Title Page
 Table of Contents
 List of Tables
 List of Figures
 Basics of optical fiber wavegu...
 Experimental technique
 Theoretical model
 "FOPAB" - A fortran program for...
 "FOPAC" - A fortran program for...
 "Acoustic" - A fortran program...
 Biographical sketch

Title: Photoacoustic spectroscopy of optical fiber waveguides
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00086025/00001
 Material Information
Title: Photoacoustic spectroscopy of optical fiber waveguides
Physical Description: xiii, 143 leaves : ill. ; 28 cm.
Language: English
Creator: Griffin, Jeffrey Wayne, 1951-
Publication Date: 1982
Subject: Optoacoustic spectroscopy   ( lcsh )
Optical wave guides   ( lcsh )
Nuclear Engineering Sciences thesis Ph. D   ( lcsh )
Dissertations, Academic -- Nuclear Engineering Sciences -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis (Ph. D.)--University of Florida, 1982.
Bibliography: Bibliography: leaves 139-142.
Statement of Responsibility: by Jeffrey Wayne Griffin.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00086025
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 000334426
oclc - 09384013
notis - ABW4066

Table of Contents
    Title Page
        Page i
        Page ii
        Page iii
        Page iv
    Table of Contents
        Page v
        Page vi
        Page vii
    List of Tables
        Page viii
    List of Figures
        Page ix
        Page x
        Page xi
        Page xii
        Page xiii
        Page 1
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        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
    Basics of optical fiber waveguides
        Page 17
        Page 18
        Page 19
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    Experimental technique
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
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        Page 104
        Page 105
    Theoretical model
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
    "FOPAB" - A fortran program for modeling the photoacoustic amplitude and phase response of a bare optical fiber on the basis of the rosencwaig-gersho theory
        Page 120
        Page 121
        Page 122
        Page 123
    "FOPAC" - A fortran program for modeling the photoacoustic amplitude and phase response of a clad optical fiber on the basis of the rosencwaig-gersho theory
        Page 124
        Page 125
        Page 126
        Page 127
    "Acoustic" - A fortran program for modeling the photoacoustic amplitude and phase response of bare or clad optical fiber on the basis of the bennett-forman theory
        Page 128
        Page 129
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    Biographical sketch
        Page 143
        Page 144
        Page 145
Full Text








to my parents, '-sse and 2o"lly Griffin,

and my w*'ife, Shirley


This experimental and theoretical work would never have reached

fruition were it not for the constant support and encouragement of my

doctoral committee chairman, Dr. Richard T. Schneider. To him I will

always be indebted. The experimental portion of this work was per-

formed in the facilities of the Electro-Optic Systems Section of

Battelle, Pacific Northwest Laboratories, Richland, Washington. Two

members of the technical staff, Dr. Michael A. Lind and Dr. John S.

Hartman, were instrumental in providing and/or procuring the necessary

instrumentation and facilities for this investigation. In addition,

their constant encouragement and evaluation undoubtedly contributed to

the success of this endeavor. Fiber samples were generously provided

by numerous members of the commercial fiber community. Most notably,

the support of Times Fiber Communications, Inc., (TFC), EOTec Corpora-

tion, and Galite, Inc., is appreciated. The polymer recladding compound

employed in the bare fiber studies was generously provided by Optelecom.

Appreciation is extended to Mr. L. Dwight Luker, Naval Research Labora-

tory, Orlando, Florida, for his helpful suggestions regarding the use

of discrete Fourier transform techniques for the determination of

signal phase. The design of the high voltage amplifier employed in

the electrostatic actuator experiments was suggested by Mr. Phillip D.

Bondurant. Mr. Timothy L. Stewart provided assistance in interfacing

the Biomation waveform digitizer to the HP1000 computer system, and

Mr. Dale A. Chaudiere answered countless questions pertaining to the

development of FORTRAN software routines. The evolution of the

manuscript into final typed form is the result of the very competent

and patient efforts of Mrs. Betty Prezbindowski. Ms. Kathy Kindali

coordinated the typing effort and bore an increased workload to ensure

that deadlines were met.

Certainly much gratitude is due my wife, Shirley, for her constant

encouragement, spiritual support, and financial backing throughout

this lengthy chapter of my life. Finally, I express deep appreciation

to my friends the Reverend Robert and Juanita Waller for spiritual

direction when the way was not so clear.







Description of the Photoacoustic Spectroscopy (PAS)
Technique 1

Historical Development 4

Photoacoustic Spectroscopy of Optical Fiber Waveguides 8

Amplitude Domain PAS Measurements on Optical Fibers 10

Phase Domain PAS Measurements on Optical Fibers 12

Summary of Present Work 15


Manufacturing Techniques and Nomenclature 17

Losses in Optical Fibers 21


Photoacoustic Response Model for a Bare Fiber
(Rosencwaig-Gersho Theory) .27

Photoacoustic Response Model for a Clad Fiber
(Rosencwaig-Gersho Theory) .34

Photoacoustic Response Model for Bare and Clad Fibers
Incorporating Acoustic Treatment of the Cell Gas
(Bennett-Forman Theory) 39


Photoacoustic Cell

Sample Illumination System


Amplitude and Phase Calibration of

Amplitude and Phase Calibration of

Optical Detector Calibration

Sample Preparation

Measurement Procedure .
n 4-


LoCk-In Am

a aG .

Hot-Wire Calibrator Experiment

Photoacoustic Data for Bare Fibers

Photoacoustic Data for Clad Fibers


Theoretical Model Results Hot Wire Calibrator

Theoretical Model Results Bare Fibers

Theoretical Model Results Clad Fibers



Summary of Results .

Discussion and Suggestions for Further Work




pl ifier .

























Material Composition Systems Used for Fibers 20

Single-Line Output of Spectra-Physics Model 165 Argon-Ion
Laser .54

Summary of Fiber Sample Parameters 80

Thermal Constants Assumed for Modeling Photoacoustic
Response ...107



1 Fiber Optic Photoacoustic Spectroscopy (FOPAS) System 9

2 Geometry for Photoacoustic Investigations of Optical Fiber
Waveguides 11

3 Propagation of Thermal Waves in an Insulating Slab 14

4 Geometries for Step-Index and Graded-Index Fibers 18

5 Spectral Loss Breakdown for a Silica Fiber .25

6 Geometry for Modeling the PAS Response of a Bare Optical
Fiber 28

7 Geometry for Modeling the PAS Response of a Clad Optical
Fiber 35

8 Geometry for Modeling the Photoacoustic Response of a
Cylindrical Rod 41

9 Fiber Module 46

10 Microphone Housing 47

11 Acoustic Response and Specifications for Bruel and Kjaer
(B&K) 4166 Condenser and Microphone Cartridge 50

12 Sample Illumination System 52

13 Microphone Calibration System 57

14 High Voltage Amplifier 59

15 Microphone Response (Electrostatic Actuator Source) Sine
Wave Input .61

16 Microphone Response (Electrostatic Actuator Source)
Triangular Wave Input .62

17 Lock-In Amplifier Calibration System 64

18 Phase Shifter/Isolation Circuit 65

19 Lock-In Amplifier Calibration Waveforms (4.0 and 10.7 Hz) 67

20 Lock-In Amplifier Calibration Waveforms (25.0 and
50.8 Hz) 68

21 Lock-In Amplifier Calibration Waveforms (75.7 and
99.6 Hz) 69

22 Comparison of Lock-In Amplifier and Discrete Fourier
Transform (DFT) Frequency Response 71

23 Optical Detector Calibration System 73

24 Absolute Spectral Calibration Curve for Spectra Physics
401B Power Meter 74

25 Absolute Spectral Calibration Curve for Fiber Throughput
Monitor (Integrating Sphere/Silicon Detector) 75

26 Linearity Confirmation for Spectra Physics 401B and Fiber
Throughput Monitor 76

27 Relative Response of Spectra Physics 401B for Multi-Line
Laser Operation 78

28 Geometries for Bare and Clad Fiber Samples and Cladding
Mode Stripper 83

29 Spectral Response of Fiber Module Constituents 84

30 Experimental Arrangement for Hot Wire Calibrator Measure-
ments 87

31 Photoacoustic Amplitude Response for Thermal Wire Source
(1 mm and 2 mm Capillaries) 89

32 Photoacoustic Phase Response for Thermal Wire Source
(1 mm and 2 mm Capillaries) 91

33 Photoacoustic Amplitude Response for Bare 125 pm and 200 pm
Silica Fibers 92

34 Photoacoustic Phase Response for Bare 125 pm and 200 pm
Silica Fibers 94

35 Spectral Response of Bare 125 pm Silica Fiber 95

36 Spectral Response of Bare 200 pm Silica Fiber 96

37 Photoacoustic Amplitude Response for Clad 125 pm (Fiber
(37.5 pm Clad) Cladding Modes Stripped and Unstripped 97

38 Photoacoustic Phase Response for Clad 125 pm Fiber
(37.5 pm Clad) Cladding Modes Stripped and Unstripped 98

39 Spectral Response of Clad 125 pm Fiber (37.5 pm Clad)
Cladding Modes Stripped and Unstripped 100

40 Photoacoustic Amplitude Response for Clad 200 pm Fiber
(25 pm Clad) Cladding Modes Stripped and Unstripped 102

41 Photoacoustic Phase Response for Clad 200 pm Fiber
(25 pm Clad) Cladding Modes Stripped and Unstripped 103

42 Spectral Response of Clad 200 pm Fiber (25 pm Clad)
Cladding Modes Stripped and Unstripped .105

43 Model Predictions for Hot Wire Calibrator (1 mm Capillary). 108

44 Model Predictions for Hot Wire Calibrator (2 mm Capillary). 110

45 Model Predictions for 125 pm Bare Fiber (2 mm Capillary) 111

46 Model Predictions for 200 pm Bare Fiber (2 mm Capillary) 113

47 Model Predictions for 125 pm Clad (37.5 pm) Fiber (2 mm
Capillary) 115

48 Model Predictions for 200 pm Clad (25 pm) Fiber (2 mm
Capillary) 116

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy




August 1982

Chairman: Dr. Richard T. Schneider
Major Department: Nuclear Engineering Sciences

A fiber optic photoacoustic spectroscopy (FOPAS) system has been

developed for the investigation of the photoacoustic amplitude and phase

response of optical fiber waveguides. Using a moderate power argon-ion

laser as the illumination source, for relatively low modulation fre-

quencies (3-100 Hz), it is possible to obtain data with acceptable

signal/noise ratio in both the amplitude and phase domains. Samples

investigated included bare and clad optical fibers of 125 pm and 200 im

core diameter. Cladding thicknesses for the two diameters were 37.5 Pm

and 25 pm, respectively. Relative spectral absorption profiles were

obtained by single-line operation of the argon-ion laser. Fiber photo-

acoustic amplitude and phase response as a function of chopping frequency

were determined in an effort to assess fiber dimensional parameters and

material thermal constants. The frequency-dependent photoacoustic

response was modeled on the basis of photoacoustic theories developed by

Rosencwaig and Gersho and Bennett and Forman. The experimental data are

in good qualitative agreement with model predictions.



Description of the Photoacoustic Spectroscopy (PAS) Technique

The photoacoustic spectroscopy technique is a calorimetric method

for detecting optical absorption in gaseous, liquid, or solid samples.

When an optically absorbing material is illuminated with light, a por-

tion of the incident photons will cause excitation of electronic, vibra-

tional, or rotational states inherent to the atom or molecule. If the

de-excitation mechanism is predominantly collisional (as opposed to

fluorescence, for example) the absorbed energy will eventually be mani-

fested as heat deposited into the sample. Consider now the case for an

intensity-modulated source with period 1/f where f is the modulation

frequency. If the source period is much longer than the excited state

lifetime, the result is a periodically varying temperature fluctuation

within the sample volume. The frequency of the temperature signal is

equal to that of the source modulation, and its amplitude is a function

of source intensity, local absorption coefficient, and physical (e.g.,

thermal) sample properties. The phase of the temperature signal is

dependent only upon physical sample properties and modulation frequency.

The PAS method is, in essence, a sensitive technique for detecting the

minute temperature signal accompanying optical absorption of modulated


In order to make optical absorption measurements utilizing the PAS

technique, the experimenter places the sample (gas, liquid, or solid) in

a hermetically sealed cell. The cell is equipped with windows to allow

illumination of the sample volume. Common to the cell volume is a

pressure piezoelectricc crystal) or displacement (microphone) trans-

ducer. In the case of gases, the transducer detects cell pressure fluc-

tuations due to internal generation of heat. For liquid and solid

samples, optical absorption may be monitored in two ways. A piezoelec-

tric transducer may be used to sense acoustic waves generated in the

sample, or a microphone connected to the cell volume may be implemented

to detect pressure variations of a cell working gas in intimate thermal

contact with the sample surface. Measurement sensitivity is enhanced by

the use of intense optical sources such as arc lamps or lasers and by

employing synchronous detection of transducer output. Spectral absorp-

tion data are obtained by varying source illumination wavelength.

The PAS technique offers some unique advantages over conventional

methods for measuring optical absorption. Since absorption of optical

radiation is required for generation of the photoacoustic signal, light

that is transmitted or scattered does not influence absorptive PAS mea-

surements. This is in marked contrast to conventional spectrophotometry

techniques. Also, since the technique does not depend on the detection

of photons, it is possible to obtain absorption spectra from completely

opaque materials. Because the PAS signal is acoustic in nature, absorp-

tion measurements may be performed over a very broad spectral range

without changing detectors. The PAS effect in solids is essentially a

radiationless energy conversion process. For this reason the technique

may be used as an indirect method for studying the phenomena of fluores-

cence and photosensitivity in matter. The unique intrinsic PAS capabil-

ity is that of depth profiling. In the case of solid sample PAS utiliz-

ing microphone sensing, detection requires that internally generated

thermal waves propagate to the sample surface in order to induce tem-

perature changes in the working gas. The attenuation and phase shift-

ing of thermal waves in a solid is a function only of source modulation

frequency for a given material. For this reason, only distinct regions

of the sample volume will be contributors to the total acoustic signal

at a given frequency. In general, for high modulation frequencies,

regions near the sample surface are the major contributors to total

signal. As modulation frequency is lowered, thermal waves generated

deeper beneath the sample surface are attenuated to a lesser degree.

In this manner the absorption profile of a material as a function of

depth along the illumination axis may be determined by deconvolution

of the frequency-dependent PAS signal. This same intrinsic PAS capa-

bility can be exploited for measurement of thin film thickness. If a

transparent thin film is interposed between an absorbing substrate and

the cell volume, thermal waves generated at the substrate/film inter-

face must propagate through the film before detection by the microphone.

Thermal waves propagating through the film experience attenuation and

thermal lag. The thermal lag results in a negative phase shift between

the modulation signal and the microphone signal. Given the thermal

diffusivity of the thin film, it is possible to derive the film thick-

ness from the phase-modulation frequency relationship.

Historical Development

The photoacoustic effect was first presented to the scientific

community in 1880 by Alexander Graham Bell. In a presentation to the

American Association for the Advancement of Science (Bell, 1880) on his

photophone research, Bell discussed the inadvertent discovery of the

photoacoustic effect. Bell's photophone consisted of a voice-actuated

mirror (modulator), a selenium cell, and a telephone receiver. Sunlight

incident on the modulator mirror was reflected to a receiver station

some distance away. At the receiver the light signal was focused onto

a selenium cell. Variations in cell illumination (due to voice modula-

tion) resulted in changes in selenium cell resistance which could be

sensed by a battery-operated telephone unit. Bell observed that if the

selenium was illuminated with a focused beam of interrupted (chopped)

sunlight, an audible signal could be observed directly without the use of

an electrical receiver. In further investigations by Bell and his asso-

ciate, Sumner Tainter (Bell, 1881), the photoacoustic effect was exam-

ined in detail. The photoacoustic "cell" became a sealed transparent

glass tube in which samples were placed. Audible signals were sensed by

coupling a hearing tube to the cell. Solids, liquids, and gases were

investigated and general relationships established between signal

strength and physical sample properties. While Bell was the first to

surmise the role of optical absorption in signal production, his explan-

ation of the sound production mechanism is now viewed as inadequate. A

year after Bell's initial introduction of the photoacoustic effect, John

Tyndall (Tyndall, 1881) and Wilhelm Roentgen (Roentgen, 1881) reported

on their photoacoustic investigations of colored and colorless (infrared

absorbing) gases.

The physical principle of photoacoustic signal production in gases

was well understood in the early 1880's since the gas laws were then

known. It was correctly surmised that periodic optical absorption in

the gas sample resulted in heating and subsequent expansion. Periodic

sample volume fluctuations could be detected by a displacement sensitive

device such as the hearing tube. Numerous explanations of the effect in

solids were offered. However, today the first correct interpretation is

deemed to be that of Mercadier (Mercadier, 1881) and Preece (Preece,

1881). Mercadier deduced that the photoacoustic signal in solids was

due to the alternating expansion and contraction of gases adsorbed on or

adjacent to the sample surface. That is, heat transfer from the opti-

cally absorbing solid to the cell working gas was a reouisite for sound

production. The investigations of Preece supported this viewpoint.

Following the initial discovery and subsequent investigations of

the photoacoustic effect in the early 1880's, further research was stag-

nated for almost 50 years until development of the microphone. In 1938

Viengerov (Viengerov, 1938) reported the results of photoacoustic exper-

iments on infrared absorbing gases using an electrostatic microphone

detector. Using blackbody infrared sources (e.g., Nernst glowers), he was

able to detect CO2 in N2 down to a few parts per thousand. Application

of the gas analyzer concept was reported by Pfund (Pfund, 1939) in 1939.

He described a gas analyzer system in use at Johns Hopkins Hospital for

measuring concentrations of CO and CO2. The first commercial differen-

tial photoacoustic gas analyzer was reported by Luft (Luft, 1943) in

1943. This instrument permitted detection of CO2 in N2 down to several

parts per million. The differential design was exploited by Viengerov

(Viengerov, 1945) resulting in the introduction of the first infrared

gas spectrometer ("spectrophone") in 1945.

In the mid and late 1940's photoacoustic investigations of gases
were pursued to provide insight into energy transfer mechanisms and

kinetics. Gorelik (Gorelik, 1946) suggested the use of photoacoustic

techniques for the study of energy transfer between the vibrational and

translational energy modes in gases. Slobodskaya (Slobodskaya, 1948)

was the first to experimentally verify Gorelik's proposal in his inves-

tigation of vibrational lifetimes of gaseous molecules.

Interest in the photoacoustic effect in solids lay dormant until

1973 when Parker reported interesting results (Parker, 1973) on his

investigations of gases. Parker found that a portion of the acoustic

signal could be attributed to absorption in the cell windows and subse-

quently derived a mathematical treatment of the effect. The first gen-

eral theory of the photoacoustic effect in solids was formulated by

Rosencwaig and Gersho (Rosencwaig and Gersho, 1975; 1976). The Rosen-

cwaig-Gersho (RG) theory derived exact expressions for the tempera-

ture at the sample gas interface; however, transport of the pressure

disturbance in the gas was treated in a heuristic manner. Bennett and

Forman (Bennett and Forman, 1976), Aamodt, et al. (Aamodt, et al., 1977),

and Wetsel and McDonald (Wetsel and McDonald, 1977a; 1977b) refined the

Rosencwaig-Gersho theory by invoking the Navier-Stokes equations for

description of the pressure disturbance transport in the gas. McDonald

and Wetsel (McDonald and Wetsel, 1978) have offered further refinements

with their calculation of the contribution of thermally induced sample

vibrations to the photoacoustic signal.

Most recently, photoacoustic studies of solids have focused on the

determination of absorption coefficients of optical materials (Hordvik

and Schlossberg, 1977; Hordvik and Skolnik, 1977; McDavid et al., 1978;

McDonald, 1979; Rosencwaig and Willis, 1980; Rosencwaig and Hindley,

1981; Fernelius, 1981). Experimental work has indicated that with

intense laser illumination the photoacoustic technique is capable of an

absorption sensitivity in solids of better than 10-5 cm. Current

interest in low optical absorption materials has been brought about

largely by ongoing research in high energy laser-induced fusion and the

rapidly expanding market for long distance fiber optic communications

systems. While photoacoustic spectroscopy has for some time been used

for the assessment of absorption in bulk samples (e.g., optical elements,

thin films, fiber reforms) (Hordvik, 1977), only recently has the tech-

nique been applied to optical fibers. Huard and Chardon (Huard and

Chardon, 1981a; 1981b) have reported observation of the photoacoustic

effect in clad optical fibers using argon ion laser (514.5 nm) illumina-

tion. Their investigations have resulted in development of a technique

for measuring attenuation (due to absorption) in optical fiber wave-

guides using photoacoustic spectroscopy.

As previously mentioned, the phase of the photoacoustic signal

contains information regarding physical (e.g., dimension) and thermal

(e.g., thermal diffusivity) properties of the sample. Investigations of

this aspect of PAS have been reported by several authors (Adams and

Kirkbright, 1976; Adams and Kirkbright, 1977; Mandelis, et al., 1979).

The use of the unique depth profiling capability of PAS has also found

wide application (Afromowitz, et al., 1977; Busse, 1979; Helander et al.,

1981; Fernelius, 1981). An excellent overview of photoacoustic theory

and methods is provided in monographs by Pao (Pao, 1977) and Rosencwaig

(Rosencwaig, 1980).

To date, reported theoretical and experimental research on the

application of PAS to the study of absorption in optical fibers has been

limited. While the groundwork for mathematical modeling exists, theo-

retical models predicting photoacoustic fiber response are nonexistent.

Experimental work on fiber absorption has been performed at only one

wavelength. In addition, no studies have yet been reported on the ampli-

tude and phase of fiber PAS signals as a function of modulation

frequency. Finally, experimental details on cell design, signal

processing, and data acquisition are obscure. It is the endeavor of

the present research effort reported herein to fill some of these voids.

Photoacoustic Spectroscopy of Optical Fiber Waveguides

The schematic diagram of a system for photoacoustic investigations

on optical fibers appears in Figure 1. The source for the fiber optic

photoacoustic spectroscopy (FOPAS) system is a medium power (1.5W multi-

line) cw argon laser. Depending on the type of measurement, it may be

desirable to operate the laser in either single line or multi-line mode.

Source modulation is accomplished with a 50% duty cycle variable speed

chopper. A microscope objective focuses modulated source radiation into

the fiber. A portion of the fiber length is passed through the hermeti-

cally sealed photoacoustic cell where fiber heating due to optical

absorption is sensed. For spectral absorption measurements,

Inteqratinq Sphere

Laser Beam Splitter


Photoacoustic Cell

Laser Power Monitor



Chopper Speed


Transmitted Light Amplitude

Sync In S' ignal

Photoacoustic Signal
Amplitude and Phase

Figure 1. Fiber Optic Photoacoustic Spectroscopy (FOPAS) System


Fiber Under Test

fiber-transmitted light is collected in an integrating sphere where the

intensity is monitored with a solid state photodiode. Photoacoustic

signal amplitude and phase are monitored with a synchronous (lock-in)

amplifier. Another lock-in amplifier monitors fiber-transmitted light

intensity. Lock-in amplifier synchronization is derived from the

chopper speed controller.

Photoacoustic investigations on optical fibers may be grouped into

one of two categories. Amplitude domain measurements are those in

which PAS signal amplitude is of prime interest. For fiber spectral

absorption measurements, signal amplitude is measured as a function of

illumination wavelength. Phase domain measurements, in which signal

phase is monitored as a function of modulation frequency, are useful for

analysis of fiber/cladding thermal properties and dimensions.

Amplitude Domain PAS Measurements on Optical Fibers

A schematic representation of bare and clad fiber geometries

appears in Figure 2. Three simplifying assumptions are made regarding

fiber physical properties and illumination geometry. First, the fiber

core and cladding regions are assumed homogeneous with respect to opti-

cal and thermal properties, i.e., the fibers are of the step index type.

Secondly, the fiber spectral absorption coefficient, 8(cm -), of the

core is assumed small. In this case the source power density in the

fiber volume is approximately independent of z (along the length of

fiber contained within the photoacoustic cell volume). Finally, inci-

dent source illumination is assumed constant across the fiber cross sec-

tion. While this condition will probably not exist at the fiber input

end (due to the Gaussian profile of a focused laser beam), such a

I(0,t)=Io/2(1+cos wt) Core

--- z


Bare Fiber Geometry


a=_ w

Clad Fiber Geometry

Figure 2. Geometry for Photoacoustic Investigations of
Ootical Fiber Wavequides

distribution will probably evolve further down the fiber length due to

mode mixing and mode coupling which is prevalent in multimode fibers

(Marcuse, 1981). The second and third assumptions establish a constant

source power density (i.e., independent or r and z) within the fiber vol-

ume for a given illumination and spectral absorption coefficient.

For mathematical convenience, the chopped incident illumination is

approximated by

I(z=O,t)=lo/2(l+cos wt) (1)

I (W/cm2) is the peak source intensity throughout the fiber cross sec-

tion and w=2nf where f is the modulation frequency. From Beer's law the

intensity along the fiber axis is given by

I(z,t)=I(O,t)exp(-Bz)=I(O,t) (2)

since B is assumed small. Optical absorption within the fiber volume

results in a thermal source H(t)(W/cm3) given by

H(t)-BI(O,t) (3)

which is constant throughout the fiber core. The linear dependence of

H(t) on B is the basis for photoacoustic spectral absorption measure-

ments. It can be shown that the photoacoustic signal amplitude is lin-
early proportional to the BI(O,t) product. Spectral scans of fiber

absorption coefficient are produced by varying source wavelength. In

practice, the accuracy to which can be determined is a function of

the accuracy to which I(O,t) is known (Huard, 1981b).

Phase Domain PAS Measurements on Optical Fibers

While PAS measurements are of value for determination of fiber

optical absorption coefficient, a considerable amount of information can

be gleaned from an examination of signal phase. The local temperature

at any point in the fiber volume, T(r,t), can be expressed as the sum of

three terms (Bennett and Forman, 1976)

T(r,t)=T +W(r,t)+e(r,t) (4)
where T is the initial equilibrium fiber temperature (room temperature),

W(r,t) is the transient temperature component (@W(r,t)/3t-+ 0 for t suffi-

ciently long), and e(r,t) is the modulated steady state component given


8(r,t)=exp(iwt)w(r,w) (5)

Modulated temperature amplitude and phase information is contained in

w(r,o). The steady state modulated temperature component can be modeled

as a superposition of traveling thermal waves in the fiber (Rosencwaig,

1980; Bennett and Patty, 1981), i.e.,

w(r,w)=Ueor+Ve-or (6)

U and V are complex constants and o=(l+i)a,i= V--. a is the wave num-

ber of the thermal waves and is given by

a= 2 (7)
where a is the thermal diffusivity of the fiber material. Just as for

the propagation of electromagnetic waves through a material, thermal

waves experience attentuation and phase shifting. The attenuation and

phase factors for a thermal wave propagating through a medium are given

by exp (-ar) and exp (-iar) respectively, where r is measured from the

source point. The phase factor is of prime interest in phase domain

photoacoustic spectroscopy measurements. Consider the case of a thermal

wave source at the boundary of a thermally insulating slab (Adams and

Kirkbright, 1977). This situation is depicted in Figure 3. The thermal

wave, in traversing the slab, suffers an attenuation exp (-ab) and a

i x




a= r~
4 72-


A(AL) -b
V7A W )


Fiqure 3. Propaqation of Thermal Waves in an Insulatinq Slab




phase lag, A given by

A4=-ab=- -v b- (8)

Notice that the phase shift is linear in VI-Wwith slope given by -b/-a&.

Consequently, if phase shift is plotted as a function of modulation fre-

quency, either slab thickness or slab thermal diffusivity may be deter-

mined from measurement of the experimental slope. The above situation

is analogous to the case for a thermal wave generated at the fiber core

boundary propagating through a cladding. In this case the phase versus

frequency information may be utilized to investigate cladding thermal

properties and thickness. Photoacoustic signal phase data can also be

used to derive information on light distribution in the fiber. For

example, if an appreciable amount of energy is propagated through a step

index fiber via cladding modes, signal phase lag would certainly be

smaller than that for core-contained propagation. In the case of graded

index fibers where the intensity across the fiber cross section is cer-

tainly not constant, the intensity distribution could presumably be

determined from comparisons of experimental data and theoretical model-

ing results. This information could be used to assess fiber index pro-

file and fiber symmetry.

Summary of Present Work

The photoacoustic investigations reported herein were performed on

bare and clad fibers of the step index type. All fibers studied were

commercially available fused silica varieties. Clad fibers were of

glass on glass construction. Core diameters for both bare and clad


fibers were 125 pm and 200 pm. Cladding thickness for the 125 pm and

200 pm core fibers were 37.5 pm and 25 pm respectively. Amplitude

domain and phase domain photoacoustic measurements were performed on

both bare and clad fibers in an effort to assess spectral absorption,

core and cladding dimensions, thermal properties, and light distribu-

tion across the fiber cross section. Theoretical photoacoustic fiber

response was modeled on the basis of work performed by Rosencwaig and

Gersho (Rosencwaig and Gersho, 1975; 1976) and Bennett and Forman

(Bennett and Forman, 1976).


Manufacturing Techniques and Nomenclature

Most optical fiber waveguides are of the step-index or graded-index

type. These two geometries are depicted in Figure 4. Step-index fibers

exhibit a sharp discontinuity in refractive index at the core-cladding

boundary. Light containment requires that the cladding be of lower

index material than the core. In graded-index fibers the core refrac-

tive index is a monotonically decreasing function of the radial coordi-

nate. For mechanical durability and to prevent degradation, optical

fibers are usually protected with a surrounding plastic jacket.

Low loss optical fibers are generally produced using chemical vapor

deposition (CVD) or modified chemical vapor deposition (MCVD) techniques

(Miller and Chynoweth, 1979). In the CVD process, an easily oxidized

reagent such as SiH4 or GeH4 is mixed with an oxidizing agent in a gas

stream highly diluted with inert gas. The dopant gas stream is then

passed through a heated fused silica tube preformm). The low reagent

concentration along with the relatively low ambient temperature insures

that the oxidation reaction takes place only on the tube walls (hetero-

geneous reaction). Reaction of the tube wall with the gaseous dopants

results in a material layer with index slightly larger than the virgin

silica. After deposition, the preform is heated and collapsed and is

Fused Silica,
Doped Fused Silica,


Fused Silica,
Doped Fused Silica,

Geometry for Step-Index Fiber



Cladding \
2 \
7J\\ n2

Doped Fused Silica


Geometry for Graded-Index Fiber

Figure 4. Geometries for Step-Index and Graded-Index Fibers


eventually drawn into a long thin fiber. With appropriate drawing para-

meters (temperature, draw rate, etc.) the index profile of the preform

can be conserved in the drawn fiber.

The MCVD process differs from the CVD process in that the gaseous

dopant species (e.g., SiC14 or GeCl4) do not react directly with the

silica preform. Instead, deposition is delayed until intermediate

species are precipitated from the gas phase (homogeneous reaction).

Particulate material is then deposited downstream from the reaction zone

onto the preform wall. The powder dopant is vitrified by localized

flame heating of the preform. Once again the preform is heated,

collapsed, and drawn to form the final fiber.

Most dopant materials increase the index of fused silica; excep-

tions are boron and fluorine compounds which actually react with silica

to form a lower index product. In this manner step-index fiber reforms

can be manufactured by exposing a heated fused silica rod to vapor phase

B or F compounds. Alternatively, fibers with silica cores and low index

borosilicate cladding can be made by first depositing a layer of boro-

silicate on the inside of the preform tube and then either depositing

a layer of pure silica or inserting a pure fused silica rod prior to

collapsing the tube. A summary of material composition systems used for

fibers appears in Table 1.

Optical fibers can support a variety of guided waveforms termed

modes (Marcuse, 1981). Single mode fibers support only one discrete

waveform which can exist in two orthogonal polarizations. Multimode

fibers can propagate up to thousands of modes. For step-index fibers

the total number of guided modes of both polarizations, N, is given by

Table 1. Material Composition Systems Used for Fibers

Core:Clad NA




Multicomponent glasses
(e.g., SiO2-B203-Na20)


loss (dB/km)










(Miller and Chynoweth,


N=1/2V2 (9)
where V=nlka V2A. n1 is the refractive index of the fiber core, a is
the core radius, and k=2l/X where A is the wavelength of the propagating
light. A is given by

2 2
A= -n2 n "-n2 for A<< (10)
2n2 n1

where n2 is the refractive index of the cladding. The numerical aper-
ture, NA, of a step index fiber is given by
2 (11)
NA=nI 2A- = n-n2 (11)
The mode number, V, and consequently the numerical aperture, NA, of a
graded index fiber is a function of input beam diameter since core index
is a function of the radial fiber coordinate.

Losses in Optical Fibers
For a single mode fiber (or for any one mode of a multimode fiber),
the power P(z) at any point along the fiber length is given by
P(z)=Poe-2YZ (12)
where Po is the initial input power and 2y is the fiber loss coefficient.
Fiber loss, L, is more commonly expressed in decibels (db) where
L=10 log10[P(z)/Po] (13)
or in db/km where
L/z=8.68y (14)
for y in km-1. In the absence of mode coupling, no unique loss

coefficient can be assigned to a multimode fiber. Each mode of the

fiber can be assigned a loss coefficient yi; however, the power propa-

gated by the fiber can no longer be expressed as a simple exponential as

in Equation 12. The assignment of a loss coefficient to a multimode

fiber requires establishment of a steady state power distribution. This

distribution represents an energy partition in which the ratio of power

propagated by the modes relative to some reference mode is not a func-

tion of the fiber length coordinate. If only low order modes are

excited, their loss coefficients are essentially the same as the loss of

the core material.

The two fundamental loss mechanisms in optical fibers are absorp-

tion and scattering. Absorption results in the removal of a portion of

the propagating electromagnetic energy and the subsequent generation of

heat while scattering redistributes light initially confined to the

fiber core. It is possible to measure the values of these two attenu-

ation components independently.

Presently, the most common methods of measuring low level optical

absorption in fibers (or in fiber reforms) are with calorimetric tech-

niques (Marcuse, 1981; Severin and van Esveld, 1981) or by spectral

transmission (fibers only) (Keck and Tynes, 1972). In calorimetric

techniques, the preform or drawn fiber is illuminated with intense

laser radiation, and the temperature rise (slope and magnitude) is moni-

tored with thermocouples or thermistors as a function of time. The

obtained data is of use not only for the determination of spectral

absorption coefficient but also for evaluation of thermal material

constants. For spectral transmittance assessment of fiber absorption,

a long length (> 0.5 km) of fiber is interposed between a spectral

source (e.g., arc lamp and monochromator) and a detector. Knowledge of

the spectral source function (intensity versus wavelength) and fiber

length allows calculation of the fiber absorptive loss coefficient.

Once again care must be exercised when applying this method to multimode


Scattering losses in optical fibers can arise from several sources.

Rayleigh scattering results from the interaction of light with particles

whose dimensions are much smaller than the illumination wavelength.

Such scattering also results from sub-wavelength dimension density and

index fluctuations in a material. The Rayleigh scattering loss coeffi-

cient, 2ys, of a single component glass (Si02) is given by

8Trr3 8 2
2ys- n0 P BTkT (15)

where X is the source wavelength, n0 is the average sample refractive

index, p is the photoelastic coefficient, BT is the isothermal com-

pressibility, k is Boltzmann's constant, and T is the glass hardening

temperature (approximately 19000K for Si02). The ~-4 dependence is a

noteworthy characteristic of Rayleigh scattering. Additional scattering

may result in optical fibers due to larger material inhomogeneities

(e.g., gas bubbles, inclusions). Finally, scattering losses may be the

result of fiber microbends induced by mechanical loading.

Scattering losses in a fiber can be quantified by measuring the

total energy scattered from the fiber as a function of input intensity.

These measurements are generally performed using an integrating sphere

(Marcuse, 1981) or an integrating cube detector (Tynes, 1970; 1971).

An integrating sphere is usually a hollow metal sphere whose inside is

coated with a white diffusely reflecting paint (Lambertian surface).

The fiber under study is passed through the sphere via two access holes

on opposite sides. An optical detector masked from direct fiber scat-

tered light views the sphere interior. Since the integrating sphere

collects all fiber-scattered light, the intensity at any point on its

inner surface is proportional to scattering magnitude. Spectral scat-

tering measurements require that the spectral reflectance of the sphere

surface be known. A variation on the integrating sphere is the inte-

grating cube. In this device, a cube is formed from six photodetectors.

Holes drilled in opposite faces allow passage of the fiber through the

cube volume. Fiber-scattered light is registered directly as detector

voltage output. The advantage of the integrating cube is its lower

inner surface absorption compared to the integrating sphere and the

resulting increased sensitivity.

The loss breakdown for a fused silica fiber appears in Figure 5.

The absorption and scattering spectra are typical. This fiber had a

doped fused silica core and a fused silica cladding. The measured

absorption (total attenuation less the scattering component) is plotted

as a function of wavelength between 250 and 1600 nm. Note that absorp-

tion in the ultraviolet and visible regions is attributable to metal

impurities (e.g., V, Cr, Mn, Fe, Co, Ni, Cu, etc.) whereas infrared

absorption is dominated by overtone and combination bands in OH.

L 0

106 t -Measured Absorption
E- Metal Impurity + OH

S10 Calculated Absorption(OH)

10 2 *t 0

== o \ -2 7

S** Scattering X-

10-1 I II i ii
200 400 600 800 1000 1200 1400 160C
Wavelength (nm)

Figure 5. Spectral Loss Breakdown for a Silica Fiber (Keck et al.,1973)



The theory of photoacoustic signal generation in solids has devel-

oped as an evolutionary process. According to the theory of Rosencwaig

and Gersho (Rosencwaig and Gersho, 1975; 1976), detection of the

PAS signal depends on the generation of an acoustic pressure disturbance

at the solid-gas interface and the propagation of this disturbance

through the cell working gas to the microphone. The periodic pressure

disturbance is the result of heat transfer from the optically absorbing

solid to the solid-gas interface. Sample vibrations and acoustic emis-

sion are ignored in the RG theory. Propagation of the pressure distur-

bance in the gas is treated in a heuristic manner (piston model) which

has been shown to be valid for most experimental conditions. Further

refinements in the photoacoustic theory of solids have included applica-

tion of the Navier-Stokes equations for a more exact treatment of the

pressure disturbance in the working gas (Bennett and Forman, 1976;

Aamodt, et al., 1977; Wetsel and McDonald, 1977a; 1977b)and treatment of

thermally induced sample vibrations (McDonald and Wetsel, 1978).

The work reported herein extends the Rosencwaig-Gersho theory to

the description of the circularly symmetric, one-dimensional heat trans-

fer problem encountered in the photoacoustic study of optical fibers. A

model is developed to predict PAS signal amplitude and phase for both

bare and clad fibers. Parameters utilized in the model include thermal

properties and dimensions of the fiber (core and cladding) and cell

parameters (dimensions and thermal properties). Also, modeling work

reported by Bennett and Forman (Bennett and Forman, 1976) on the

photoacoustic signal generated by low absorption glass rods is extended

for the prediction of PAS signal amplitude and phase of bare and clad

optical fiber waveguides.

Photoacoustic Response Model for a Bare Fiber (Rosencwaig-Gersho Theory)

A schematic of the geometry for modeling the PAS response of a bare

fiber appears in Figure 6. The fiber is contained in a hermetically

sealed, circular, transparent tube (photoacoustic cell) and is coaxial

with the tube centerline. Dimensions are as noted on the figure. The

thermal source is assumed to be of constant power density and limited

to the fiber core volume. The cell working gas (air) and the cell walls

are assumed to be optically transparent and are therefore not contribu-

tors to the PAS signal. All temperatures are referenced to ambient

(room) temperature.

Light intensity at the fiber input end is modeled as a chopped sinu-

soid of the form
I(z=0,t)=Io/2(l+cos wt) (16)

where w=2rf, f is the chopping frequency, and t is the time variable.

I1 is the peak-to-peak intensity swing. According to Beer's Law

I(z,t)=I(z=O,t)e-6z (17)
where p is the spectral absorption coefficient (cm-~) and z is the fiber

length coordinate. If B is small (B 10-5cm-1) and the cell length is

limited (L<10 cm), the light intensity along the fiber (within the cell

volume) is essentially independent of z. Assuming the fiber does not

Quartz Cell

Fiber Core

Air Space

Temperature Profile
Assumed Linear in
Air Space and
Cell Wall Reqions

Temperature Profile Assumed
Parabolic in Core Region
3 l1(r,t)
r r=O=0

Region 3

Region 2

IRegion 1

Figure 6. Geometry for Modeling the PAS Response of
a Bare Optical Fiber


fluoresce (i.e., all optically excited states eventually decay collision-

ally), the thermal power source (W/cm3) within the fiber volume is then
constant and is given by
H(t)=o10/2(1+cos wt)-E(1+cos wt) (18)
where E=BIo/2. Note that the source can be expressed as the real part

(Re) of a complex valued function, i.e.,
H(t)=RelE(l+eiWt)] (19)
The thermal diffusion equation in the fiber core, taking into account
the distributed heat source, is

D2I (r,t) 1 Oae(r,t) int
2 E(l+e ) (r 3r 91 at

where 61(r,t) is the complex radially dependent core temperature and a,
is the core thermal diffusivity. The real part of 61(r,t) is the temper-
ature of physical interest. The total temperature at point r in the
fiber core is
T(r,t)=Re[el1(r,t)] +TO (21)
where TO is the ambient temperature. Likewise, the diffusion equations
in the gas and cell wall regions take the form

S2 2(r,t) 1 0e2(r,t) a Sr2 a2 at

2 3(-r,t) 1 3(rt) (a+b)<(a+b+c) (23)

Dr2 a3 ta

One set of solutions to the above system of equations is given by
61(r,t)=A1+A2r2+(Bleolr+B2e-ar+B3)e it
62(r,t)=A3 ryal A4+[B4eo2(r-a)+B 5e-2(r-a)]eiw t a a 2 ]t)e= a3r

63(rt)=A5(r-a-b) Ag+[B6e-3(r-a-b)leit (a+b)

A1, A2, A3, A4, A5, and A6 are real constants whereas B1, B2, B3, Ba, B5,
and B6 are complex valued constants. o=a(l+i) where a=w/2ct and i=
-\FT. Notice that the solutions contain a steady-state and an oscilla-
tory term. In the core region the steady state component is assumed to
be parabolic (A1+A2r2) while the oscillatory term is a superposition of
oppositely traveling thermal waves (Bleolr+B2e-al)e i1 t and a source
term B3ei1t. In the gas region the steady state term is assumed linear
(A3+(r-a)A4/b) while the oscillatory term, [B4ea2(r-a)+B5e-a2(r-a)e it
consists of a superposition of traveling thermal waves. The inward trav-
eling thermal wave component, B4e2 (r-a)ei t, allows for the occurrence
of thermal wave reflection at the cell wall. Finally, in the cell wall,
the steady state component, A5+(r-a-b)A6/c, is assumed linear and the
oscillatory term, B6e-a3(r-a-b)e it, is a decaying thermal wave. The An
and Bn are determined from boundary conditions on temperature and flux
continuity. Temperature continuity requires that
1: 61(a,t)=62(a,t) and 2: e2(a+b,t)=93(a+b,t) (27)
Flux continuity requires that
361(r,t) 362(r,t) D62(r,t) 363(r,t)
3:K r r=a2 r=a 4: r ra+br r=a+b (28)
1 3r r=a 2 Br r=a *2 ar r=a+b 3 3r r=a+b (28)

where K is the thermal conductivity. The boundary conditions apply
separately to the steady-state (D.C.) component and the oscillatory
(A.C.) component of the solution. For the D.C. component, the coeffi-
cients are derived as follows:
[Applying 1 to 8l(r,t) and e2(r,t)] A1+a2A2=A3 (29)
[Applying 2 to 02(r,t) and 03(r,t)] A3+A4=A5 (30)

[Applying 3 to and (r,t) and 2(r,t) 2aKA2= 2 (31)

K2A4 K3A6 (32)
[Applying 4 to e2(r,t) and e3(r,t)] -4 b c(

Requiring the D.C. temperature component at the outer cell wall to equal
ambient gives
A5+A6=0 or A5=-A6 (33)
The final equation is determined by insertion of 81(r,t) into Equation
20 with the result
A2=-E/2 (34)
The coefficients for the A.C. component of the solutions are generated
in the same manner,

[Applying 1 to 61(r,t) and e2(r,t)] eClaB1+e-a aB2+B3=B4+B5 (35)
[Applying 2 to 02(r,t) and 03(r,t)] eo2bB4+e-a2bB5=B6 (36)
[Applying 3 to 0l(r,t) and 62(r,t)] Kolle laB -Klale-olaB2=
K202B4-K 22B5 (37)

[Applying 4 to 02(r,t) and e3(r,t)] K K2a2eo2bB4-K22e-C2bB5
-K303B6 (38)
Application of the forcing function (Equation 20) to 0l(r,t) gives

B3- 2

Finally, since the temperature field is assumed circularly symmetric
about the r=0 axis,

ae1 (r,t)
r r=0

= 0



This condition requires that

B1=B2 (41)
Since the photoacoustic signal is essentially determined by the A.C.

temperature component, further discussion will be limited to the evalu-

ation of the B The equations relating the B are summarized below.


+e- aB2

+ B3

K GlealaB, Kir1 F1l aB2

-B4 -B5 =0 (35)

eG2bB4 + e-o2bB5 B6=0 (36)

-K2 2B4 + K228B5 =0 (37)
K22ea2bB4-K2o2e-2bB5g+K33B6=0 (38)

B1 B2 =0 (41
This system of equations can be expressed in matrix form
[G] [B] = S (4;

where G is the complex coefficient matrix, B is the column vector com-
posed of the B and S is the column vector composed of complex

constants. This system is easily solved for the Bn by matrix inversion



techniques or iterative schemes (Gaussian elimination). The coefficients
of interest are primarily B4 and B5 since they determine the A.C. temper-
ature distribution in the cell gas. Recalling that
Sgas(r,t)=(D.C. component) +[B4ea2(r-a)+B5e-a2(r-a)]eiwt (43)
the spatially averaged A.C. temperature amplitude in the cell gas is
given by r=a+b

f B4ea2(ra)+B5e-2(r-a)]dr

M r=a (44)


Notice that M is a complex valued constant for a given chopping fre-
quency, i.e., M can be expressed as
M= IMI e16 (45)
wherelMI=rRe(m)]2+[Im(M)]2 and 6=tan-1 [Im(M)/Re(M)]. Re(M) is the real
part of M and Im(M) is the imaginary part of M. The phase of the PAS
signal relative to the source function, e Wt, is given by 6. From the
ideal gas law we have
pV=nRT or dp- dT (V constant) (46)

where p is pressure, V is volume, T is absolute gas temperature, n is
the number of moles of gas, and R is the gas constant. The amplitude
swing, Ap, in cell pressure is then given by
Ap ATR (21M) (47)
and the phase is given by 6.

A FORTRAN program ("FOPAB") which implements the Rosencwaig-Gersho
theory for modeling the photoacoustic response of bare fibers appears

in Appendix A. Results of the model calculations and a comparison with

experimental data appear in Chapter V.
Photoacoustic Response Model for a Clad Fiber (Rosencwaig-Gersho Theory)
The photoacoustic response for a clad fiber is modeled in essen-

tially the same manner as for the bare fiber. A schematic of the geome-
try for modeling the PAS response of a clad fiber appears in Figure 7.
Notice that introduction of the cladding results in an additional set of
temperature and flux continuity conditions at the core-clad interface.

Also, recall that no light is assumed to be absorbed in the cladding.

The thermal diffusion equations for all regions (core cladding, air

space, and cell wall) are

a el(r't) 1 ael(r,t)
= -E(1 + cos at) O ar2 at

92 2(r,t) 1 ae2(rt) a ar2 O2 at

203(r,t) 1 ae3(r,t) (a+b) 3r2 '3 at

a2e4(r,t) 1 ao4(r,t) (a+b+c) r2 a 4 at

Fiber Cladding

Fiber Core

Air Space __

Temperature Profile
Assumed Linear in
Fiber Claddinq,
Air Space,
and Cell Wall

Temperature Profile Assumed
Parabolic in Core Region
ar r=00

Figure 7. Geometry for Modeling the PAS Response of
a Clad Optical Fiber

where E is defined as in Equation 18 and a is the material thermal
diffusivity. The solutions are again modeled as the sum of a steady
state (D.C.) component and a modulated (A.C.) component which is a
superposition of traveling thermal waves. The general solutions are
01(r,t)=A1+A2r2+(B e lr+B e-lr+B )eit 0

e2(r,t)=A3 ra) A4+[B 4e2(r-a)+B 5e-2(ra) let a

03(r,t)=A5(r-a-b) A6+IB6ea3(r-a-b)+B7e-03(r-a-b) eiWt

4(r,t)=A7(r-b-c) A +B e-4(ra-b-c )eit (a+b+c)

Notice that the solution in the cladding region is a superposition of
forward and backward traveling thermal waves. Temperature continuity
at the interface requires that
1: e1(a,t)=e2(a,t)
2: e2(a+b,t)=e3(a+b,t)
3: e3(a+b+c,t)=04(a+b+c,t) (56)

Flux continuity at the interface requires that

ael(r,t) a8e2(r,t)
4: 1 ar r=a K2 r r=a

a 62(r,t) a03( rt)
5: aK r r=a+b =3 r r=a+b

6: K3 3e3(r,t) K e4(r,t)
6: K4K- (57)
Sr r=a+b+c ar r=a+b+c(5
Once again these constraints apply separately to the D.C. and A.C. com-
ponents of the solution. For the D.C. component, the results are:

[Applying 1 to el(r,t) and e2(r,t)] A +a2A2=A3 (58)
{Applying 2 to e2(r,t) and e3(r,t)] A3+A4=A5 (59)
[Applying 3 to 03(r,t) and e4(r,t)] A5+A6=A7 (60)

[Applying 4 to 06(r,t) and 62(r,t)] 2aKlA2 =-A4 (61)

K K3
lApplying 5 to e2(r,t) and e3(r,t)] 6- A4-c3 A6 (62)

[Applying 6 to 63(r,t) and 64(r,t)] c A6 d A7 (63)
Requiring the D.C. temperature at the outer cell wall to equal ambient
A7+A8=0 or A7=-A8 (64)
From the forcing function (Equation 48) we have
A2 E (65)

This completes the set of simultaneous equations for the eight A .

The coefficients for the A.C. temperature are generated in the same
The results are

[Applying 1 to 1 (r,t) and 92(r,t)l] eclaB +e-1laB2+B3=B4+B5 (66)

[Applying 2 to 02(r,t) and 03(r,t)] ea2bB4+e-a2bB5=B6+B7 (67)




1 (r,t)



[Applying 5 to 02(r,t) and

[Applying 6 to e3(r,t) and

Application of the forcing

of 01(r,t) gives

64(r,t)] e3CB6+e-a3CB7-B8

e 2(r,t)] + K 0elaB1-K 1e-aB2


e3(r,t)] K202eo2bB4-K2o2e-o2bB5=

K3a3B6-K3 3B7
64(r,t)] K3G3eU3CB6-K 33e-03CB7=

function (Equation 48) to the periodic

B3-E 2







Finally, symmetry of the core solution requires that its slope equal

zero at r=0 with the result

Since the B

equation set

eolaB +

determine th

is summarize


K11 ealaB -K 1 el aB2

photoacoustic response, the A.C. component





K 22ea2bE


+e-G2bB5-B6 -B7


34 +K202B5
34 -K202e 2 B 5-K33B 6+K30`3B7

K3G3eG3CB6 K30`3 e3cB7+K 44B8






B1 -B2

=0 (73)




Once again the above set of simultaneous linear equations determines the
B The coefficients of interest are primarily B6 and B7 since they

determine the A.C. temperature distribution in the cell gas. The

temperature solution in the cell gas is then

egas(r,t)=(D.C. component)+[B6e3(r-a-b)+B7e-3(r-a-b)]eiWt (74)
The A.C. temperature component can again be spatially averaged to give

a complex constant, M=IMI eia, where IMI is the average temperature

amplitude and 6 is the phase. Application of the ideal gas law (Equation

46) gives the predicted PAS pressure response (magnitude and phase).

A FORTRAN program ("FOPAC") which implements the Rosencwaig-Gersho
theory for modeling the photoacoustic response of clad fibers appears in

Appendix B. Results of the model calculations and a comparison with

experimental data appear in Chapter V.

Photoacoustic Response Model for Bare and Clad Fibers Incorporating
Acoustic Treatment of the Cell Gas (Bennett-Forman Theory)
The Rosencwaig-Gersho theory of solid state photoacoustic response

treats propagation of the pressure disturbance in the gas in a heuristic

manner. An accurate analysis of acoustic pressure waves generated in
the gas as a result of modulated heat transfer from the solid to the gas

requires application of the three hydrodynamic equations (Bennett and
Forman, 1976). These equations are the equation of continuity, the

Navier-Stokes equation, and the energy transport equation. Assuming that

the gas temperature [TG(r,t)], density [pG(r,t)], pressure E(pG(r,t)],

and material particle velocity [i*G(r,t)] can be linearized as sums of

zero order and first order terms I(i.e., TG(r,t)To+e(r,t);

PG(r,t)=po+P(r t); G=Po+P(r,t); and uG(r,t)=0+u(r,t)], we have:
1) The equation of continuity
3p(r,t) + po.((r,t)=0 (75)
a t

2) The Navier-Stokes equation
P 3ui(r,t) T ij(r,t)
Po =0 (76)
at ax

where ui(r,t) is the it component of i(r,t), Tij(r,t) is the stress
tensor (i=1,2,3 and j=1,2,3), and x is the jth component of vector x.
3) The energy-transport equation

PoC r,t) KGV28(rt)+Po o-1C (y-1)C(rt)=O (77)

where O(r,t) is the gas temperature relative to ambient; CV is the speci-
fic heat at constant volume, y=(C /CV); KG is the gas thermal conducti-
vity; and Bo is the isobaric coefficient of thermal expansion.
The above relations are the starting point for the derivation of the
photoacoustic response of an axially illuminated highly transparent glass

rod (Bennett and Forman, 1976). Since the calculations are reported in
some detail, the method and relevant results are only briefly summarized
here. The photoacoustic cell geometry and dimensional notation are
reproduced in Figure 8. A cylindrically symmetric laser beam (step
function intensity distribution) axially illuminates a highly transparent

cylindrical glass rod of length R. The radii of the laser beam, rod, and
cell are rL, rS and rI respectively. The temperature solution in the

Heat Sink at T

Figure. 8 Geometry for Modeling the Photoacoustic Response of
a Cylindrical Rod (Bennett and Forman,1976)

Gas(aG K G,

*Laser Beam I
Glass Rod(as,Ks,Ps)


solid is derived in the same manner (thermal diffusion) as in the Rosen-
cwaig-Gersho theory. The photoacoustic term, i.e., the modulated steady
state solution, has the form
OS(r,t)=wS(r,w)eiw t (78)
wS(r,w) is given by
WS(r,w)=ASIo(.Sr)-iQL r WS(r,w)=ASIo(ESr)-iESrLQL[K1(SrL)Io(ESr)+Il(ESrL)Ko(ESr)] rL where AS is a complex constant; Io, I. and K and K1 are the zeroth and
first order modified Bessel functions of the first and second kind res-
pectively; QL=(mBSWLaS/KSr 2 m) where m is the source modulation depth
(oI1), BS is the spectral absorption coefficient, WL is the laser
power, caO is the thermal diffusivity, and KS is the sample thermal con-
ductivity; and e = exp(ir/4) where ES=(m/aS) / 2
The temperature solution in the gas is of the form

BG(r,t) = wG(r,w)eiWt (81)
Application of the hydrodynamic equations (Equation 75-77) gives
WG(r,w)=wa(r,w)+wt(r,w) (82)
where wa(r,w) is the acoustic term given by
wa(r,w)=AGJo( ar)+BGYo( ar) (83)
and wt(r,w) is the thermal diffusion term given by
wt(r,w)=CGIo [tr expCi7/4)]+DGKo[ctr exp (ir/4)] (84)
AG, BG, CG, and DG are complex constants; Jo and Yo are the zero order
Bessel functions of the first and second kind respectively; Ea=m/cG
where cG is the speed of sound in the gas; and t=(Wy/KG)12. The magni-
tude of the A.C. component of the normal pressure on the photoacoustic
cell wall is equal to the magnitude of the trace of the stress tensor

[Trr(rl,w)]. Normalizing the A.C. component to ambient pressure, p the
result is

Trr(r ) ) [-a(r,)+iY1_6(y-l)wt(ri,w)] (85)
po (y-1)

where To is the ambient temperature and 6 = oxG/CG2. This is the modu-
lated pressure signal which would be detected by a microphone situated
at the cell wall. Notice that once again there are five unknown coeffi-
cients, namely AS, AG, BG, CG, DG. The equations relating these coeffi-
cients are generated by applying boundary conditions. First, the temper-
ature at r=rI equals To at all times so that

wG(rI,w)=0 (86)
Assuming that the interfaces at r=rI and r=rS are rigid with respect to
the acoustic wave [i.e., u(r1,t)=u(rSt)=0] from the Navier-Stokes
equation, we have

Trr(r,) Trr (r) (87)
r r=r r r=r (87)

Temperature and flux continuity at the solid-gas interface require that

wS(rSw)=wG(rS,w) (88)

and K S(rw) G (r,w) (89)
Dr r=rS =r r=rS

These five relationships determine the complex coefficients.
Application of the above model to the case of photoacoustic response
of a bare fiber is accomplished by setting rL=r (i.e., the laser beam

fills the sample volume). Once again uniform illumination of the fiber

cross section is assumed. Extension of the Bennett-Forman relations to

modeling step-index clad fiber response is possible if three assumptions

are made. First, the core and cladding should be in intimate thermal

contact. This premise is not unreasonable since most glass on glass

fibers are drawn from a monolithic preform. Secondly, the thermal

diffusivity of the core and cladding materials should be identical.

While the core and cladding regions of doped fused silica step-index

fibers are certainly different on a microscopic scale, their thermal

diffusivities presumably differ little since doping concentrations are

relatively small. This assumption is difficult to verify. Finally, all

source light should be excluded from the cladding region. This condition

concurs with the assumption of a step function source involved in the

Bennett-Forman theory. Given validity of the above assumptions, a clad

fiber is modeled by setting the laser beam radius, rL, equal to the core

radius and the sample rod radius, rS, equal to the overall fiber radius.

A FORTRAN program ("ACOUSTIC") which implements the Bennett-Forman

theory for modeling the photoacoustic response of bare and clad fibers

appears in Appendix C. Results of the model calculations and compari-

son with experimental data appear in Chapter V.


Photoacoustic Cell
The photoacoustic cell for investigation of optical fibers consists

of two components, the fiber module and the microphone housing. The

two components are depicted schematically in Figures 9 and 10. The fiber

module is constructed from a quartz or fused silica capillary tube. The

fiber under study is positioned coaxially with the capillary centerline

and is secured with optical adhesive at either end. Prior to fiber

mounting a cut is made (via an abrasive wheel) into the tube wall mid-

way along its length to provide access to the active volume.

There are several design criteria for a satisfactory fiber module.

First, the module should be constructed from quartz or fused silica of

high optical transparency. This is especially critical since the fused

silica fibers under study exhibit minimal optical absorption. Scatter-

ing of some light into the cell walls is inevitable; therefore, wall gen-

erated photoacoustic signals can only be minimized by minimizing cell

wall optical absorption. This design philosophy is in marked contrast

to conventional PAS cell design practices. In more conventional PAS

cell designs, the walls are generally of high thermal conductivity, high

reflectivity metal (e.g., aluminum). The walls therefore act as heat

sinks and rapidly dissipate modulated temperature fluctuations generated

by optical absorption at the surface. A major drawback to this type of

Quartz Capillary Tubing

Outside Diameter
I .25(Nominal)

Inside Diameter
1 or 2mm(Nominal)

.040 Fiber
Optical A(
C 1.5-- r

Cut to Capillary Surface

All Dimensions in Inches

Figure 9. Fiber Module

4 22-22- U L1111A -




All Dimensions in Inches

.088 Drill

Drill and Tap
for #2-56 Scre


.25 Mill(Half-Round)

Figure 10. Microphone Housing

design, which is very relevant to fiber studies, is the lack of sample

visibility. Excessive fiber scatter, propagation of cladding modes,

fiber mounting defects, and faulty module seating are not observable

with an opaque cell. The use of a transparent cell module is also jus-

tified by the fact that while there may be some light scattered to the

walls, the incident intensity is certainly several orders of magnitude

lower than the intensity throughout the fiber cross-section. The wall

and sample photoacoustic signal components scale in roughly the same


The adhesive with which the fiber is mounted into the capillary

should be of high optical transparency. Since light absorbed in the

adhesive will cause generation of extraneous signals, every effort should

be made to exclude light from this region. For the mounting of clad

fibers in which the sealant comes into contact with the cladding, if

possible the adhesive should possess a lower refractive index than the

cladding material. This condition encourages reflection of light

incident on the cladding-sealant interface back into the cladding. In

the case of bare fibers, a thin layer of low index material (e.g., poly-

mer) should be deposited on the fiber at the fiber contact points prior

to sealing the fiber into the module.

For a given module length, the active volume should be minimized

in order to encourage the largest possible A.C. pressure variation for

a given fiber temperature excursion. The limit to this minimization is

the onset of physical interaction of the fiber with the cell wall. Since

coaxial mounting of the fiber is a tedious operation, the bore diameter

should be large enough to avoid fiber-wall contact in the presence of

moderate fiber bending. Such wall contact results in coupling of light

out of the fiber core or cladding (resulting in an increase in wall sig-

nal amplitude) and invalidates model calculations based on coaxial sym-

metry. The fiber module length should be chosen with regard to minimiz-

ing end effects (i.e., signal generation due to optical absorption in the

adhesive volume) and physical convenience. Outer module diameter is gen-

erally dictated by the availability of fused silica capillary stock.

The microphone housing is fabricated from aluminum bar stock. The

module saddle platform and microphone tube are joined with machine

screws and the joint is sealed with vacuum grease. Fiber modules are

greased and seated in the saddle with their access port coincident with

the pressure channel. A vent screw in the saddle stem prevents micro-

phone diaphragm overpressure during sample mounting. This vent is

closed during measurements.

The pressure transducer incorporated in the photoacoustic cell is

a Bruel and Kjaer (B&K) Model 4166 condenser microphone cartridge (Bruel

and Kjaer, 1977). The acoustic response of this cartridge along with

additional specifications are reproduced in Figure 11. The cartridge

is sensed by a B&K Model 2619 preamplifier. Operating voltages for both

the microphone and preamplifier are provided by a battery-powered B&K

Model 2804 microphone power supply. For installation in the microphone

tube, the protective grid is removed from the cartridge in order to mini-

mize cell volume. Since the Model 4166 is a back-vented microphone, room

pressure fluctuations outside of the sealed cell volume will result in

spurious microphone output. To minimize this problem, all joints along



Reference= v/Pa
(1Pa=1N/m2= Odynes/cm=1 Obar

-n I I -- --

50 100 200 500 1K 2K
Source Frequency (Hz)

5K 10K 20K

Open-Circuit Pressure Response (Electrostatic Actuator Source) for
B&K Condenser Microohone-Cartridqe Type 4166 (Serial #871360)

Open Circuit Sensitivity at 1013 mbar=
-26.7 db or 46.2 mv/Pa

Cartridge Capacitance=20.8DF

Gain of B&K 2619 Preamplifier=-0.2db

Figure 11. Acoustic Response and Specifications for
Bruel and Kjaer(B&K) 4166 Condenser
Microphone Cartridge(Manufacturer's Specifications)
(Bruel and Kjaer,1977)

the microphone length (i.e., cartridge-preamplifier interface, cable

ferrule) are sealed either with vacuum grease or teflon tape.

The photoacoustic cell is mounted in a vertical V-grooved optical

holder for measurements. The optical holder is equipped with a magnetic

base for easy positioning and securing of the cell. The entire fiber

optic photoacoustic spectroscopy system (FOPAS) is contained on a

vibration isolated optical table (Newport Research Corporation) in order

to minimize the effect of extraneous acoustic and vibrational noise.

The microphone output is synchronously detected and amplified with

a Princeton Applied Research (PAR) Model 5204 lock-in analyzer (PAR

1976a; 1976b; 1976c). Synchronization for this amplifier is provided by

the modulator. This mode of signal detection is necessary to extract

the feeble photoacoustic signal from incoherent background noise result-

ing from vibrations, ambient pressure fluctuations, and acoustic sources

(PAR, 1968). Photoacoustic signal amplitude and phase (relative to the

modulated source) are simultaneously obtainable. Output analog signals

(voltages) proportional to photoacoustic amplitude and phase appear at

individual panel jacks which are monitored by Hewlett-Packard Model

3438A digital multimeters.

Sample Illumination System

A schematic of the sample illumination system appears in Figure 12.

The optical source for all measurements is a Spectra-Physics Model 165

argon ion laser. This laser provides either single-line or multi-line

illumination depending on the rear reflective element. For multi-line

operation, a planar dielectric reflector element is used; whereas

Hypodermic Needle
(#18 or #20)

Syrinqe Tip


fl Optical Mount

. Sample Illumination System



single-line operation requires the use of a Littrow prism assembly. The

output wavelengths and specified power levels are tabulated in Table 2.

The laser controller provides for either constant plasma tube current

stabilization or stabilization of light output intensity. For single-

line operation, some line intensities are insufficient for proper opera-

tion of the intensity control feedback circuit, so output is stabilized

using current regulation. This problem is not encountered in multi-line

operation since output intensity is high and therefore intensity stabi-

lization is implemented. The laser beam is directed to the optical mod-

ulator via a set of steering mirrors. Prior to entering the modulator,

the beam is split with a quartz plate to allow monitoring of source

intensity. Laser power is monitored with a Spectra-Physics Model 401B

power meter (0-100mW). Since the detector element in this meter is

silicon, its use over an extended wavelength range (457.9-514.5 nm)

requires that a spectral calibration be made.

Laser source intensity is modulated with a PAR Model 192 variable

speed chopper. The rotational range of the chopper drive varies from

less than 2.5 revolutions per second (rps) to 100 rps. With a two

aperture blade (butterfly) the modulation frequency can be varied from

approximately 3 Hz to 200 Hz. Frequency stability is +0.2%/hour. A

chopper-derived synchronization signal (0 to +5V) is generated by a

photodiode pickoff in the blade housing. This signal is used for inter-

nal frequency stabilization and as a reference for the lock-in ampli-

fier. Chopper frequency is monitored with a Fluke 1910A multi-counter.

Table 2. Single-Line Output of Spectra-Physics
Model 165 Argon-Ion Laser

Wavelength (nm)

Peak Output









Power (mW)









(Spectra-Physics, 1972)

After traversing the chopper, the modulated source beam is focused

onto the fiber input face with a 5X, 0.10 numerical aperture microscope

objective (Edscorp). Given a laser beam diameter D and an objective

with focal length f, light of wavelength A is focused to a spot of dia-

meter d given by (O'Shea et al., 1977)

4h f
d- D (90)
r D

For a 2 mm laser beam diameter (Gaussian profile, TEMoo mode, A =

514.5 nm) and a 5X objective (focal length = 32 mm), the focused spot size

is 10.5 lim. This diameter is sufficiently small to avoid overfilling

the fiber face. The numerical aperture was chosen so as not to exceed

that of the clad fibers. This constraint prevents the injection of an

excessive amount of light into the fiber cladding.

Precision positioning of the fiber input face is accomplished with

an optically mounted (three-point) fiber jig. The jig consists of a

truncated hypodermic needle (18 or 20 gauge) pressed onto the end of a

sawed-off glass syringe cylinder. During sample mounting, the fiber end

is passed through the hypodermic to the focal plane of the microscope

objective. Positioning of the fiber end in the focal plane is accom-

plished with adjustment screws on the optical mount.

Ideally, light exits the fiber output end with a cone angle estab-

lished by the input beam numerical aperture. For spectral photoacoustic

spectroscopy measurements, fiber-transmitted light is collected with an

integrating sphere equipped with a silicon detector/amplifier in the

output port. The detector module output is synchronously detected and

amplified with a PAR Model 186A Synchro-Het lock-in amplifier. Syn-

chronization is provided by the chopper pickoff. Analog output was

monitored with a HP Model 3465B digital multimeter. The sphere is a

commercial model (Labsphere) of 6-inch diameter with an inner coating

of Eastman 6080 (barium sulfate, binder, and solvent). Once again the

spectral response of the sphere/detector system must be determined by a

calibration procedure.


Amplitude and Phase Calibration of Microphone

In order to perform accurate amplitude and phase measurements of

photoacoustic signals, it is necessary to know the amplitude and phase

response of the microphone system (cartridge and preamplifier) as a

function of frequency. Therefore, for a given frequency, microphone-

induced amplitude attenuation and phase shift must be quantified. The

general procedure for this calibration is to observe the microphone out-

put for a known input. For condenser microphones the best standard

source is an electrostatic actuator. With this device the microphone

diaphragm is electrostatically deflected according to some input wave-

form and the microphone output amplitude and phase (relative to the

source) is monitored to determine the transfer function.

A diagram of the microphone calibration system appears in Figure

13. The electrostatic actuator is a B&K Model UA0033 and consists simply

of a perforated metal disk with an electrode attached. The actuator is

electrically isolated from the microphone diaphragm by three equally

spaced insulating feet. The electrical ground connection is made at

the microphone casing. Drive voltage for the actuator is derived from

B&K UA0033
Electrostatic Actuator

B&K 4166 Cartridge

2619 Preamplifier

Oscilloscope Monitor

Figure 13. Microphone Calibration System


a high voltage amplifier. The electronic schematic for this amplifier

appears in Figure 14. To prevent frequency doubling, it is necessary to

bias the actuator at a high D.C. level and simultaneously superimpose

an A.C. voltage. For a bias level of 800 VDC and a peak to peak A.C.

component of 85 volts, a peak pressure of about 1 Pa (1 Pa=IN/m2
10 dynes/cm2=10pbar) acts on the diaphragm. Power for the high voltage

amplifier is provided by a Fluke Model 405B high voltage power supply

and a HP Model 6236B low voltage power supply. Actuator voltage (ampli-

fier output) is monitored with an oscilloscope using a Teletronix Model

P6013A high voltage probe. The reference signal (amplifier input) is

derived from an Interstate F-41 high voltage function generator and

monitored on an oscilloscope.

The electrostatically induced microphone signal is monitored with

the PAR Model 5204 lock-in amplifier. The synchronization reference is

derived from the TTL (transistor-transistor logic) synchronization out-

put of the Interstate F-41. Additional measurements were performed to

insure that the TTL output and signal output exhibited a constant phase

relationship over the frequency range of interest (3-100 Hz).

Ideally the high voltage amplifier input and output voltage wave-

forms should be 1800 out of phase with one another due to the circuit

arrangement (i.e., a voltage peak at the input produces a voltage mini-

mum at the output). Since there are no capacitive or inductive elements

in the amplifier circuit and since operation is limited to low frequen-

cies, the 1800 phase relationship is assumed to hold throughout the mea-

surement range. This being the case, any observed frequency-dependent

100 V


High Voltaqe


+15 VDC



(10-15 V Peak to Peak)

-' 500-700VDC




-15 VDC

Figure 14. High Voltage Amplifier

phase variation between microphone output and reference input is attri-

butable to the microphone (cartridge and/or preamplifier).

Amplitude and phase response curves for the B&K 4166 cartridge/

2619 preamplifier appear in Figures 15 and 16. In Figure 15 the ampli-

tude response and microphone-induced phase shift is plotted as a function

of source frequency for a sinusoidal input. Actuator drive voltage

(D.C. + A.C.) was maintained constant throughout the measurement.

Amplitude response of the microphone is essentially constant throughout

the measurement range. Notice however that the microphone output voltage

leads the applied actuator voltage throughout the frequency span. Con-

sequently, the phase of photoacoustically generated signals must be

corrected (phase lead subtracted off) if a true frequency-dependent

phase relationship is to be established. The phase curve in Figure 15

is used for all corrections of photoacoutic signal phase versus fre-

quency data. As an additional check, a microphone calibration was per-

formed using a triangular input waveform to ascertain the effect of

higher frequency Fourier components on microphone response. The obtained

data appears in Figure 16. It can be observed that the microphone

response for both sinusoidal and triangular forcing functions is essen-

tially the same.

Amplitude and Phase Calibration of Lock-In Amplifier

The lock-in amplifier (synchronous detector) is by design most

accurate for amplitude and phase measurements when the input signal wave-

form consists of a single frequency (sine wave). The photoacoustic sig-

nal output is, however, a complex periodic function. Not only do ampli-

tude and phase vary widely over the measurement frequency range

B&K 4166 Cartridge/2619 Preamplifier

Actuator Voltage

D.C. 650 VDC
A.C. 100 V Peak to Peak

I-Q- 06--

Microphone Amplitude Response
S.......Microphone-Induced Phase Lead

60. 0 80.

Source Frequency (Hz)


100. 0

--1 0.00
120. 0

Figure 15. Microphone Response (Electrostatic Actuator Source) Sine Wave Input







-a I


40. 00

30. 00

20. 00 0-



10. 00

20 _

0. 0

20. 0

I I* .11p- .0 ....

40. 0

ff- -


B&K 4166 Cartridqe/2619 Preamplifier

Actuator Voltage
D.C. 550 VDC
A.C. 100 V Peak to Peak

Microphone Amplitude Response
.... ..Microphone-Induced Phase Lead

0. 0

.4n. inl I

20. 0

40. 0

60. 0

80. 0

100. 0

I 0.00
120. 0

Source Frequency (Hz)

Fiqure 16. Microphone Response (Electrostatic Actuator Source) Triangular Wave Input




S-. CD
4- 4



,I 1 L

. 40


30. 00


- 20. 00 o.



40. 00

'0 .

'_P':1: P..4oh.

(3-100 Hz), but waveform symmetry varies also. For this reason it was

deemed necessary to determine the amplifier response for a variety of

waveforms at several fundamental frequencies throughout the range of


A schematic of the system developed for calibration of the PAR 5204

appears in Figure 17. Independent signal phase and amplitude measure-

ments are initiated by first acquiring the digital waveforms (signal

and reference) using a Biomation 8100 waveform recorder. The waveform

recorder is capable of simultaneously acquiring a discrete record (1024

words in length) of time-dependent signal voltage for both channels.

Sample interval is adjustable and ranges 0.5 ms to 0.02 ms for the

reported measurements. Amplitude resolution is 1 part in 256 (8 bits).

In order to simulate the frequency dependent photoacoustic signal, a 50%

duty cycle voltage pulse was applied to the input of a phase shifter/

isolation circuit. The voltage pulse was derived from the high imped-

ance (600 0) output of an Interstate F-41 high voltage function gener-

ator. The TTL synchronization output served as a reference waveform for

both the lock-in amplifier and digitizer measurements. The electronic

schematic for the phase shifter/isolation circuit appears in Figure 18.

The phase shift network consists of the 2KM resistor and 47 pf capa-

citor. The 50 0 terminator serves to prevent the D.C. input component

from reaching an excessive level. Because the digitizer input impedence

is low (50 0), it is necessary to decouple the phase shifter signal with

a voltage follower to prevent loading of the function generator. For

this same reason a 470 0 isolation resistor is inserted between the

Interstate F-41

TTL Sync Signal
TTL.Sync Signal

Phase Shifter/Isolator


PAR 5204

Input I I
r- 50n

Biomation 8100


Figure 17. Lock-In Amplifier Calibration System

Figure 18. Phase Shifter/Isolation Circuit



function generator TTL output and reference channel digitizer input.

Source frequency is monitored with a Fluke 1910A multi-counter.

The digitized signal and reference waveforms are passed to the disk

storage unit of an HP1000 computer via a HP2240A measurement and control

processor. The quantized signal and reference data strings are stored

as relocatable named files. A computer algorithm allows extraction of

the magnitude and phase of the fundamental component of both waveforms

using the discrete Fourier transform (DFT) (Frederick and Carlson, 1971).

For a periodic waveform consisting of M samples spaced equally in time

(the M samples correspond to an integral number of periods of the wave-

form), the amplitude of the n th discrete Fourier component is given by

c(Mn)= Z v(m)exp(-i2nnm/M) n=O,1,...M-1 (90)

where v(m) is the m th voltage sample and i =VY--. Notice that the c(n)

are complex constants with amplitude, c(n) given by

c(n) =\-[Re c(n)]2 + Jm c(n)]2 (91)
and phase, 4, given by

S= tan-[Im c(n)/Re c(n)]. (92)

A given Fourier component is then completely specified by c(n). Since
the lock-in amplifier is sensitive only to the fundamental of the signal
waveform, n is set equal to 1 and the M data points correspond to one

complete cycle of either the signal or reference waveform.

Experimental data for the lock-in amplifier amplitude and phase

calibration are reproduced in Figures 19-21. In addition to plots of

100. 00

Source Frequency=4.0Hz
75.00 PAR 5204:Normalized Amplitude=1.0, Relative Phase=83.2
DFT:Normalized Amplitude=l.0, Relative Phase=80.7'

SZ. --

50. 00

-25. -00Si

...... Reference

100. 0 1 1 1
0.00 200.00 400.00 600.00 800.00 1000.00
Channel Number(Sample Interval=0.5msec)

J 25.00

0. 00

-25. 00

-50. 00

.00 400.00 b00.00 ma 00. 00
Channel Number(Sample Interval=U.Zmsec)


Figure 19. Lock-In Amplifier Calibration Waveforms (4.0 and 10.7 Hz)

100. 00

75. 00

50. 00


-50. 00

-75. 00

-100. 00

200.00 400. 00 600.00 800.00
Channel Number(Sample Interval=O.05msec)

200.00 400. 00 500.00 800. 00
Channel Number(Sample Interval=O.05msec)

Figure 20. Lock-In Amplifier Calibration Waveforms (25.0 and 50.8 Hz)

200. 00 400.00 80O. 00 800.00
Channel Number(Sample Interval=O.02msec)

200.00 400.00 O00.00 800.00
Channel Number(Sample Interval=0.O2msec)

Figure 21. Lock-In Amplifier Calibration Waveforms (75.7 and 99.6 Hz)

Source Frequency=75.7Hz
PAR 5204:Normalized Amplitude=.56, Relative Phase=35.2"

DFT:Normalized Amplitude=.65, Relative Phase=37.5


..... Reference


75. 0 L_

50. 00

-' 25.00


0. 00

S-25. 00

-50. 00




75. 00

55. 55


-50. 00

-75. 00

-10. 00
0. 0

Source Frequency=99.6Hz
PAR 5204:Normalized Amplitude=.47, Relative Phase=27.4'

DFT:Normalized Amplitude=.SS, Relative Phase=30.4


..... Reference

I I I I I i _


1000. 00


I -

Ill)' I I I I I 1 I I I

signal and reference waveforms, phase and amplitude data derived from

both the PAR 5204 lock-in amplifier and the DFT technique are tabulated.

A summary plot of frequency-dependent signal amplitude and phase pre-

dicted by both techniques appears in Figure 22. Notice that the lock-in

and DFT measurements differ by at most 13.6% in normalized amplitude and

by 3.0 in relative phase. Since the lock-in and DFT techniques each

possess inherent methodical errors, it is difficult to quantify the abso-

lute accuracy with which phase and amplitude can be determined with the

PAR 5204. For the DFT method, inaccuracies arise principally from signal

quantization errors. The major lock-in errors arise from a 1/n sensi-

tivity to odd harmonics of the waveform fundamental frequency (PAR,

1980). However an inherent advantage of the lock-in amplifier is the

ability to average over many signal cycles. Given the data in Figure 22

and assuming the DFT results as correct, the maximum error in normalized

signal amplitude for the PAR 5204 is taken as 13.6%. The error in rela-

tive signal phase is taken as the average of the absolute difference

between DFT and lock-in amplifier data which is 2.1.

Optical Detector Calibration

During photoacoustic measurements the laser source intensity is

continuously monitored with a Spectra Physics Model 401B power meter.

Since the detector element in this instrument is silicon, its response is

spectrally dependent. The same is true for the integrating detector

system which monitors fiber-transmitted light during spectral photo-

acoustic measurements. The response of this system is slightly more

complicated due to the spectral reflectivity variation of the integrating

20. 0 40. 0 60. 0 80. 0

Source Frequency (Hz)

100. 0

75. 00


60. 00




__30. 00 -


120. 0

Fiqure 22. Comparison of Lock-In Amplifier and Discrete Fourier Transform (DFT) Frequency Response









0. 0

sphere surface. This intrinsic spectral response variation requires

that both the beam power monitor and the fiber throughput monitor be


The optical detector calibration system appears in Figure 23.

Absolute beam power measurements are made with a Laser Precision Model

RS 3964 electrically-calibrated pyroelectric radiometer. The chopper

for this radiometer provides beam modulation (15 Hz) and synchronization

for the fiber throughput monitor. To minimize the effects of spatial

reflectivity variation within the integrating sphere, the laser beam is

expanded with a quartz lens ahead of the input port.

Absolute spectral calibration curves for both the laser power moni-

tor and the fiber throughput monitor are reproduced in Figures 24 and 25.

The laser was operated in intensity feedback mode for power stabiliza-

tion. This feedback system is most effective for the high intensity

spectral line (514.5, 496.5, 488.0, 476.5, and 457.9 nm) and the reported

curves are compiled from data collected at those wavelengths. A manu-

facturer's spectral sensitivity curve is included for the Spectra Physics

401 B power meter.

A linearity check was performed for both detectors using the cali-

bration system depicted in Figure 23. For these measurements the laser

was tuned to 514.5 nm and operated in intensity feedback mode. The

results are reproduced in Figure 26 where relative detector output is

plotted against beam power measured with the pyroelectric radiometer.

In multi-line operation of an argon-ion laser, the relative power

distribution between spectral lines is generally not constant throughout

the range of plasma tube operating current. This situation will give

Detector Head Chopper

Spectra Physics
165 Argon Laser

Inteqratinq Sphere I


PAR 186A

Reference Signal

Fiber Throughput------------ Monitor
Fiber Throughput Monitor

Figure 23. Optical Detector Calibration System


+ Experimental Data

-- -- Manufacturer's Specification


460.0 470.0 480. 0 490.0 500.0 510.0 520.0
Laser Wavelenqth (nm)

Figure 24. Absolute Spectral Calibration Curve for Spectra Physics 401B Power Meter



0.00 L





001 1 I I i i I

450.0 460.0 470.0 480.0 490.0 500. 0
Laser Wavelength (nm)

Figure 25. Absolute Spectral Calibration Curve for Fiber
(Inteqratinq Sphere/Silicon Detector)

510.0 520.0

ThrouqhDut Monitor

50. 00

40. 00 L

30. 00 _



20. 00 L-

10. 00 L


+-Spectra Physics 401B
O-Fiber Throuqhout Monitor


0.0 20. 0

40.0 60.0
Incident Beam Power(514.5nm) mW

Figure 26. Linearity Confirmation for Spectra Physics 401B and Fiber Throughput Monitor

50. 00

40. 00 _

30. 00 __

10. 00 _


- mJ


90. 0

100. 0


Z l


rise to slight errors when a spectrally variant detector is used to

monitor multi-line beam power. To quantify this effect, the relative

multi-line power of the attenuated laser beam (i.e., that portion

reflected from a 10% quartz beam splitter) was measured with the

Spectra Physics 401B as a function of beam power (measured with the

pyroelectric radiometer). The results are reproduced in Figure 27.

Note the departure from linearity for large beam powers. Since the

laser power monitor is only utilized to provide a rough estimate of

intensity at the fiber input face, this slight non-linearity is of no


Given an initial laser output power POUT(W), beam splitter trans-

mittance TBS, and microscope objective transmittance TMO, the power

delivered to the fiber input face, PI, is given by

where TBS can be calculated from beam splitter reflectance, RBS, as

TBS=1-RBS. The maximum theoretical average intensity, I1(W/cm2), across

the focused beam assuming a 5X, 0.1 numerical aperture microscope

objective (beam diameter = 10.5 pm) is

10=(1.2 X 106)P (W/cm2) (94)

where Equation 90 has been used to calculate the focused spot size for a

2 mm laser beam diameter. If the light upon entering the fiber core

redistributes its energy among guided modes resulting in uniform cross

section illumination, the intensity at any point is constant and is

given approximately by (ignoring coupling losses)

40. 00


30. 00 __


20. 00 __

10. 00 _

rA rA r





0. 0 20. 0 40. 0 60. 0 80. 0 100. 0
Incident Multi-Line Beam Power (mW)

Figure 27. Relative Response of Spectra Physics 401B for Multi-Line Laser Operation



40 (94)

where D is the fiber core diameter.

For spectral photoacoustic measurements on optical fiber samples,

the laser output power varied from 3 mW at 465.8 nm to 300 mW at 514.5nm

for maximum plasma tube current. These power levels resulted in approxi-

mate average fiber cross-section intensities of 7.3 W/cm2 and 730 W/cm

respectively, for a fiber with core diameter of 200 pm (TBS=0.90,

TMO=0.85). For measurements in which the effect of modulation frequency

on photoacoustic amplitude and phase was investigated, the laser was

operated in multi-line mode at maximum power (POUT=IW). The result is

an average fiber cross-section intensity (200 pm core) of 2430 W/cm2

Recalling that the heat source term within the fiber volume is given by

BIO where B is the spectral absorption coefficient (cm-1), we have for
10-8cm -1l<10-5cm- a thermal power density ranging from 24.3 pW/cm3 to

24.3 mW/cm3

Sample Preparation

The photoacoustic studies reported in this investigation were per-

formed on four different fiber samples. The sample parameters are sum-

marized in Table 3. The bare (i.e., unclad) samples are obtained by

stripping the plastic jacket and silicon cladding from commercial fibers

(EOTec EPC BN125 and EPC BN200). This is accomplished by soaking a por-

tion of the as-received fiber in paint remover (active ingredient methyl

methacrylate) to swell the jacket and clad, and fingertip removal. A

short length of jacket and clad are left intact at the fiber input end

to limit the numerical aperture. This protective sheath also serves to

Table 3. Summary of Fiber Sample Parameters

Core Diameter (pm)





Cladding Thickness (pm)












Galite 5020



isolate the fiber from the metal wall (hypodermic needle) of the posi-

tioning jig. The clad fibers (Galite 5020 and TFC Step-Index) are both

coated with a silicon jacket which is removed in the same manner. Once

again a short length of silicon jacket is left intact for numerical

aperture limiting and for decoupling of light propagating in the clad-

ding. After stripping, all fibers are cleaned with isopropyl alcohol.

The fiber input and output ends are cleaned to assure a clean, uniform

optical interface.

In the case of clad fiber samples, no further preparation is neces-

sary prior to mounting. For bare samples, fiber contact with the optical

adhesive at the module input and output ends results in the decoupling

of large amounts of light from the fiber core. This is due to the

larger refractive index of the optical adhesive (n=1.56) compared to

that of the fiber (n=1.46). For this reason the portions of the bare

fiber in contact with the adhesive must be reclad. The contact areas

of the fiber are reclad with Optelecom low index plastic cladding com-

pound. This compound, which consists of a polymer dissolved in acetone,

is applied with a brush applicator and is heated with a hot air gun to

shrink and homogenize the dried coating. The low recladding index

(n=l.4) prevents decoupling of light from the fiber volume.

The fiber module is constructed from a 7.5 cm (3 inch) length of

quartz capillary tubing. Capillary inside diameter is 2 mm and outside

diameter is 6.35 mm (0.25 inch). Midway along the module length a slot

is cut (abrasive wheel) in the tube wall to provide access to the capil-

lary. The module blank is then cleaned with isopropyl alcohol. The

fiber sample is positioned coaxially with the capillary centerline

using a horizontal mounting jig. Once the fiber is positioned, Norland

N61 optical adhesive is applied to either end of the fiber module.

Capillary action draws the adhesive inward (approximately 6 mm) pro-

viding a uniform, competent hermetic seal. The adhesive is cured for

five minutes using a 275 W sunlamp.

A schematic depicting bare and clad fiber parameters appears in

Figure 28. Note that the clad fiber samples are somewhat longer to

allow incorporation of a cladding mode stripper. The stripper is com-

prised of two microscope slides separated by spacers. The open gap is

filled with mineral oil (n=1.6). The higher index of the oil compared

to that of the fiber cladding allows decoupling of cladding modes from

the cladding. This is especially important in chopping frequency depen-

dent photoacoustic studies where heat generated in the cladding can

result in significant contributions to the signal.

A prime concern in the construction of fiber modules for photo-

acoustic investigations is the inherent spectral absorption of the cell

components. For obvious reasons the cell constituents (i.e., capillary

tubing, optical adhesive, recladding compound, and sealing grease)

should exhibit very low optical absorption. This desired trait was

experimentally verified for all components utilized in cell construc-


Experimental curves for the measured spectral absorptance of

Optelecom low index plastic cladding compound and Dow Corning silicone

vacuum grease (fiber module microphone housing interface sealant)

appear in Figure 29. The cladding and grease samples were of thickness

0.006 inches and 0.06 inches respectively. Spectral absorptance is

All Dimensions in cm

----3 ----i

- 2(- 3-^ ----------
e F 7.5 Sam
Bare Fiber Sample Geometry

Original Plastic Jacket
and/or Cladding

I+--- t"

Quartz Capillary Tube
------- --,--

Cladding Mode Stripper

Clad Fiber Sample Geometry
Clad Fiber Sample Geometry

- 14.5


S7.-75 -


Mineral Oil

e2.5 --S
, =' Metal Spacer

I =I


Cladding Mode Stripper

Figure 28. Geometries for Bare and Clad Fiber Samples and Claddinq Mode Stripper


1 -_L-




Spectral Transmittance
Norland N61 Optical Adhesive
(Manufacturer's Curve)

Vacuum Grease(O.060"-Thickness)
Recladdinq Compound(0.006"-Thickness)

1-=. ..B .. ... EG>.. .-. .... ... ,.. . ...8)...

Figure 29. Spectral Response of Fiber Module Constituents

1. 00

. 80


. 201


450. 0

460.0 470.0 480.0 490.0 500.0 510. 0

Wavelenqth (nm)

520.0 530. 0

"' "





Yt U 3 T-- -7 YJ U 4J W--

computed as the difference between unity and the sum of hemispherical

transmittance and hemispherical reflectance. The Norland N61 optical

adhesive exhibits high optical transparency. A portion of the manufac-

turer's relative transmittance curve is reproduced in Figure 29.

Measurement Procedure

Prior to mounting the fiber module in the microphone housing

saddle, the mating surface of the module is coated lightly with Dow

Corning silicone vacuum grease and the microphone vent is opened. After

seating the module and closing the vent, proper sealing is confirmed by

observation of the microphone signal on an oscilloscope. The module is

secured to the microphone housing by an elastic band. The entire photo-

acoustic cell is then positioned by passing the fiber input end through

the positioning jig to within one focal length of the focusing micro-

scope objective. The fiber throughput monitor is positioned at the

fiber output end.

The fiber input face is positioned by slowly translating (via an

optical mount) the fiber in the image plane of the microscope objective.

Proper alignment is accomplished when the fiber face completely shadows

the positioning jig and when minimal light is observed to scatter from

the fiber module input and output ends. The shadowing criterion insures

that the fiber face is centered in the objective image plane and the low

module scattering constraint demonstrates that excessive light is not

being propagated in the cladding. In addition, every effort is made

to maximize fiber-transmitted light as indicated by the fiber through-

put monitor.

For all measurements the lock-in analyzer (PAR5204) time constant

is maintained at 10 sec. A 60 sec. (six time constants) settling time

is allowed between the adjustment of parameters (i.e., laser wavelength

or chopping frequency) and the acquisition of data. During spectral

photoacoustic measurements, five quantities are monitored and recorded

for each data point. These quantities are laser wavelength (not

directly measured), photoacoustic signal amplitude, photoacoustic signal

phase, fiber throughout monitor output, and laser beam power. For

frequency domain measurements, the laser wavelength variable is replaced

by chopping frequency. The fiber throughput monitor output is logged

at each modulation frequency to verify experimental system stability.


Hot Wire Calibrator Experiment

As a baseline for the analysis of experimental photoacoustic data

on optical fibers, two data runs were performed using a resistance wire

heater as the thermal source. The objective of this experiment was to

ascertain effects of the fiber module and microphone housing on photo-

acoustic response. Since metals generally exhibit much higher thermal

conductivities than glasses, sample-induced attenuation and phase shift

effects on the thermal signal are minimized. To ascertain the effect of

capillary diameter on photoacoustic response, data was collected for two

capillary widths (1 mm and 2 mm).

The experimental arrangement for the hot wire calibrator measure-

ments appears in Figure 30. The sample modules are constructed by pass-

ing a taut length of nichrome wire (#44 AWG) through the capillary and

Nichrome Wire(#44 AWG)

PAR 5204

Figure 30. Experimental Arrangement for Hot Wire Calibrator Measurements


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