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Transmittance and Reflectance Spectroscopy of Diffractive Optical Devices

Permanent Link: http://ufdc.ufl.edu/UFE0043760/00001

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Title: Transmittance and Reflectance Spectroscopy of Diffractive Optical Devices
Physical Description: 1 online resource (1 p.)
Language: english
Creator: Koukis, Dimitrios I, Sr
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

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Subjects / Keywords: arrays -- diffractive -- metallic -- periodic -- spectrosopy -- transmittance
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
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theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
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Electronic Thesis or Dissertation

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Abstract: Investigations of the optical response of sub-wavelength structure arrays perforated in thin metal films have revealed surprising phenomena, including unexpectedly high transmission of light. Many theories attempt to explain these effects, like the resonant excitation of surface plasmon polaritons (SPPs), or approaches involving composite diffraction of surface evanescent waves (CDEW), or electromagnetic modes trapped in the holes. This work discusses the various aspects of this phenomenon through the experimental measurement of the transmittance and reflectance spectra of various diffractive optical devices. The spectrum of a typical nano-fabricated such device consists of a non-resonant and a resonant contribution. Our study reveals that the resonant spectrum becomes the dominant contributor in the index matched case for normal incidence, where the transmittance amplitudes can reach values as great as seven times the open area fraction. We discuss the validity limits of theoretical calculations that approach the two-dimensional gratings for normal and oblique incidence till 65 degrees. Our measurements of periodic cross like structures on a suspended thin foil make suggestions about the role of the structure shape. The universal character of the phenomena is revealed as the presented data extend from the visible to the far infrared part of the electromagnetic spectrum.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Dimitrios I Koukis.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Tanner, David B.

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Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043760:00001

Permanent Link: http://ufdc.ufl.edu/UFE0043760/00001

Material Information

Title: Transmittance and Reflectance Spectroscopy of Diffractive Optical Devices
Physical Description: 1 online resource (1 p.)
Language: english
Creator: Koukis, Dimitrios I, Sr
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: arrays -- diffractive -- metallic -- periodic -- spectrosopy -- transmittance
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Investigations of the optical response of sub-wavelength structure arrays perforated in thin metal films have revealed surprising phenomena, including unexpectedly high transmission of light. Many theories attempt to explain these effects, like the resonant excitation of surface plasmon polaritons (SPPs), or approaches involving composite diffraction of surface evanescent waves (CDEW), or electromagnetic modes trapped in the holes. This work discusses the various aspects of this phenomenon through the experimental measurement of the transmittance and reflectance spectra of various diffractive optical devices. The spectrum of a typical nano-fabricated such device consists of a non-resonant and a resonant contribution. Our study reveals that the resonant spectrum becomes the dominant contributor in the index matched case for normal incidence, where the transmittance amplitudes can reach values as great as seven times the open area fraction. We discuss the validity limits of theoretical calculations that approach the two-dimensional gratings for normal and oblique incidence till 65 degrees. Our measurements of periodic cross like structures on a suspended thin foil make suggestions about the role of the structure shape. The universal character of the phenomena is revealed as the presented data extend from the visible to the far infrared part of the electromagnetic spectrum.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Dimitrios I Koukis.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Tanner, David B.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043760:00001


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AMERICAN PHYSICAL SOCIETY One Physics Ellipse, College Park, MD 20740 http://www.aps.org December 1, 2011 Dimitrios Koukis Ph.D. student University of Florida Gainesville, FL Ref # 10867 Thank you for your permission request dated on November 29 2011 W e are pleased to grant you a non exclusive, non transferable permission, English and German ri ghts limited to print and electronic format provided you meet the criteria outlined below. Permission is for a one time use and does not include permission for future editions updates, databases, translations, or any other matters. Permission must be sought for each additional use. This permission does not include the right to modify APS material. Please print the required copyright credit line on the first page that the material appears: Reprinted (abstract/excerpt/figure) with permission from [FU LL REFERENCE CITATION] as follows: authors names, journal title, volume number, page number and year of publication. Copyright (YEAR) by the American Physical Society. The following language must appear somewhere on the website: Readers may view, brow se, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without p rior written permission from the American Physical Society Provide a hyperlink from the reprinted APS material ( the hyperlink may be embedded in the copyright credit line). APSs link manager tec hnology makes it convenient and easy to provide links to individual articles in APS journals. For information, see: http://link.aps.org/ You must also obtain permission from at least one of the authors for each separate work, if you havent done so already. The authors name and address can be found on the first page of the published Article. Use of the APS material must not imply any endorsement by the American Physical Society. Permission is granted for use of the following APS material only Fig. 4, PRL 97, 067403 (2006) Permission is limited to the single title specified or single edition of the publication as follows: A PhD dissertation entitled "Transmittance and Reflectance Spectroscopy of Diffractive Optical Devices" to be published by Dimi trios Koukis If you have any questions, please refer to the Copyright FAQ at: http://publish.aps.org/copyrightFAQ.html or send an email to H assocpub@aps.org Sincerely, Eileen LaManca Publications Marketing Coordinator



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TRANSMITTANCEANDREFLECTANCESPECTROSCOPYOFDIFFRACTIVEOPTICALDEVICESByDIMITRIOSI.KOUKISADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2011

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c2011DimitriosI.Koukis 2

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Tomyfamily 3

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ACKNOWLEDGMENTS Thisworkistheproductoftheeffortofalargenumberofpeopleanditisanhonorformebothtohaveparticipatedandtobeabletoreportitinthisbook.ThepeopleIhavemetduringtheveandahalfyearsofmystudyintheUniversityofFloridahavenotdenedonlythecontextofthisdissertation,butalsothewaythatIthinkandthewaythatIapproachlife.Iwouldliketoexpressmycompletegratitudetoeachandeveryoneofthem.FirstofallIwanttothankmyfamilyfortheirunconditionallove,adviceandsupportformydecisions.AmongallthepeoplethatIknow,theyaretheonesthathavedonethesacricesnecessaryformetobeabletoclaimsomesmallachievementstoday.SinceIjoinedtheTannerlabin2007,aspecicpersonhasneverseizedtoamazeme,bothwithhisprofoundknowledgeinphysics,hisabilitytocomprehendthephenomenafastandhispersonality.IthasbeenthegreatesthonorformetomeetmyadvisorProfessorTanner.Hehasbeenveryinspiringandsupportive,butaboveallhehasbeenaparagonforme.IwouldliketothankalltheProfessorsthatservedasmembersofmycommittee.Dr.Hebard'sadviceandhisunconditionalhelpweremaincontributorstomyefforts.Dr.Shabanov'stheoreticalresultshavebeenthebiggestinspirationformanystudentstodealwithdiffractiveopticaldevices.SpecialthanksalsotoDr.ReitzeandDr.Hollowayfortheirinterestandvaluablecontributiontomyresearch.DuringthelastfouryearsIhadthefortunetomeetpeoplethatservedmenotonlyasseniorstudentsandcoworkers,butalsoasvaluablefriends.Mycharactertochallengeeverythingestablished,andmytendencytoapproachlifewithajokingmood,Ifoundonapersonfullofgoodnessandtalents.ItisthegreatestpriviledgeformetomeetDr.DanielArenas.IwouldalsoliketothankmyroommateformanyyearsandcoworkerinphysicsKonstantinosNinios,forhiscare,trustworthinessandgreatinuencetomycharacterandtomyperceptionoflife.AlsoIwouldliketothankDr. 4

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SinanSelcukforhisfriendship,careandhelp.Hewastheonethathelpedmeonthebeginningofmyresearch,whichisthehardestpart,tomakesureitwouldnotbeashardforme.Iamverythankfultoallmylabmatesforallthehoursthatwehavespenttogetherworkinginexperimentalphysicsanddiscussing.Itisthegreatestprivilegetobelongtoacommunitythatconsistsofveryintelligentpeople,withawidebandofknowledge.HardworkingDr.CatalinMartinforhispatienceandhelp,andDr.JungseekHwang.AlsomyfriendsDr.NaveenMargankunte,Dr.AndrewWint,Dr.NathanHeston,RichardOttens,JeffreyHoskins,XiaoxiangXi,KevinMiller,ZahraNasrollahi,NaweenAnand,EvanThatcher,BerikUzakbaiuly,ChangLongandLuyiYan.Alsomycollaboratorsfromotherphysicslabs,especiallyDr.Hebardsgroup.FinallymycollaboratorandfriendfrommaterialsciencedepartmentDonghaShim.IwouldalsoliketothankalltheProfessorsofmyclassesfortheircarefulpresentationofthetopicsandfortheirhelptomybetterunderstanding.AlsoIwouldliketothankmyclassmatesfortheirsmile,willingnesstohelpandforcreatinganiceenvironmentforstudy.AlsospecialthankstomylabstudentsofmyrstyearinUniversityofFlorida,forgivingmethechancetohelpthemwithmyphysicsknowledgeandfortheirtoleranceonmyspokenEnglishskills.IwouldliketothankthepeopleinNIMETforteachingmehowtouseveryspecializedhightechnologyequipmentandtheirwillingnesstohelpmewheneverIneededanything.SpecialthankstoDr.AppletonandJoelFridmannforthevaluabletimetheyspenthelpingmewithmyproject.AlsoIwanttothankthemachineshopandelectronicshoppeople,fortheirbrilliantdesignsandfabricationsthathelpeverygraduatestudentintheUniversityofFlorida. 5

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 13 CHAPTER 1INTRODUCTION ................................... 14 1.1Motivation .................................... 14 1.2EnhancedTransmissionPhenomenon .................... 15 1.3ManipulationoftheElectromagneticSpectrum ............... 17 1.4DissertationSummary ............................. 19 2THEORETICALAPPROACH ............................ 20 2.1ReviewofPlasmonics ............................. 20 2.2SurfacePlasmonPolaritons .......................... 22 2.3AnalysisoftheDiffractionEquation ...................... 24 2.4OtherTheoreticalApproaches ........................ 27 3EXPERIMENTALSETUP .............................. 32 3.1SampleFabrication ............................... 32 3.2ThinGoldFoilSampleDescription ...................... 36 3.3ZeissMPM-800MicroscopePhotometer ................... 40 3.4Bruker113vFourierSpectrometer ...................... 43 3.5FourierTransformSpectroscopy ....................... 45 3.6FabricationConcerns ............................. 48 3.7AtomicForceMicroscopy ........................... 49 3.8ElectronBeamLithography .......................... 52 4PERIODICHOLEARRAYSINSILVERFILMS .................. 55 4.1Prologue .................................... 55 4.2NormalIncidenceTransmittance ....................... 55 4.3NormalIncidenceReectance ........................ 59 4.4AnalysisofTransmittanceandReectanceData .............. 64 4.5EffectsoftheDielectricEnvironment ..................... 70 4.6AngularDependence .............................. 78 6

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5PERIODICHOLEARRAYSINTHINGOLDFOIL ................. 95 5.1AngleDependenceofTransmittance ..................... 95 5.2ReectanceMeasurements .......................... 102 5.3CalculatedTransmittancePlusReectanceSpectra ............ 107 5.4NormalizedTransmittance ........................... 109 6SUMMARY ...................................... 121 6.1Conclusions ................................... 121 6.2FutureWork ................................... 122 APPENDIX AATOMICFORCEMICROSCOPEIMAGES .................... 124 BNORMALIZEDTRANSMITTANCEDATA ...................... 126 CFURTHERANALYSISOFTHINFOILSAMPLE .................. 130 REFERENCES ....................................... 133 BIOGRAPHICALSKETCH ................................ 136 7

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LISTOFTABLES Table page 4-1TablewiththecalculatedrstfourdiffractionthresholdsforthesamplewithDg=6.0m. ..................................... 58 4-2TablewiththecalculatedrstfourdiffractionthresholdsforthesamplewithDg=8.0m. ..................................... 58 4-3TablewiththecalculatedrstdiffractionthresholdsattributedtoZinc-Selenideforholearrayswithvariousperiodicities. ...................... 65 4-4Tablewiththecalculatedrstdiffractionthresholdsattributedtofusedsilicaforholearrayswithvariousperiodicities. ...................... 69 4-5TablewiththecalculatedrstfourdiffractionthresholdsforthesamplewithDg=6.0mincludingtheremainingphotoresistS1813. ............. 73 4-6TablewiththecalculatedrstfourdiffractionthresholdsforthesamplewithDg=1000nm. .................................... 76 4-7Tablewiththecalculatedpositionsofthedipstodifferentdiffractionorders. .. 82 4-8S-polarization(substrateattributed)peaksanddipsforsilveronfusedsilica. 83 4-9S-polarization(airattributed)peaksanddipsforsilveronfusedsilica. ..... 84 4-10P-polarization(substrateattributed)peaksanddipsforsilveronfusedsilica. 84 4-11P-polarization(airattributed)peaksanddipsforsilveronfusedsilica. ..... 85 5-1Tablewiththecalculatedpositionsofthedipstozeroandrstdiffractionordersamplewith:Dg=66.2mandL=39.3m. ................... 99 5-2Tablewiththecalculatedpositionsofthedipstozeroandrstdiffractionorderforthesamplewith:Dg=8.64mandL=4.93m. ............... 102 5-3Tablewiththepositionsofthepeaksanddipsfor(i=0,j=1)forthesamplewith:Dg=66.2mandL=39.3m. ....................... 110 5-4Tablewiththepositionsofthepeaksanddipsfor(i=-1,j=0)forthesamplewith:Dg=66.2mandL=39.3m. ....................... 110 5-5Tablewiththepositionsofthepeaksanddipsfor(i=0,j=1)forthesamplewith:Dg=8.64mandL=4.93m. ....................... 111 5-6Tablewiththepositionsofthepeaksanddipsfor(i=-1,j=0)forthesamplewith:Dg=8.64mandL=4.93m. ....................... 111 8

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LISTOFFIGURES Figure page 1-1Scienticeldsrelatedtothemanipulationoftheelectromagneticspectrum. .. 18 2-1Diffractiononatwodimensionaldevice. ...................... 25 2-2Transmittanceplusreectancepredictionsofthetrappedmodestheory. .... 28 3-1Typicalholearraysamplewithgeometricalproperties:Dg:Holearrayperiod,a:Holedimension. .................................. 32 3-2Samplepreparationprocess ............................ 35 3-3SEMimageofthesideofthegoldfoilmeasuringitsthickness. ......... 37 3-4SEMimageofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3m. ................................ 38 3-5SEMimageofthegoldfoilsamplewithcharacteristicgeometry:Dg=8.64mandL=4.93m. ................................ 39 3-6ThemicroscopephotometerusedformeasurementsofsampletransmittanceandreectanceintheVIS/NIRpartsofthespectrum. .............. 40 3-7Theeffectthattherefractionofthesamplehasonthemeasurementofthemicroscopephotometer. ............................... 42 3-8SchematicdiagramoftheBruker113vFourierspectrometer. .......... 43 3-9SchematicdiagramoftheMichelsoninterferometer. ............... 45 3-10AFMimageofaperiodicholearraysamplewithgeometricalcharacteristicsDg=1200nmanda=537nm. .......................... 49 3-11AFMimageofaperiodicholearraysamplewithgeometricalcharacteristicsDg=600nmanda=268nm(initial). ....................... 50 3-12AFMimageofaperiodicholearraysamplewithgeometricalcharacteristicsDg=600nmanda=268nm(nal). ........................ 51 3-13SEMimageofasamplewithDg=500nm,a=200nm. ............. 53 3-14SEMimageofasamplewithDg=1000nm,a=300nm. ............ 53 3-15SEMimageofsecondsamplewithDg=500nm,a=200nm. ......... 54 4-1TransmittancespectraofthreedifferentholearraysamplesonZinc-Selenidesubstrate. ....................................... 56 4-2ReectancedataforthesilveronZinc-Selenidesamples. ............ 59 9

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4-3Extinctiondatafortwosampleswithdifferentopenareafractionsandcomparisonwithsimulationsbasedontrappedmodestheory. .......... 60 4-4Reectance+TransmittanceforsilveronfusedsilicaholearraysamplewithDg=800nm,a=400nm,(f=0.25). ....................... 62 4-5Normalizedtos=1168nmReectance+TransmittanceforsilveronfusedsilicaholearraysamplewithDg=800nm,a=400nm,(f=0.25). ....... 63 4-6TransmittanceforsilveronZinc-Selenideholearraysampleswithvariousperiodicitiesandopenareafractions. ........................ 64 4-7NormalizedtotherstdiffractionthresholdtransmittanceforsilveronZinc-Selenideholearraysamples. ......................... 65 4-8Transmittanceandreectancedataforsilveronfusedsilicasamples. ..... 66 4-9Normalizedtotherstdiffractionthresholdattributedtothefusedsilicasubstratetransmittance. ............................... 67 4-10CalculatedReectance+Transmittancespectraforsilveronfusedsilicaholearraysamples. .................................... 68 4-11NormalizedtotherstdiffractionthresholdReectance+Transmittancespectraforsilveronfusedsilicaholearraysamples. ............... 69 4-12TransmittancedataforaholearraysampleonZnSewithDg=6.0m,a=4.0m. ........................................ 72 4-13Transmittancedataforsilveronfusedsilicasamplesatstage5ofthedevelopingprocess. ................................. 74 4-14Transmittancedataforsilveronfusedsilicasamplesatstage6ofthedevelopingprocess. ................................. 75 4-15Analysisofasilveronfusedsilicaholearraysampletransmittance,withDg=1000nm,a=316nm. ................................ 77 4-16S-polarizeddataofsilveronfusedsilicasamplewithcharacteristics:Dg=800nm,a=400nm,(f=0.25),forvariousanglesofincidence. ........ 79 4-17P-polarizeddataofsilveronfusedsilicasamplewithcharacteristics:Dg=800nm,a=400nm,(f=0.25),forvariousanglesofincidence. ........ 80 4-18Reectance+Transmittanceat45degreesincidentangle. ............ 86 4-19S-polarizationanalysisofsilveronfusedsilicasample,forvariousanglesofincidence(rstgure). ................................ 88 10

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4-20S-polarizationanalysisofsilveronfusedsilicasample,forvariousanglesofincidence(secondgure). .............................. 88 4-21P-polarizationanalysisofsilveronfusedsilicasample,forvariousanglesofincidence(rstgure). ................................ 89 4-22P-polarizationanalysisofsilveronfusedsilicasample,forvariousanglesofincidence(secondgure). .............................. 89 4-23P-polarizationanalysisofsilveronfusedsilicasample,forvariousanglesofincidence(thirdgure). ............................... 90 4-24TransmittanceofsilveronfusedsilicasamplewithDg=800nmanda=400nm,illuminatedbyun-polarizedlightforvariousanglesofincidence. ...... 90 4-25Angledependentpositionofthetwopeaksandthetwodipsfor(i=0,j=1). 91 4-26Angledependentpositionofthetwopeaksandthetwodipsfor(i=-1,j=0). 92 4-27Sin()dependentpositionofthetwopeaksandthetwodipsfor(i=0,j=1). 93 4-28Sin()dependentpositionofthetwopeaksandthetwodipsfor(i=-1,j=0). 94 5-1Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3mfors-polarizedlight. ......... 95 5-2Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3mforp-polarizedlight. ......... 96 5-3Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=8.64mandL=4.93mfors-polarizedlight. ......... 97 5-4Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=8.64mandL=4.93mforp-polarizedlight. ......... 98 5-5Reectanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3mfors-polarizedlight. ..................... 103 5-6Reectanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3mforp-polarizedlight. ..................... 104 5-7Reectanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=8.64manda=4.93mfors-polarizedlight. ..................... 105 5-8Reectanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=8.64manda=4.93mforp-polarizedlight. ..................... 106 5-9Normalizedtransmittance+reectancespectraofthetwogoldfoilsamples. .. 107 5-10Normalizedextinctionspectraofthetwogoldfoilsamples. ............ 108 11

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5-11Angledependentpositionofthemainpeakanddipforthesamplewith:Dg=66.2mandL=39.3m(s-polarization). ..................... 113 5-12Sin()dependentpositionofthemainpeakanddipforthesamplewith:Dg=66.2mandL=39.3m(s-polarization). ..................... 114 5-13Angledependentpositionofthemainpeakanddipforthesamplewith:Dg=66.2mandL=39.3m(p-polarization). ..................... 115 5-14Sin()dependentpositionofthemainpeakanddipforthesamplewith:Dg=66.2mandL=39.3m(p-polarization). ..................... 116 5-15Angledependentpositionofthemainpeakanddipforthesamplewith:Dg=8.64mandL=4.93m(s-polarization). ..................... 117 5-16Sin()dependentpositionofthemainpeakanddipforthesamplewith:Dg=8.64mandL=4.93m(s-polarization). ..................... 118 5-17Angledependentpositionofthemainpeakanddipforthesamplewith:Dg=8.64mandL=4.93m(p-polarization). ..................... 119 5-18Sin()dependentpositionofthemainpeakanddipforthesamplewith:Dg=8.64mandL=4.93m(p-polarization). ..................... 120 A-1AFMimageofasamplewith:Dg=1200nmanda=537nm. ......... 124 A-2AFMimageofasamplewith:Dg=1000nmanda=447nm. .......... 125 A-3AFMimageofasamplewith:Dg=800nmanda=358nm .......... 125 B-1Normalizedtransmittanceofsamplesatstage5ofthedevelopingprocess. .. 126 B-2Normalizedtransmittanceofsamplesatstage6ofthedevelopingprocess(rstplot). ....................................... 127 B-3Normalizedtransmittanceofsamplesatstage6ofthedevelopingprocess(secondplot). ..................................... 128 B-4Normalizedtransmittanceofthetwoperiodiccrossarraysinthingoldfoil. ... 129 C-1Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3mforUn-polarizedlight. ........ 130 C-2Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3mfor45degreespolarizedlight. ... 131 C-3Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=8.64mandL=4.93mforUn-polarizedlight. ........ 132 12

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyTRANSMITTANCEANDREFLECTANCESPECTROSCOPYOFDIFFRACTIVEOPTICALDEVICESByDimitriosI.KoukisDecember2011Chair:DavidTannerMajor:PhysicsInvestigationsoftheopticalresponseofsub-wavelengthstructurearraysperforatedinthinmetallmshaverevealedsurprisingphenomena,includingunexpectedlyhightransmissionoflight.Manytheoriesattempttoexplaintheseeffects,liketheresonantexcitationofsurfaceplasmonpolaritons(SPPs),orapproachesinvolvingcompositediffractionofsurfaceevanescentwaves(CDEW),orelectromagneticmodestrappedintheholes.Thisworkdiscussesthevariousaspectsofthisphenomenonthroughtheexperimentalmeasurementofthetransmittanceandreectancespectraofvariousdiffractiveopticaldevices.Thespectrumofatypicalnano-fabricatedsuchdeviceconsistsofanon-resonantandaresonantcontribution.Ourstudyrevealsthattheresonantspectrumbecomesthedominantcontributorintheindexmatchedcasefornormalincidence,wherethetransmittanceamplitudescanreachvaluesasgreatasseventimestheopenareafraction.Wediscussthevaliditylimitsoftheoreticalcalculationsthatapproachthetwo-dimensionalgratingsfornormalandobliqueincidencetill65degrees.Ourmeasurementsofperiodiccrosslikestructuresonasuspendedthinfoilmakesuggestionsabouttheroleofthestructureshape.Theuniversalcharacterofthephenomenaisrevealedasthepresenteddataextendfromthevisibletothefarinfraredpartoftheelectromagneticspectrum. 13

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CHAPTER1INTRODUCTION 1.1MotivationTheworkisthecontinuationofaseriesofeffortsthatinvestigatethepropertiesofdiffractiveopticaldevices.Themainfocuswillbeonperiodicarraysofholesfabricatedonmetallms.Thesetypesofopticaldevicesareofspecialinteresttoday,astheypresentthepotentialformanydifferenttypesofapplications.Thepropertythatcharacterizesthesedevicesisthatthedimensionsoftheirconstituentpartsareasmallfractionofthewavelengthofthelight.Ifweattemptapreviewontoday'stechnologicalprogress,wecansaythatithasbeenhelpedalotbytheadvancesinthemanipulationofelectromagneticsignalsmainlybyusingelectronicprocessors.Somedecadesago,practicalapplicationswerelimitedbythelargesizeofthedevicesthatwereperformingthismanipulation.Todaythough,thesizesofthedeviceshaveshrunktotensofnanometersorsmaller.Atthesametimethetechnologicalprogresshasachievedasignicantincreaseinprocessingspeeds.Thegreatlyenhancedpowerofprocessorscomesalongwiththeinterestofusingthemtosolveproblemsofgreaterdifcultyandincorporatetheminapplicationsofgreatercomplexity.Tosatisfythatneedtherehavebeenmanyscienticapproaches,includingafurtherincreaseinprocessingspeed.Unfortunatelyprocessingusingelectricalsignalsforcommunicationofconstituentpartshasmetalimittoday.EventhoughresearchhaspushedthespeedlimitsofthedevicestospeedsofTHz,andnobodycanpredictwhattheprojectioninthefuturecanbe,stillthereisafundamentallimitationtotheseefforts.Thatistheshrinkageofthedevicesizecomesalongwithparasiticcapacitiveeffects,whichposeanupperlimittotheirspeed.Whiletheresearchonthecurrentstateprocessingmethodsstillcontinues,newapproacheshavebeensuggestedtoo.Thedevicestodaycanstillbeapproachedmacroscopicallyasthecharacteristicsizesofthesignalsused(wavelengthinthe 14

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opticalcase),arealotlargerthananycharacteristicdimensionofthedevice.Astheunderstandingoftheatomicworldgetsbetter,therearisesuggestionsthatmakeuseofthevariousquantumpropertiesofmatterforapplications.Alotofresearchgoesonforexploitingthismicroscopicapproach.HoweverthesimplestideatowardsthecontinuationofthecurrentscienticapproachistryingtoexploittheelectromagneticspectruminevengreaterfrequenciesintheTHzrange.Atsomepointwehavetodealwiththemanipulationoflight.Manipulatinglightsignalshasthegreatadvantageofitsveryhighfrequency,whichwouldallowspeedsordersofmagnitudehigherthancurrentones,dependinguponhowsuccessfulthenewopticaldeviceswouldbe.Ontheotherhandthepropertiesoflightandmainlythediffractionlimitposealsolimitations.Tounderstandthisbetter,letussupposethatweuselightof500nmwavelength(greenlight)toachievethecommunicationoftwo'opticaltransistors'ofsizes90nm,sizenottoosmallforcurrentstateCMOStechnology.Itisapparentthatasthesizeofthedevicesissomuchsmallerthanthewavelengthofthelight,thesignalcannotinteractwiththosedevicesintheclassicalway,whichissomeofitsenergybeingabsorbedbythedeviceandthentranslatedasaninformationexchange.Onewouldsaythatwecanstillusedevicesaslargeasnecessary,tomanipulatethoselongwavelengthsandthisisthetopicofthepartofresearchinopticswhichcanbecalledphotonics.Thephotonicdevicesmakeuseofintrinsicphysicalpropertiesofthematerials,likethegapbetweenthevalenceandconductionbandsandalsoopticalphenomenaonthewavelengthscalelikediffraction.Sotosummarizethisparagraph,photonicsisthestudyoflightmanipulationusingstructurescomparabletothewavelengthofthelight. 1.2EnhancedTransmissionPhenomenonAsanotherexample,anarrayofsub-wavelengthholesfabricatedonanopticallythickmetallmshouldnotposesignicantdifferencesthanthesamemetallmwithout 15

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theholes,accordingtotheclassicalapproachbytheelectromagnetictheory.TheapproachisquantiedbyBetheusingstandardaperturetheory.[ 1 ]Thepredictionwasthatthetransmittance,normalizedtothesquareholecoveredarea,fornormalincidenceonanopticallythickmetallm,canbegivenby: T18a 4(1)whereaisthedimensionofthesquareholesandthewavelength.Equation 1 wasderivedbasedontheassumptionthata/<<1.Thetransmittancewouldbeevensmallerforobliqueincidence.Weseethatforsub-wavelengthholeswedonotexpectanysignicantportionofthelighttobetransmittedthroughthelm.Forexampleinourexperimentswestudyperiodicholearrayswithholesizea300nmusinglightofwavelength1400nm.Equation 1 wouldthengive:T3.8%,thatisverysmallincomparisontotheobservedtransmittedintensity.Sothestandardaperturetheorypredictionwasprovenwrongbytheexperimentsandthisleadtonewtheoreticalconsiderations.Insomecasesthetransmittancenotonlyisnon-zero,butgetsgreatervaluethanthefractionofthesampleareathatisperforatedbytheholes.Thisjustiesthename'enhancedtransmissionphenomenon'.Historicallythediffractionpropertiesofperiodicgratingsattractedthescienticattentionaftertheobservationofanomalousreectiveproperties.TheseWood'sanomalieswereinterpretedbyLordRayleighandFanoandlateritwasrealizedthattheywererelatedtotheexcitationofevanescentelectromagneticmodesboundtothegrating.[ 2 10 ]TheenhancedtransmissionphenomenonwasrstobservedintheopticalpartoftheelectromagneticspectrumbyEbbessenandhisco-workers,butasimilarphenomenoninthemicrowaverangewasknownlongbeforehiswork.[ 11 ].Inourstudythetransmittanceamplitudesobservedcanreachvaluesashighasseventimestheopenareafractionofthediffractiveopticaldevice. 16

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Eventhoughtheelectromagneticeldofthelightcannotpenetrateinsidethebulkofthemetallm,thereexistotherinterestingphenomenathathavetodowiththeexistenceofaninterfacebetweenthesurfaceofthelmandthedielectricenvironmentthatusuallysurroundsit.Thesephenomenaallowthemanipulationoflightinawaythathadnotbeenimaginedbefore.Theelectromagneticeldinducessurfacechargesandcurrentsonthemetalliclm,thatcangiverisetosurfacewavesthatevanescentlydecayintheperpendiculardirection,ortheelectriceldistrappedintheholescreatingplacesofverystrongandweakelds,orwecanapproachitthroughstudyingthetotaldiffraction.Thesurfacephenomenawecancollectivelycallplasmonsandthevariouseffortsandschemesproposedfortheirstudy,gaverisetothedevelopmentofplasmonics.Plasmonicdevicesmanipulatelightsignalsusingpropersub-wavelengthgeometricalpropertiesandpropertiesoftheinterfacesthatgiverisetoaneffectivemacroscopicbehaviour.Thereforeweseethatthestudyofplasmonsisaveryinterestingtopicthatisnotwellunderstoodwhileexploringtherelatedpropertiescangiverisetoaneweraoftechnologicaladvancements. 1.3ManipulationoftheElectromagneticSpectrumTheneedforgreaterprocessingspeedsleadtotheexplorationofthedeepThzpartoftheelectromagneticspectrum.TheThzradiationisenergeticenoughtoexcitephenomenathatareintrinsicforsolidstatematerials.Forexample,theinter-bandtransitionsthatoccurinthesefrequenciesforspecicmaterialsgiverisetolasing.Exploitingthesepropertieswehavetodaylaserdevices,likethequantumcascadelaser,thathaveaidedmanytechnologicalapplications.Diffractionphenomenaalsohelpalotintheexploitationofthemoreenergeticpartofthespectrum.BraggX-raypeaksthatgivesovaluableinformationaboutthecrystalstructure,followthediffractionlawsofphysicaloptics.Thedevelopmentofphotonicdevices,suchasphotoniccrystals,wasbasedontheexplorationofthesedescribedphenomena.Thesephenomenaarethetopicofthegeneralstudyofphotonics,but 17

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Figure1-1. Scienticeldsrelatedtothemanipulationoftheelectromagneticspectrum.TheneedforexploringtheThzrangegaverisetophotonics.Theneedtomanipulatesub-wavelengthpropertiesgaverisetoplasmonics. alsoposethelimitationstothephotonicsapplications.Duetotheselimitationswecaningeneraldenethestudyoftheinteractionofhigherthan1GHzelectromagneticradiationwithgreaterthan1msizestructures,asthetopicofphotonics.Ashasbeenexplained,whenthesizesshrinktosmallerdimensionsthereoccurphenomenathatstillhavenotbeencompletelyunderstoodandexplored.Veryinterestingsuchphenomenahavebeentheoreticallypredictedandfascinatingnewtechnologicalapplicationshavebeensuggested.Oneexampleisthedevelopmentofmetamaterials,thathavealreadyfoundapplicationsintheGhzrange.Thedevelopmentofmetamaterialsistechnologicallyverypromising,asveryexcitingapplicationslikesuper-lensingandcloakingarerelatedtothem.Themanipulationoflightusingsub-wavelengthstructuresisthetopicofplasmonics.Figure 1-1 summarizesthecurrentstateoftheelectromagneticspectrumexploitingscience. 18

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1.4DissertationSummaryThisworkismainlyfocusedonthestudyoffabricatedsub-wavelengthperiodicstructuresthatfallwithinthetopicofplasmonics.Itisorganizedinsixchapters.Chapter1istheintroductiontoourstudy.Chapter2dealswiththevarioustheoreticalapproachesthatwillbeusedduringthestudyfortheexplanationofourresults,whileChapter3isfocusedontheexperimentalset-up.TheexperimentalresultsregardingourfabricatedsamplesarepresentedinChapter4alongwiththeirdiscussion.Chapter5presentsastudyofthetransmittanceandreectancespectraofaperiodicarrayofcrosslikestructuresperforatedin1.2mthickgoldfoils.Chapter6summarizesourwork. 19

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CHAPTER2THEORETICALAPPROACH 2.1ReviewofPlasmonicsAsiswellknown,metalsarecharacterizedmainlybytheirhighdensityoffreecarriers.Thusthespacingsbetweentheelectronenergylevelsarealotsmallerthanthethermalexcitations.Alsothemetallmsthatconstitutethedevicesthatwefabricate,havecharacteristicdimensionsoftheirelements,muchsmallerthanthewavelengthofthelightused,sowecancallthemduringthiswork:sub-wavelengthstructures.TheconclusionisthatwecanapproachourstructuresusingthemacroscopicMaxwell'sequations: rD=ext(2) rB=0(2) rE=)]TJ /F5 11.955 Tf 13.68 8.08 Td[(@B @t(2) rH=Jext+@D @t(2)IntheabsenceofexternalchargesandcurrentswecancombineEquation 2 andEquation 2 toderivetheequationsfortheelectromagneticwavesinsidethemetal: rrE=)]TJ /F5 11.955 Tf 9.3 0 Td[(0@2D @2t(2) K(KE))]TJ /F7 11.955 Tf 11.96 0 Td[(K2E=)]TJ /F5 11.955 Tf 9.29 0 Td[((K,!)!2 c2E(2)Wecandistinguishbetweentwodifferentpolarizationsoftheelectriceld.ForatransversewaveKE=0,sowederivethefollowingdispersionrelation: K2=)]TJ /F5 11.955 Tf 9.3 0 Td[((K,!)!2 c2(2)ForlongitudinalwavesEquations 2 and 2 give: (K,!)=0(2) 20

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Weseethatlongitudinalwavescanexistinthemetalonlyatthezerosofthedielectricfunction.TodenethedielectricfunctionwewillusetheDrudefreeelectrongasmodel.Accordingtothatwehave: (!)=1)]TJ /F5 11.955 Tf 29.62 8.95 Td[(!2p !2+i!(2)Where!pistheplasmafrequencyandisthecollisionfrequencythatisthedampingmechanismintheDrudemodel.1isinsertedtomodelthebehaviouroftheboundelectronsandhasavalueoftheorderof1formostmetals.Theparameters!p,and1arecharacteristicsofthemetal.Forlargefrequencies,closeto!pthedampingbecomesnegligiblesoEquation 2 becomes: (!)=1)]TJ /F5 11.955 Tf 13.15 8.95 Td[(!2p !2(2)Inthefollowinganalysiswewillreplace1withthevalue1astheanalysisconsidersmainlythefreeelectrons.NowusingEquation 2 intoEquation 2 wederivethedispersionrelationfortravellingwaves: !2=!2p+K2c2(2)AsisclearfromEquation 2 for!
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ofonewavelength,wecanrewritethewaveequationas: r2E)]TJ /F5 11.955 Tf 16.57 8.09 Td[( c2@2E @2t=0(2)ForharmonictimedependencewederivetheHelmholtzequation: r2E+k20E=0(2) 2.2SurfacePlasmonPolaritonsWewillapplyEquation 2 tondtheallowedsolutionsforaatinterfacebetweentwoisotropicmediawithdielectricfunctionsmandd.Weassumepropagationoftheelectromagneticwavealongthex-directionandhomogeneityinthey-direction.Thez=0surfaceistheinterfacebetweenthetwomediaandfornegativevaluesofzweareinsidethemediumwithm,whileforpositiveweareinthemediumwithd.Alsowelimitourselvestothecaseoftransversemagneticelds.Forp-polarizedelectromagneticwave(TMwave),themagneticeldisperpendiculartotheplaneofincidenceandtheelectriceldisintheplaneofincidence.ThentheH-eldhastobealongthey-axisandtheE-eldisinthex-zplane.Thus,theEandHeldsineachregioncanbeexpressedas: ~E1=(A,0,B)exp[i(kx)]TJ /F5 11.955 Tf 11.95 0 Td[(!t)]exp[)]TJ /F7 11.955 Tf 9.29 0 Td[(a1z],(z>0)(2) ~H1=(0,C,0)exp[i(kx)]TJ /F5 11.955 Tf 11.95 0 Td[(!t)]exp[)]TJ /F7 11.955 Tf 9.3 0 Td[(a1z],(z>0)(2) ~E2=(D,0,E)exp[i(kx)]TJ /F5 11.955 Tf 11.96 0 Td[(!t)]exp[)]TJ /F7 11.955 Tf 9.3 0 Td[(a2z],(z<0)(2) ~H2=(0,F,0)exp[i(kx)]TJ /F5 11.955 Tf 11.95 0 Td[(!t)]exp[)]TJ /F7 11.955 Tf 9.3 0 Td[(a2z],(z<0)(2)WhereA,B,C,D,E,Faretheamplitudesofthecomponentsoftheelectricandmagneticeldsintherstandinthesecondmedium.TheboundaryconditionthatneedstobeconsideredisthatthecomponentsofEandHparalleltothesurfaceare 22

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continuousattheinterface,(z=0),thatis: ~E1xjz=0=~E2xjz=0(2) ~H1xjz=0=~H2xjz=0(2)Solvingforthedispersionrelation,usingMaxwell'sequationswederivetheresult: kx=! cr 12 1+2(2)Equation 2 isofgreatsignicanceasitshowsthattherearespecicconditionsthattheassumptionofsurfacewaves,canbetrue.TheseelectromagneticexcitationsthatareconnedontheinterfacebetweenadielectricandaconductorarecalledsurfaceplasmonpolaritonsandEquation 2 istheirdispersionrelation.Similarlywecanshowthattherearenosurfaceplasmonmodesfors-polarization(TransverseElectricorTEmodes),whichsuggeststhatthetwodifferentpolarizationsshouldgiveusverydifferentexperimentalresults,whichissomethingthatwillbeconrmedbyourexperimentaldata.Ashasbeenexperimentallyshowntherearetwowaystoexcitethesurfaceplasmonpolaritons.Therstmethodusesadielectricprism.Thesecondusesperiodicstructuresonthemetalsurface,creatingagrating.Theadditionalmomentumenablestheexcitationofthesurfaceplasmonpolaritonsonthetopandthebottommetal/dielectricinterfaces.Theholesprovidethenecessarycouplingbetweenthetwosidesandveryhightransmittedintensitiescanbeachieved.[ 11 ]Variousexplanatoryschemesarebasedonthismatchingofthewavevectorofthesurfaceplasmon,withtheBraggconditionforscatteringbytheholearray.[ 12 20 ]Forthepurposesofourstudywealsousedthegratingmethod.Ourgratingsconsistofsquareholeswithcharacteristicsize(a)andarefabricatedonopticallythickmetallms.ThedistancebetweentheholesremainsconstantandwewilldenoteitasDginthefollowing. 23

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Nowifweconsidermomentumconservationonatwodimensionalgratingonthemetalsurface,wederivetheequationthatpredictsthewavelengthssp,wheretheincidentlightexcitesthesurfaceplasmonpolaritons.Theseareresponsiblefortheenhancedresonanttransmission,sotheycorrespondtothepositionsoftheresonantpeaksontheexperimentaldata.Theequationhasthefollowingform: sp=Dg i2+j2)]TJ /F7 11.955 Tf 9.29 0 Td[(isin+r (i2+j2)dm d+m)]TJ /F7 11.955 Tf 11.96 0 Td[(j2sin2(2)Wherei,jareintegernumbers,istheangleofincidenceandm,d,arethedielectricfunctionsofthemetalandthedielectricrespectively.OurexperimentfocusesonexaminingvariouspredictionsbasedonEquation 2 .ExpandingtheratioofthedielectricsinsidethesquarerootofEquation 2 ,consideringthat:jmjdintheinfraredwavelengthsanddroppinghigherthanrstordertermswederivethefollowingresult: peaks=Dg i2+j2)]TJ /F7 11.955 Tf 9.29 0 Td[(isin+r (i2+j2)d(1+jd mj))]TJ /F7 11.955 Tf 11.96 0 Td[(j2sin2(2)TheformofEquation 2 takesintoconsiderationthefactthatthedielectricconstantofthemetalisnegativewithveryhighabsolutevalue,whiletheonesforthedielectricsusedarepositivewithvaluescloseto1.Equation 2 approximatesthepositionsoftheresonanttransmittancepeaks.Ifwekeeponlythelowestinjd/mjtermwederive: dips=Dg i2+j2)]TJ /F7 11.955 Tf 9.3 0 Td[(isin+q (i2+j2)d)]TJ /F7 11.955 Tf 11.96 0 Td[(j2sin2(2)Equation 2 isrelatedtothepositionsofthedipsofourexperimentaldata,asitagreeswiththediffractionequationforthecaseoftotallydiffractedlight. 2.3AnalysisoftheDiffractionEquationForthederivationofthegeneralsurfaceplasmonequation(Equation 2 )thesquareshapeoftheholesistakenintoconsiderationduringtheapplicationofthemomentumconservation.Sothesquareshapeisincludedinthediffractionequation(Equation 2 )too.HoweverthenalformofEquation 2 suggestsspecic 24

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Figure2-1. Diffractiononatwodimensionaldevice.Astheanglexgetssteeperthesurfaceexcitationremainsalmostunaffected.Astheangleygetssteeperthewavesplitsintoared-shiftedoneandablue-shiftedonecorrespondingtotheelectriceldcomponentsparallelandperpendiculartothesurfaceplane. dependenceoftheenhancedtransmissionphenomenonuponthesample'sproperties,thatwillbeanalysedinthisparagraph.Therstthingthatwemustobserveisthatthewavelengthsofthecharacteristictransmittancedipsdonotdependuponthesizeofthesquarehole.ThedominantroleinthedenitionofthesecharacteristicwavelengthsisascribedtothedielectricconstantofthedielectricenvironmentofthemetallmandtheholeseparationDg.Thesamplesthatwefabricateduseaproperlyselecteddielectricsubstratethatallowsthetransmittanceoflightwithoutabsorptioninthewavelengthsofthemeasuredspectrum 25

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andmechanicallysupportsthedepositionofthemetallm.Thisdielectricsubstratehasapositivedielectricconstantthatisgreaterthanthatoftheair.Ontheothersideofthelmthereisair,whileforspecicstudiesoftheeffectwehavealsodepositedproperdielectrics.Equation 2 suggeststhattwoseparategroupsofresonanceswillbesupported,eachattributedtothetwodielectrics.ThepositionsofthecorrespondingdipscanbecalculatedusingEquation 2 .ComparingtheapproximationEquation 2 forthepositionsofthepeakstoEquation 2 ,weseethateverypeakhasacorrespondingdiponitsshorterwavelengthsideasthereisanadditivepositiveterminsidethesquarerootforEquation 2 .Alsoweneedtoconsiderthedifferencesbetweenonedimensionalanalysisandthetwodimensionalcasethatisthetopicofourstudy.Equation 2 showsdependenceupontwointegernumbersiandjthatcantakeanypositiveornegativevalues.Thetwointegerscorrespondtothetwodimensions.Itisinterestingtoobservethatinthegeneralcase,Equation 2 impliesthatforadiffractiveopticaldevicethetwodimensionsarenotequivalent,asitisnotsymmetricwithrespecttotheinterchangebetweeniandj.Thetwodimensionsbecomeequivalentonlyinthecaseofnormalincidence=0.ThecaseisdescribedschematicallyinFigure 2-1 .Weseethatastheanglexbecomessteepertheelectriceldisintheplaneofthemetallmwithoutchange.OntheotherhandastheangleybecomessteeperTheelectriceldacquiresanincreasingperpendiculartothesurfacecomponent,whilethecomponentinthesurfaceplanegetsweaker.Figure 2-1 impliesthatfornormalincidenceandastheanglexgetssteeperthesurfaceexcitationremainsalmostunaffected(theeffectofjinEquation 2 isweakandnotalteredforpositiveandnegativevalues),representedbythegreenwave.Whentheangleygetssteepertheinitialgreenwavesplitsintoared-shiftedoneandablue-shiftedone,asthewavelengthscorrespondingtopositivediffractionorders 26

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(positivevaluesfori)aredifferentthantheonescorrespondingtonegativediffractionorders(negativevaluesfori). 2.4OtherTheoreticalApproachesInthissectionwewilldiscussthevariousapproachestotheenhancedtransmissionphenomenon.Thefollowingpresentdifferentwaysofdescribinglocalizedelectromagneticeldsinthevicinityofthescatteringstructures.Thetrappedmodestheoryisbasedonthestandardscatteringtheory,whereanyscatteringresonanceisassociatedwithaquasi-boundstatelocalizednearthescatteringstructure.Itisaccuratelydenedasasolutionofthewaveequationunderspecialboundaryconditions(Sommerfeld'sradiationboundaryconditions).Inquantumresonantscatteringtheory,thesestatesarewellknownasSiegertstates.Themorenarrowtheresonance,thelongerthecorrespondingSiegertstatelivesafteritsexcitationbyanincidentwave.AsasolutiontoMaxwell'sequations,aSiegertstatedependsonboththestructuregeometryandthedispersionpropertiesofthestructurematerial.NowtheconstructionofaSiegertstateisthemaintheoreticalconcernofthedifferentapproachestotheenhancedtransmissionphenomenon.Ingeneralsharpdropsinthetransmittanceatspecicwavelengthsaretypicalthresholdphenomenaassociatedwiththeopeningofdiffractivescatteringchannels.Thetransmittancepeakscanbeattributedtoaresonantscatteringoflightviatrappedelectromagneticmodes.ThesearedenedastheeigenvalueproblemsolutionsofMaxwell'sequationswithradiatingboundaryconditions.[ 21 ]Theelectromagneticeldsaretrappedinthevicinityofthestructuresandtheenergydensityofthecorrespondingtrappedmodecangetverylargevaluesthere.Theslowdecayoftheseelds,causetheemissionofnearlymonochromaticradiation.Computersimulationsleadtotheconclusionthatthetrappedmodesareindeedthescatteringresonances.AlsotheysuggestthatthepeaksofOhmiclossesinthemetalmatchthetransmittancepeaks. 27

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Thetheorycanpredictthepositionsofthedipsintransmittance.Thesewillbethethresholdsfortheopeningoftheproposeddiffractionchannels.Fornormalincidencethesediffractionthresholdsaregivenby: s=Dgnd p i2+j2(2)Wherend=p distheindexofrefractionofthedielectricenvironmentofthemetallm.Equation 2 agreeswithEquation 2 ,thatwasderived,afterkeepingthezeroordertermofthesurfaceplasmonpolaritonequationandalsowiththeequationthatpredictsthewavelengthsfortotaldiffraction,fromthediffractiontheory. Figure2-2. Transmittanceplusreectancepredictionsofthetrappedmodestheory,nears=1appearontheleftpanel.Therightpanelsshowtheenergydensityofthecorrespondingtrappedmode.Thecolorcodevariesfromdarkbrown(zero)tobrightyellow(maximum)onalinearscale.[Reprintedgurewithpermissionfrom[ 21 ].Copyright(2006)bytheAmericanPhysicalSociety]. 28

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NumericalsimulationsbasedonthetrappedmodestheorygivetheresultsthatappearinFigure 2-2 forthepredictedformofthesumoftransmittanceandreectance.InFigure 2-2 sdenotesthenormalizedtothediffractionthresholdpredictedbyEquation 2 wavelength.Alsofdenotestheopenareafractionthatistheratiooftheareacapturedbytheholestothetotalareaofthesample.Ontherightsideweseesimulationsoftheintensityoftheelectriceld,thatgetsveryhighvaluesontheedgesoftheholesandalsoit'sdependenceupontheopenareafractionf.Weseethatforsmallerholesthetrappedelectriceldshowsveryhighintensities.Foranon-idealconductorwithohmiclosses,weunderstandthattheohmiclossesaregreaterforgreaterstrengthsoftheeldandthatexplainsthelossintheamplitudesofbothtransmittanceandreectanceasmoreenergyisabsorbedbythemetal.Theresultisthatthedipnexttothediffractionthresholdgetsdeeperforsmallerholes,revealingtheroleoftheholesizetothephenomenon.Thesetheoreticalconsiderationsandpredictionsaregoingtobetestedexperimentallyduringthisstudy.TheremarkablethinginFigure 2-2 isthatthepredictedbehaviouroftransmittanceplusreectance,dependsonlyupontheopenareafraction.Totestthispredictionwefabricatedmanysamplesondifferentsubstratesandwithvariousopenareafractions.Toclosethisgeneralreviewonthevarioustheoreticalschemes,weshouldrefertootherexistinginterpretations,basedondynamicaldiffractioninperiodicslitandholearraysorvariouskindsofresonantcavitymodesinone-dimensional(1D)slitsandslitarrays.[ 22 23 ]Alsonewnumericalstudiesandmeasurementshavemotivatedthedevelopmentofanewmodelofsurfacewaveexcitation,namelythecompositediffractedevanescentwave(CDEW)model.[ 24 25 ]TheCDEWmodelattemptstoexplainpropertiesoftheenhancedtransmissionphenomenonthatcannotbeexplainedbytheinitialapproachfromsurfaceplasmonpolaritontheory.Forexample,thepredictedtransmittancepeaksfromEquation 2 29

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arereallyclosetothecorrespondingdiffractionthreshold(Equation 2 )onthelongerwavelength,leadingtoverysharpresonances.Inthemidinfraredandfarinfraredpartsofthespectrum,wherethedielectricfunctionofthemetalgetsverylargenegativevaluesthewidthoftheresonancesbecomesinnitesimal.Experimentallywetestedthispredictioninalargepartoftheelectromagneticspectrum.Thebroadeningoftheresonancesthatwemeasured,isverylargeanditcannotbeexplainedbyexperimentalerrors.Also,asthedielectricconstantofthemetalgoestominusinnity,weseethatthereisnocouplingconditionforsurfaceplasmonpolaritons,whichimpliesthatperfectconductorscannotsupportthephenomenon.[ 26 ]Theseareweakpointsofthesurfaceplasmonpolaritontheoryasourexperimentsandtheexperimentsofothersshow.Alsonon-metallicphotoniccrystalshavebeenshowntosupportbeamingeffects.[ 27 29 ]Thecompositediffractedevanescentmodelclaimsthatacompositesurfacewaveistheresultofalargedistributionofdiffractedevanescentinhomogeneousmodes.[ 25 30 31 ]Eachofthesemodesisevanescentinthedirectionnormaltothesurface.Theslitorthegrooveisthelaunchsiteofthewavepacketandtheamplitudedecreasesinverselywiththedistancefromthesite.Themodelisbasedonasolutiontothe2-DHelmholtzEquation 2 ,andfortheinterfacebetweentwomediaitreducestoascalarresult.[ 32 33 ]ThisimpliesthattheCDEWmodelcanbeappliedto1-Dsystemslikeperiodicslitarrays.Aswehaveanalysedourdiffractiveopticaldevicesare2-Dandthetwodimensionsarenotequivalent.Sothescalarapproachcanbeusefulonlyforthederivationofqualitativeconclusions.Anothermodelexplainingtheenhancedtransmission,isunifyingthesurfaceplasmonandthediffractionmodel.ThisunifyingmodelproposesananalysiswithFanoproleintransmissionspectra,whichisattributedtoasuperpositionoftheresonantandnon-resonantprocesses.[ 34 42 ]Theresonantprocessisthesurfaceplasmon 30

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contributiontothespectrumwhilethenon-resonantisthedirectlytransmittedlightthroughtheopenapertures.Recently,A.G.Borisovetal.proposedanotherdiffractionmodelfortheenhancedtransmissionofsub-wavelengthstructures.[ 43 45 ]Theysuggestedthattheenhancedtransmissionofsub-wavelengthholearraysisduetotheinterferenceofdiffractiveandresonantscattering.Thecontributionoftheresonantscatteringcomesfromtheelectromagneticmodestrappedinthestructures.Thistrappedelectromagneticmodeisalong-livedquasistationarymodeandoffersanexplanationtotheextraordinaryresonanttransmission. 31

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CHAPTER3EXPERIMENTALSETUP 3.1SampleFabricationWeusedvariousadvancedfabricationtechniquestocreateperiodicarraysofsquareholesinthinmetallms.Forthebetterstudyoftheenhancedtransmissionphenomenonwefabricatedavarietyofsamplesthatdifferaccordingtosomecharacteristicdimensions.Figure 3-1 presentsthosesamplecharacteristics.Theywillbedescribedinthissection,astheyplayaverysignicantroleindeningtheopticalproperties. Figure3-1. Typicalholearraysamplewithgeometricalproperties:Dg:Holearrayperiod,a:Holedimension. AssketchedinFigure 3-1 ,adenotestheholedimension,Dgdenotesthedistancebetweenconsecutiveholes,orholearrayperiod.Usingthesetwoquantitieswecandenetheopenareafractionasf=(a/Dg)2.Wewillusethisnotationconsistentlythroughoutthisstudy.Asourexperimentsandtheexperimentsofothersshow,thesediffractiveopticaldevicesshowaresonanttransmissionatwavelengthsoflightthatareproportionaltoDg.Alsothephenomenonisdescribedasenhancedtransmission,becauseinsomecasesthetransmitted/incidentlightintensityratio,isgreaterthanthe 32

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openareafraction.Aninitialapproachtothestudyofthephenomenonistovarythosetwo(aandDg)geometricalproperties.Ingeneralatypicalholearraysampleispreparedusingthefollowingsteps.Asarststepwehavetoselectthesubstrate.Thebasiccriteriaforthisselectionaretheproperopticalproperties(verylowabsorptionatthespectralrangethatweintendtomeasure),thepropermechanicalpropertiestowithstandthefabricationprocessandalsotheabilityofthemetalusedtostickwelltothepolishedsurface.Toenhancethislastsubstratepropertyweuseinsomecasesaverythinlayerofchrome(Cr)betweenthedielectricsubstrateandthemetal.Thethicknessofthislayerneverexceeds30Asothatitdoesnotinterferewiththepropertiesthatweintendtomeasure.Thenextstepisthedepositionofanabout100nmthinlmofmetalontopofthesubstrate.Onmostofoursamplesthemetalofchoicewassilvermainlyduetothegoodqualityofthenalsamples.Forthispurpose,weusedtwodifferentmethods.Thermaldepositionatarateofabout5A/secgivesverygoodresults,intermsoflmstabilityandroughness.Themetalsusedforthermaldepositionaresilverandgold.ForthepurposeweusedthethermalevaporatormachinefromProfessorHebard'slab.Alsoanothermethodofdepositingveryhighqualitylmsisionsputteringdeposition.ForthepurposesweusedtheSputterDeposition,KJLCMS-18Multi-SourcedeviceattheNanoscaleResearchFacilityoftheUniversity.Thedepositionratevariesaccordingtotherecipeandiongunused,butforourdepositionsitwas10A/sec.Exceptfromtheveryhighqualityofdepositions,anotheradvantageisthatthemachinesitsinsidethecleanroomsothesampleneverleavesthecleanenvironmentuntiltheendofitsfabrication.ThefabricationprocesscontinueswiththespincoatingoftheproperliquidresistthatforthiscaseisPMMAPoly-(MethylMethacrylate).WeusedMicro-chem'sPMMA450A4andPMMA950A4inAnisole.AnisoleislesshazardouschemicalfortheuserthanChlorobenzene.Howevercollaboratorshavereportedsuccessinfabricationof 33

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verysmallgeometriesusingthechlorobenzenetype,buttheresultishighlyunlikelytodependonthesolvent.Differentspin-coatingspeedsresultindifferentthicknesses.Wetestedthequalityofoursamplesforspeedsfrom3000RPMto4000RPM.Thesampleisthenplacedinaconvectionovenat120degreesCelsiusfor30minutes.Analternativewaytopre-bakethesample,istoplaceitfor1minuteonahotplateat120degreesCelsius.Thepurposeofthepre-bakingfabricationstepistosolidifythePMMAbyevaporatingitssolvents,mainlyanisoleforourpurposes.ThenweexposethePMMAtotheselectedholearraypatternusingelectronbeamlithography.AftertheexposurethesampleisdippedintoapropermixofliquiddeveloperMIBK(MethylIsobutylKetone)withisopropanolforasuitableamountoftimethatrangesbetween5and20seconds.ThepartsofthePMMAexposedtotheelectronbeamareremovedbythedeveloperleavingbehindanarrayofsquareholes.Followingthedevelopingprocess,thesampleisplacedintheRIE/ICPUnaxisSLRdryetchingRFdevice,wherea500eVargonionbeamisusedtoetchawaythemetalinthelocationsoftheholes.TheremainingPMMAisthenremovedinanacetonerinse.ThefullprocessisdescribedinFigure 3-2 thatfollows.InFigure 3-2 wecanseealsoanoptionalnalstepwhereontopofthelmwecanspin-coatadielectricsubstanceinordertoalterthedielectricenvironmentofthelm.Ourmeasurementsfocusontheinfraredandvisibleportionsoftheelectromagneticspectrum.Tobeabletostudyabigproportionofthisspectralrangewefabricatedtwodifferenttypesofsamples.Forthenearinfrared(NIR)andvisible(VIS)partsofthespectrumwefabricatedseveralsamplesonfusedsilicasubstrate,asthisdielectricshowsaattransmissionspectruminthisspectralrange.Therefractiveindexofthesubstratewillbeusedforthecalculations(nf.silica1.46inNIR/VISspectralrange).Weusedelectronbeamlithographytopatternthearraysofsquareholes,onthemetallm.Usingthistechnique,wesucceededinfabricatingsquareholesofdimensionsthatrangebetween250nmand500nm.Theholearrayperiodofoursamples,rangebetween600 34

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Figure3-2. Samplepreparationprocess.1)A100nmthinmetallmisdeposited,2)PMMAisspin-coatedontopofit,3)PMMAisexposedtoe-beamanddeveloped.4)Metalisetchedawayfromtheholes,5)RemainingPMMAisremoved,6)(Optional)Adielectricisspin-coatedontopofthesample. nmand1200nm.Aswewilldiscussbeingabletofabricateevensmallerholes,mightresultinveryinterestingexperimentaldata.OnthenextsectionswewilldiscussthelimitationsTomeasuretheholearraysonfusedsilicasubstrateweusedamicroscopephotometerinthespectralrangeof200nmto2000nm.Thisdevicehastheadvantageofhighsignaltonoiseratioevenforsampleareasthatareassmallas104nm2.Thelightisincidentasaconecorrespondingtoarangeofanglesofabout5degreesoneverysideofazaxis(normaltothesample)asisshowninFigure 3-1 .Thiswillresultinsmalldeviationsofourdatafromthetheoreticalpredictions,butwillnotalterthequalitativeconclusions.Thesecondsetofsamplesisintendedforstudyinthemid-infrared(MIR)andfar-infrared(FIR)regionsoftheelectromagneticspectrum.ThedielectricsubstrateusedforthisstudyismadeofZinc-Selenide(ZnSe)witharefractiveindexthatrangesfromnZnSe=2.415at=8mtonZnSe=2.315at=19m.Theholedimensionsofthosesamplesrangebetween3mand4mwhiletheholearrayperiodrangesbetween6mand8m.Thefabricationstepsaresimilartotheprevioussetofsamplesexcept 35

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thatinthiscaseweusephotolithographyinsteadofelectronbeamlithographyduetothemuchlargersizeoftheholes.Inthephotolithographycaseontopofthemetallmwespin-coattheS1813photoresistandprebakeonahotplateat120degreesCelciusfor1minute.WeplacethesampleonaKarlSussMA6maskalignerandontopofthesamplewealignamaskwiththedesiredpattern.Lightof405nmwavelengthexposesthephotoresist.Usingthesuitableliquiddeveloperweremovetheexposedphotoresist.TheprocessthatfollowsisasdescribedforthePMMAresistcase.ThesamplesthatarefabricatedonZnSesubstratearemeasuredusingaBruker113vFourierspectrometerinthespectralrangeof2mto25m.Forthereectanceweuseastage,wherethesampleismeasuredatnearnormalincidence(about10degreesoffaxis).Thissmallincidenceanglewillpresentasmallcontributiontotheexperimentalerrorofourdata.Thenaldataarederivedafteraveragingthespectraofmanyscansforincreasingthesignaltonoiseratio.Exceptfromthesamplesthatwefabricated,onthisdissertationwepresentthemeasurementsoftwosamplesthatwereprovidedtous.Thesamplesconsistofa1.2mthickgoldfoilsuspendedonanickelringandperforatedbycrosslikeperiodicallyspacedholes.Thetwosampleshavedifferentperiodicitiesandholesizesandweremeasuredinthefarinfraredandmidinfraredpartsofthespectrum. 3.2ThinGoldFoilSampleDescriptionThedatathatarepresentedinChapter4,aremeasurementsofsamplesthatwehavefabricatedinthenanoscaleresearchfacilityoftheUniversityofFlorida.Thefabricatedsampleshadthelimitationofalwaysusingasubstratefortheirmechanicalstability.Thepropertiesofthesubstratelikeitsrefractiveindex,causedeviationsofourresultsfromthepredictedones.Alsoaswewillexamineinthestudyofthedielectricenvironment,iteffectstheenhancedtransmissionphenomenonbecauseitcausesbadindexmatching,thuswecannotseeverystrongresonances.InChapter5wewill 36

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Figure3-3. SEMimageofthesideofthegoldfoilmeasuringitsthickness(imagetakenbyAndresTruccoofAdvancedPlasmonicscompany,samplefabricatedbyLakeshoreCryogenics). examineperiodicstructuresperforatedonathingoldfoil.ThesampleswerepreparedbyLakeshoreCryogenicscorporationandweregiventousformeasurementsbyourcollaboratorsNaradaBradmanandAndresTruccoofAdvancedPlasmonicsCompany.Weareverythankfultothem.Chapter5referstothemeasurementsthatwereperformedonthesesamples.Inthissectionwedescribetheirgeneralcharacteristics.Theyconsistofa1.2mthickgoldfoilthatissupportedbyanickelring.Theinnerdiameteroftheseringsis19mm.OnasmallcutofthefoilourcollaboratorsexaminedthesamplethroughSEMimaging.Figure 3-3 showsagoodimageofthecutwerethethicknessofthesamplecanbeexperimentallydened.Thestructuresthatwereperforatedinthetwosamplesthatwemeasuredwerecrosslike.ByselectingtheproperperiodicitiesLakeshoreCryogenicsintendsto 37

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fabricatebandpassltersintheinfraredfornormalincidence.Exploitingbettertheinfraredpartofthespectrumisoneobviousapplicationofthediffractiveopticaldevicesthatwestudy.Thethicknessofthefoilallowsthefabricationofsamplesinthefarinfraredandmidinfraredpartsoftheelectromagneticspectrum.Thetwoltersthatwemeasuredshowtheirresonanttransmittancepeaksonthisrangetoo,soforthemeasurementsweusedtheBruker113vFourierspectrometer. Figure3-4. SEMimageofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3m(imagetakenbyAndresTruccoofAdvancedPlasmonicscompany,samplefabricatedbyLakeshoreCryogenics). Figure 3-4 showsanSEMpictureofthesamplewithintendedresonancewavelengthat80m.WeseeperiodiccrosslikestructureswithaperiodicityofDg=66.2m.Thetotallengthoftheperforatedstructuresis:L=39.3m(whereLdenotesthetotallengthofthearmofthecross)andthethicknessofthecrossesisabout6.62m.Thecalculatedopenareafractionis:f0.10whichisverysimilartothethirdcaseinthesimulationsbasedontrappedmodestheorythatwaspresentedinFigure 2-2 .Thefoil 38

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isthickenoughanddoesnotneedasubstratetosupportit,thustheonlydielectricenvironmentisvacuumwithrefractiveindexnvac=1.ThevacuumiscreatedasthesamplesareplacedinsidethetransmissionorreectioncompartmentoftheBruker113vinstrumentandthenthewholeinstrumentisevacuated.Thenwecanchangetheincidentangleorswitchbetweensamplesusingknobs.ForthesamplethatwaspresentedinFigure 3-4 wedirectlyknowthatthediffractionthresholdfornormalincidencewillexistat:s=Dg=66.2m.Thisallowustoselecttheproperset-upoftheBruker113vinstrumentformeasurementsinthispartofthefarinfraredspectrum. Figure3-5. SEMimageofthegoldfoilsamplewithcharacteristicgeometry:Dg=8.64mandL=4.93m(imagetakenbyAndresTruccoofAdvancedPlasmonicscompany,samplefabricatedbyLakeshoreCryogenics). Thesecondsamplethatwemeasuredhascharacteristicgeometricaldimensions:Dg=8.64mandL=4.93mandthusshowsitscharacteristicresonanttransmittancespectruminthemidinfraredpartofthespectrum.Figure 3-5 showstheSEMpicture 39

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thatwastakenbyourcollaboratorsonthatsample.Againtheopenareafractionisf0.10andwecancomparetheresultstothetheoryoftrappedmodes.Onecharacteristicofthissamplethatweneedtoremarkisthatthecrosslikestructuresdonothavetheperfectshapethatweobservedinthepreviouscasebuttheyshowdeviationandmainlytheopeningbecomeswiderclosertothecenteroftheperforatedstructure.Thisisprobablyafabricationsideeffect,asitgetshardertofabricatestructureswithsizescomparabletothethicknessofthegoldfoil.Asithasbeenshownbyothersandourdatawillsuggest,theshapeofthestructuresplaysaroleindeningitstransmittancespectrum.Sointhatsensethetwosamplesthatweexamineinthisdissertation,showsomesmalldifferencesinshapethatwewillobserveinthecorrespondingspectratoo. 3.3ZeissMPM-800MicroscopePhotometer Figure3-6. ThemicroscopephotometerusedformeasurementsofsampletransmittanceandreectanceintheVIS/NIRpartsofthespectrum. Forthemeasurementsofthevisible(VIS)andnearinfrared(NIR)spectralranges(200nmto2000nm),weusedtheZeissMPM-800microscopephotometerthatis 40

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sketchedinFigure 3-6 .Thisinstrumenthasafewadjustableparts,sothatitcaneasilyswitchmodefromreectiontotransmission.Alsointernalmirrorscanipaccordingtotheinstructionsgivenbytheuser,toselectbetweendifferentsourcesanddetectors.Thespectrumisdividedintotworegionsthatoverlapwitheachother.TheVISregion(200nmto800nm)iscoveredbytheuseofaXenonarclampwithaseparatemonochromator(otherthanthatofFigure 3-6 ).Thenthecomputerthatoperatestheinstrumenthastheoptiontobypassthemonochromatorthatsitsinfrontofthedetector.Thedetectorthatweuseisaphotomultiplier(PMT).TheNIRspectralregion(600nmto2000nm)ismeasuredusingatungstenlampandaPbSdetector.AllthewavelengthsofthelightilluminatethesampleandthenareseparatedatthemonochromatorofFigure 3-6 .Topreparetheinstrumentfortransmissionmeasurementsweneedtoattachthesourcescompartmenttothebottomposition(Figure 3-6 )andalsotoinstallthecondensorlensunderneaththesampleplatform.Theslitontopofthesampleiscoveredwithanemptyboxtoallowthetransmissionoflighttothedetector.Asweseetherearealsopositionsforplacinganopticaliristhatconcentratesthebeamonlyonthesamplearea.Developingbiggerareasamplesposestheconcernofmuchlongerelectronbeamexposuretimes,sothesampleareasarekeptaround200x200m2.Forreectionwehavetoattachthesourcecompartmenttothehighposition(Figure 3-6 ).Alsoweneedtoreplacetheemptyboxontopofthesamplewithaboxthatcarriesthebeamsplitters.Theboxhasthreedifferentcompartments.Theonethatisusedforreectancehasonlythebeamsplitterattachedtoit.Theothertwoareusedforphotoluminescenseandtheyhaveproperltersinstalled.Theentranceltereliminatesallwavelengths,exceptthedesiredilluminationwavelengththatthenexposesthesample(resonanceopticallter),whiletheexitltercropstheilluminatingwavelengths(lowpassopticallter). 41

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Figure3-7. Theeffectthattherefractionofthesamplehasonthemeasurementofthemicroscopephotometer. Onthetransmissionmodethelightaftertheiriscomesasanearlyparallelbeamtothecondensorlens.Thelensconcentratesthelighttothesampleandthetransmittedintensityiscollectedbyanotherlens.Thisimpliesthatthelightisformingacone,thatisequivalenttothesamplebeingilluminatedspatiallybybeamsthatdeviateinangleofincidencefrom0degreestoabout5degrees.AlsothesamplecancauserefractionofthelightasFigure 3-7 shows,thatbecomesimportantforthicksamplesoflargerefractiveindex.Thismightcausesomeoftheintensityofthelightthatwascollectedonthebackgroundmeasurement,todeviatefromthecollectinglensandthetransmittancewillturnoutsmallerthanitsactualvalue.AlsoasEquation 2 shows,thepositionofthecharacteristicwavelengthsoftheenhancedtransmissionphenomenondependupontheangleofincidence.Soevenwhentheconcernthatwejustdescribedisnotpresent,stillweexpectsomea-priorismalldeviationofourtransmittanceresultsfromtheiractualvalues.Alltheseconsiderationswillbecomeveryclearwhenwewillpresentourexperimentalresults. 42

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Figure3-8. SchematicdiagramoftheBruker113vFourierspectrometer.Numbersdenotethedifferentparts.1)Globarsource,2)Mercuryarcsource,3)Sourceselectingmirror,4)Nonmovablemirror,5)Aperture,6)Opticallter,7)Beamsplitter,8)Iris,9)Scanneronitstrack,10Channelselectingmirror,11)Reectancestage,12)Transmissionchannel,13)Sample,14)DTGSdetector,15)Siliconbolometer. 3.4Bruker113vFourierSpectrometerForthemeasurementsofthesamplesthatpresentresonancesinthemid-infrared(MIR)andfar-infrared(FIR)partsoftheelectromagneticspectrumweusedaBruker113vFourierspectrometer.ItsfunctionisbasedoncollectingtheinterferogrambytheuseofaMichelsoninterferometer.ThelightbeaminaMichelsoninterferometertravelsinitstwoarmsafterbeingpartiallytransmitted/reectedbythebeamsplitter.Thelengthofonearmisconstantwhilethereisamovablemirroronthesecondarmthatchangesitslength.Whenthelengthsofthetwoarmsareequal,thereisconstructiveinterferenceofallthewavelengthsandthesignalonthedetectorismaximum.Asthemovablemirrormovesawayfromthatposition,differentwavelengthshavedifferentinterferencepositions,whichiswhatgivestothecollectedinterferogramtheinformationofthedifferentwavelengths.AsshowninFigure 3-8 forourspectrometerthereisa 43

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scannerthatmovesadoublesidedmirroronaspeciedtrack,changingbotharmsatthesametime,onebecominglargewhiletheotherbecomesshorter.Figure 3-8 showsthedifferentpartsoftheBruker113vFourierspectrometerthatweusedforourstudy.Thepathofthelightbeamstartsatthesourcecompartment.Thiscompartmenthousestwodifferentsources.Aglobarsourceforthemeasurementofthemid-infraredspectralrangeandamercuryarcsourceforthefar-infrared.Theselectingmirroripsbetweenthetwopositionstoselectthesource.Thebeamthentravelsthroughanapertureselectedbyamechanism,totheinterferometercompartment.Therewecanselecttheproperopticallterandalsotheproperbeamsplitter,viatwoseparatewheelmechanisms.Thescannermovesonitstrackwithnearlyconstantspeedthatcanbeselectedbytheuser.Thescannermovesthemainbigdoublesidedmirror,butalsomovesasmallermirrorthatproducesaninterferogramforaredlasersourceandawhitelightsource.Thecenterburstonthewhitelightinterferograminitiatesthedatacollectionwhilethezerocrossingsofthelaserbeamarethepointswheretheanaloguetodigitalconvertercollectseachpointofthemaininterferogram.Thecollectedinterferogramissinglesidedandwecanachieveresolutionsof0.1cm)]TJ /F9 7.97 Tf 6.59 0 Td[(1.ThefastFouriertransformisappliedtotheinterferogramofeachscanningcircletoderivethespectrum.Thenastheinterferogramissingle-sidedtheproperphasecorrectiontechniqueisapplied.Theresultsfromeachscanarestoredinacomputermemory.Usuallyeverymeasurementistheaverageofmanyscans,sothatthesignaltonoiseratioisimproved.AsweseeinFigure 3-8 forthetransmittancemeasurementsthereisanincomingconeoflightandthismeanssomecomponentsofthebeamhavenon-zeroanglesofincidence.Thustherefractionandgeometricalconcernsthatwediscussedinthemicroscopephotometersectionapplyalsotothiscase.Alsothereectancemeasurementsaretakenatanangleofabout10degreesoffthenormaltothesample 44

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axis.Theseinstrumentationlimitationscausesmalldeviationsofourresults,fromtheirtruevalues. 3.5FourierTransformSpectroscopyInthissectionwewillpresentthebasicprinciplesofFouriertransformspectroscopy.ThemaincomponentoftheBruker113vspectrometerthatweusedforourmeasurements,istheMichelsoninterferometer.TheMichelsoninterferometerconsistsofthesource,thebeam-splitterthatsplitsthebeamintoitstwoarmswiththexedandmovablemirrorandthedetector.AschematicdiagramappearsinFigure 3-9 .Thebasicprincipleofoperationisquitesimple. Figure3-9. SchematicdiagramoftheMichelsoninterferometer.Themaincomponentsarethesource,beam-splitter,xedandmovablemirrorsandthedetector.Thetwoarmsoftheinterferometerhavelengthsl1andl2. ForunderstandingpurposesletussupposethatthesourceemitsamonochromaticbeamofwavenumberandintensityB()thatisincidentonthebeam-splitter.Thebeam-splitterhasamplitudereectioncoefcient(r)andtransmissioncoefcient(t).So 45

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partofthebeamwillbereectedtowardsthearmwithlengthl1,whiletheotherpartwillbetransmittedtothearmwithlengthl2.Thetwobeamsarereectedbythemirrorsandrecombineonthebeam-splitter.Thebeamcomingfromthexedmirrorisreectedbythebeam-splitter,whiletheonereectedfromthemovablemirroristransmittedandbothmovetowardsthedetector.Sobothbeamshavebeenoncetransmittedandoncereectedbythebeam-splitter.Itisobviousthatwhenthetwoarmsoftheinterferometerhaveequallengthsl1=l2,wehaveconstructiveinterferenceofthetwobeamsandallthesignalB()iscollectedbythedetector.Whenweintroduceapathdifference=l1-l2throughthemovablemirrorthetwobeamsgetoutofphasesotherecombineddetectedsignalfortheidealcaser=0.5andt=0.5willbe: IR()=B() 2[1+cos(2)](3)Nowletsconsiderthegeneralcaseofapolychromaticsource.Theincidentamplitudeoftheelectriceldtothebeam-splitterwillbe: E(z,)d=E0()expfi(!t)]TJ /F4 11.955 Tf 11.96 0 Td[(2)d(3)Withzthedistancebetweenthesourceandthebeam-splitter.Therecombinedamplitudewillbe: ER(l1,l2,)d=rtE0()[expi(!t)]TJ /F4 11.955 Tf 11.95 0 Td[(2l1)d+expi(!t)]TJ /F4 11.955 Tf 11.96 0 Td[(2l2)d](3)Fortheintensitywithrespecttothewavenumberwehave: I(l1,l2,)d=ER(l1,l2,)ER(l1,l2,)(3)Substitutingweget: I(l1,l2,)d=2E20()jrtj2[1+cos(2)]d(3) 46

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Sothetotaldetectedintensityis: IR()=Z10I(,)d=2jrtj2[Z10E20()d+Z10E20()cos(2)d](3)Ifweconsiderthevalueofthedetectedintensityfor=0thenwederivethenalformoftheinterferogramthatis: IR()=1 2IR(0)+2jrtj2Z10E20()cos(2)d(3)IR(0)isjustanadditiveconstantthatonlyshiftstheleveloftheinterferogram.Whileitsvalueisnotimportantinthecalculationofthespectrum,deningwithgoodaccuracywhere=0is,isverycrucialespeciallyforsinglesidedinterferograms.Equation 3 describestheidealsinglesidedinterferogram,thatisaninterferogramthatiscollectedbymovingonlyononesideoftheposition=0(centerburst).Ourspectrometerstartscollectingdataalittlebitbeforethecenterburst.InarealworldcasethepathdifferencecannotbeinnitesotheintegralinEquation 3 shouldhavenitelimitsandthustheresolutionofanyinterferometerisnitetoo.Thereasonthatwecollectsinglesidedinterferogramsistoexploitallthedistancethatthescannercantravel,thusimprovingtheresolution.Alsotheimperfectionsthatexistonthedesignofanysystem,causeerrorsthatcanbeinsertedinthetheorythatwaspresentedasdistortionsinthephaseofthecosineterm.Toderiveandcorrectthesephasedistortionsthereexistmanytechniquesandoneofthemiscollectingadoublesidedinterferogram.Intheidealcaseitwillbeperfectlysymmetricwithrespecttothecenterburst,butinrealcasesitisnot.Thenphasecorrectiontechniquesareapplied,butananalysisofthosewillnotbeattemptedforthepurposesofthiswork.ForourmeasurementsweusedtheMertzphasecorrectionmethod.Oncewehavethecorrectedinterferogram,wecanderivethespectrumby 47

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applyingtheFouriercosinetransform. B()=1 jrtj2Z10[IR())]TJ /F4 11.955 Tf 13.15 8.09 Td[(1 2IR(0)]cos(2)d(3) 3.6FabricationConcernsInthissectionwewilldiscusssomeconcernsrelatedtothefabricationprocess.Usuallytherewerenoseriousconcernswithourphotolithographysamples.Thesesamplesrangeinholesizesfrom2mto6m,whiletheperiodicityDgisneversmallerthan4m.Thismeansthatwedealwithlargegeometricalcharacteristicsincomparisontothewavelengthoftheexposinglight(405nm),soeffectslikeroundingofsquarefeaturesarenotveryimportant.Alsothephotoresistlayerusedisalotthicker,whichallowsustonotbetoocautious,selectingtheaccelerationvoltagesandsputteringtimeduringtheetchingprocess.Themainconcerniswiththesamplesthatarefabricatedonfusedsilicasubstratesthatneedtohavethesmallestgeometricalcharacteristics.Onthenoblemetalsused(silverandgold)thevolumeplasmonappearsintheircharacteristicplasmafrequency,whichisintheultravioletpartofthespectrum.Aswewillseefromourdata,thevolumeplasmonappearsasanotherresonanceintheultraviolet,butthistimewillnotbeattributedtothegeometricalcharacteristicsofthesamplebuttothenaturalpropertiesofthemetallm.Nowiftheholeseparationgetsverysmallthentheexcitationfrequenciesofthesurfaceplasmonsgetclosetotheplasmafrequency.Resonancesattributedtothegeometry,behaveonaspecicwaywhentheirexcitationfrequenciesgetcloser.Theinteractionbetweenaresonanceduetogeometryandthevolumeplasmonissomethingthatwewantedtoexperimentallystudy.Wesuspectthatthevolumeplasmon'scharacteristicswillchange,asforexampletheacousticpropertiesofanemptyroomchangewhentheroomislledwithfurnitureandotherobjects.Toconductsuchanexperimentweneedtofabricatesampleswithholeseparationsmallerthan500nm.Thisneedstheuseofelectronbeamlithographyandforthe 48

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purposeweusedtheRaith150machineinsidethecleanroomoftheNanoscaleReasearchFacility.EventhoughthewavelengthoftheelectronsandthespotsizeoftheRaith150instrumentpracticallydonotposeanylimitations,fabricatingsmallgeometriescanbetricky,asthereareassociatedproblemsthatwewillbrieydiscussinSection3.8.AidingusinthiseffortwehavealotofsampleimagingtechniquesthatwewilldiscussinSections3.7and3.8.Opticalimagingusingthemicroscopephotometerisnotveryusefulinourcaseasthegeometryistoosmall,tobeabletoextractconclusionsabouttheareaqualityanddepthofthefabricatedfeatures.Soweusedtwoimagingtechniques,AFM(AtomicForceMicroscopy)andSEM(ScanningElectronMicroscopy). 3.7AtomicForceMicroscopy Figure3-10. AFMimageofaperiodicholearraysample,afterdevelopingthePMMAresist.Thecharacteristicdimensionsofthesampleare:Dg=1200nmanda=537nmcorrespondingtoanopenareafractionf=0.20.Thesamplewasdevelopedin5:1MIBK/IPAfor30seconds. TheAtomicForceMicroscopeisaninstrumentthatallowsveryaccurateimagingofverysmallstructures,withresolutionmuchbetterthantheopticaldiffractionlimit.It'smainadvantageoveropticalimagingandSEMisthatitcangiveusathreedimensionalimageofthesample.Itusesacantileverwithaverysharptiponitsend.Thetipcanfollowthefeaturesofaholearraysample,givingusaveryaccurateestimateofthe 49

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Figure3-11. AFMimageofaperiodicholearraysample,afterdevelopingthePMMAresist.Thecharacteristicdimensionsofthesampleare:Dg=600nmanda=268nmcorrespondingtoanopenareafractionf=0.20.Thesamplewasdevelopedin5:1MIBK/IPAfor20seconds. depthoftheholes.Weuseditinnoncontactmode,whereapiezoelectriccrystalallowsfortinyandveryprecisemovementsofthecantilever,afewnanometersoverthesurfaceofthesample.Theaccuratemeasurementofthepositionofthecantileverisperformedusingthetimeofightofalaserbeamthatisreectedoffitsbacksurface,toanappropriatedetector.Figure 3-10 showstheresultsofanAFMmeasurementofasuccessfullydevelopedsample.TheimageistakenafterthedevelopingofthePMMA.Usingthetechniquewecancomparedifferentdevelopingrecipes,tondtheoptimumone.Inthiscasethesamplewasdippedinsidea5:1mixtureofdeveloper/stopper(MIBK/IPA)for30seconds.Theholesizeis:a=537nmandtheholeseparationis:Dg=1200nmtokeeptheopenareafractionatf=0.20.Aftersavingthethreedimensionalimageontheinstrumentscomputer,wecanmeasurethedepthofthePMMAalongselecteddirections.Inthedirectionoftheredlineonthetwodimensionalpreview,thesampleproleisshown.Onthesameprolewehaveapproximatedthedesiredhole 50

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Figure3-12. AFMimageofaperiodicholearraysample,afterdevelopingthePMMAresist.Thecharacteristicdimensionsofthesampleare:Dg=600nmanda=268nmcorrespondingtoanopenareafractionf=0.20.Thesamplewasdevelopedin5:1MIBK/IPAfor30seconds. sizewiththegreenverticallines.The950A4PMMAwasspin-coatedat3600RPMcorrespondingtoathicknessofabout220nm,asshowninFigure 3-10 .TheprolepictureisconsistentwithMicrochem'sdata.Ageneralremarkisthattheproleofthissampleisverypromisingforthefabrication.TobetterunderstandhowAFMimagingcanhelpusoptimizethedevelopingprocess,thesameAFMimagesarecollectedforasamplewithholeseparationDg=600nmandf=0.20openareafraction.Thespin-coatingspeedwas3600RPMandthedeveloper/stopperratiowas5:1.Figure 3-11 showstheAFMimagesfor20secondsdevelopingtime,whilefortheimagesofFigure 3-12 weexposedthesamplefor10moresecondsforatotalof30seconds.Theimagesprovideevidenceofhowcrucialisforthedevelopingofsmallgeometriestheoptimizationofthedevelopingprocess.ThePMMAtendstoacquireverysharpcharacteristicsatthebeginningofthedevelopment.ThenthePMMAwallstendtogiveintoaroundingeffect. 51

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Alsotheygiveusafeelingofthecharacteristicsoftheelectronbeamthatexposedthesample.Inthisnothighqualitysamplecase,theenergyoftheelectronbeamseemsconcentratedmainlyinthecenterofthehole,cominginwithaconeshapeleavingpartiallyexposedtherestoftheholearea.Thisisanindicationofnotverygoodfocusofthebeaminthesurfaceofthesample.TheelectronbeamfocusproblemswillbediscussedinSection3.8.Usinghigherdevelopertostopperratiosforsmallertimesofexposure,gavebetterresultsforthisgeometry.MoreAFMimagesarepresentedonAppendixA. 3.8ElectronBeamLithographyAswehavediscussedintheprevioussectionsthefabricationofverysmallstructuresposessomedifculties.Fortheperiodicholearrayscasethedifcultiesariseforholeseparationssmallerthan600nm.Asthesesizesarecomparabletothelightusedinthephotolithographyfabrication(405nm),thistechniquecannotbeused.ForthisfabricationsweusedtheRaith150electronbeamlithographymachine.Thissectionpresentsourconcernsregardingthisprocess.Thestructuresthatwefabricateconsistofametallmsosurfacechargingbytheelectronbeamisnotsomuchofaconcern.Toeliminateanysuchpossibilityoncethesampleismountedtothespeciallydesignedmetallicplatformoftheinstrument,wemakesurethatthereisverygoodelectricalcontactbetweenthelmandtheplatform.ForthispurposeweremovethePMMAonthepointsofcontact.Theinstrumentgivesustheoptiontoselectbetweenvariouselectronacceleratingvoltagesinarangebetween1kVoltand30kVolts.Ontherstfabricationswewereusing10kVoltsacceleratingvoltageand100Coulombcurrentdose.Tofabricateevensmallerstructuresweexperimentedwithmanydifferentacceleratingvoltagesanddosages.NowafteralotofexperimentationwiththeRaith150machinewederivedthefollowingconclusions.ThemainconcernwiththePMMAontopofsilversamplesistheveryblurryimagethatinsomecasesthesecondaryelectronscreate,whichresultsina 52

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Figure3-13. SEMimageofaperiodicholearraysampleafterdevelopmentofthePMMAresist(Dg=500nm,a=200nm).ThesamplewasfabricatedusingRaith150at20kVoltandthepicturewastakenusingJEOL5700at5kVolt. Figure3-14. SEMimageofaperiodicholearraysampleafterdevelopmentofthePMMAresist(Dg=1000nm,a=300nm).ThesamplewasfabricatedusingRaith150at20kVoltandthepicturewastakenusingJEOL5700at5kVolt. badfocusoftheelectronbeam.Thebadfocusjustdistractsabittheperfectshapeoftheholesinaholearraysamplewithlargeholeseparation.ButforsmallerseparationsallofthePMMAresistisexposedbytheelectronbeamandtheresultistoyawayatthedevelopingprocess.ThebadfocusisrelatedtothePMMAonsilveronfusedsilicasubstratesamples,aswehadnoproblemfocussingonothertypesofsamples,like 53

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PMMAonsiliconsubstrateforexample.TheimagesinFigure 3-13 andFigure 3-14 arethebestimagesthatwecouldtakeforthespecicreferredsamples,withtheJEOL5700SEM,afterexperimentingwithvariousparameters.ThesameproblemswithfocussingwehadduringtheirfabricationwiththeRaith150.Figure 3-15 ontheotherhandhasalotbetterqualityandthefocuswasprettygoodduringthefabricationtoo.Theproleoftheexposurethoughisnotveryuniform,butithasashapelikethenumber8. Figure3-15. SEMimageofaperiodicholearraysampleafterdevelopmentofthePMMAresist(Dg=1000nm,a=300nm).ThesamplewasfabricatedusingRaith150at30kVoltandthepicturewastakenusingJEOL5700at10kVolt. 54

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CHAPTER4PERIODICHOLEARRAYSINSILVERFILMS 4.1PrologueInChapter4wearegoingtopresentourexperimentaldataonourfabricateddiffractiveopticaldevices.ThegeneralconclusionsderivedfromthesedataagreeinbothNIR/VISandFIR/MIRspectralregions,suggestingtheuniversalityoftheenhancedtransmissionphenomenon.Thefabricationfollowedthestepsthathavebeendescribed.Onthebeginningtheenhancedtransmissionphenomenonwillbepresentedandonthenextsectionsthemaindifferentattributesofthephenomenonasdenedbyourexperimentswillbeextensivelystudied.ForthestudyoftheinuenceofthedielectricenvironmentwehaveusedtheoptionalfabricationstepashasbeenpresentedinFigure 3-2 .ThemaintheoreticalapproachhasbeentheuseofthepredictionsofthetrappedmodestheorywhileforthecalculationofthediffractionthresholdsEquation 2 hasbeenused.Thisapproachtakesintoconsiderationonlytheeffectsoftheholearrayperiodinthedeterminationofthespectrum.Chapter4willclosewiththestudyofthepolarizationandangleofincidenceeffectsonthespectrum. 4.2NormalIncidenceTransmittanceOurexperimentalstudybeginswiththemeasurementsofthetransmittancespectraofperiodicholearraysonZinc-Selenidesubstrates.Wedeposited100nmthicksilverlmsandweperforatedperiodicarraysofsquareholeswithdifferentperiodicitiesandopenareafractions.ThetransmittancespectrawasmeasuredfornormalincidenceoflightusingtheBruker113vFourierspectrometer.Figure 4-1 presentsthenormalincidencetransmittanceofthreedifferentsamples.Thethreesampleshavecharacteristicgeometricaldimensions1)Dg=6.0m,a=4.0m,(f=0.44),2)Dg=6.0m,a=3.0m,(f=0.25)and3)Dg=8.0m,a=4.0m,(f=0.25). 55

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Figure4-1. TransmittancespectraofthreedifferentholearraysamplesonZinc-Selenidesubstrate.Blackverticallinesshowtheattributedtothesubstratediffractionthresholdsandcyantothevacuum,forthebluegraph(Dg=8.0m).Greenandmagentalinesshowtheonesattributedtosubstrateandtovacuumcorrespondinglyfortheothertwosamples(Dg=6.0m). Inthesedataweclearlyobservetheenhancedtransmissionphenomenon,astheresonanttransmittancepeaksareexceedingtheopenareafractionnotedonthegraph,forthegreenandtheblueplots.Alsotheseresonancesappearatwavelengthsthatexceedbyalotthedimensionoftheholes,suggestingthatthetheoreticalapproachshouldbedifferentfromthatbasedontheaperturetheory.Theshapeofthetransmittanceplotsisageneralcharacteristicofthesedevicesasitissimilarinallthecasesthatwestudied.Specicallythereisoneresonancepeakthathasthemaximumamplitude,followedbyotherprogressivelyweakeronesthatappearatshorter 56

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wavelengths.Theresonanceatthelongerwavelengthsusuallyexceedstheopenareafractionforawellfabricatedsample.WeobservetwomaincharacteristicsoftheenhancedtransmissionphenomenoninFigure 4-1 .Therstcharacteristichastodowiththeamplitudesofthetransmittancepeaks.Weseethattheresonancesofthesampleswiththesameopenareafractions(f=0.25)haveapproximatelythesameamplitudes,whilethesamplewithf=0.44hasmuchstrongerresonances.Thisisareasonableexperimentalresult,butaquantitativeexplanationcannotbefoundintheaperturetheoryofclassicalelectrodynamics.Tounderstandthiswecancalculatetheamplitudeoftransmittedlightat19.6mforasamplewith:Dg=6.0m,a=4.0m,(f=0.44).Equation 1 givesthenT=3.12%,whileinFigure 4-1 weseethatthetransmittancereaches:T=33%avaluemorethan10timeshigher.Thesecondmaincharacteristicisthatthetwosamplesthathavethesameholearrayperiod(Dg=6.0m)showtheirstrongestcharacteristicresonancesatthesamewavelength.Theothercharacteristicresonantpeaksalsoappearatalmostthesamewavelengths.ThesamplewithDg=8.0mshowsthecharacteristicresonancesatdifferentwavelengthswhilethestrongestappearsatalongerwavelength.Thisfacthasbeenobservedinallofthecasesthatwestudiedandsuggeststhatforsquareholestheholearrayperioddenesthepositionsofthecharacteristicpeaks.ThisisingoodagreementwiththetheoryofsurfaceplasmonsasthereisnoholesizedependenceinEquation 2 .Alsotheresonantpeaksareaccompaniedbyadipontheirleftside,whichisrelatedtotheopeningofthediffractionchannelsofthetrappedmodestheory.ThesearethediffractionthresholdsandfornormalincidencecanbecalculatedusingEquation 2 .Table 4-1 showsthecalculatedcharacteristicdiffractionthresholdsfortherstfourdiffractionorders,(differentvaluesofi2+j2inEquation 2 )forthetwosampleswith:Dg=6.0m.Thecalculationstakeintoconsiderationthetwodifferentdielectrics 57

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(Zinc-Selenidesubstrateandvacuum)thatsurroundtheopticallythicksilverlms.TherefractiveindexofZinc-Selenideisnotconstantinthemeasuredspectralrangesoitschangeistakenintoconsiderationforamoreaccurateprediction.InTable 4-1 wealsopresenttheexperimentallydenedvaluesattributedtothesubstrateandthevacuum. Table4-1. TablewiththecalculatedrstfourdiffractionthresholdsforthesamplewithDg=6.0m. SampleDiffractionRefrac.dipdipdipdipperiodicityorderindex(subst.)(vacuum)(exp.subst.)(exp.vac.)nZnSe(m)(m)(m)(m) Dg=6.0mi2+j2=12.37614.256.0014.05.8i2+j2=p 22.40610.204.2410.0i2+j2=22.4217.263.007.3i2+j2=p 52.4236.502.685.8 ForthesamplewithDg=8.0mwepresentthecalculateddiffractionthresholdsinTable 4-2 Table4-2. TablewiththecalculatedrstfourdiffractionthresholdsforthesamplewithDg=8.0m. SampleDiffractionRefrac.dipdipdipdipperiodicityorderindex(subst.)(vacuum)(exp.subst.)(exp.vac.)nZnSe(m)(m)(m)(m) Dg=8.0mi2+j2=12.32018.568.0018.07.8i2+j2=p 22.38613.505.6613.2i2+j2=22.4109.644.009.4i2+j2=p 52.4158.643.587.8 Weseethatthecalculatedpositionsforthediffractionthresholdscorrespondverywelltothepositionsofthedips,withthesmalldifferencesattributedtoexperimentalerror.Sothedatasuggestacrucialroleofthegeometricalcharacteristicsoftheholearrayinthedenitionofthespectrum,thatcanbestudiedusingthetheorypresentedinChapter2.Thereasonthatweselecttocheckthevalidityofourtheoreticalconsiderationsbycalculatingthepositionsofthediffractionthresholds(dipsinthegraph),isthatitgivesverygoodapproximationtotheexperimentalresults.Thedielectricconstantofsilver 58

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inthemidinfraredrangehasaverylargenegativevalue(inthehundreds)rangesothedielectricratioinEquation 2 ispracticallyzero.SothepositionsofthepeaksalmostcoincidewithpositionsofthedipscalculatedinTable 4-1 andTable 4-2 .Thisisoneoftheweakpointsofthesurfaceplasmontheoryaswehavediscussed,whilethediffractionthresholdapproachisbetterinthiscase. 4.3NormalIncidenceReectance Figure4-2. ReectancedataforthesilveronZinc-Selenidesamples(solidlines).Thedashedlinespresentthecorrespondingtransmittancedata. Tofurthertestthevalidityofthetheoreticalconsiderationswemeasuredthereectanceofoursamples.Thereectancedataofthetwosamplesthathavethesameopenareafraction(f=0.25)arepresentedinFigure 4-2 .InFigure 4-2 wealsopresentthetransmittanceofthesesampleswiththedashedlinesforcomparison. 59

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Thereectancealsoshowsgreatsimilaritiesbetweensampleswithdifferentholearrayperiodsbutsameopenareafractions.Thesesimilaritieswhereobservedinthetransmittancespectratoo.Weobservethatthewavelengthsofthetransmittancepeaksapproximatelycorrespondtoreectancedipsandtheopposite.Howeverweneedtotakeintoconsiderationthatthereectancedatahavebeentakenatnearlynormalincidence(10degreesoffaxis).Theeffectofthesmallangleofincidenceisthesplitofthereectancediponthelongerwavelengthsideofthecalculateddiffractionthreshold,intotwoseparatedips.Thespectrumdependenceupontheangleofincidencewillbestudiedthoroughlyonaseparatesection.FornowletssaythatthisbehaviourcomplieswithEquation 2 forthecaseofnegativeandpositivenon-zerovaluesofintegeri. Figure4-3. Extinctiondatafortwosampleswithdifferentopenareafractionsandcomparisonwithsimulationsbasedontrappedmodestheory. 60

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Wecanderiveveryusefulconclusionsabouttheopeningofthediffractivechannelsandtheohmiclossesrelatedtotheholesizeandthemetallm,byaddingthetransmittanceandreectancedata.FromthiswecanderivetheextinctiongraphE=1-T-Rthatcanbecomparedtotheoreticalsimulationsbasedonthetrappedmodestheory,thathavebeenpresentedinFigure 2-2 .Wecalculatedtheextinctionforthetwosamples1)Dg=6.0m,a=4.0m,(f=0.44)and2)Dg=6.0m,a=3.0m,(f=0.25)thathavedifferentopenareafractions.ThenormalizedtothresholdwavelengthextinctionispresentedinFigure 4-3 .Onthesameplotweseetheplotsderivedfromthesimulationsforcomparison.Weseethatthegeneraltrendsareinagreementbetweentheoryandexperimentwithinthelimitsofexperimentalerror.Themainsourceoferroristhenon-normalincidence(10degreesoffaxis)forthereectancedata.Thetwosamplesthatwerejustpresentedhavegreatopenareafractionsandtheextinctiondipattributedtoohmiclossesfromthetheoryisnotverydeep.Alsothenon-normalincidenceforthereectanceandtheconeshapeoftheexposingbeamshouldgiveshiftofthatdipandingeneralbroadeningoftheresonantfeatures.Thevalidityofthesimulationswillbebettertestedwhenwecomparereectanceandtransmittancemeasuredatthesameangleofincidence.Wealsotestedtheagreementbetweentheoryandexperiment,inthenearinfrared/visiblerange.Forthispurposewefabricateda100nmthicksilversampleonfusedsilicasubstrate,withperiodicity800nmandholesize400nm.Thetransmittance(T)andreectance(R)weremeasuredusingamicroscopephotometerusingun-polarizedlightinthe600nmto2000nmspectralrange.TheexperimentalresultsalongwiththecalculatedT+RarepresentedinFigure 4-4 .AlsoFigure 4-5 presentstheT+Rdatawiththewavelengthnormalizedtothediffractionthreshold(s=1168nm).Againthereectancegraphiscomplementarytothetransmittance.Theobservedsplitinthereectancedataisattributedtotherangeofincidentanglesthatthe 61

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Figure4-4. Reectance+TransmittanceforsilveronfusedsilicaholearraysamplewithDg=800nm,a=400nm,(f=0.25). microscopephotometeruses.Thesamereasoncausesthebroadeningofthetransmittanceplot.Thiseffectsalongwiththefactthattherearediffractionthresholdsclosetothestrongestresonanceat=1400nmcausethesmalldeviationoftheexperimentallydenedshapefromthepredictions.ThegeneralconclusionisthattheformofthecalculatedT+Ragreeswellwiththesimulatedform.Alsoweneedtoremarkthatthemainresonanceofthissamplereachestransmittanceof50%,whileitsopenareafractioniskeptsmallf=0.25.Sotheenhancedtransmissionphenomenonismoreclearinthiscasewhileournextexperimentshaveshowntransmittanceamplitudesthatcanexceedbyalottwotimestheopenareafraction. 62

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Figure4-5. Normalizedtos=1168nmReectance+TransmittanceforsilveronfusedsilicaholearraysamplewithDg=800nm,a=400nm,(f=0.25). Accordingtothetheoryoftrappedelectromagneticmodesthephenomenoniscausedbythegreatenhancementoftheelectriceldamplitudesinthevicinityoftheholes,atwavelengthsclosetoitsresonantvalue.Thisleadstolargerproportionoftheenergybeingdissipatedbytheohmiclossesinthemetalatthosewavelengths.Atshorterthanthediffractionthresholdwavelengths,morediffractionchannelsareopen,soenergyislostfromthemeasurementinthehigherdiffractionorders(thezerodiffractionorderismeasured).Figure 4-4 andFigure 4-5 showsclearlythesepointsbothinthesimulatedandtheexperimentalplots.Atlongerwavelengthstherearenopredictedresonancesandthediffractiveopticaldevicebecomesopaqueintransmittance,whileitsreectanceapproachesR=1,assilverisaperfectreectorinthesewavelengths. 63

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Figure4-6. TransmittanceforsilveronZinc-Selenideholearraysampleswithvariousperiodicitiesandopenareafractions. 4.4AnalysisofTransmittanceandReectanceDataForthebetterunderstandingofthespectroscopicpropertiesofthediffractiveopticaldeviceswewillperformananalysisofthetransmittanceandreectancecharacteristicsofmanydifferentperiodicholearraysamples.Figure 4-1 presentsthedataforthreedifferentsamplesfabricatedonZinc-Selenidesubstrate.Figure 4-6 showsthosedataalongwithtwoothersilveronZinc-Selenideholearraysamples.Theperiodicitiesofallthepresentedsamplesrangefrom4mto8mandthesampleshavetwodifferentopenareafractions(f=0.25andf=0.44).AlsotheroleoftheholearrayperiodcanbebetterexaminedifwenormalizeallthegraphsofFigure 4-6 withrespecttotherstcalculateddiffractionthreshold.The 64

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Figure4-7. NormalizedtotherstdiffractionthresholdtransmittanceforsilveronZinc-Selenideholearraysampleswithvariousperiodicitiesandopenareafractions. calculatedvaluesofthediffractionthresholdsappearinTable 4-3 .ThenormalizedtransmittanceappearsinFigure 4-7 Table4-3. TablewiththecalculatedrstdiffractionthresholdsattributedtoZinc-Selenideforholearrayswithvariousperiodicities. SampleRefractivedipperiodicityindex(substrate)nZnSe(m) Dg=4.0m2.4109.64Dg=6.0m2.37614.25Dg=8.0m2.32018.56 Figure 4-7 showsclearlytheeffectthatthegeometricalpropertiesoftheperiodicholearrayhaveonthespectrum.Weseethatthesampleswiththelargeopenarea 65

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Figure4-8. Transmittanceandreectancedataforsilveronfusedsilicaholearraysampleswithvariousperiodicitiesandopenareafractionf=0.20.Thicksolidlinespresentthetransmittancedatawhilethethinlinespresentthereectance. fraction(f=0.44)showthegreatestamplitudesontheirresonanttransmittance,whilethenon-resonantbackgroundonthesmallerwavelengthsalsogetshigherforlargerholesandopenareafractions.Thedifferentorderresonancesscalegoodwitheachotherfordifferentgeometrysamplesandwealsoobservenarrowerresonancesforlargergeometrysamples.Inthecasesofthesampleswith8.0mperiodicitythereisacontributionfromtheZinc-Selenidesubstratethatstartscuttingoffatthewavelengthsafterthegreatresonanttransmittancepeak.Butingeneralweexpectthatthelargergeometrysamplesarebetterfabricatedasthefabricationgetseasierwhenthestructuresgetbigger. 66

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Figure4-9. Normalizedtotherstdiffractionthresholdattributedtothefusedsilicasubstratetransmittance,forsilveronfusedsilicaholearraysampleswithvariousperiodicitiesandf=0.20openareafraction. Alsoweperformedthesametestsinthenearinfraredandvisiblerangeofthespectrum.Forthispurposewefabricatedthreedifferentsampleswiththesameopenareafractionf=0.20.Thesampleswerefabricatedona100nmthicksilverlmonfusedsilicasubstrate(nf.silica1.46).Thegeometricalcharacteristicsofthesamplesare:SampleA(Dg=800nm,a=358nm),SampleB(Dg=1000nm,a=447nm),SampleC(Dg=1200nm,a=537nm).ThetransmittanceandreectancedataappearinFigure 4-8 .Thesedataalsoshowthegoodcorrespondencebetweentransmittancepeaksandreectancedips.Allofthesampleshavehigherthantheopenareafraction 67

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Figure4-10. CalculatedReectance+Transmittancespectraforsilveronfusedsilicaholearraysampleswithvariousperiodicitiesandf=0.20openareafraction. transmittanceofaboutthesamelevel.Themainreectancedipsreachalsothesamelevel,whileforlongerwavelengthsthereectanceapproachesR=1,thatisthereectanceofsilverwithoutholes.Forshorterthantherstdiffractionthresholdwavelengths,wehaveenergyradiatedtohigherdiffractionorderssothemeasuredzeroorderreectionhassmallvalues.Theeffectoftheperiodicityisstudiedbynormalizingourtransmittancedatawithrespecttotherstdiffractionthreshold.ThecalculationsoftherstsarepresentedinTable 4-4 andthenormalizedtransmittancedataarepresentedinFigure 4-9 68

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Figure4-11. NormalizedtotherstdiffractionthresholdReectance+Transmittancespectraforsilveronfusedsilicaholearraysampleswithvariousperiodicitiesandf=0.20openareafraction. Table4-4. Tablewiththecalculatedrstdiffractionthresholdsattributedtofusedsilicaforholearrayswithvariousperiodicities. Sampledipperiodicity(substrate)(nm) Dg=800nm1168Dg=1000nm1460Dg=1200nm1752 InFigure 4-9 weobserveagainthescalingwithrespecttotheperiodicity.Alsoweseethatastheperiodicityincreasesthemainresonanttransmittancepeakgetsclosertothediffractionthreshold,somethingthatweobservedalsointhestudyofthesamplesfabricatedonZinc-Selenidesubstrates.Theindexofrefractionoffusedsilica 69

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getssmallerforlongerwavelengths,butthechangeislessthan0.5%inthespectralrangeofinterestandthusisnegligible.Thethreesampleswerefabricatedonthesamesubstrate,andthismeansthattheywentthroughthesamefabricationprocesses.Ingeneralasthedatasuggestdifferentsamplegeometriesrequireslightlychangeddevelopingandetchingrecipes,foroptimumresults.UsingthetransmittanceandreectancedatawecalculatedtheT+Rspectraofthedifferentsamples.TheresultsappearinFigure 4-10 .Tobeabletocomparetheresultstothepredictionsfromthesimulationsbasedonthetrappedmodestheory,weagainnormalizedthedatawithrespecttotherstdiffractionthreshold.TheexperimentalresultsalongwiththetheoreticalpredictionsareshowninFigure 4-11 .InFigure 4-11 werstobservethatthethethreegraphshaveverysimilarcharacteristicshapes.Allofthemshowasmallpeakatthediffractionthresholdwavelength,followedbyadeepdipatthelongerwavelengthsideofthediffractionthresholdandthenT+Rstartsrisinguntilitslimitvalueof1.Thisbehaviourisverysimilartothebehaviourpredictedfromthesimulationsbasedonthetrappedmodestheoryforasamplewithf=0.25openareafraction(upperplotinFigure 4-11 ).Thedominantcharacteristicintheseplotsisthedipafterthediffractionthresholdwavelength,thatisrelatedtogreaterohmiclossesinthatregion.Thisissimilartothesimulatedplotforasamplewithf=0.11openareafraction(lowerplotinFigure 4-11 ).Sothedatasuggestthatourfabricatedperiodicholearraysampleswithf=0.20haveintermediatecharacteristicsbetweenthetwosimulatedplots. 4.5EffectsoftheDielectricEnvironmentIngeneraltheresonantpropertiesofperiodicstructurescanbeunderstoodwiththehelpoftheconceptofcoupledresonanceswhichhasbeendevelopedandextensivelystudiedinquantumscatteringtheory.Thecouplingbetweenresonancescanchangetheirpositionandtheirwidth,orcanstabilizeoneresonanceturningitintoaboundstate 70

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intheradiationcontinuum.Theresonancescaninteractthroughtheradiativeeldsaswellasthroughevanescenteldsifthedistancebetweenthestructuresisnotverylarge.Inthissectionwewillanalyzetheroleofthedielectricenvironmentonthecharacteristicsofthetransmittancespectraofperiodicholearraysonmetallm.Therstobservationsoftheenhancedtransmissionphenomenontriggeredinterestinthecouplingbetweenlightandsurfaceplasmons.[ 11 ]Thiscouplingoccursviadiffractionoftheperiodiclatticeandenablesefcientexcitationofasurfaceplasmonmodeononeofthemetaltodielectricinterfaces.[ 46 ]Nowplasmonsonasingleinterfacecanbecoupledtoawaveguidemode.[ 35 37 ]Thecouplingmechanismcanbeimprovedbythegeometricalpropertiesandthedielectricenvironment.Thetwoexcitedsurfacemodescaninteractthroughtheholesaswellasbecomecoupledtotheradiationcontinuum.Aperiodicperforationnaturallyleadstoquantizationofthesurfaceplasmonwavevector,fromwhichitfollowsthatsurfaceplasmonpolaritonscanbeexcitednearthediffractionthresholds.Thiscouplingbetweenexcitationsondifferentinterfacesismoredifculttoobservebecauseinthegeneralcasetheplasmonresonancesondifferentsidesofthemetallmaredetunedinfrequency.[ 46 ]Thisisbecauseoftheasymmetrythatononesideofthelmwehavethesubstrate,whileontheotherwehaveingeneraladifferentdielectricmaterial(airusually).Theseconsiderationswereexperimentallystudied,byvaryingthedielectricontopofthesilverlmandtheresultsarepresentedonthissection.Forthispurposewefabricateda100nmthicksilverlmonZnSesubstrate.Thecharacteristicdimensionswere:Dg=6.0m,a=4.0m,(f=0.44).ThesamplewasmeasuredontheFIR/MIRattwodifferentstepsofthefabricationprocess.Therstmeasurementwasatthestage4ofthedevelopingprocessasispresentedinFigure 3-2 .Duringthisstagearesidueofthephotoresistusedremainsontopofthesample.TheindexofrefractionoftheS1813photoresistis:nS18131.6inallof 71

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Figure4-12. TransmittancedataforaholearraysampleonZnSewithDg=6.0m,a=4.0m,(f=0.44).Theorangeplotpresentsthedatafromstage4ofthedevelopingprocesswherethereisstillphotoresistresidueontopofthesilverlm.Thegreyplotshowsthedataatstage5whenallthephotoresisthasbeenremoved. thespectralrangeofourmeasurements.Accordingtothetheoreticalanalysisthathasbeenpresented,wecanuseEquation 2 tocalculatethecharacteristicdiffractionthresholdsattributedtoeachofthemetaltodielectricinterfaceincludingtheS1813photoresist.ThecalculatedpositionsarepresentedinTable 4-5 .Figure 4-12 presentstheexperimentalresultsatstages4and5ofthedevelopingprocess.Atstage5weusestandardcleanroomsolventstoremovetheremainingphotoresist.OnthesameplottheverticallinesrepresentthecalculatedinTable 4-5 characteristicdiffractionthresholdwavelengthsattributedtotheair,ZnSesubstrate,andS1813photoresist. 72

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Table4-5. TablewiththecalculatedrstfourdiffractionthresholdsforthesamplewithDg=6.0mincludingtheremainingphotoresistS1813. SampleDiffractionRefractivedipdipdipperiodicityorderindex(substrate)(air)(S1813photoresist)nZnSe(m)(m)(m) Dg=6.0mi2+j2=12.37614.256.009.60i2+j2=p 22.40610.204.246.79i2+j2=22.4217.263.004.80i2+j2=p 52.4236.502.684.29 Atstage5ofthedevelopingprocessweobservethattheamplitudeofthestrongestresonanceissmallerthanthelargeopenareafractionofthisspecicsamplef=0.44.Themaincharacteristicofthesampleatthisstageisthegreatmismatchbetweentheindexesofrefractionbetweenthedielectric/metalinterfacesoftwosidesofthelm.Thesubstrateofthelmhas:nZnSe2.4,whileontheairsidewehave:nair1.0.SoasweseeinTable 4-5 thediffractionthresholdsonthetwosidesoccuratwavelengthsthatarefarapartfromeachother.Forthatreasonthetransmittancespectrapresentasmootherpattern.Onlythehigherintegerindexordersofthesubstrate/metalinterface,caninteractwiththerstindexordersoftheair/metalinterface.Ontheotherhandatstage4ofthedevelopingprocessweobservethatthebignumberofseparatediffractionthresholdsgiverisetomanyseparateresonances.TheattributedtotheS1813photoresistresonancesaddalotmorefeaturestothetransmittanceplotthanthestage5one.TheS1813refractiveindexnS18131.6isinbetweentheonesforsubstrateandairsoasTable 4-5 showstheattributeddiffractionthresholdsfallinbetweenthetwo.Alsowecanremarkthehighertransmittanceamplitudesofthetworesonancesat:15.0mand10.8m,atstage4ofthedevelopingprocess.Themaximumtransmittanceinthiscaseexceedstheopenareafraction.Thephotoresistresiduehasanindexofrefractionhigherthanthatofair,sotheattributedresonancesshiftclosertotheonesattributedtothemetal/substrateinterface.Thedatasuggestthatresonancesoneachsideofthemetallmcaninteract.Thebehaviourofthestrongestresonance 73

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thatappearsatthelongerwavelengths(15.0m)suggeststhattheinteractionfavourstheamplitudeoftheresonancesatthelongerwavelengths. Figure4-13. Transmittancedataforsilveronfusedsilicasamplesatstage5ofthedevelopingprocess. Inordertoexaminebetterthislaststatementwefabricatedthreedifferentsamplesonfusedsilicasubstrate.Wetookcaresothatallofthesesampleshavethesameopenareafraction,thatwekeptsmallatf=0.10.Thethreesampleshavecharacteristicgeometricaldimensions1)Dg=800nm,a=253nm,2)Dg=1000nm,a=316nmand3)Dg=1200nm,a=379nm.Allthreesampleswerefabricatedonthesamepieceofsubstrate.Thisspecicsampleshowssomeimperfectionsinthefabrication.Itwasprobablyunder-etched,asthisprocessisnotabsolutelycontrollable,andsampleswiththespecicpropertieshaveshownalothighertransmittances.Inthiscasesilvermetal 74

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remainsinsidetheholesblurringtheenhancedtransmission.Howeveritisidealforourstudyasitshowedthegreatestchangewiththealtereddielectricenvironment.ThemeasuredtransmittanceofthesamplesatnormalincidenceintheNIR/VISspectralrangeatstage5ofthedevelopingprocess(Figure 3-2 )ispresentedinFigure 4-13 Figure4-14. Transmittancedataforsilveronfusedsilicasamples.ThesolidlinespresentthemeasurementsafterPMMAhasbeenspincoatedontopofthesample.Thedashedlinescorrespondtostage5ofthedevelopingprocess. Becauseofthefabricationimperfectionsthatwedescribedthetransmittanceofthesampleismuchlowerthantheopenareafraction.Atstage5ofthedevelopingprocess(Figure 3-2 )thesubstrate/metalinterfacecontributesthestrongresonancesthatweseeatlongerwavelengths.Theresonancesattributedtotheair/metalinterfacearemuchseparatedfromthose,sothereisonlyverysmallinteractionbetweenthesetwotypesof 75

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resonances.Thisisbecausetheindexofrefractionofthedielectricaboveandtheonebellowthemetallmareverydifferentfromeachother(nair1.0whilenf.silica1.46).Thepurposeofthisexperimentwastostudyasamplethatconsistsoftwometal/dielectricinterfaces,wherethedielectricshavethesameindexofrefractioninthemeasuredspectralrange.Forthispurposeweaddedtheoptionalstage6ofthedevelopingprocessinFigure 3-2 .Abovethemetalwespin-coateda200nmthicklayerofPMMA,thathasanindexofrefraction:nPMMA1.55intheNIR/VISspectralrange.Thisisveryclosetotheindexofrefractionoffusedsilicanf.silica1.46.Thisconditionisdescribedas:nearlyindexmatching.Figure 4-14 presentsthemeasurementsofthesampleafterthelastfabricationstep.WecanseeforcomparisonthedataofFigure 4-13 withthedashedlines.Asourdatasuggesttheinteractionbetweentworesonancesonnearlyindexmatchedsamples,favoursalottheamplitudeoftheresonanceatlongerwavelengths.Itisremarkabletoobservethatbeforetheindexmatchingtheamplitudeoftheresonanceswerenotapproachingtheopenareafraction,whileaftertheindexmatchingthelongerwavelengthresonancesexceedtheopenareafractionbyagreatamount.Theindexmatchingisnotperfectsoweseemanyseparateresonances.Foraquantitativeapproachtothephenomenonwecalculatedthediffractionthresholdsattributedtothedielectricenvironmentofthesilverlminstages5and6ofthedevelopingprocessforthesamplewith:Dg=1000nm,a=316nm,usingEquation 2 .Table 4-6 presentstheresults. Table4-6. TablewiththecalculatedrstfourdiffractionthresholdsforthesamplewithDg=1000nm. SampleDiffractiondipdipdipperiodicityorder(PMMA)(fusedsilica)(air)(m)(m)(m) Dg=1000nmi2+j2=1155014601000i2+j2=p 210961032707i2+j2=2775730500i2+j2=p 5693653447 76

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Figure 4-15 comparetheplotsatstages5and6ofthedevelopingprocessforthatsample.TheverticallinesshowthewavelengthsofthecharacteristicdiffractionthresholdsfromTable 4-6 Figure4-15. Analysisofasilveronfusedsilicaholearraysampletransmittance,withDg=1000nm,a=316nm,(f=0.10).Thebluegraphcorrespondstostage5)ofthedevelopingprocess.Theyellowgraphcorrespondstostage6)withPMMAspincoatedontopofthesilverlm. Thedataverifythesuggestionthattheresonancesinteract,withtheinteractionfavouringtheamplitudeoftheoneatlongerwavelengths.Examiningthestrongestresonanceat1600nmweseethatatstage6thewavelengthofitspeakisslightlyshiftedtothehigherwavelengthssideasthePMMAhasaslightlyhigherindexofrefraction.Theinteractionoftheclosedcoupledresonancesisverystrong,leadingtoafourtimesstrongerpeak.Betweenthetworesonanttransmittancepeaksat 77

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1600nmand1250nm,weseesomestructurethatcannotbeexplainedasresonanttransmission.Itisprobablethatsmallquantitiesofresiduesofsolventsandphotoresists,fromthefabricationprocessremainontopofthelm,withindexesofrefractionbetween1.0and1.55,causingthosestructures. 4.6AngularDependenceSofarwehavepresentedexperimentaldatafortransmittanceandreectanceatnearlynormalincidence.ThemeasurementsusingthemicroscopephotometerandmainlythereectancemeasurementsontheBruker113vFourierspectrometer,showedsomesmallsystematicdeviationsfromtheexpectedresults.Mostofthesedeviationscanbeexplainedaslimitationsoftheexperimentalmeasuringtechniques.Thelimitationthataffectsthesemeasurementsthemostisthenon-normalincidenceofthelight.Wedecidedtoinvestigatefurthertheeffectofnon-normalincidencebymeasuringaholearraysampleatvariousanglesofincidence.Thesampleconsistedofa100nmthicksilverlmdepositedonfusedsilica,withgeometricalcharacteristics:Dg=800nm,a=400nm,(f=0.25).Thetransmittanceofthesamplewasmeasuredatthespectralrangefrom600nmto2000nm,usingthemicroscopephotometer.Thepolarizationofthelightplaysaverysignicantroleonthesemeasurementssothedataareorganizedintwoseparatesets,oneforp-polarizationandthesecondfors-polarization.Thetransmittancesetupthatweusedrotatesonlythesampleagainstaconstantbeamthatisalmostperpendicular(beamlookslikeaconeofincidentandtransmittedlight)tothemetalsurface.Theaxisofrotationliesonthemetalsurfaceandisperpendiculartoanedgeofthesquareholes.Whenthesampleisrotatedsothatthereisnoelectriceldcomponentnormaltothesurfaceofthesamplewecollectours-polarizationdata.Whenthereexistsanormalelectriceldcomponent,thatincreaseswithincreasingangleofincidencewehavethep-polarizationcase.Themaximumanglethatwewereabletoreachwas46degrees,whichissteepenoughtoobserveagreateffectonthespectrum.Thelimitationstoincreasingthe 78

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angleofincidenceevenmore,comemainlyfrommechanicaldifcultyofplacingthesamplebetweenthetwoobjectivesofthemicroscopephotometerandalsofromthenecessitytoreducethesizeofthebeamastheanglegetssteeper,duetotheniteareaofthemetalthatiscoveredbyholes.EffortstofurtherincreasetheincidentanglemightgiveveryinterestingresultsasBrewster'sangleforfusedsilicais:55degrees.Thesignalcanbeincreasedatsteepangles,byfabricatingsampleswithbiggerareacoveredbyholes.Thearealimitationstemsfromthemuchgreatertimes,neededduringthee-beamexposure.Figure 4-16 presentsourexperimentaldataforthes-polarizationcasewhilethep-polarizationcaseispresentedinFigure 4-17 Figure4-16. S-polarizeddataofsilveronfusedsilicasamplewithcharacteristics:Dg=800nm,a=400nm,(f=0.25),forvariousanglesofincidence. 79

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Figure4-17. P-polarizeddataofsilveronfusedsilicasamplewithcharacteristics:Dg=800nm,a=400nm,(f=0.25),forvariousanglesofincidence. Anobviousremarkontheseplotsisthatdifferentlightpolarizationsleadtosignicantlydifferentresultsfornon-normalincidence.Acommoncharacteristicinallthedataisthattheamplitudeoftheresonantpeaksisdecreasing,astheangleofincidenceincreases.Inthenormalincidencecases-andp-polarizationcannotbedenedandweexpectthetransmittancetobethesameforanypolarizationthatisparalleltooneoftheedgesofthesquareholes.Thenastheangleofincidenceincreases,thewavelengthofthestrongestresonantpeak(1400nm)isnotalteredbymuchinthes-polarizationcase.Incontrastthesamepeakinthep-polarizationcaseissplitintomany,thatmovefurtherawayfromeachother,astheangleofincidenceincreases.Examiningtheamplitudesofthese 80

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resonancesandthewavelengthsoftheirappearanceweseethatthephenomenonhasallthecharacteristicsoftheinteractionsofenhancedtransmissionresonances,thatwehavestudiedintheprevioussections.UsingEquation 2 wecancalculatethewavelengthswherethediffractionthresholdsexist.TheresultsarepresentedinTable 4-7 .ForthedatainTable 4-7 wehaveomittedsolutionstoEquation 2 forhigherthantheseconddiffractionordersasthewavelengthsoftheirappearancecannotaffecttheresonancespectrum.Equation 2 issymmetricinthechange(j=N)to:(j=-N)withNinteger,astheintegerjappearseverywheresquared.Soweneedonlythepositivevaluesforthecalculationofthediffractionthresholds.ThatisnottruefortheintegerianditsrolehasbeendiscussedinChapter2.Thesolutionsforpositiveihavebeenomittedastheymoveveryfasttowardsshorterwavelengthswhentheincidenceanglegetssteeper.Theygetoutofthemeasuredspectralrangeandtheycannotaffecttheresonantspectrum.Alsofortheairsideattributeddiffractionthresholdsweusedaneffectiverefractiveindexofne=1.14.Thereasonthatwedidthatisthatthecalculatedcharacteristicwavelengthsagreebetterwiththeexperimentalresults.Wecanjustifythischoiceasforthefabricationweusedchemicalsofrefractiveindicesbetweenthatoffusedsilicaandair,thatsomeresiduemightremain.Qualitativetheresultisnotalteredasthethresholdsmovetothecorrectdirectionwithrespecttotheincreasingangle,foranyvalueoftheairrefractiveindex.Inthes-polarizationcasethishypothesisthatthediffractionthresholdattributedtotheairsidemovesthewaythatacalculationbasedonEquation 2 suggestsischallengedthemost,aswecanseeontheanalysisthatfollows.AccordingtoTable 4-7 thesolutionsforthetwodielectric/metalinterfaceswithi=0andj=1,appeartoslightlyshifttowardssmallerwavelengths,astheangleofincidenceincreases.Amoredetailedanalysisshowsthatthesesolutionscandescribe 81

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Table4-7. Tablewiththecalculatedpositionsofthedipstozero,rstandseconddiffractionorder. dipdipdipdipdipdipAnglesubstratene=1.14substratesubstratene=1.14substrate(deg.)(i=0,j=1)(i=0,j=1)(i=-1,j=0)(i=-2,j=0)(i=-1,j=0)(i=-1,j=1)(nm)(nm)(nm)(nm)(nm)(nm) 011689121168584912826411679101224612967853161147885138969511329282011358701442720118595124112285214937461237972301097820156878413121001361069782163881913821026421038739170385214471048461016708174388114871061 verywellthechangeofthetwotransmittancedips,at1200nmandat900nminthes-polarizedincidentbeamcase,astheyalsoappeartoshifttosmallerwavelengths.Otherdiffractionthresholdsinthecloseproximityofthepositionsofthosedipsexistalsobetween20degreesand30degreesangleofincidence,fori=-1andj=1.Theinteractionoftheseresonanceswiththemainresonancesdescribedabove,giverisetothesmallpeaksthatweseearound1140nm,inthes-polarizedcase,attheseanglesofincidence(Figure 4-16 ).Alsotherangeofincidentangles(5degreesoffnormalaxis)ofthemicroscopephotometer,impliesthatthereisasmallcontributionofp-polarizedlighttothes-polarizedcaseandviceversa.Thisisapossiblecauseofsmalldeviationsofthedatafromtheirexpectedvalues.Similarlyinthep-polarizationcase(Figure 4-17 ),weseethatthedipsmovetolongerwavelengthswhilenewresonancesalsoappear,astheangleofincidencegetssteeper.ThissituationcanbedescribedbythesolutionstoEquation 2 for(i=-1,j=0),(i=-2,j=0)and(i=-1,j=1).AdetailedanalysisshowsthatthereisgoodcorrespondencebetweenthosesolutionsandthepositionsofthedipsinFigure 4-17 .Thesolutions(i=-1,j=1)playamoresignicantrolethaninthep-polarizedbeam 82

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case.Figures 4-21 4-22 4-23 presenttheanalysisforfourdifferentangles.Weselectedthesefouranglesforpreservingagoodclarityoftheplots.Sothelightpolarizationappearstoplayasolutionselectingrole,leadingtoverydifferentresultsfors-andp-polarizations.OnFigure 4-19 andFigure 4-20 wemarkthecalculatedpositionsofthediffractionthresholds.Theexperimentclearlysuggeststhatthesolutionsthatdenethes-polarizationbehaviourare(i=0,j=1)and(i=-1,j=1),whileforthep-polarization(i=-1,j=0),(i=-2,j=0)and(i=-1,j=1)withthelaterplayingamoresignicantrolethaninthep-polarizationcase.Fornospecicpolarizationofthelight(un-polarized)wegetFigure 4-24 .Weseethatthisplotcanbederivedasasuperpositionofthecharacteristicsofthes-polarizationandthep-polarizationcases. Table4-8. Tablewiththecalculatedpositionsoftheattributedtofusedsilicasubstratepeaksanddipsfors-polarization(i=0,j=1),forthesilveronfusedsilicasamplewithgeometricalcharacteristics:Dg=800nmanda=400nm. AnglempeakdipExperimentallyExperimentally(silver)(i=0,j=1)(i=0,j=1)denedpeakdeneddip(nm)(nm)(nm)(nm) 0deg.-7211851168141412094deg.-72118411671416120716deg.-70116511471434120520deg.-69115411351448120024deg.-68114011221456119830deg.-63111811971499113136deg.-61109111691521111942deg.-58106211381564111046deg.-541043111615111099 Foramorequantitativecomparisonbetweenthetheoreticalpredictionsandourexperimentaldataweshowplotsofthepositionsofpeaksanddipswithrespecttotheangleofincidence.Wehaveexaminedtheexperimentallydenedpeaksanddipsfor(i=0,j=1),(i=-1,j=0)attributedtobothdielectrictometalinterfaces,bothwithrespecttotheangleandtosin().ForthecalculationsofthepeakpositionsweassumedDrudemodelbehaviourforthedielectricconstantofthesilver.Theparameters 83

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Table4-9. Tablewiththecalculatedpositionsoftheattributedtoairpeaksanddipsfors-polarization(i=0,j=1),forthesilveronfusedsilicasamplewithgeometricalcharacteristics:Dg=800nmanda=400nm. AnglempeakdipExperimentallyExperimentally(silver)(i=0,j=1)(i=0,j=1)denedpeakdeneddipE.M.(n=1.14)E.M.(n=1.14)(nm)(nm)(nm)(nm) 0deg.-4292691211388904deg.-42925910113689016deg.-39901885113588820deg.-38886870113888424deg.-36870852114487130deg.-3384082097884136deg.-3080578295982742deg.-2776573994180646deg.-25739708914768 Table4-10. Tablewiththecalculatedpositionsoftheattributedtofusedsilicasubstratepeaksanddipsforp-polarization(i=-1,j=0),forthesilveronfusedsilicasamplewithgeometricalcharacteristics:Dg=800nmanda=400nm. AnglempeakdipExperimentallyExperimentally(silver)(i=-1,j=0)(i=-1,j=0)denedpeakdeneddip(nm)(nm)(nm)(nm) 0deg.-7211851168146812304deg.-80124012241515134216deg.-103139513891560142320deg.-111145214421590146224deg.-119150314931629148230deg.-131157715681694154236deg.-144164716381745159242deg.-156171117031797166446deg.-1631751174318501714 forsilverthatweusedare:1=5.0,!p=9.216eVand=0.0212eV.Asourstudyisperformedinthenearinfraredandvisiblepartsofthespectrum,wewillneglectthedampingandthedielectricfunctionwillbegivenby:Equation 2 .Forthes-polarizationcasethecalculatedpositionsareshowninTable 4-8 andTable 4-9 .Forthep-polarizationcasethedataareshowninTable 4-10 andTable 4-11 .Forthecalculationsweusedthevalueofthedielectricconstantofsilveratthewavelengthoftheexaminedpeakordiptoimprovetheaccuracyoftheresults.Also 84

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Table4-11. Tablewiththecalculatedpositionsoftheattributedtoairpeaksanddipsforp-polarization(i=-1,j=0),forthesilveronfusedsilicasamplewithgeometricalcharacteristics:Dg=800nmanda=400nm. AnglempeakdipExperimentallyExperimentally(silver)(i=-1,j=0)(i=-1,j=0)denedpeakdeneddipE.M.(n=1.14)E.M.(n=1.14)(nm)(nm)(nm)(nm) 0deg.-4292691211609004deg.-48980967118893216deg.-67114111321216103220deg.-73119311851253105024deg.-80124512371340129130deg.-90131913121374135036deg.-101138813821399139142deg.-111145314471436138346deg.-1171493148714931416 againfortheairsideweusedaneffectiverefractiveindex(E.M.nair=1.14).AlsoinFigure 4-16 andFigure 4-17 weobservethatourpeaksanddipsareverybroadandsothereisanassociatederrorintheirexperimentaldenition.Fromthedenedvalueofapeakwecheckedthewavelengthsoftheplotforminus3%ofthetransmittancevalue.Thiswaywecandeneonewavelengthontheleftofthepeakandoneontheright.Wedenedtheerrorasthedifferenceofthesevaluesdividedbythewavelengthofthepeak.Takingasampleofvalueswedenedanaverageerrorinthedenitionofapeakoradipwavelengthat3.3%.UsingtheseconsiderationsandthepresenteddataweconstructedFigure 4-25 forthes-polarizationcaseandFigure 4-26 forthep-polarization.Theerrorbarsshowtheapproximateerrorinthedenitionofthewavelength.Theseplotsshowthegoodcorrespondencebetweenthedipsandthecalculateddiffractionthresholds.Thes-polarizationpeaksshowadiscrepancytothelongerwavelengthsfromthepredictedvalue.Thisistheresultofthebroadresonantspectrumofthemeasuredperiodicholearraysample.Thefactorsthatcontributetothisbroadeninghavebeendiscussed.Thep-polarization(i=-1,j=0)peaksshowagoodagreementwiththetheoretically 85

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predictedvaluesasthespectrumcoversabroaderrangeandtheinteractionsbetweenseparateresonancesareweaker.Wealsopresentthesamedatawithrespecttosin()inFigure 4-27 forthes-polarizationcaseandFigure 4-28 forthep-polarization.Duetothechangeinthedielectricconstantofsilverfordifferentwavelengthsthetheoreticalplotsappearcurved,butthecurvatureisverysmallinthep-polarizationcasefor(i=-1,j=0),wheretheequationsthatgivethepeakanddipwavelengthsbecomelinearfunctionsofsin(). Figure4-18. (Orange)Un-polarizedtransmittancedataofaholearraysamplewith:Dg=800nm,a=400nm,(f=0.25)at46degreesangleofincidence.(Blue)Un-polarizedreectancedatafor45degreesangleofincidence.(Black)R+T.Thesmallgraphpresentsthenormalincidencereectance(blue)andT+R(black). 86

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Alsowemeasuredreectanceofthesamesampleat45degreesangleofincidence.Thephotometermeasuresnormalincidencereectancebyusingabeamsplitterthatseparatestheincomingfromthereectedlight.Thereectionat45degreesanglewasmeasuredbyplacingamirrorwithitsplanenormaltothesurfaceofthesample.Thelightthatwasreectedbythesurfaceofthesample,wasreectedalsobythatmirrortotravelbacktotheobjectiveofthemicroscopephotometer.Usingthetechniquedescribedabovewemeasuredun-polarizedreectancefor45degreesangleofincidence.Thesampleareareductionduetothesteepangle,washardertoovercomeinthatcase.Sothemeasurementsusingpolarizedincidentbeamarepending,astheinterferedpolarizerwoulddecreaseevenmorethesignal.TheresultsareshowninFigure 4-18 ,whereforcomparisonweseealsothereectanceofthesampleatnearlynormalincidence,thatwaspresentedinFigure 4-4 .Withintheexperimentallimitationsthathavebeenexplainedweseethatthetransmittanceandreectancedataarecomplementarytoeachother.TheselimitationsexplainthestructuresshownintheR+Tplotandalsoitslowerthanexpected,amplitudeforlongerwavelengths.Theremarkablethingaboutthesedata,isthatthecharacteristicstructurethatweobserve,inthenormalincidencecase(smalldipfollowedbysmallpeakfollowedbygreatdip),appearsatthreedifferentpartsofthespectrumat45degreesangleofincidence,correspondingtothedifferentsolutionsfors-andp-polarizations. 87

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Figure4-19. S-polarizationanalysisofsilveronfusedsilicasamplewithDg=800nmanda=400nm,forvariousanglesofincidence.Thewavelengthsofthediffractionthresholdsattributedtosubstratefor(i=0,j=1)and(i=-1,j=1)aremarkedbythearrows. Figure4-20. S-polarizationanalysisofsilveronfusedsilicasamplewithDg=800nmanda=400nm,forvariousanglesofincidence.Thewavelengthsofthediffractionthresholdsattributedtoairfor(i=0,j=1)aremarkedbythearrows. 88

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Figure4-21. P-polarizationanalysisofsilveronfusedsilicasamplewithDg=800nmanda=400nm,forvariousanglesofincidence.Thewavelengthsofthediffractionthresholdsattributedtosubstratefor(i=-1,j=0)and(i=-2,j=0)aremarkedbythearrows. Figure4-22. P-polarizationanalysisofsilveronfusedsilicasamplewithDg=800nmanda=400nm,forvariousanglesofincidence.Thewavelengthsofthediffractionthresholdsattributedtoairfor(i=-1,j=0)and(i=-2,j=0)aremarkedbythearrows. 89

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Figure4-23. P-polarizationanalysisofsilveronfusedsilicasamplewithDg=800nmanda=400nm,forvariousanglesofincidence.Thewavelengthsofthediffractionthresholdsattributedtosubstratefor(i=-1,j=1)aremarkedbythearrows. Figure4-24. TransmittanceofsilveronfusedsilicasamplewithDg=800nmanda=400nm,illuminatedbyun-polarizedlightforvariousanglesofincidence. 90

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Figure4-25. Angledependentpositionofthetwopeaks(upperplot)andthetwodips(lowerplot)thatcorrespondtotheinterfacesmetal/fusedsilicaandair/silver(ne=1.14)for(i=0,j=1).Thesolidlinesshowthetheoreticallypredictedvalues,whilethetriangulardotsshowtheexperimentaldata. 91

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Figure4-26. Angledependentpositionofthetwopeaks(upperplot)andthetwodips(lowerplot)thatcorrespondtotheinterfacesmetal/fusedsilicaandair/silver(ne=1.14)for(i=-1,j=0).Thesolidlinesshowthetheoreticallypredictedvalues,whilethetriangulardotsshowtheexperimentaldata. 92

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Figure4-27. Sin()dependentpositionofthetwopeaks(upperplot)andthetwodips(lowerplot)thatcorrespondtotheinterfacesmetal/fusedsilicaandair/silver(ne=1.14)for(i=0,j=1).Thesolidlinesshowthetheoreticallypredictedvalues,whilethetriangulardotsshowtheexperimentaldata. 93

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Figure4-28. Sin()dependentpositionofthetwopeaks(upperplot)andthetwodips(lowerplot)thatcorrespondtotheinterfacesmetal/fusedsilicaandair/silver(ne=1.14)for(i=-1,j=0).Thesolidlinesshowthetheoreticallypredictedvalues,whilethetriangulardotsshowtheexperimentaldata. 94

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CHAPTER5PERIODICHOLEARRAYSINTHINGOLDFOIL 5.1AngleDependenceofTransmittance Figure5-1. Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3mfors-polarizedlight. FortherstexperimentswiththethingoldfoilsampleswemountedeachoneonthespeciallydesignedangleofincidencechangingplatformthatwehavedescribedinChapter4.Wemadesurethattheelectriceldatnormalincidenceisorientedparalleltoonesideofthecrosslikestructures.Weusedapolarizerthatworksinthefarinfraredforthesamplewithgeometry:Dg=66.2mandL=39.3mandpolarizedmidinfraredlightforthesamplewith:Dg=8.64mandL=4.93m.Thes-polarizedandp-polarizedmeasurementsfortherstsampleappearinFigure 5-1 andFigure 5-2 95

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Figure5-2. Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3mforp-polarizedlight. respectively.TheonesforthesecondsampleappearinFigure 5-3 andFigure 5-4 respectively.Therearealotofcommentsthatwecanmakeabouttheseplots.Thesesamplesdonothaveasubstratesotheycangiveusaverygoodbasisforcheckingthevalidityofthetheoreticalpredictions.Alsothesimilaritiesanddifferencesbetweenthetwowillhelpusderiveinterestingconclusions.ForaquantitativeunderstandingofthesituationwesolveEquation 2 forthediffractionthresholdsintheexperimentallymeasuredregion.TheresultsarepresentedinTable 5-1 .Againonlythesolutionswithi=)]TJ /F4 11.955 Tf 9.29 0 Td[(1arepresented,asthesolutionswithi=1moveveryfasttowardsmuchshorterwavelengthswiththeincreaseinthe 96

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Figure5-3. Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=8.64mandL=4.93mfors-polarizedlight. incidenceangleandtheycannotaffecttheresonantspectrum.Allotheromittedorders,alsocannotcontributetotheresonantspectrum.Letsbegintheanalysisbyexaminingthesamplewith:Dg=66.2mandL=39.3m.Therstthingthatweobserveinthes-polarizationcase(Figure 5-1 )isthatthestrongestresonanttransmittancepeaksfornearlynormalincidencehaveamplitudesofabout:T=0.80.Thisisveryremarkableifwecompareittotheopenareafractionf0.10.Thegreatenhancementofthetransmissionismainlybasedontheperfectrefractiveindexmatchingbetweentheupperandthelowerdielectric/metalinterfaces.Theresonancesthatareexcitedonthetwosidesofthefoilareperfectlytunedgivingrisetothisremarkableincreaseintransmittance. 97

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Figure5-4. Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=8.64mandL=4.93mforp-polarizedlight. Ournextcommentisabouttheangledependenceofthestrongestpeak.WeseethatasinthecaseofFigure 4-16 ofourfabricatedsamples,thewavelengthofthispeakdoesnotchangeatallwiththeincreaseintheangleofincidence.Alsotheamplitudeofthepeakdecreaseswhentheanglegetssteeperfavouringtheamplitudeofthesmallresonancethatweseeonitsleftside(at69.0m).ThesetwopeaksaretheonlydominantcharacteristicsinFigure 5-1 andthiscreatesaverysimplepicture.Onethingweshouldremarkinthiscaseisthatthedipontheleftsideofthestrongestresonancemovestoslightlylongerwavelengthswiththeincreaseintheincidenceangle,whileinFigure 4-16 wehadseenthedipmovingtoshorterwavelengths.Thebehaviourinthatcasecouldbeexplainedastheshiftofthesubstrate 98

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Table5-1. Tablewiththecalculatedpositionsofthedipstozeroandrstdiffractionorderforthegoldfoilsamplewithgeometricalcharacteristics:Dg=66.2mandL=39.3m. Angledipdipdip(i=-1,j=0)(i=-1,j=1)(i=0,j=1)(m)(m)(m) 0deg.66.246.866.25deg.72.049.665.910deg.77.752.265.215deg.83.354.663.920deg.88.856.762.225deg.94.258.760.030deg.99.360.357.335deg.104.261.854.240deg.108.863.050.745deg.113.063.946.850deg.116.964.742.655deg.120.465.338.060deg.123.565.633.165deg.126.265.927.970deg.128.466.122.6 solutionstoEquation 2 fori=0,j=1withthesteeperangle.InthepresentcasethesesolutionsfromTable 5-1 shifttoshorterwavelengthsfastersotheircontributiontotheformationofthestrongestresonancepeak,isblurredbytheexistenceofthesmallerresonanceat69.0m.SothepresenteddatainTable 5-1 donotexplainthebehaviourofthetransmittanceresonances,forthes-polarizationcase.ThemaindifferencewiththecasesstudiedinChapter4isthecrosslikeshapeofthestructures.Inthefarinfraredpartofthespectrumthefabricatedstructurescanbeperfectcrosses,sotheirbehaviourcanbeunderstoodasasuperpositionofthecharacteristicsoftwoseparatesamples.Thetwosamplesconsistofaperiodicrectangularholearray.Thesizeofeachrectangleis:L1=39.3m,L2=6.62maswecanseeinFigure 3-4 .Theonesamplehasthelongsideoftherectanglesparalleltotheelectriceld,whiletheotherhasitperpendiculartotheelectriceld. 99

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Experimentsperformedinourlabwithrectangularholearraysonsilverlmshaveshownthatwhentheelectriceldisparalleltothelongaxisasmallfeatureontheleftsideofthestrongestresonanceappears,veryclosetothediffractionthreshold,liketheonethatweseeinFigure 5-1 .[ 33 ]Inourcasethefeaturedoesnotexistfornormalincidenceastheindexmatchingcreatesaverystrongmainresonancethatinteractswithitandabsorbsitcompletely.Whenthemainresonancegetssmallerweareabletoseetheshaperelatedfeatureat69.0m.Whentheelectriceldisinthesampleplaneandperpendiculartothelongedgetheresonancepeakappearsatawavelengthfurtherawayfromthediffractionthreshold.Beforeweleavethes-polarizationcasewecanremarkthattheplotforthe5degreesangleofincidenceappearstobehigherthantheoneat0degrees.Thisisnotduetoerrorsindeningthezeroangleasthes-andp-measurementswereperformedataspecicanglebyrotatingthepolarizer.SocomparingwithFigure 5-2 weseethatthisbehaviourisprobablyduetobetterexperimentalconditionsfortheenhancedtransmissionphenomenoninourparticularset-upat5degreesangleofincidence.Thesituationismorecomplicatedinthep-polarizationcasewhereweseeagainthatthemainpeaksplitsintodifferentpeaks.Thisispredictedfromthediffractionequation(Equation 2 )asthedifferentordersofintegerimoveindifferentdirections.OnthefabricatedsamplesthatwestudiedinChapter4wehadattributedthediffractionthresholdsthatcorrespondtotothelongerwavelengthresonancepeak,tothesolutionsofEquation 2 with:i=-1,j=0.Againthesolutionswith:i=1,j=0movefasttoshorterwavelengths,sotheycannotcontributetotheresonanttransmittancespectrumandarenotpresented.Weseethatagainthesesolutions(i=-1,j=0)showthecorrectbehaviour,followingtheshiftofthedipthatexistsontheleftsideofthestrongresonancepeaktowardslongerwavelengths.Quantitativelytheagreementbetweenthetheoreticalvaluesandtheexperimentallydenedcharacteristicwavelengthsisverygoodtoo.Sofarwehaveshownstrongargumentsthatthissolutionplayssignicant 100

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roleindeningtheresonantspectrum,whiletheshapeandsizeofthestructuresdoesnotaltertheresults.Alsotheamplitudeofthelongerwavelengthpeakdecreasesastheanglegetssteeper,whilewehavetheappearanceofabroadpeakat70mthatgetsstronger.Thispeakappearstocontainthecontributionoftworesonancesthatarecloseinwavelength.Ifweattemptamoreaccuratedenitionoftheirpositionwehavetwopeaksat73.2mandat68.0m.Theresonancepeakappearingatsteeperanglesinthes-polarizationcaseisat:69.0mwhichisveryclosetothesecondpeakdescribedbefore(68.0m).ThisisanindicationthattheshapeplayssomeroleindeningtheactualshapeofthepeakbutwehaveseenasimilarsituationinFigure 4-17 .Inthiscasethestrongestpeakatnormalincidencemovesawaysotheresonancethatisveryclosetothediffractionthresholdcangrowinamplitude.Thebehaviourofthesamplewithgeometry:Dg=8.64mandL=4.93misverysimilartothatofthesamplethatweextensivelyanalysed.Duetothesmallersizeofthestructuresthefabricationposesgreaterdifculties.Theshapeofthesampleisalteredfromtheidealcrossesthatweexamined.Nowthereismoreopenspaceinthecenterofthestructure.AlsowecanseeinFigure 3-5 thattheperiodicityisnotconstantandthecrossshapesdonotrepeatidentically.Theseimperfectionshaveameasurableeffectinthetransmittancespectrum.Thecalculateddiffractionthresholdwavelengths(Equation 2 )appearinTable 5-2 .Inthes-polarizationcasethemaindifferencethatweobserveisthatthestrongestpeakstartsmovingtoshorterwavelengths,tillanincidenceangleof30degreesandthenitstartsmovingbacktoitsinitialwavelengthforevensteeperangles(Figure 5-3 ).Alsotheweakeroneforsteepanglesappearatshorterthanthecalculateddiffractionthresholdwavelength.Thisbehaviourcanbeexplainedascontributionsofthesampleimperfections.Inthep-polarizationcaseagainthestrongestatnormalincidence 101

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Table5-2. Tablewiththecalculatedpositionsofthedipstozeroandrstdiffractionorderforthegoldfoilsamplewithgeometricalcharacteristics:Dg=8.64mandL=4.93m. Angledipdipdip(i=-1,j=0)(i=-1,j=1)(i=0,j=1)(m)(m)(m) 0deg.8.646.118.645deg.9.396.478.6110deg.10.146.818.5115deg.10.877.128.3520deg.11.607.418.1225deg.12.297.667.8330deg.12.967.877.4835deg.13.608.067.0840deg.14.198.216.6145deg.14.758.356.1150deg.15.268.445.5555deg.15.728.524.9660deg.16.128.574.3265deg.16.478.613.6570deg.16.768.632.96 resonance,movesaccordingtothesolutionsofEquation 2 for(i=-1,j=0)(Figure 5-4 ).Wecanbetterexaminethebehaviourofthemainpeakandtheescortingdipbydeningtheirpositionswithrespecttotheincreasingangle.Thenwecancomparetheresultstothetheoreticalpredictions. 5.2ReectanceMeasurementsOurspectroscopicstudyofthethingoldfoilsamplescontinuedwithreectancemeasurements.Ourmaingoalistoexaminethebehaviouroftheexpectedreectancedipthatexistsatthelongerwavelengthsideofthediffractionthreshold:s=Dg.Thebehaviourthenwecancomparetothesimulationsbasedonthetrappedmodestheory.Againweusedthepolarizerstoexamineseparatelythes-andp-polarizationcases.Thereectancemeasurementsareperformedatanangleofincidenceof10degreesduetoourexperimentalset-uplimitations.Aswesawinthetransmittanceplots 102

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Figure5-5. Reectanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3mfors-polarizedlight. ofthethingoldfoilsamples,thewavelengthofthestrongestresonancepeakchangesastheangleofincidenceincreases,especiallyinthep-polarizationcase.Soweexpectthatwecanderivebetterconclusionsaboutthepropertiesofthesediffractiveopticaldevicesbycomparingtransmittanceandreectancedataatthesameangleofincidence(10degrees).Forthesetwosamplestheresonanceshaveveryhighamplitudesandareverysharp,soasmallshiftoftheirwavelengthcancausegreatproblemsduringtheanalysis.Westartpresentingourdatabythes-polarizationcase(Figure 5-5 )andthep-polarizationcase(Figure 5-6 )forthesamplewithgeometry:Dg=66.2manda=39.3mthatshowsitsresonantpeaksinthefarinfraredpartofthespectrum.Forthe 103

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Figure5-6. Reectanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3mforp-polarizedlight. understandingofthecrucialroleoftheangleofincidencewepresentthetransmissionplotsforallmeasuredanglesfrom0degreesto20degrees.Weobserveespeciallyinthecaseofp-polarizedlight(Figure 5-6 )thatthestrongestresonantpeakinthe10degreesincidencetransmittance,appearsataboutthesamewavelengthasthegreatdipinthereectance.Ifweaddthedifferentincident-angletransmittanceplotsplusthereectance,wegetareasonableresultonlyforthecaseof10degreesincidencetransmittance.Especiallyinthep-polarizationcasetheotherdegreeresultsshowpeaksthatexceed:T+R=1,whichdeestheenergyconservationlaw.Weobservethatinthes-polarizationcase(Figure 5-5 )themainreectancedipistheonlystrongfeature.Theotherfeaturesatshorterthanthediffractionthreshold 104

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Figure5-7. Reectanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=8.64manda=4.93mfors-polarizedlight. wavelengthsareveryweak.Thecaseisdifferentin(Figure 5-6 ),whereweseeabigdipinreectanceforwavelengthsaroundthediffractionthresholdandshorter.Asthediffractionchannelsarenotopeninsomeofthesewavelengths,comparingthes-polarizationwiththep-polarizationcasedrivesustotheconclusionthattheohmiclossesaregreaterinthelatercase.Soourexperimentsuggeststhattheperpendiculartothesurfaceofthefoilcomponentoftheelectricelddrivesstrongercurrentsinthevicinityofthecrosslikestructures.Thereectancemeasurementsofthesamplewithgeometricalcharacteristics:Dg=8.64manda=4.93m,fors-andp-polarizationsappearinFigure 5-7 andFigure 5-8 respectively.Theresonantcharacteristicsofthissampleappearinthe 105

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Figure5-8. Reectanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=8.64manda=4.93mforp-polarizedlight. midinfraredpartofthespectrumbutthegeneralconclusionsthatwederivedfortheprevioussamplearestillvalid.Againweseetransmittancestrongestpeakandreectancegreatdiptocoincidefor10degreestransmittanceinthes-polarizationcase.Thep-polarizationcaseisveryinterestingforthissample.Thereasonisthattheshiftofthereectancedipthatwehavediscussedtothelongerwavelengths,allowsthedipinitsshorterwavelengthsidetogrow.TheshortwavelengthdipinFigure 5-7 isstrongerthanthelongerwavelengthdip.Theirinteractionshouldfavourthedipatlongerwavelengthsaswehavediscussed,butthisdoesnotsuppresstheshortwavelengthdipinthiscase.Thissuggeststhatthemechanismthatcreatestheshorterwavelengthdipisstrongerforthissample.Possiblereasonsarethemoreenergeticradiationinthemid 106

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infraredrangeoftheelectromagneticspectrum,alongwiththegreaterimperfectionsofthissamplebothinperiodicityandintheshapeofthecrosslikestructures.Thesamereasonscontributetotheincreaseintheamplitudeofthetransmittancepeakat8.5minFigure 5-7 for10degreesincidentangle. 5.3CalculatedTransmittancePlusReectanceSpectra Figure5-9. Normalizedtransmittance+reectanceofthetwogoldfoilsamplesfors-polarizedandp-polarizedlightat10degreesangleofincidenceandcomparisonwithsimulationsbasedontrappedmodestheory. Usingthecollectedreectancedataandthedatafortransmittanceat10degreesangleofincidence,wecalculatedtheT+Rspectrumforthetwogoldfoilsamplesforbothpolarizations.Also,tobeabletocomparetheresultswiththesimulationsbasedonthetrappedmodestheory,wenormalizedthedatawithrespecttothediffractionthresholds=Dgforthetwodifferentsamples.TheresultsappearinFigure 5-9 .For 107

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Figure5-10. Normalizedextinctionofthetwogoldfoilsamplesfors-polarizedandp-polarizedlightat10degreesangleofincidence. comparisonweshowthetheoreticallypredictedvaluesforopenareafractionsf=0.11andf=0.25.AlsoinFigure 5-10 weshowthenormalizedtotherstdiffractionthresholdextinction(E=1-T-R)forabroaderrangeofwavelengths.OurrstcommentabouttheplotsinFigure 5-9 isthattheyallappearatthesameT+RlevelwithvaluesbetweenT+R=0.5andT+R=1.Theremarkablethingaboutthemisthattwosampleswithcharacteristicresonancesatcompletelydifferentpartsoftheelectromagneticspectrumshowsimilarbehaviourforthesamepolarizationconditions.Thetwocurvesreferringtop-polarizationshowgreatsimilarities.Wehaveanalmostatregionintheshortwavelengthsidefollowedbyadipthatreachesmaximum 108

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depthafterthediffractionthreshold.ThenitiscominguptoformasmallpeakthatisfollowedbytheregionwherethereectanceapproachesR=1andthetransmittanceapproachesT=0.Thisbehaviourisverysimilartothesimulatedplotforopenareafractionf=0.11,thatshowsadipafterthediffractionthresholdattributedtoohmiclossesinthemetal.Sincetheopenareafractionsofthesamplesareveryclosetothatvalueweclaimthatthereisverygoodcorrespondencebetweentheoryandexperiment.Againthedatasuggestthattheperpendiculartothesurfaceofthefoilelectriceldcomponentcausesstrongercurrentsinthevicinityofthestructures.Similarcommentswecanmakeaboutthes-polarizationcasesinFigure 5-9 .Duetoexperimentalerrorsthesimilaritytoeachotherisnotperfectlyclearasinthecaseofp-polarization,butthetrendsareagainthesame.AgainwehaveaatregionofsmallT+Rvaluesintheshortwavelengthsside,followedbyasmalldipclosetothediffractionthresholdandthencomestheregionofhighreectancevalues.Inthiscasewedonotobserveacleardipclosetothediffractionthreshold.Thissuggeststhattheohmiclossesinthiscasearesmallerandtheplotsstartresemblingmorethesimulatedf=0.25case(Figure 5-9 ).Thisagainsupportstheargumentthatthelossesaregreaterforperpendicularelectricelds.Finallyweshouldremarkthattheresultsaresuspecttotheexperimentallimitations.ThetheoreticallypredictedformsofR+Tarebasedontheassumptionofnormalincidence.Ourexperimentalresultsarebasedondatafor10degreesangleofincidenceoflightwhilethebeamhasaconeshape,thusincludesashortrangeofangles.Theselimitationscausethefeaturestoshiftfromthepredictedwavelengthsandalsocausebroadeningofthewidthoftheresonantcharacteristics. 5.4NormalizedTransmittanceInthissectionwewillpresentananalysisofourdataregardingthesamplesfabricatedinthingoldfoil.Wewillexamineeachsampleandeachpolarizationseparately.Firstwedenedtheexperimentalpositionsofthemainpeakandthe 109

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Table5-3. Tablewiththepositionsofthepeaksanddipsfor(i=0,j=1)forthegoldfoilsamplewithgeometricalcharacteristics:Dg=66.2mandL=39.3m. AngledipExperimentallyExperimentallysin()(i=0,j=1)deneddipdenedpeak(m)(m)(m) 0deg.066.268.281.05deg.0.087265.968.481.010deg.0.173665.268.581.215deg.0.258863.966.881.620deg.0.342062.270.381.825deg.0.422660.071.281.230deg.0.500057.371.480.635deg.0.573654.271.780.440deg.0.642850.771.980.845deg.0.707146.872.281.050deg.0.766042.673.281.455deg.0.819238.073.581.260deg.0.866033.173.682.065deg.0.906327.973.382.2 Table5-4. Tablewiththepositionsofthepeaksanddipsfor(i=-1,j=0)forthegoldfoilsamplewithgeometricalcharacteristics:Dg=66.2mandL=39.3m. AngledipExperimentallyExperimentallysin()(i=-1,j=0)deneddipdenedpeak(m)(m)(m) 0deg.066.268.381.05deg.0.087272.069.381.610deg.0.173677.773.883.615deg.0.258883.377.586.520deg.0.342088.882.090.425deg.0.422694.286.794.630deg.0.500099.391.699.035deg.0.5736104.296.3104.140deg.0.6428108.8100.8108.645deg.0.7071113.0105.5113.150deg.0.7660116.9107.5117.655deg.0.8192120.4110.2121.260deg.0.8660123.5112.8123.965deg.0.9063126.2115.0125.7 110

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Table5-5. Tablewiththepositionsofthepeaksanddipsfor(i=0,j=1)forthegoldfoilsamplewithgeometricalcharacteristics:Dg=8.64mandL=4.93m. AngledipExperimentallyExperimentallysin()(i=0,j=1)deneddipdenedpeak(m)(m)(m) 0deg.08.649.069.875deg.0.08728.619.049.9010deg.0.17368.518.949.9215deg.0.25888.358.769.7820deg.0.34208.128.599.6325deg.0.42267.838.279.5430deg.0.50007.488.429.4535deg.0.57367.088.579.4140deg.0.64286.618.739.4845deg.0.70716.118.849.5950deg.0.76605.558.939.7055deg.0.81924.969.069.8360deg.0.86604.329.199.94 Table5-6. Tablewiththepositionsofthepeaksanddipsfor(i=-1,j=0)forthegoldfoilsamplewithgeometricalcharacteristics:Dg=8.64mandL=4.93m. AngledipExperimentallyExperimentallysin()(i=-1,j=0)deneddipdenedpeak(m)(m)(m) 0deg.08.648.969.815deg.0.08729.399.199.9610deg.0.173610.149.6310.515deg.0.258810.8710.311.120deg.0.342011.6011.011.825deg.0.422612.2911.712.530deg.0.500012.9612.313.135deg.0.573613.6013.213.840deg.0.642814.1913.814.445deg.0.707114.7514.315.050deg.0.766015.2614.815.555deg.0.819215.7215.416.060deg.0.866016.1215.816.4 111

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escortingdipforthesamplewithDg:66.2mfors-polarization.TheresultsappearinTable 5-3 ,whileforp-polarizationthedataappearinTable 5-4 .SimilarlyweconstructTable 5-5 andTable 5-6 forthesamplewithDg:8.64m.Thetheoreticalpredictionthatwecancomparethetwopolarizationsdatatotheexperimentaldataisthecalculateddiffractionthresholdsfor(i=0,j=1)and(i=-1,j=0)respectively.ThecaseissimilartotheangledependentanalysisthatweperformedinChapter4.Inthiscasehoweverthedielectricfunctionofthesilvergetsverylargevaluesandaccordingtothetheoreticalconsiderationsthatwehavepresentedtheresonanceacquiresinnitesimalwidth.Soaccordingtothetheory,eachpeakappearsatthesamepositionwiththecorrespondingdip.Thentheonlydielectricthatweneedtoconsideristhatofvacuum.Theexperimentalandcalculatedpositionsofthepeaksanddipsdonotcoincideinthes-polarizationcase(Figure 5-11 andFigure 5-15 )asthesefeaturesremainpracticallyatthesamewavelengthinourexperiment,whilethetheoreticallineshowscurvaturetowardsshorterwavelengths.Thisaswehavediscussedsuggeststheroleofthecrosslikeshape.Ontheotherhand,astheplotsinFigure 5-13 andFigure 5-17 show,thecorrespondencebetweenexperimentandtheoreticalpredictionisverygoodinthep-polarizationcase.Thetheoreticallinecrossesinbetweenthepointsfortheexperimentaldipsandthepeaks.Thereasonshavebeenanalyzedontheprevious,butthewavelengthversusangleplotscangiveusabetterinsightoftheassociatedproperties.Forthatreasonwehavealsoplotthedatawithrespecttosin(),whereweseethatinthep-polarizationcases(Figure 5-14 andFigure 5-18 )thetheoreticallypredictedplotisastraightline,whiletheexperimentalpointsshowgoodagreementtothetheory. 112

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Figure5-11. Angledependentpositionofthemainpeak(upperplot)anddip(lowerplot)forthesamplewith:Dg=66.2mandL=39.3m(s-polarization). 113

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Figure5-12. Sin()dependentpositionofthemainpeak(upperplot)anddip(lowerplot)forthesamplewith:Dg=66.2mandL=39.3m(s-polarization). 114

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Figure5-13. Angledependentpositionofthemainpeak(upperplot)anddip(lowerplot)forthesamplewith:Dg=66.2mandL=39.3m(p-polarization). 115

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Figure5-14. Sin()dependentpositionofthemainpeak(upperplot)anddip(lowerplot)forthesamplewith:Dg=66.2mandL=39.3m(p-polarization). 116

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Figure5-15. Angledependentpositionofthemainpeak(upperplot)anddip(lowerplot)forthesamplewith:Dg=8.64mandL=4.93m(s-polarization). 117

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Figure5-16. Sin()dependentpositionofthemainpeak(upperplot)anddip(lowerplot)forthesamplewith:Dg=8.64mandL=4.93m(s-polarization). 118

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Figure5-17. Angledependentpositionofthemainpeak(upperplot)anddip(lowerplot)forthesamplewith:Dg=8.64mandL=4.93m(p-polarization). 119

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Figure5-18. Sin()dependentpositionofthemainpeak(upperplot)anddip(lowerplot)forthesamplewith:Dg=8.64mandL=4.93m(p-polarization). 120

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CHAPTER6SUMMARY 6.1ConclusionsWestudiedthetransmittanceandreectancespectraofvariousmetallmsperforatedwithperiodicarraysofholes.Thesediffractiveopticaldevicespresentanextraordinarilyhightransmittancethatcannotbeexplainedusingaperturetheory.Varioustheoriesprovideexplanationstosomeaspectsofthephenomenon.[ 26 27 47 56 ]Thisworkinvestigatesthevariouspredictions,bycomparisontoexperimentalresults.Itwasshownthattheresonanttransmissionpeaksaredenedbythegeometricalpropertiesoftheperiodicholearrays,thedielectricenvironment,andthepolarizationoflightandangleofincidence.Theexperimentaldataextendfromthefarinfraredtothevisiblepartsoftheelectromagneticspectrum.Forthispurposewefabricatedvariousdiffractiveopticaldevicesontwodifferentdielectricsubstrates,fusedsilicaandzinc-selenide.Wealsomeasuredthetransmittanceandreectancespectraoftwoperiodiccrosslikestructuresperforatedin1.2mthingoldfoilssuspendedonanickelring.OurdatashowgoodagreementwithsimulationsofT+Randextinctionbasedonthetrappedmodestheory.Alsoweshowedthatthesurfaceplasmontheoryisquantitativelyvalidforspecicpredictions,likethewavelengthofthestrongestresonantpeakforp-polarizedlightfornormalandobliqueincidence.Byalteringthedielectricenvironmentofthelmwecancontrolthewavelengthswhereresonanttransmittanceoccurs.Theamplitudesoftheresonancesgetveryhighvalueswhentherefractiveindexesofthedielectricsaboveandbelowthemetallmmatch.Eveninthecasesofunder-etchedsamples,whereopticallythinsilverlmstillremainsinsidetheholes,thetransmittanceamplitudecanexceedalottheopenareafractionintheindex-matchedcase.Theresonanttransmittanceofthethinfoilsamples 121

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reachedvaluesmorethan7timestheopenareafractionfornormalincidence.Thesepropertiesareexplainedbythecouplingbetweentheexcitationsintheupperandlowermetal/dielectricinterfaces,throughtheopeningoftheholes.Thecouplingisbetterforlargeropenareafractions,andgoodindex-matching.Ourexperimentaldatasuggesthowthecouplingmechanismworks.Whentwosuchresonantpeaksapproacheachother,weobservedaninteractionphenomenon,whichfavourstheamplitudeoftheresonanceatlongerwavelength.Theamplitudeissignicantlyenhancedwhentheexcitationwavelengthsofthetworesonancescoincide,whilethewidthoftheresonancegetssmaller.Finallyourdatasuggestthatthepolarizationofthelightplaysadiffractionthresholdsolution-selectingroleleadingtomuchdeviatingresultsforthetwodifferent(s-andp-)polarizations,astheangleofincidenceincreases.Measuringat10degreesandcomparingwiththereectancedatathatweretakenatthatangle,hasbroughtourexperimentaldatatoverygoodagreementwiththepredictionsbasedontrappedmodestheory.Inthisstudyweacquiredveryinterestingresults,thatgiveusinsightonthediffractionpropertiesandtheroleofohmiclossestothespectra.Theuniversalityofthephenomenonwasshownasourexperimentcoverfromthefarinfraredtothevisiblepartoftheelectromagneticspectrum. 6.2FutureWorkThesofaracquiredresultssuggestdirectionstocontinueresearchintheeld.ForexampleinFigure 4-14 weobservethebulkplasmonofsilverat330nm.Thisisanotherresonantcharacteristicofoursamplesthatmightcontributetotheenhancedtransmittanceproperties.Toinvestigateapossibleinteractionweneedresonanttransmittancepeaksthatappearatwavelengthstotheproximityof330nm.Thiscanbeachievedbyfabricatingsampleswithsmallergeometricalcharacteristics,whichposessomedifcultiesforussofar.Alsowecanuseadifferentmetalthatshowsabulkplasmonatlongerwavelengthsthansilver.Howeversamplesfabricatedon100nmgold 122

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lms(measuredbulktransmittanceresonanceat500nm)havenotgivenacceptableresults.Intherefractiveindexmatchingexperiments,wecanuseavarietyofdielectrics,tostudytheinteractionsoftheresonanttransmittancepeaks.Inthestudiedcasesofthegoldfoils,vacuumistheonlydielectricsurroundingthestructuresinthemetalleadingtoperfectindex-matching.ThenextstepinthepolarizedangledependentexperimentsismeasuringatanglesthatexceedBrewster'sangle.Thiscanrevealveryinterestingaspectsofthestudiedphenomena,butposesexperimentalchallengesthathavetodowiththedecreaseoftheeffectivesampleareaatsteeperanglesandalsorefractivephenomenafromthesubstrate.Anothersuggestioncouldbethemeasurementofthebacksidereectanceofoursamples.Ingeneralthereectanceofanysampleisdifferentforlightincidentonthefrontorthebackside.Alsoasthetrappedmodestheorysuggestsandourexperimentaldataconrmtheelectriceldacquireshighamplitudesinthevicinityoftheholesonaperiodicholearraysample.Aninterestingsuggestionthatwehavestudied,butwithoutthedesiredsuccessisllingtheholeswithnon-linearmaterialforsecondharmonicgeneration.Theideaisthattheinteractionbetweenthenon-linearmaterialandtheradiationisstrongersoitmightleadtostrongersecondharmonicgeneration.Ourexperimentsonthiswerenotconclusivesotheworkonthisneedstobecontinued.Thestudyofthediffractiveopticaldevices,fallswithintheregionofplasmonicsandhasgreatpotentialapplications.Inthefuturethesedeviceswillallowthemanipulationoflightsignalsusingsub-wavelengthfabricatedstructures. 123

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APPENDIXAATOMICFORCEMICROSCOPEIMAGESImagesusingtheatomicforcemicroscopewereveryusefulindeningthefabricationconditionsthatgivethebestresults.Duringthefabricationmanyparameterscanbeoptimized.ForexampleatomicforcemicroscopeimagesofthedevelopedPMMAbroughtustousefulconclusionsaboutthethickness,thechemicaldeveloper/stopper(MIBK/IPA)ratioanddevelopingtime.Figures A-1 A-2 A-3 presentsuccessfullydevelopedsampleswithdifferentperiodicitiesandholesize.TheexperimentallydenedoptimumPMMAthicknesswas:200nmto250nm,whilethedevelopingratiohasbeenstandardizedinthenanoscaleresearchfacilityto3:1MIBK/IPA,duetoverygoodresults.Ourdevelopingtimesvariedfrom8secto15sec. FigureA-1. AFMimageofaperiodicholearraysample,afterdevelopingthePMMAresist.Thecharacteristicdimensionsofthesampleare:Dg=1200nmanda=537nmcorrespondingtoanopenareafractionf=0.20.Thesamplewasdevelopedin3:1MIBK/IPAratiofor8seconds. 124

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FigureA-2. AFMimageofaperiodicholearraysample,afterdevelopingthePMMAresist.Thecharacteristicdimensionsofthesampleare:Dg=1000nmanda=447nmcorrespondingtoanopenareafractionf=0.20.Thesamplewasdevelopedin3:1MIBK/IPAratiofor8seconds. FigureA-3. AFMimageofaperiodicholearraysample,afterdevelopingthePMMAresist.Thecharacteristicdimensionsofthesampleare:Dg=800nmanda=358nmcorrespondingtoanopenareafractionf=0.20.Thesamplewasdevelopedin3:1MIBK/IPAratiofor8seconds 125

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APPENDIXBNORMALIZEDTRANSMITTANCEDATA FigureB-1. Transmittanceofthreesliveronfusedsilicasamplesnormalizedtotherstdiffractionthresholdatstage5ofthedevelopingprocess. 126

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FigureB-2. TransmittanceofthreesliveronfusedsilicasamplesnormalizedtotherstdiffractionthresholdattributedtoPMMAatstage6ofthedevelopingprocess.Forcomparisonthenormalizedtransmittanceatstage5ofthedevelopingprocessisshownwithdashedlines. 127

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FigureB-3. Transmittanceofthreesliveronfusedsilicasamplesnormalizedtotherstdiffractionthresholdattributedtofusedsilicaatstage6ofthedevelopingprocess.Forcomparisonthenormalizedtransmittanceatstage5ofthedevelopingprocessisshownwithdashedlines. 128

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FigureB-4. Normalizedtothediffractionthresholdtransmittanceofthetwoperiodiccrossarraysinthingoldfoil.Thepresenteddatashowthep-polarizationands-polarizationcasesatthelimitwheretheincidentanglegoestozero. 129

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APPENDIXCFURTHERANALYSISOFTHINFOILSAMPLE FigureC-1. Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3mforUn-polarizedlight. 130

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FigureC-2. Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=66.2mandL=39.3mfor45degreespolarizedlight. 131

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FigureC-3. Angledependenttransmittanceofthegoldfoilsamplewithcharacteristicgeometry:Dg=8.64mandL=4.93mforUn-polarizedlight. 132

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BIOGRAPHICALSKETCH DimitriosKoukiswasborninAthens,GreeceandlivedwithhisparentsandhisyoungersisteruntilhisadulthoodinSalamina,asmallbeautifulisland.Hewasalwaysinterestedinmathematics,physicsandengineering,soattheageof18helefttojointhecommunityofthePhysicsDepartmentoftheUniversityofPatras.WhenhegraduatedwithBachelorofSciencein2004hefeltequallyfascinatedbyexperimentalphysics,astronomy,andelectronicsengineering.HeenrolledintheElectronicsandComputersEngineeringprogramoftheUniversityofPatras,wherehewasamazedbythedevelopmentofcurrentstateelectronicdevicetechnologyandprogressofmodernsolidstatedevices.Aftergraduationin2006,heenrolledforPh.D.studiesattheUniveristyofFlorida.In2007hejoinedtheInfraredstudygroupofProfessorTannerandheworkedonthepropertiesofdiffractiveopticaldevicesandothercondensedmatterexperiments,untilhisgraduationinDecember2011 136