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An Experimental study of frequency modulation of the laser by the Zeeman effect

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Title:
An Experimental study of frequency modulation of the laser by the Zeeman effect
Added title page title:
Frequency modulation study
Creator:
George, Rhett Truesdale, 1933-
Publication Date:
Copyright Date:
1965
Language:
English
Physical Description:
iv, 62 leaves : illus. ; 28 cm.

Subjects

Subjects / Keywords:
Atoms ( jstor )
Frequency modulation ( jstor )
Laser beams ( jstor )
Lasers ( jstor )
Light beams ( jstor )
Magnetic fields ( jstor )
Magnetic mirrors ( jstor )
Mirrors ( jstor )
Neon ( jstor )
Zeeman effect ( jstor )
Dissertations, Academic -- Electrical Engineering -- UF
Electrical Engineering thesis Ph. D
Lasers ( lcsh )
Magnetooptics ( lcsh )
Radio frequency modulation ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis - University of Florida.
Bibliography:
Bibliography: leaves 60-61.
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Also available on World Wide Web
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Manuscript copy.
General Note:
Vita.

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AN EXPERIMENTAL STUDY OF FREQUENCY

MODULATION OF THE LASER BY THE

ZEEMAN EFFECT


















By
RIIETT TRUESDAI.E GL-ORGE,. Jl.


A DLbS[ETATION iREt.EN ID 10 1MtE L~PAPUATE LOUNCJL OF
THE LINJ.'LR.IlTY O FLOFIDA
IN PARTIAL FULFILLMENT OF THL EQULIPFMENTl FOR THE
DEGREE OF DOC-OR OF PHJLOsOPHY










UNIVERSITY' O: FLORIDA
I Ie, r-i ly v 1













ACKNOWLEDGErMENTS


The author wishes to express his appreciation to Dr.

T. L. Bailey and other members of his supervisory committee

for their valuable assistance in the research, and to the

late Dr. M. J. Larsen for his assistance in procuring the

research equipment. Appreciation for technical aid is

expressed to Mr. H. R. King, Mrs. Joanna George, and to

many others.














TABLE OF CONTENTS


ACKIOWLEDGEMENTS

LIST OF ILLUSTRATIONS

ABSTRACT

Chapter

I INTRODUCTION

II PHYSICAL PRINCIPLES

The Laser
Stimulated Emission of Radiation
Optical Configuration
The Zeeman Effect
Fundamentals of Frequency Modulation
Methods of Frequency Modulation
Details of Frequency Modulation by the
Zeeman Effect

III THE ZEEMAN EFFECT FREQUENCY MODULATED LASER

The Light Beam Transmitter
Discharge Tube Configuration
Mirror Configuration
Frequency Pulling
Four Experiments
The Receiver

IV THE EXPERIMENTAL STUDY

Details of the Experiment
Excitation System
Modulation System
The Receiver System
Preliminary Tests

V MEASUREMENTS AND RESULTS

VI SUIMARY AID CONCLUSIONS

LIST OF REFERENCES

BIOGRAPHICAL SKETCH













LIST OF ILLUSTRATIONS


Figure Page

1. Grotrian Diagram for Helium and Neon
Levels Pertinent to-.the Laser 9

2. Laser Mirror Configurations 11

3. Laser with External Mirrors 13
4. Laser with Internal Mirrors 14

5. Energy Levels and Spectral Lines of the
Zeeman Effect 17

6. Emission Pattern Due to the Zeeman Effect 18

7. Spectral Lines as a Function of Current 23

8. Spectral Lines as a Function of Current 23

9. Sample One-Way Laser Communication System 25

10. Response of Cavity 33

11. Basic Internal Mirror Laser 42

12. Exciter Diagram
(a) Radio Frequency Driver 44
(b) Radio Frequency Amplifier 45

13. Receiver System 48

14. Filter Network and Response 49

15. Magnetic Field Beam Orientation Polariza-
tions 55














Abstract of Dissertation Presented to the Graduate Council
in Partial Fulfillment of the F.equirements for the Decree of
Doctor of Philosophy


AN EXFEr.IT'C:TAL STUDY
OF FFEQUEijCY :*I:DULATIOi; OF THE LASER
BY THE :EE;!Ai EFFECT



Fhett Truesiale George, Jr.

December 18, 1965


Chairman: Dr. "hom-a: L. Bailey
'lajor Department: Electrical Engineering


The purpose of this experimental study is to explore

the use of the Zeenan effect to frequency modulate a gas

laser for communication purposes. Lasers are used with

mirrorss outside the discharge tute and within it, and uith

axial and transverse masc-tic fields from zero to seventy

gauss. The laser iz a heliun-neon type with confocal nir-

rcrs, operating at 6328 A. Ho experiments involving the

Zeeman effect for modulation in either internal or external

mirror cas lasers have been reported In the literature, and

it isr believed that these are original.

Ieon is excited in the laser discharge tube to a meta-

staole state from uhich laser action at 6323 A may occur.

A resonant cavity formed by multiple dielectric mirror: at







vi
each end of the discharge tube reflects radiation necessary

to stimulate other neon atoms in the metastable state to

emit. In the resonant cavity, an integral or half-integral

number of light wave lengths may be maintained. For a mir-

ror separation of 128 centimeters, the frequency difference

between standing waves of visible light, or axial modes, is

117 mcps.

The Zeeman effect is a splitting of an energy level

into sublevels in the presence of a magnetic field, resulting

in splitting of the corresponding spectral line. The light

viewed parallel to the field axis contains the a+ and o-

beams, which are circularly polarized. By modulating the

field, the frequency difference between the a and o- beams

will be modulated, making frequency modulation possible.

The receiver is a photomultiplier tube whose photocathode

has a square law characteristic which makes detection

possible. Several peculiarities exist when using the Zeeman

effect to frequency modulate this type of laser, including

linear polarization of the light and frequency pulling due

to the optical cavity.

The study was made using PEK LT-11 and LT-12 laser

tubes, Optics Technology, Inc., mirrors, and an internal

mirror laser built in the laboratory. Preliminary tests

for excitation power, beam display and mirror alignment

were made.

The LT-11 laser tube was used with external mirrors,









Brewster-angle windows, and an axial magnetic field. The

Zeeman effect could not be detected, although the axial mode

beats and the transverse mode beats were detected. Similar

results were obtained with the LT-12 tube with external mir-

rors, Brewster-angle windows, and a transverse magnetic

field. It is concluded that strong polarizing action of

the Brewster-angle windows prohibits or greatly diminishes

the Zeeman effect.

The internal mirror laser with a transverse magnetic

field exhibited the Zeeman effect with the field applied,

as well as the transverse and axial mode beats. A field of

sixty gauss gave a o' a- line splitting of 1000 cps which

was then modulated over a frequency range of 20 to 200 cps

and received. It was concluded that this system is useful

for narrow-band, economical signal transmission by laser

beam.












T

INTRODUCTI Ot


Since the time of the mathematical description of the

laser, or optical maser, by A. L. Schawlcu and C. H. To-.nes

[1], the variety of applications of the laser has Frown

almost as rapidly as the number of speculations on its

possible uses. The purpose of this research .was to study

experimentally the frequency modulation of a gas laser by

means of the Zeeman effect. The gas laser was chosen over

the ruby and the junction diode lasers for its narrow line

width, continuous uave operation, and lack of special temper-

ature requirements.

Frequency modulating of the laser by the Zeeman effect

would offer a simple, economical communication system. The

modulator would be simple and economical to construct, and

the receiver ,would be no more complicated than f-m receivers

presently used at radio frequencies.

The study was made using sealed laser discharge tubes

with Brewster-angle windcus and eternal mirrors, and also

with demountable discharge tubes with internal mirrors,

normal windes, and a gas-fillinr apparatus.

Experiments ..ith a magnetic field applied to the Cas

laser :ith external mirrors have not been reported in the

literature, Also, modulation of an external magnetic field






2

passing through an internal mirror gas laser, and design and

operation of an f-m receiver of the type used have not been

reported. It is believed that this work is original.












II
PHYSICAL PRINCIPLES


The Laser


Laser is an acronym for light amplification by stimu-

lated emission of radiation. In nearly all cases the light

amplifier has sufficient positive feedback to make it

behave as an oscillator or generator. The helium-neon

laser, the most common form of gas laser, uses an electrical

discharge to excite the helium atoms. In several of its

transitions back to the ground state, the helium atom gives

up internal energy directly to the neon atom in a collision,

rather than by radiation. Several of the energy levels to

which the neon atom may be excited are metastable. If

radiation corresponding to a downward transition from a

neon metastable state to a lower excited state or to the

ground state interacts with another metastable neon atom,

the atom can radiate by stimulated emission, in addition to

spontaneous emission. The laser tube is fitted with high

reflectance mirrors at each end of the tube so that this

radiation builds up in intensity.

The laser to be discussed here is the gas laser,

specifically the helium-neon laser. The essential parts are:

a sufficient number of atoms whose electronic energies can








be raised to a metastable state so that a population inver-

sion will occur; a means of exciting these atoms; and a

high frequency optical cavity which will support standing

waves at a frequency corresponding to a desirable downward

transition.


Stimulated Emission of Radiation

Schawlow and Townes [1] have discussed the theory of the

laser and have shown that there are two requirements for

-amplification by stimulated emission. These are: a popu-

lation inversion between the electronic states involved in

the laser operation and a radiation power gain due to this

population inversion which is equal to the sum of all power

losses.

Population inversion is necessary if there is to be an

increase in, or amplification of, the energy density of the

radiation passing through an active laser medium, We con-

sider for simplicity a system in which there are only two

electronic energy levels. There are three processes per-

taining to electronic energy Jumps of atoms between these

two states and radiation of a frequency, f, corresponding

to the energy difference between these two states. The first

process is absorption of energy in the radiation resulting

in an increase in electronic energy equal to Wm Wn, where

Wm is the energy of the higher energy state, m, and Wn is -

that of the lower state, n. The number of atoms making

this jump per unit of time equals Nnu B where u is
n an amn mn


jiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii






5

the energy density of the radiation and Bm is the Einstein

coefficient for absorption.

The other two processes are emission processes. One is

stimulated or induced emission which corresponds to stimulat-

ed or induced absorption discussed above. This is a direct

interaction with the radiation, in which the photons emitted

have a constant phase relationship with the radiation, adding

to the energy density. The number of atoms making this

emissive jump per unit time equals NmmrnBmn, where Im is the

number of atoms in the state m. The Einstein coefficient

Bmn will be shown to equal Bm in the discussion of the two

state system below. The second emission process is sponta-

neous emission; the number of atoms making this emissive

jump equals N mA n. tote that no radiation field is necessary

for the spontaneous emissive jump.

If the two state system described above is in thermo-

dynamic equilibrium with the radiation field, the population

of each state is constant. Then

nBnm mn mB mnu mn mA mn

In equilibrium, 11M < 1n unless Amn is zero. According to the

Boltzmann distribution,

!m Sm e-kT/Wm 2.
Nin gn e-kT/~,

where &m and g, are the statistical weights of the two states,

k is the Boltzmann constant, and T is absolute temperature.

If 6m and g5 are equal, then 11M < n .








Assuming gm equals gn and that NmAmn c mBmnumnU if

Nm >. 1n, amplification of the radiation of energy density,

Umn, will take place. This is because more atoms are stimu-

lated to emit in a jump from m to n than are induced to

absorb in a jump from n to m, or

I"mBmn un > JBnmumn 3.

The number of n-m transitions is

Bnmn dt
n rm in

and the absorbed energy is

dWab 11nB nmmn h fn'

where h is Planck's constant. Similarly, the number of stimu-

lated m-n transitions is

NmBmn um dt

and the emitted energy is

dUem = 11MBmnUmn h fn dt.


The net emitted energy rate, or power, is

d(We- ) = ( ) mn) h fn 4.

Obviously -d(em- Wab) is positive only if Nm > Nn. This

net emitted power is evidenced in an increased umn.

At this point, it is noted that as T approaches infinity,

e-kT/Wm
e-kT/Wn 1

For gm equal to gn,









+- 1
n

Also, umn -

Then


BmnUmnllm


and

Bn = Bm 5.


as asserted earlier. Since B and B are microscopic in

nature and are not temperature dependent, this equality holds

for all values of T. By substituting the exponential ratio

of Nim/ln in equation 1 ,

mn /Bmn
en hf/kT-i

Comparing this with the Planck radiation formula,

8nf2 hf
ufdt = c2 hf/'T_1 df


where c is the speed of light and df is a small band of

frequencies about f, the following equation is obtained:

Sof2
Amn = 2 h Bn .
c-
low the energy lost in the spontaneous m-n transitions may

be calculated relative to the energy added to um by

stimulated emissions.

The second requirement is that the power gain achieved

above and described in equation 4 equal the sum of power








looses in the total radiation system, of the laser; except

of course, for absorption, airea.dy accounted for. Tri e

losses occur in the rirrors, in the *'indous which may be in

the basic system, in non-active Eas, and in dizperi,.-c

m..dia.

In the laser used in this experiment, the discharge

tuLe *:as 'illea i.ltn a mixture of about ten parts of helium

to one part neon, to a total pressure of one nicro.. An-

eiectrical dischargcr ex:.-ites the neliun to a nur.ser of

different energy sta-tes. T-1he helium. dec-ay- blac: to the

ground ztare by meant of a number of transitions, usually

em.ittin: radiation a-pontaneousl: ',:ith each transition. There

are zseeral inelastic collisions in .*.hich electronic excita-

tion ene:6y is e::changea bet.ieen helium ana neon atoms.

These include:

HeI213) + Ne(CS i He1'5) + l:e(3s2)
6.
HeC23Z) t 1Nee(13; Iell'So) + te(2z2)

In eacn of these collisions the neon is excited to a meta-

statle state from which stinulates emission can ta::e place.

From the lowest energy electronic state, 2p, neon atm.s

decay rapidly. to the- ground state sy spontaneous emission.

Tne Grctrlan diagram of energy levels for this cycle, begin-

ning with helium in the excited state, is given on the next

page in rilure 1.

In this figure, the dotted line indicates the collision

described by the first part of equation 6 and the solid

line indicates the collision described by the second part



















o c r

rJ rj
m Lu-.


0








Lft
'2)j
Y.







I1 /'/'';
en rj c-'



IA





(~1








E
.,I
rCA

H II'
'C,


ti H- 0% CA\ CO %0
c Nj rr r- -1 C Hi


r-)


-- ("U

- 0


co







i.
0
t-
rl,





c"
L.





0
L.

-I















Cr.








of equation 6. Stimulated emission due to the downward

transition from each neon metastable state is indicated by

a wavy line; the emission wavelength is also given. The

rapid decay time for the Ne(2p) energy level permits the

necessary population inversion between this state and the

metastable 3s and 2s states.


Optical Configuration

The stimulated emission described above must reflect

back and forth in the laser tube to stimulate more emission.

The gain per pass is small; an attenuation of two to three

per cent could stop the laser operation. Therefore, mirrors

used must have very high reflectance. Typical values of the

reflectance for gas lasers are 99.0 to 99.5 per cent. Of

the remaining .5 per cent of the light beam, probably 0.3

per cent is absorbed and 0.2 per cent transmitted. Mirrors

commonly used in laser applications have nine to thirteen

layers of dielectric coatings, usually with two different

dielectrics alternating, which are applied in precise

thicknesses to substrates whose surfaces are controlled to

one tenth wave length or better. The surface may be flat or

curved for optical configurations of parallel plane, confocal,

spherical or combination mirror systems [2,3]. Several

configurations are shown on the next page as Figure 2 [1,33.

The confocal mirror configuration was used in this

experimental study for both the internal and external mirror

lasers. The mirrors, produced by Optics Technology, Inc.,












































0




E *,
C) C
rt


rl
(-
r-


1" 2-3


CT r-


0

3 i
TI n





C,
U C



LL


o L

L.
- r1



1-1





L.2 -I


rli








are shaped for a nominal separation of 125 centimeters and

are multiple dielectric coated. The PEK laser tubes required

that the mirrors be external. Later investigations required

that internal mirrors be mounted on a laser tube built by

the author. The external mirrors are victims of atmospheric

dust, the internal mirrors are subject to electron and ion

bombardment during operation; each of these effects decreases

reflectivity.

A laser with external mirrors and Brewster-angle windows

is shown on the next page in Figure 3. Brewster-angle win-

dows [1] are used because incident radiation which has its

electric vector parallel to the plane of incidence suffers

no reflection. A laser with internal mirrors is shown in

Figure 4 on page 14.



The Zeeman Effect

Excited atoms may be in a degenerate energy level. If

such atoms are placed in a magentic field, this degeneracy

(in general) is removed; the excited energy level splits into

a number of sublevels. If the spectrum of transitions

between the two levels is observed, what had been a single

line now becomes several individual lines. This is the

Zeeman effect [4]. For the hydrogen atom, the number of sub-

levels is determined simply by the quantum number m. As the

number of electrons in an atom increases the number of sub-

levels and the system of energy coupling between the electrons















Li-








cd -0
'1J'i H


I I Is


I,-

-O
C: 44









0 0



3 T :













0C O
0 0

SL 1






15
become complicated. In their paper, Statz, Paananen, and

Foster [5] suggest that j-l coupling be used for neon. This

is also called Racah or extreme coupling. Knowledge of the

coupling was used to determine the Lande-g factor, which, in

turn, was used to determine the splitting of the levels.

Statz, et al. [5] calculated g = 1.33 for the 2s, state,

used the value of 1.3 for the 2p, state, and quoted the

experimental value for the 3s2 state as 1.295. The dominant

stimulated neon transition in the visible spectrum is the

3s?-2p4 transition, for which a Land,-g of 1.3 will be used.

Removal of the energy level degeneracy by placing the

two state system previously discussed in a magnetic field

makes possible emissive transitions from one or more sub-

levels in state m to one or more sublevels in state n. The

energy separation among the zublevels of m and among the sub-

levels of n is quite small compared with the m-n transition

emitted energy. This variation in the m-n transition energy

may be calculated by the quantum mechanical first order per-

turbation theory. The energy differences among the sub-

levels is interaction energy, between the magnetic moment of

the atom, denoted by u, and the magnetic flux density B of

the applied field.

W = -u*E T

The theories for L-S coupling are most widely used and will

be summarized here to demonstrate the dependence of the

interaction energy W on the Land4-g factor. A g factor






16

based on j-1 coupling rather than L-S coupling will then

be used.

The net magnetic moment u is the vector sum of the

orbital magnetic si of all v electrons of an atom.

u0- [ -() 1i + E
i=1

= ( ) (L + 2S)
Ir m -

6- e J + )
2 m

where J = L + S

Then

U (J + ) B.
2 m -

From a consideration of the vector quantities and their

various rates of processing, the following equations are

developed:

e [(J + S)-J] [J.B]
2 m [J l

1 eB [lJ 2 + (|J_12 + [S2 IL21)] J


where J'S = (IJIr + IS2 ILl2). The quantum mechanical

operator for the interaction energy, W, is just the operator

for the quantity in the right hand member of the above

equation. The shift in the energy of a quantum state

specified by the quantum numbers L, S, J, and Mj is, accord-

ing to first order perturbation theory, given by

1 eB J(J+1)+t[J-(J+1)+S(S+1)-L(L+1)]
7w 7 ;14+ + ] +j.)








1 ehB
W= 7 m g r"


where g has the value of the quantity in large brackets in

the proceeding equation.

The energy differences become

1 efB
Em 2 m bm "Jm and
9.
1 eiB
n 2 E2 n m Jn .


The levels and transitions involved in the two state

system are depicted below, along with the resultant spectral

lines. The system with gm equal to gn exhibits a "normal"

type of Zeeman effect, though with an abnormal line separa-

tion unless the g factors equal one. The system with gm

unequal to g exhibits the anomalous Zeeman effect.


State m



gm= gn


n



Spectral
Lines


0 I 0
-- i 0
o~ n o+


Figure 5. Energy Levels

of the Zeeman


mT












II Ii a
n








and Spectral Lines

Effect








The radiation emitted by the atoms is not uniform

spatially. The emission of the a and w components of the

radiation is governed by quantum selection rules, the results

of which are indicated below in Figure 6.




1 S o' only
circularly
polarized

vertically horizontally
polarized polarized


Figure 6. Emission Pattern Due to the Zeeman Effect



Fundamentals of Frequency Modulation


Frequency modulation is a neans of modulating the

carrier with a signal such that the frequency of the carrier

deviates from its center frequency a number of times per

second which is equal to the frequency of the signal, and

deviates a number of cycles per second from the center fre-

quency according to the amplitude of the signal. Expressed

mathematically [6] for a carrier of amplitude A and a signal

frequency of the form B sin wst, the frequency modulated

signal is

A(t) = A sin (w,+ m B sin u t)t 1D.


where uc is the center frequency of the carrier and m is the

modulation index.

Phase modulation is similar to frequency modulation






19

e::cept that the phase cf the carrier is changed accordin-

to the signal, or

A(t) = A sin (.t+ m B sin "st)


= A sin (t + m B sin t)i


where 4-= t. To relate phase modulation to frequency
C C
modulation, the parenthetical part of the above equation

is differentiated with respect to time to obtain d.,'dt, or

frequency, to compare with equation 10.

d (CWt + m B sin u t) = ,e + n B cos L t
dt p c p -
If, before the mcdulation took place, the signal were inte-

grated, it uould be of the form

JB sin L.t dt = I B cos mt.


Replacing the signal ,ith its integral in the derivative above,

(, ct m B cos u t)=(w + m sin L..', 11.


Equation 11 no'' has the same fern as the parenthetical part

of equation 10. Therefore, i'.'en a phase modulatian device,

frequency modulation will result if the signal is first

integrated. Since a frequency modulated signal may te

obtained, several r1eans of pha.e modulaticn ?'ill be discussed.

I:. appl.'.in; the laser to comnur.ications work, information

must be put on the bean of light using either aTplitude or

frequency modulation. Here, :-aplitude -modulation includes

most formn of pulse modulation and frequency nodulation in-

cludes phase modulation. Only frequenc:.y nodulation will be









considered here.

riethods of Frecuencv Modulation


There are at least four methods of frequency modulating

the laser beSm. The first, the subject of this paper, em-

ploys the Zeeman effect. This method will be discussed in

greater detail in the next section. The second uses an

electromechanical transducer to *.ary the position of one of

the nigh reflectance mirrors [7]. This rives a Dopoler

shift to the light reflected and a change of optical cavity

frequency. This motion is

S= + k D sin w-t 12.


where 1 is the transducer coefficient, Z is the mirror

separation, and B sin u-t is the signal. For a constant

mirror displacement

Z = 0


there will be a chance in the cavity frequency, but no

Doppler shift. The result of changing the optical cavity

frequency is discussed in Chapter III,

The third method makes use of an electro-optic material,

that is, a -material in which the velocity of light in the z

direction is a function of the voltage applied in the y

direction. T:-.o such materials, which are crystalline, arc

-nmmonium dihydroren phosphate, ADP, and potassium dihydrogen

phosphate, 1.DP. This method involves placing one of these

crystals in the optical cavity, [3. This changes the







21

velocity of light in the :avity:, giving a Doppler shift to

the light frequency and a change of optical cavity fre-

quency. The fourth method uses the ADP or ZDP crystal out-

side the optical system, '*'hnre the output bean will pass

through it [9], This cgies only a Doppler shift to the

lilht fremuenc-., but has the advantage of no addeJ item with-

irn the optical system of the laser c-sllator, which could

cauze diffraction or attenuation of the beam, possibly

stopping oscillation.


Details of Frequency Modulation by the Zeeman Effect


Unlike the second, third and fourth methods just listed,

the first methcd of frequency nodulaticn by the Zeeman effect

is achieved directly--phase modulation by D.oppler zhift is

not an intermediate process. From the discussion of the

Zeeman effect, the following equations are obtained:

U = E E


and
E E :'1 f .
= .LE nE 2 (mg Jm EnJn)
M n 2 m m"m nJn

A quantum selection rule states that I.J = J + 1, ,Jm'

'J.- 1. The spectral lines are due to in not equal to

r"Jm. A.:uminr. that gm equals gn and :Jjn equals RiJm- 1,

then

M H u e
U in






22

The frequency difference between the a and i rays is Civen

by the following equation

F = GpfD/h.

Finally

C/D = g 1.1 mcps 14.


where f is the difference between the 1 ray frequency and the

o ray frequency, B is the magnetic field strength, g is the

Landc-g factor, u,. is the magnetic moment component in the

direction of the applied H field, and h is Planck's constant.

This assumes that gj = 6J+.' From both experiment and theory,

the Lande-g factor is known to be approximately 1.3 for

transitions of interest in this work.

For the general case, which produces the external mag-

netic field, let the coil be excited by a current which is

l(t) = Io + I sin wut 15.


where I0 is a constant or bias current and Is sin wst is the

signal. Uith a proportionality constant k' relating the

current I(t) to the flux density B(t), the frequency expres-

sion becomes

f = 1.3(1.4) k' (Io + Is sin wut) mcps. 16.


With Io equal to zero, the center frequency of the

light beam will be the same as the frequency for zero mag-

netic field. Figure 7 is a plot of the beam frequencies for

a certain input.
















I(t) 1=0 Is sin st

Figure 7. Spectral Lines as a Function of Current

lith circular polarizers it may be possible to separate the

+ and the oa beam components. Otherwise the signal may be

lost or may be recoverable only with a large second harmonic

component.

With Io greater than IIs sin tstj the center frequencies

will be shifted away from the zero field frequency. Figure

8 is a plot of the beam frequencies.




f(t) fo
~o-



I(t) i=0 I0+ Is sin st


Figure 6. Spectral Lines as a Function of Current


The beam components now have a definite separation and may

lend themselves to considerably simpler detection techniques.

In Figures 7 and 8, the w component is included, although,

under certain conditions to be described, it will not be in

the output beam.


f(t)t fo













III

THE ZEE::'.:N EFFECT FREQL'UE:iCY i!CDULATED LACER


The physical principles pertinent to the laser which

is frequency modulated using the Zeeman effect hsve been

discussed. Certain operational peculiarities appear when

a magnetic fieli is applied to a laser. These will no', te

discussed *.:ith emphasis cn the helium-neon laser operating

at 6328 A with external mirrors and Erewster-angle ',indo"s

on the dircharre tabe. Cev.eral experiments performed b-

others, .thich are concerned with the Zceman effect and some

of the peculiarities will be discussed also. Finally, a

means of receiving the light signal will be described.

A transmitter cornistin, of a laser with its modulator

and a receiver are needed for a one-'w-ay' com.municaticn system.

The simplified system ;ho.:n in Figure 9 on the next pafe is

similar to the actual system which :'.as constructed for this

experiment, described in the ne::t chapter. The simplified

system is reminiscent of the system enploying a reflex:

klysvtron in the transmitter, ..here signal voltage is merely

applied to the klystron reflector and a frequency modulated

signal is obtained.


The Liht Ecamn Transmitter


The laser with the magnet is the essential part of















"4 0
4- a1
.-
'-4 Ci
0. 4)

a.

1.- 4-


+ ---

1>3
ci -|
LLl






C
0




ui















EE
A >O












td ri


>- oJ o
J 11







C







Li





0O
<-4












C'S cii LO
c a.






26

the transmitter. The transmitter performance is affected by

the discharge tube configuration, the optical configuration,

and by "frequency pulling." These three factors will now be

discussed.


Discharge Tube Confiruration

The discharge tube may have the mirrors built in, or it

may be constructed for use with external mirrors. In either

case, there are windows at each end of the tube through

which the beam passes. These windows must be optically flat

if the wave front is to be undistorted. As discussed in the

chapter on physical principles, Brewster-angle windows are

commonly used for the external mirror configuration, since

they permit the electrical field vector to pass through in

one polarization without reflection. This means that the

beam which builds up within the cavity is linearly polarized;

so, also, is the output beam. If internal mirrors are used,

the windows are usually perpendicular to the axis to avoid

a polarizing effect.

An axial magnetic field applied to a laser will split

the energy levels as shown in Figure 5 on page 17. Based

on the calculations in the section on the Zeeman effect, the

Landd-g factors for the initial and final states are assumed

to be 1.3. The spectral line simplicity (but not the

spacing) of the normal Zeeman effect will be observed. If

the laser has internal mirrors and perpendicular windows,

the axial field will cause the output beam to split and be








made up of two components, the a+ and a- circularly polar-

ized rays. As the w ray does not exist in the axial direc-

tion, there will be no stimulation for the transition which

produces the n ray.

An axial magnetic field applied to a laser with external

mirrors and Brewster-angle windows will produce the a+ and a-

circularly polarized beams within the discharge tube. On

passing through the Brewster-angle windows, the electric

vector perpendicular to the plane of incidence is partially

reflected, and the emerging beam is elliptically polarized.

With no laser excitation, the perpendicular field component

would be lost rapidly in the optical cavity. With laser

excitation, the loss for the perpendicular component due to

window reflection is large enough to prevent laser oscillation

in this field component. The contribution to the perpendi-

cular field component per pass will be small, resulting in

an output made up of two linearly polarized beams, one at the

a+ frequency and one at the a" frequency.


Mirror Configuration

The mirror configuration presents no special problems

beyond those already discussed in the chapter on physical

principles.in operating a laser with an axial magnetic field.

This statement is made with regard to mirror shape--confocal,

hemispherical, etc., and the mirror location, whether inside

or outside the discharge tube. Mirror separation does

present certain problems which will be discussed next under







28

the topic "frequency pulling." Mirror reflectance, which

determines the Q of the optical cavity, also affects fre-

quency pulling.


Frequency Pulling

Frequency pulling is a familiar phenomenon. In the case

of two mechanical oscillators moderately to strongly coupled

without buffering, when one is tuned rather closely to the

frequency of the other, the two will tend to lock and oscil-

late at one frequency. A strongly tuned cavity will pull the

frequency of a microwave oscillator if the two are tuned

near the same frequency. The laser, with two resonant

systems, exhibits frequency pulling also. The two systems

are: the assembly of excited neon atoms, which are radi-

ating by stimulated emission; and the optical cavity, which

will support an integral or half-integral number of wave

lengths.

If two similar resonant systems, A and B, with quality

factors QA and QB, tuned to slightly different frequencies

fA and fB, are coupled together, the combined resonant fre-
quency, fo, will be approximately (fA+ fB)/2. If QA and QB

are not similar, then for QA greater than QB, fo will be

closer to fA than to f A first approximation can be made

by letting the "willingness to change frequency" be inverse-

ly proportional to the Q or

QA (f0- fA) -0(f- B) QB 17.






29
This is similar to the resultant gain of two tuned ampli-

fiers whose individual gains are

A =A 1
A AO w WA 18.
1 + jQ(n -)
1
AB AB -B
0 1 + jQB( 19.
B 19.

The total gain is

1 1
A = AAAB = AAAB WA B 20
0 0 1+jQA(U -U) 1+jQB(B- -)

The imaginary component vanishes at the system resonant

frequency:
S WA i 0B
J(QA(Zc ) + QB( =)) 0


or

(o- A)('O+ A) ( 0- B )(O +B) 2.
quW- A)( 0 A O B 0 B 21.
A "AO B WBO

For A approximately equal to uB,

A B22.

and

0 + WA "O + "B 23.

Then

Q C ) -Q s 24.
A .0 A Be 0 B17

which is the same as equation 17.






30

In their article, Gordon, Zeiger, and Townez [10]

gave the following expression for frequency pulling for a

He-:e laser, analogous to equation 24:

B B 25.



or

= U+v BVn- v Al B-'B) '' B L+ -C) 26.

where v, is the output frequency, vB is the neon transition

frequency, &vB is the half-w:idth of the emission line of

neon, VC is the cavity resonant frequency, and s', is the

half-width of the cav.ity modes. This equation has also been

deri'.ved by Bennett [11]. For example, if the cavity is

initially tuned to the center of the neon line :vC = vB),

the second term on the rirht will be zero. If now the

cavity is tuned to a higher frequency, the amount of the

frequency increase will not be .C- vp, but rather

AVB
",_ B v


Ihe nominal frequency of the neon transition and its

band'.idth or line-':idth are constant;. The cavity fre-

quency is a function of the nirror separation, and the

cavity Q is a function of the mirror reflectance. The neon

bandwidth ir approximately 1000 mcps, due mainly to Doppler

broadning. At thes .a'avelengths the cavity has a resonant

point every 120 mcps for 125 cm. mirror separation. It -was

shown in Figure 2. on page 11 that for confocal mirrors of







31

125 cm. focal length, separated to 128 cm., that a point 2
o
mm. from the center of one mirror is 750 A closer to the

other mirror center than is the center of this mirror. This

is a very large operational attitude. The mirror reflec-

tance is such that one per cent of the energy is lost per

pass, giving Q of approximately 100. This is a bandwidth of

1.2 mcps, or a line half-width of 0.6 mcps. Frequency

pulling may be calculated using these values; it may oe

more accurately calculated using known values for the par-

ticular equipment. The large operational attitude men-

tioned above offers some relief from pulling, but only at

the expense of having the beam wander about on the mirror.

This is unlikely because the mirrors are focused. Usually

different modes occupy different parts of the mirror.

Consequently, a large expected shift in frequency due to the

Zeeman effect in the presence of a magnetic field becomes,

in actuality, a small shift, due to the frequency pulling

of the cavity.

The frequency pulling expected in the laser usea in

this experimental study will now be calculated. Beginning

with the equation for frequency pulling, 25 the frequency

difference between the o+ and o- beams will be calculated.

(vgCVC + AVBVC)
O = (AVB + AvC)


Let


vgE = AvC + C







32


C ( + ca+a c

cjv


VC 4AV B C

,,,here vO0 is beam frequency, v B is neon line center frequency,

6v B is neon line width, v C is cavity center frequency, and

A,)C is cavity bandw,,idth. Since the cavity remains tuned to

the zero magnetic field be-am frequency, c is the frequency

shift produced by the Zeeman effect, or the frequency dif-

fernce between the o n beams. Due to frequency pul-

ln, however, the expected observed difference is





The band)idth 6v C of the optical cavity may be determined

by considering, the Q c, or quality factor, and the resonant

fexcuency increments of the cavity


energy dissipated acn


Dielectric i-,irrors of reflectance R will reflect R nor cent

of the E vector of the light ( and consequently R ner cent of

the H vector) and transmit (100 R) per cent, Power is

proportional to the square of the magnitude of the E vector.

The expression for Q may be written as



(100 F)2

where R is given in percentage. With 99 per cent reflectance

mirrors, Q c is (99/1)1 or approximately 104.








The resonant frequency increments may be determined by

the number of integral or half-integral standing waves the

cavity will support. Let n be the number of half wave-

lengths supported in the cavity, X1 the wavelength, and fl

the corresponding frequency. The n + 1 will represent the

number of half wavelengths supported in the cavity for a

slightly different frequency, and f, the corresponding

frequency. The mirror separation used is 1.28 meters.

Then

1.28 _1.28 2.56fi
n = l e 3"lOs
S 3xl08 3108
2f1

2.56f2
n + 1 = ----
3.108


f f = 3108 = 117 l106 cps
2.56

The approximate response of the cavity is shown below.



Ability
to
Support
Standing
Waves
ii 7 mcps-- f*



Figure 10. Response of Cavity


Based on the calculated Q and the axial mode separation,

AvC is ll7"x10/Qc, or 11,700 cps.

Doppler broadening of the neon line amounts to 500 to







34

1000 mcps. Using the latter figure, AvB = 109. For

H = 10 gauss and g = 1.3,

c = 1.4.1.310h0'10

= 1.82 107cps


The frequency separation is

S- VC 1.e82x1071.17i10 = 210 cps.
109+1.17.104

The calculated frequency separation between the 0+ and a

beams is 420 cps, using a Doppler broadening of 1000 mcps,

and 840 cps, for a Doppler broadening of -500 mcps. Mag-

netic field intensities from 0 to 70 gauss were used in

the experiments so that the audio range would be covered.



Four Experiments


Three experiments have been described in the literature

in which frequency pulling is studied. In two of these,

the Zeeman effect is studied. Each of the first three

experiments to be described was performed with the helium-

neon laser operating on the 11,522 A line, the laser being

equipped with internal plane mirrors. Bennett [11] describ-

ed an experiment where frequency pulling is measured.

Approximate expressions to account for this pulling were

derived. He did not deal with frequency shifts and conse-

quent pulling due to the Zeeman effect, but with pulling

due to the cavity, the gaseous medium in the cavity, and






35

the population levels of the excited gas.

The second, by Statz, Paananen, and Koster E[5, was an

experiment to determine the Zeeman effect. They used a

linear polarizer to convert the circularly polarized waves

to linearly polarized waves of varying amplitude which were

then detected with an infrared phototube. The output with

the earth's magnetic field parallel to the laser tube was

1050 cps, indicating that the o+ and o- rays were rotating

in opposite directions at the rate of 525 revolutions per

second. Assuming the field to be 0.5 gauss, they calculated

a rotation of 300 rps. With an imposed field of one gauss,

they calculated a rotation of 610 rps and measured 625 rps.

Culshau, iennelaud, and Lopez [12) measured the Zeeman

effect superimposed on the 120 mcpz beat note detected

between oscillations in adjacent cavity modes. They in-

serted a Nicol prism to polarize the output wave and de-

tected it with an infrared phototube. Both a 4 gauss per-

pendicular field and a 30 gauss axial field were used in the

experiment, With the 30 gauss field, a modulation of 80

kcps was measured; a modulation of 130 kcps was calculated.

This calculation included frequency pulling. These results

compare favorably with those of 3tatz, et al.[5].

The last experiment to be discussed, performed by Kiss

[133,deals with the Zeeman effect in the CaF :Dy + solid

state laser. This laser is photon exicted or light pumped

and is operated at 27K. The optical cavity consists of






.6

high reflectance r.irrors deposited on the end: of crystals,

whichh are spherical. Small magnetic fields up to ?0 gauss

and large fields of 10,000 gauss uere used. The results

:.ere as follc's.: the ~ n, and o- beam components werc

observed in the axial direction. A separation of the axial

components of 150,000 mcps was observed ':ith the use of a

10,000 gauss magnetic field. Usinr small fields, frequency

modulation *.a; obtained with av.'ities having a low Q and

amplitude modulation with cavities having a high Q. The

magnet system used homogenous and inho.nogenous fields.



The Receiver


The frequency modulation receiver used in the present

experiments employs a photomultiplier tube for the first

detector stage. This tube i. sensitive to instantaneous

variations in incident light [10, 11, 12, la] such as the

beat or difference frequency between the o rays. The output

signal from the photomultiplier is amplified, then d-modula-

ted in an f-i detector to obtain the original signal.

Caddes and ::cr-urtr: [15] discuss photodetectors, giving

a conversion equation as foilo-:s:


0 light e


where Plint is average light input power, n is quantum

efficiency of the photon-electron convcrsion, e is electron

charge, h is Flanck's constant and v is light frequency.






37

The magnitude of the output current is proportional to the

square of the input light vector. For an input consisting

of the oa and a- beams,

Io = k(A cos w.t + B cos w2t)2

= A2cos2 it + 2AB cos wut cos w2t + B2cos2W

A2Cos2t + Bzcos2,t + AB(cos(l+ w2)t

+ COs(wj- w2)t)


where k is a constant of proportionality, A is the magnitude

of the E vector of oa, u is the frequency of a+, B is the

magnitude of the E vector of C-, and w2 is the frequency of

a -. If o+ and a- differ by a few hundred to a few thousand

cycles per second, the difference in frequency will occur in

the audio range. Let there be two axial modes of oscillation,

identified as Beam 1 and Beam 2. For Beam 1, containing o+

and o s, separated 117 mcps from Beam 2, at and a,

Io = k(Alcos uit + Bicos W2t + Acos w21t

+ Bzcos L,2t)


where k is a constant of proportionality, Al and Wl, are

magnitude and frequency of E vector of a, B1 and Li, of

0o A2 and w2I of 0o, and B2 and u22 of o. The a and o

separations will be approximately the same for Beams 1 and

2. If this separation is in the audio range of frequencies,

then Io ~ill contain this audio frequency, the 117 mcps fre-

quency, and sidebands separated from the 117 mcps component

by the audio frequency. If






38

7 (I 1 w12) = fA


where fA is an audio frequency, then I contains fA, 117

mcps, 117,000,000 a fA cps, and others. The signal in fre-

quency modulated form is contained in fA'














IV

THE EXPERIMENTAL STUDY


The experimental study was conducted from July, 1963,

to June, 1965. At that time, there were no gas lasers in

the College of Engineering. Part of the time was spent

building associated laser equipment, building laser dis-

charge tubes, and making mirrors. The associated equip-

ment will be discussed under Details of the Experiment.

Several laser discharge tubes were built. These consisted

of Pyrex tubes, usually thirty-six inches long and six to

eight millimeters inside diameter, supported on end pieces.

The end pieces were metal cups or fittings with windows,

mounted on a sturdy base. A fitting at one end of the tube

had a connection to the vacuum pump and the gas-filling

apparatus. Several means of sealing the windows and the

tube to the end pieces were used at different times, includ-

ing vacuum wax, O-rings, and tin-indium glass to metal sol-

der. These sealing systems allowed the tube, but not the

end pieces, to be baked out.

Some plane mirrors were made on flat glass substrates

using aluminum, and later, silver. The high reflectivity of

magnesium made it attractive as a mirror coating, but the

vacuum obtained in the evaporator used was inadequate for








giving good quality mirrors. The magnesium bettered the

atmosphere of the bell jar, and the deposition was a com-

bination of magnesium oxide and magnesium salts. At this

point, multiple dielectric mirrors of confocal design were

purchased from Optics Technology, Inc. These mirrors were

fitted to the laboratory laser and a number of unsuccessful

attempts to obtain laser action were made.

The gas filling apparatus consisted of a helium tank,

a neon flask, a mercury manometer built for the laboratory,

valves, and a thermocouple gauge. After evacuation, the

laser tubes were filled with neon and then with helium to a

final pressure of 0.5 torr to 1.0 torr. The gas composition

was varied from pure neon to one part neon to ten parts

helium. Windcus perpendicular to the axis and Brewster-

angle windows were tried. lo evidence of laser action was

observed with these tubes. It is believed that the lack of

laser action may be attributed to windows which were barely

of laser quality, to outgassing of the tube, and to impuri-

ties in the gases (which were not of spectroscopic grade).

In the last stage of this work, the windows were checked in

the optical cavity of an operating laser and found to be

below laser quality.

Two commercially assembled laser tubes, PEK LT-11 and

LT-12 were obtained and mounted on a previously constructed

base. The PEK LT-11 and LT-12 have the gas mixture of helium

and neon sealed in, are forty-seven inches over the Brewster-






41

angle windows, and have an inside diameter of six milli-

meters. Ilo difficulties were experienced in obtaining

laser action.

For later experiments, another laser discharge tube

was built in the laboratory. This laser discharge tube was

constructed with internal mirrors and windows normal to the

beam. Mirror mounts were constructed which employed bellows

to allow for mirror alignment adjustments. The Optics Tech-

nology mirrors were placed in the bellows mount with tin-

indium solder. A connection was provided in one mount for

the gas-filling apparatus linkage. A drawing of the basic

unit appears on the next page in Figure 11.

The evacuation and back-filling equipment represents

another change from the original experiments. A laser mix-

ture of helium and neon, premixed in a one to seven ratio

was obtained from the Linde Company. Evacuation to 10l-

torr (10-7 torr at the pump) used first a mechanical pump

and then an ion pump, followed by heat gun bakeout of tubu-

lation and discharge tube, but not mirror mounts. Then, gas

was admitted through a leak valve into the tube to a pressure

of about one torr. Laser action was easily obtained over a

range of pressures near one torr.



Details of the Experiment


The large quantity of support equipment necessary for

a laser experiment was in part built for the experiment and













.- r .


t..
a> 03


- U7
I: y o






43

modified from equipment already in the laboratory.


Excitation SYstem

This system consists of a radio-frequency e :citer,

matching netw::rk-, and recitation electrodes, a3 shoin in

Figure 12. The e:;citer includes a 14.4 mncs driver and an

amplifier. The amplifier use- three 807 tubes connected in

parallel and has independently variable plate and screen

grid power supplies. The s:'stemr operate: in a shielded de-

sign to minimize radiation. The amplifier i3 locp-coupled

to a tank circuit in which the capacitance is made up large-

ly of the capacitance in the electrode structure mounted or

the laser tube. Several structures were tried; the finzl

design consists of alternate ground and high voltare elec-

trcdes wrapped partly around the tube and connected to the

Icngitudinal ground or high voltage buss. The busses are

separated by ccrnjriic spacers and the whole structure is hunE

from the tube. There are five high-voltage electrodes and

six ground electrodes.


The Ilodulation S"ston

Cev eral modulation na:nets were constructed for the

experiment in order that the direction of the externally

applied magnetic field through the laser might be varied.

The LT-11 tube w;a fitted with a solenoid three inches in

diameter, forty inches long, and wound :.ith t-.o forty-turn

windingg. Calculations and measurements showed that this











0 --r ,-.
orl

P


cu
mO >

i O

ob
0r C



Ci

[ 0
C4





v
















C -a
co



E- cu-'



LL


,1) r-I
Q. >
-4 D.O
C-,









S.i G
0 C, > >
E-, r-. 0'--



C0
co Dl





CJ







46

solenoid produced an axial magnetic field with less than

110 per cent variation of field strength over the length of

the discharge.

For the LT-12 tube, a pair of rectangular coils about

two and one half inches by forty inches, each having a total

of eighty turns were constructed. These were placed one on

each side of the tube with aSout three inches separation and

connected so that the fields produced were in the same direc-

tion. rMeaurements showed a variation in this transverse

field of less than -8 per cent.

The rectangular coils described above were used with the

internal mirror laser. At the field strengths necessary for

observing the Zeeman effect, the coils heated rapidly. A

similar set of rectangular coils three and one-half inches

by forty inches were built, each having approximately 2500

turns. These were placed one on each side of the discharge

tube with two and one-half inches separation. Measurements

again indicated a variation in transverse field strength of

less than 18 per cent.


The Receiver S/stem

The optical portion of the receiver consists of two

first-surface glass dielectric reflectors (reflection taking

place at the air-glass boundary) set at the polarizing

angle, and a photonultiplier tube. The reflectors remove

the component of light which has the E vector in the plane

of incidence, this being the w component. The o components






47

are transmitted. The photonultiplier cathode is a square

la.j detector which has all the original, sun, and difference

frequencies in its output. Due to the low'-pass nature of

the electron multiplier section of the tube, the electrical

output is made up solely of the lower difference frequencies.

The output frequencies include the a;:ial mode beat fre-

quencies in the 115 to 125 mcps spectrum, recoverable with

a conventional receiver which tunes to this range, the fre-

quency difference between the o+ and oa rays in the audio

range when a magnetic field is applied, and the beat fre-

quencies between the transverse modes in the audio range if

more than one exists.

The f-m receiver used consisted of a wide-band amplifier

0 20 mcps, driving a monostable vibrator. The multivi-

brator output passed through a diode gate and into a low

pass filter. The filter output drives an audio type ampli-

fier and speaker. This is a type of frequency counter in

wnich the output voltage varies as the input frequency which

controls tht repetition rate of the multivibrator. The wide-

band amplifier and multivibrator used are part of the cir-

cuitry of a Tektroni:; IModel 541 oscilliscope. The receiver

diagram is shown in Figure 13 on page 48 and the lou-pass

filter schematic and response curve in Figure 14 on page 149



Preliminary Tests


Tne LT-11 laser was u-ed first with an exciter of low








48








r-







0.


r;







i--4












-*- 4






LiI.











in
O r"













L. .. -o a-
--[ -- ^ ^ ^ 5
*" I I
; p (




t



i^,4
(U / l










o \ n
O. -




































0


















r--1


C























I






U
o


-^t/-



















J


r


C
'


l"
r
0
a
tj





C[
CJ










C-,





1 -4

I"













C-








power. It provided sufficient excitation for single trans-

verse mode lasing at 50 to 60 vatts and multiple transverse

mode losing at 70 to 80 watts. With ambient dust in the air,

the beams intensity was observed to be much greater in the

cavity than outside the cavity, This is normal, since the

reflectivity quoted for the mirrors was 99.5 per cent. The

transmission as probably 0-.2 pe cent. The ratio ofrelc

tion to transmission was-probably 500 to 1.----

Tolerance of miro ralsignment was next observed.- With-

80 watt excitation, lasting was maintained ovear a range of




or a deviation fro-m alignment center of ten minutes. Atth

same time, another beam with brightness of from 10 to 50pe

cent of the main beam was observed. This beam reflected

from the Brewster-angle window at an angle apparently equal

to the angle of incidence. The spot size, observed on the

ceilinG, indicated that this was a reflected beam and not

just light scattering from imperfections or dust on the win-

dow. The intensity of the beam transmitted through the mir-

ror is approximately 0.2 per cent of that of the internal

beam. Therefore, the reflected beam is from 0.02 per cent

to 0.1 per cent of the intensity of the beam within the

cavity. This indicates that the beam, without a magnetic

field, is essentially linearly polarized; the reflection may

come from a slight deviation from linear polarization in the






51

discharge tube, slight non-parallelism of the Erewster-

angle windows, or from slight angular displacement of the

polarization by the confocal mirrors.

A large glass cylinder uith Glass ends was filled with

benzene to see if the bean could be observed as it passed

through. The benzene did not diffuse the beam. It could

be ob-erved if a diffusing material were suspended in the

benzene. Tap uater gav'e no results either. The beam was

visible as it passed through a jar filled uith smok.e.

A photographic slide i;as made on Kodachrome II film.

The beam intensity was measured with a light meter, the

diapnragm and inutter speed were set and the picture taken.

The result was a completely over-exposed spot in the center

of an otherwise blacl: slide. The fact that the camera dia-

phragm opening has no effect on the intensity of light

incident on the film was o'.'erlooked; over-exposure could have

been avoided only by increa-lin the chutter speed.












V

MEASURE.rIITS AND RESULTS


The first experiments were made with the LT-11 laser

tube and the axial field solenoid. When several transverse

modes were present, the beat frequencies between them were

detected in the audio range. Decreasing of the exciter

power and realignments of the mirrors returned the system to

single transverse mode operation and the beat frequency out-

put ceased. The axial transverse mode beats were detected

at 117 mcps using a narrow band all-frequency receiver.

With increased exciter power, the multiple transverse mode

beats appeared as modulation on the axial mode beats. Next

the magnetic field was applied in the range of 0 to 70 gauss.

The beat frequency between the oa and o- rays could not be

found. Calculations for frequency pulling were made, in-

dicating that an output should be observable in the 10 to

20 gauss range. however, the Zeenan effect did not go

entirely unnoticed. A beam disturbance detected electrically

as an impulse was observed each time the magnetic field was

applied or removed. This is possibly caused by a change in

vY due to the Zeeman effect which resulted in sufficient de-

tuning to cause one of the axial modes to cease or begin to

oscillate. Under conditions of low exciter power and slight

mirror misalignment, lasing would occur only if the magnetic







53
field .ere present, again po:s.ibly due to a change in v'

due to the feeman effect.

Due to the effect of the Ereuzster-a.n.le windows, the

beam remained lin-arl:. polarized throughout the ranTe of the

mnrnetic field used. This was determined usinc double di-

electric reflector: of the type mentioned in the dic-ussion

:n the receiver system mounted at each end of the laser itn

the paths of the cutput beam;.

The LT-12 tube .Jas ne:t used with trans'.erse manetic

field coils.. :ith no magnetic field applied, the results of

the e::perirents for the trns','erse node beats and the a:..ial

mode beats i.ere the sa1me as those obtained with the LT-11

tube. The traneveree magnetic field was applied succes-

si.el: in 'two directions, fir=t to pass the c rays through

the Erewster-angle indooror unreflected, and second to pass

the r ray unreflected. In each e-periment, the Zeeman

effect ::as not obser.'ed. Electrical impulses in the output

:.ere obtained upcn sudden application or removal of the

field, but the beat frequency betw-en the ,+ and a- ra','3

with the field applied wa- not detected ''ith field strengths

up to 50 causs.

The internal mirror laser described on page 41 4'-1 s

ueea next, noting that careful attention to good vacuum

technique: was ne:ezsarv, to assure reliable operation.

The transverse mode beat frequencies again zould be obtain-

ed and removed by e.citsr pcwer control and mirror adjust-







511

mert. The axial node beats were obtained at 121 ncps, the

change due to a reduced mirror separation. The Zeenan

effect '.as observed 'ith field strengths of 50 to 70 gauss.

The need for higher magnetic fields was anticipated due to

the nature of the laser, the Q of the cavity should be

greater than that of the earlier systems as this system

does not contain Brecster-anrle windo.s. The Zeeman split-

ting did not run smoothly up from 0 gauss, but appeared

suddenly in the 4C0O to E00 cps range with about 50 gauss

applied. The Zeeman effect w'as obtained with single trans-

verse mode laser operation. The frequency output, or amount

of splitting, depends both on the strength of the applied

field and the exciter power level. This splitting dependency

has been reported by Statz, et al.[5].

With a field level of 60 gauss and a lowr exciter level,

a splitting of the line of 100 cps '.as obtained and used as

a carrier frequency. The field :wa then modulated over a

range of 20 to 200 cps. The frequency nodulated signal was

detected over this same ranCe of signal frequencies usinr

the receiver. The inductance of the transverse magnetic

coils and the lou-pass characteristics of the receiver fil-

ter precluded the use of higher modulation frequencies. It

is interesting to note that photomultiplier alignment was

not critical for detection of the Zeeman effect. Parallel-

ism between the ben and a vector normal to the photocathode

of within 2 to 3 degrees was adequate.












VI

SUI:':A'AR. AUlD CO:ICLUSIO;S


At the beginning of this experimental research, use of

only the LT-11 laser tube and axial field solenoid was

planned. The negative results obtained in this experiment

and later with the LT-12 laser experiments made it necessary

to enlarge the scope of this experimental study tuice to

achieve positive results. The conclusions based on the LT-

11 and the LT-12 laser tubes will be given first.

At no time was a signal detected which would indicate

frequency modulation by means of the Zeeman effect with the

external mirror lasers. The three measurements concerned

the different orientations between beam polarization, E,

and the magnetic field *y. These are shown below in Figure

15.






Beam 2eam Beam

Hf


(a) (b) (c)

Figure 15. Magnetic Field Beam

Orientation Polarizations








The first measurement ,'as made according to Figure

15(a). The Zeeman effect indicates that the beam uill

contain the o+ and o- rays which will be circularly polar-

ized in opposite directions. The optical cavity contains

two Breoster-angle windows which are thought to prevent

amplification of a circularly polarized i;ave. This was

found to be the case. :Jo beam. was found with the electric

vector perpendicular to the plane of incidence. Prohibition

of circular polarization may prevent the frequency shift due

to the Zeeman effect.

The second measurement was made according to Figure 15

(b). Here, the beam should contain the o+ and 0- components

plane polarized in the plane of incidence. Again, no signal

was found, apparently because of the strong effects of the

plane polarization, or perhaps because of much greater fre-

quency pulling chat that believed to be present.

The third measurement was made according to Figure

15(c). There, the seam should contain only the component.

Again, no a components were detected.

The axial modes, spaced every 117 mcps, were detected.

With more intense beams, which permitted laser operation

in several transverse modes, audio frequency whistles and

squeals were detected. These frequency differences between

transverse modes are due to slight path length differences.

It appears that the detector does operate properly.

Based on these observations and on the four experiments







57

in the section on the Zeeman effect frequency modulated

laser, it is concluded that this laser structure witl

external mirrors and Bre::ster-angle windows cannot be fre-

quency modulated using the Zeeman effect with magnetic

fields from 0 to 50 gauss.

The Zeeman effect may be observed in spontaneous

emission provided that the a rays can reach the detector.

In laser operation, the neon atom radiates downward from a

higher energy level whichh is metastable. If the a rays are

discriminated against by the optical structure, specifically

the Erewster-angle windows, there t:ill not be enough gain

to support laser action in the J ray mode. Then there will

be no rays to stimulate emission from those metastable

atoms jith H, 0.

The internal mirror laser does not contain any strong

polarizer in the form of a Brewster-angle window. Outside

the optical cavity, uindous are used which are normal to

the beam so that there is no polarizing influence there.

The only polarizer which ray be present, excluding the mag-

netic field, is a mirror imperfection, and this is not large.

The Zeeman effect was observed repeatedly using the internal

mirror laser and transverse magnetic fields in the ranCe of

50 to 70 gauss with ao a frequency differences of approx-

imately 1000 cps. The magnetic field strength was modulated

directly with the signal. The signal was recovered from

the frequency modulated light beam using the receiver.






56

It is noted that from the results of the frequency

pulling equations, the Zeeman effect will be small, even in

a laser cavity which will support circular polarization.

Therefore the range of carrier frequencies and useful modu-

lation frequencies will be small for easily achieved mag-

netic field strengths. Additionally, at a sufficiently

high field strength, the ao and lines may jump to the

next axial mode, establishing an upper limit to the useful

modulating frequency. By shortening the length of the

optical cavity, the axial mode frequencies are raised.

Frequency modulation by the -eeman effect does offer

several important advantages. First, it is simple and

economical. The magnet structure is simple, and modulating

the magnetic current produces frequency modulation of the

carrier, which is the difference between the a+ and c- rays.

The system is less sensitive to vibration than a moving

mirror system, and does not contain ADP or KEP crystals,

inch are expensive and which require high driving voltage.

The polarizer may be mounted on the laser in the output

beam path to lessen the alignment problem between trans-

mitter and receiver. Since both the a+ and a- rays are

transmitted, the receiver photomultiplier tube functions

as the first detector of a superheterodyne receiver with

the carrier and the local oscillator signals both coming

from the transmitter. In the experiment, the corresponding

intermediate frequency is centered at 1000 cps. 'With this









system, there is no need for a second laser to function as

a local oscillator, eliminating what has been, up to now, a

significant stability problem. Elimination of the second

laser is an added economic factor.

From thiz research, it is concluded that frequency

modulation by means of the Zeeman effect is practical only

for narrow bandwidth applications, but offers significant

advantages in that area. These advantages are simplicity

and low cost of the modulator magnet, simple modulator

electronics and receiver design which is no more complicated

than f-m receivers at radio frequencies. As the modulator

magnet does not come in contact with the discharge tube or

optical system, the way is left open for comblninc this

system with other systems. Further, the Zeeman effect is

not only influenced by the Q of the optical cavity, but

also by the nature of the polarizers within the cavity.














LIST OF REFERENCE,


1. A.L. Schawolo, and C. H, Tounes, "Infrared and Optical
:asers," Physical Revie!, Vol. 112, December, 195),
p. 140.

2. W. U. Rigrod, H. cgelnik, D. J. Brangaccio, and D. R.
Herriot, "Gaseous Optical !!aser :ith E:ternal Concave
Mirrors," Journal of Aonlied Physics, Vol. 33,
February, 16-2, pp. 73-744.

3. A. L. Bloon, "Properties of Laser Re:onators Givinr
Uniphase '.!ave Fronts," Laser Technical Bulletin il. 2.
Spectra-Physics, Inc., Mountain View, Caiifornia.

4. Gerhard Herzberr, Atomic goectra and Atomic Structure.
Dover Publications, !We York, 194l .

5. H. Statz, R. Paananen, and G. F. Foster, "Zeeman Effect
in Gaseous ielium-!eon Optical 'aser," Journal of
Asplied Physics, Vol. 33, February, 1962, pp. 14'-744.

6. T. L. Martin, Jr., Electronic Circuits. Prentice Hall,
Inc., EnClewood CliTff, 1955.

7. P. Rabincwitz, J. LaTourette and G. Gould, "AFC Optical
Heterodyne Detector," Proceedings of the IRE, Vol. 50,
July, 1962, pp. 1686-87.

8. F. S. Earnes, "On Modulation of Optical [lasers," Pro-
ceedinrs of the IRE, Vol. 50, January, 1963, pp. 177-
153.

9. C. J. Peters, "Gisacycle Bandiidth Coherent Light
Travelin-!Wav.-e Phase :lodulator," Proceedings of the
IEEE, Vol. 51, January, 1963, pp. 147-153.

10. J. P. Cordon, H. J. Zeiger and C. H. Townes, "The Haser-
New Type of licrouave Amplifier, Frequency Standard and
Spectrometer Physical Revie'w, Vol. 99, August, 1955,
pp. 1264-1274.

11. W. R. Bennett, Jr., "Hole Burning Effect in a He-Ne
Optical Maser," Ph.sical Review, Vol. 126, April, 1962,
pp. 580-593






61

12. W!. Cul1hau J. ::annclaud, ana F. Lo-,e, "Zeeman Effect
in the Helium-.:Jon Planar Laser," Ph'.-ical 7e'ie*:,
;ol. 12:, :ij.oencer, 1962, pp. 1747-1 7i6.

13. Z. J. Kiss, "Zeeman TuninT of the CaF,:D:,. Cptical
;laser," [Paper prezentc at the ricroronr'e Pesearch
Institute :3mpo iumn cn Cpticta iiaser, Pol:.technic
Insti ute of brol:l;.n, April, 1963.]

14. P. A. Lindsay, S. F. Paik, K. D. Gilbert and S. A.
Focney, "Cptical ii.inn- in Fhototube ," Proceedinrs
if the IRE, Vol. 50, IIcvermber, 1962, pp. 238-2-31.

15. D. E. zadde; and E. J. iic;iurtry, "E-.aluating Light
Demodulator ," Electr rnice, 'lol. 37, April, 196I ,
pp. 5'-61.














BIOGRAPHICAL SKETCH


Rhett Truesdale George, Jr., was born on !:ay 2, 1933,

in Columbia, South Carolina. In June, 1951, he was graduated

front Boys' Hi7h School in Anderson, South Carolina. In June,

1955, he received the degree of Bachelor of Science in

Electrical Enlineering from Puke University. He received

the degree of Mascer of Science in Engineering from the

University of Florida in 1956. Fron 1957 to 1961 and during

tne fall of 1?62, he taught Electrical Enginecrinz at fuke

University. In the Fall of 1961, he enrolled in the

Graduate School of the University of Florida and has pursued

his ';ork toward the degree of Doctor of Fhilosophy until the

present time. From 1961 to 1963, he worked as a graduate

assistant on the Ford Foundation program in the department

of Electrical Engineerine. From Septenber,1963, to August,

1964, he was on the Duke University advanced degree program

for faculty. From September, 1964, to the present time, he

has been teaching Electrical Engineering at Duke University.

Rhett Truesdale George, Jr., is married to the former

Joanna :arie Huffer. He is a member of Sigmra X:, Phi Beta

Kappa, Tau Beta Fi, Eta Kappa Nu, and Ormicrcn Delta Kappa.












This dissertation was prepared under the direction of

the chairman of the candidate's supervisory committee and

has been approved by all members of the committee. It was

submitted to the Dean of the College of Engineering and to

the Graduate Ccuncil, and was approved as partial fulfill-

ment of the requirements for the degree of Doctor of

Philosophy.


December 18, 1965



Dean, College of Engineering



Dean, Craduate School


Supervisory CorrTrittee:



Chairman



\ ^ .3\. .,.



--- v >t77 < --- ^-




Full Text

PAGE 1

AN EXPERIMENTAL STUDY OF FREQUENCY MODULATION OF THE LASER BY THE ZEEMAN EFFECT By RHETT TRUESDALE GEORGE, JR. A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA ! >^ ember, I N

PAGE 2

ACKNOWLEDGEMENTS The author wishes to express his appreciation to Dr. T. L. Bailey and other members of his supervisory committee for their valuable assistance in the research, and to the late Dr. M. J. Larsen for his assistance in procuring the research equipment. Appreciation for technical aid is expressed to Mr. H. R. King, Mrs. Joanna George, and to many others. ii

PAGE 3

TABLE OF CONTENTS ACKNOWLEDGEMENTS ii LIST OF ILLUSTRATIONS iv ABSTRACT V Chapter I INTRODUCTION 1 II PHYSICAL PRINCIPLES 3 The Laser 3 Stimulated Emission of Radiation 4 Optical Configuration 10 The Zeeman Effect 12 Fundamentals of Frequency Modulation 18 Methods of Frequency Modulation 20 Details of Frequency Modulation by the Zeeman Effect 21 III THE ZEEMAN EFFECT FREQUENCY MODULATED LASER 24 The Light Beam Transmitter 24 Discharge Tube Configuration 26 Mirror Configuration 27 Frequency Pulling 28 Four Experiments 34 The Receiver 36 IV THE EXPERIMENTAL STUDY 39 Details of the Experiment 4l Excitation System 43 Modulation System 43 The Receiver System 46 Preliminary Tests 47 V MEASUREMENTS AND RESULTS 52 VI SUMMARY AND CONCLUSIONS 55 LIST OF REFERENCES 60 BIOGRAPHICAL SKETCH 62 iii

PAGE 4

LIST OP ILLUSTRATIONS Figure Page 1. Grotrian Diagram for Helium and Neon Levels Pertinent to'
PAGE 5

Abstract of Dissertation Presented to the Graduate Council in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy AN EXPERIMENTAL STUDY OF FREQUENCY MODULATION OF THE LASER BY THE ZEEMAN EFFECT by Rhett Truesdale George, Jr. December 18, 1965 Chairman: Dr. Thomas L. 3ailey Major Department: Electrical Engineering The purpose of this experimental study is to explore the use of the Zeeman effect to frequency modulate a gas laser for communication purposes. Lasers are used with mirrors outside the discharge tube and within it, and with axial and transverse magnetic fields from zero to seventy gauss. The laser is a helium-neon type with confocal miro rors , operating at 6328 A. No experiments involving the Zeeman effect for modulation in either internal or external mirror gas lasers have been reported in the literature, and it is believed that these are original. Neon is excited in the laser discharge tube to a metao stable state from which laser action at 6328 A may occur. 'A resonant cavity formed by multiple dielectric mirrors at

PAGE 6

vi each end of the discharge tube reflects radiation necessary to stimulate other neon atoms in the metastable state to emit. In the resonant cavity, an integral or half-integral number of light wave lengths may be maintained. For a mirror separation of 128 centimeters, the frequency difference between standing waves of visible light, or axial modes, is 117 mcps. The Zeeman effect is a splitting of an energy level into sublevels in the presence of a magnetic field, resulting in splitting of the corresponding spectral line. The light viewed parallel to the field axis contains the a + and o" beams, which are circularly polarized. By modulating the field, the frequency difference between the a + and o~ beams will be modulated, making frequency modulation possible. The receiver is a photomultiplier tube whose photocathode has a square law characteristic which makes detection possible. Several peculiarities exist when using the Zeeman effect to frequency modulate this type of laser, including linear polarization of the light and frequency pulling due to the optical cavity. The study was made using PEK LT-11 and LT-12 laser tubes, Optics Technology, Inc., mirrors, and an internal mirror laser built in the laboratory. Preliminary tests for excitation power, beam display and mirror alignment were made. The LT-11 laser tube was used with external mirrors,

PAGE 7

vii Brewster-angle windows, and an axial magnetic field. The Zeeraan effect could not be detected, although the axial mode beats and the transverse mode beats were detected. Similar results were obtained with the LT-12 tube with external mirrors, Brewster-angle windows, and a transverse magnetic field. It is concluded that strong polarizing action of the Brewster-angle windows prohibits or greatly diminishes the Zeeman effect. The internal mirror laser with a transverse magnetic field exhibited the Zeeman effect with the field applied, as well as the transverse and axial mode beats. A field of sixty gauss gave a o + o~ line splitting of 1000 cps which was then modulated over a frequency range of 20 to 200 cps and received. It was concluded that this system is useful for narrow-band, economical signal transmission by laser beam.

PAGE 8

I INTRODUCTION Since the time of the mathematical description of the laser, or optical maser, by A. L. Schawlow and C. H. Townes . [1], the variety of applications of the laser has grown almost as rapidly as the number of speculations on its possible uses. The purpose of this research was to study experimentally the frequency modulation of a gas laser by means of the Zeeman effect. The gas laser was chosen over the ruby and the junction diode lasers for its narrow line width, continuous wave operation, and lack of special temperature requirements. Frequency modulating of the laser by the Zeeman effect would offer a simple, economical communication system. The modulator would be simple and economical to construct, and the receiver would be no more complicated than f-m receivers presently used at radio frequencies. The study was made using sealed laser discharge tubes with Brewster-angle windows and external mirrors, and also with demountable discharge tubes with internal mirrors, normal windows, and a gas-filling apparatus. Experiments with a magnetic field applied to the gas laser with external mirrors have not been reported in the literature. Also, modulation of an external magnetic field

PAGE 9

2 passing through an internal mirror gas laser, and design and operation of an f-m receiver of the type used have not been reported. It is believed that this work is original.

PAGE 10

II PHYSICAL PRINCIPLES The Laser Laser is an acronym for light amplification by stimulated emission of radiation. In nearly all cases the light amplifier has sufficient positive feedback to make it behave as an oscillator or generator. The helium-neon laser, the most common form of gas laser, uses an electrical discharge to excite the helium atoms. In several of its transitions back to the ground state, the helium atom gives up internal energy directly to the neon atom in a collision, rather than by radiation. Several of the energy levels to which the neon atom may be excited are metastable. If radiation corresponding to a downward transition from a neon metastable state to a lower excited state or to the ground state interacts with another metastable neon atom, the atom can radiate by stimulated emission, in addition to spontaneous emission. The laser tube Is fitted with high reflectance mirrors at each end of the tube so that this radiation builds up in intensity. The laser to be discussed here Is the gas laser, specifically the helium-neon laser. The essential parts are a sufficient number of atoms whose electronic energies can

PAGE 11

be raised to a metastable state so that a population inversion will occur; a means of exciting these atoms; and a high frequency optical cavity which will support standing waves at a frequency corresponding to a desirable downward transition. Stimulated Emission of Radiation Schawlow and Townes [1] have discussed the theory of the laser and have shown that there are two requirements for amplification by stimulated emission. These are: a population inversion between the electronic states involved in the laser operation and a radiation power gain due to this population inversion which is equal to the sum of all power losses. Population inversion is necessary if there is to be an increase in, or amplification of, the energy density of the radiation passing through an active laser medium. We consider for simplicity a system in which there are only two electronic energy levels. There are three processes pertaining to electronic energy Jumps of atoms between these two states and radiation of a frequency, f, corresponding to the energy difference between these two states. The first process is absorption of energy in the radiation resulting in an Increase in electronic energy equal to W W , where W m is the energy of the higher energy state, m, and w~ n is that of the lower state, n. The number of atoms making this jump per unit of time equals N u B , where u Is n mn nm* ran

PAGE 12

the energy density of the radiation and B nm is the Einstein coefficient for absorption. The other two processes are emission processes. One is stimulated or induced emission which corresponds to stimulated or induced absorption discussed above. This is a direct interaction with the radiation, in which the photons emitted have a constant phase relationship with the radiation, adding to the energy density. The number of atoms making this emissive jump per unit time equals N m u mn B mn , where N m is the number of atoms in the state m. The Einstein coefficient Bmn will be shown to equal B rm in the discussion of the two state system below. The second emission process is spontaneous emission; the number of atoms making this emissive jump equals N m A mn . Note that no radiation field is necessary for the spontaneous emissive jump. If the two state system described above is in thermodynamic equilibrium with the radiation field, the population of each state is constant. Then N n B nm u mn = N m B mn u mn + Vtan' 1 ' In equilibrium, N m < N n unless A mn is zero. According to the Boltzmann distribution, % , Sm ekT / W m 2 . N n " 6 n e -kT/W n where g m and g n are the statistical weights of the two states, k is the Boltzmann constant, and T is absolute temperature. If ^ and g n are equal, then N m < N .

PAGE 13

6 Assuming g m equals g n and that N m A mn « N m B mn u mn , if N m >: :N n , amplification of the radiation of energy density, u mn , will take place. This is because more atoms are stimulated to emit in a jump from m to n than are induced to absorb in a jump from n to m, or N m B mn u mn > VW^nn 3. The number of n-m transitions is N B u dt n nm mn and the absorbed energy is dW ab " N n B nm u mn h f mn' where h is Planck's constant. Similarly, the number of stimulated m-n transitions is N B u dt "m mn mn and the emitted energy is dW em = N m B mn u mn h f mn dt The net emitted energy rate, or power, is dT (W emW ab> = B mn u mn h f mn' *• Obviously ^(W^W ab ) is positive only if N m > N n . This net emitted power is evidenced in an increased u . mn At this point, it is noted that as T approaches infinity, e-*T/W m e -kT/W n 1 For g m equal to g n ,

PAGE 14

N m W n Also, u mn Then and inn m "mn 11 !^ m mn nm ^ as asserted earlier. Since B and B,,,,, are microscopic in mn nm r nature and are not temperature dependent, this equality holds for all values of T. By substituting the exponential ratio of N m /N n in equation 1 , u _ A mn /B mn 11111 ehf/kT.! Comparing this with the Planck radiation formula, 8TTf 2 hf u f df = c 2 ghf/kT.! df where c is the speed of light and df is a small band of frequencies about f, the following equation is obtained: 8*f 2 A mn = 2 h ^ B mn • Now the energy lost in the spontaneous m-n transitions may be calculated relative to the energy added to u mn by stimulated emissions. The second requirement is that the power gain achieved above and described in equation 4 equal the sum of power

PAGE 15

3 losses in the total radiation system of the laser; except of course, for absorption, already accounted for. These losses occur in the mirrors, in the windows which may be in the basic system, in non-active gas, and in dispersive media. In the laser used in this experiment, the discharge tube was filled with a mixture of about ten parts of helium to one part neon, to a total pressure of one micron. An electrical discharge excites the helium to a number of different energy states. The helium decays back to the ground state by means of a number of transitions, usually emitting radiation spontaneously with each transition. There are several inelastic collisions in which electronic excitation energy is exchanged between helium and neon atoms. These include: He(2 1 S) + NeC^) He( l S ) + Xe(3s 2 ) He(2 3 S) + NeOSo) * He ( x S ) + i\ T e(2s 2 ) In each of these collisions the neon is excited to a metastable state from which stimulated emission can take place. Prom the lowest energy electronic state, 2p, neon atoms decay rapidly to the ground state by spontaneous emission. . The Grotrian diagram of energy levels for this cycle, beginning with helium in the excited state, is given on the next page in Figure 1. In this figure, the dotted line indicates the collision described by the first part of equation 6 and the solid line indicates the collision described by the second part

PAGE 16

CO

PAGE 17

10 of equation 6. Stimulated emission due to the downward transition from each neon metastable state is indicated by a wavy line; the emission wavelength is also given. The rapid decay time for the Ne(2p) energy level permits the necessary population inversion between this state and the metastable 3s and 2s states. Optical Configuration The stimulated emission described above must reflect back and forth in the laser tube to stimulate more emission. The gain per pass is small; an attenuation of two to three per cent could stop the laser operation. Therefore, mirrors used must have very high reflectance. Typical values of the reflectance for gas lasers are 99.0 to 99.5 per cent. Of the remaining .5 per cent of the light beam, probably 0.3 per cent is absorbed and 0.2 per cent transmitted. Mirrors commonly used in laser applications have nine to thirteen layers of dielectric coatings, usually with two different dielectrics alternating, which are applied in precise thicknesses to substrates whose surfaces are controlled to one tenth wave length or better. The surface may be flat or curved for optical configurations of parallel plane, confocal, spherical or combination mirror systems [2,3]. Several configurations are shown on the next page as Figure 2 [1,33 • The confocal mirror configuration was used In this experimental study for both the internal and external mirror lasers. The mirrors, produced by Optics Technology, Inci,

PAGE 18

11 n na cp C=3 T in cd h in c\j in c\j cd o o Cm c o o o in oo C\J o o c-, c o o

PAGE 19

12 are shaped for a nominal separation of 125 centimeters and are multiple dielectric coated. The PEK laser tubes required that the mirrors be external. Later investigations required that internal mirrors be mounted on a laser tube built by the author. The external mirrors are victims of atmospheric dust, the internal mirrors are subject to electron and ion bombardment during operation; each of these effects decreases reflectivity. A laser with external mirrors and Brewster-angle windows is shown on the next page in Figure 3. Brewster-angle windows [H] are used because incident radiation which has its electric vector parallel to the plane of incidence suffers no reflection. A laser with Internal mirrors is shown in Figure h on page Ik, The Zeeman Effect Excited atoms may be in a degenerate energy level. If such atoms are placed in a magentlc field, this degeneracy (in general) is removed; the excited energy level splits Into a number of sublevels. If the spectrum of transitions between the two levels is observed, what had been a single line now becomes several individual lines. This is the Zeeman effect [H], For the hydrogen atom, the number of sublevels is determined simply by the quantum number m. As the number of electrons in an atom increases the number of sublevels and the system of energy coupling between the electrons

PAGE 20

13

PAGE 21

14
PAGE 22

15 becomes complicated. In their paper, Statz, Paananen, and Koster [53 suggest that j-1 coupling be used for neon. This is also called Racah or extreme coupling. Knowledge of the coupling was used to determine the Lande*-g factor, which, in turn, was used to determine the splitting of the levels. Statz, et al. [5] calculated g = 1.33 for the 2s 2 state, used the value of 1.3 for the 2p 4 state, and quoted the experimental value for the 3s 2 state as 1.295* The dominant stimulated neon transition in the visible spectrum is the 3s ? -2p k transition, for which a Lande"-g of 1.3 will be used. Removal of the energy level degeneracy by placing the two state system previously discussed in a magnetic field makes possible emissive transitions from one or more sublevels in state m to one or more sublevels in state n. The energy separation among the sublevels of m and among the sublevels of n is quite small compared with the m-n transition emitted energy. This variation in the m-n transition energy may be calculated by the quantum mechanical first order perturbation theory. The energy differences among the sublevels is interaction energy, between the magnetic moment of the atom, denoted by u, and the magnetic flux density B of the applied field. W = -U*B_r j^ The theories for L-S coupling are most widely used and will be summarized here to demonstrate the dependence of the interaction energy W on the Lande*-g factor. A g factor

PAGE 23

16 based on j-1 coupling rather than L-S coupling will then be used. The net magnetic moment u is the vector sum of the orbital magnetic s, of all v electrons of an atom, v a-!.£
PAGE 24

17 1 eftB 8. where g has the value of the quantity in large brackets in the preceeding equation. The energy differences become 1 eftB ^ " 2 m Sm M Jm and ,„ _ 1 eftB ^n ~ "SS« M . 9. 2 m n Jn • The levels and transitions involved in the two state system are depicted below, along with the resultant spectral lines. The system with ^ equal to g exhibits a "normal" type of Zeeman effect, though with an abnormal line separation unless the g factors equal one. The system with g^ unequal to g exhibits the anomalous Zeeman effect. State m >m~ S n .J. I * 1 !! !L m Snr s n £=*=; Spectral Lines L j_ v jj L Figure 5. Energy Levels and Spectral Lines of the Zeeman Effect

PAGE 25

18 The radiation emitted by the atoms is not uniform spatially. The emission of the o and it components of the radiation is governed by quantum selection rules, the results of which are indicated below in Figure 6. > W /' f s l^o* only rJ „+ m B sin u t)t 10. « s where w is the center frequency of the carrier and m is the modulation index. Phase modulation is similar to frequency modulation

PAGE 26

19 except that the phase of the carrier is changed according to the signal, or A(t) = A sin ( + m B sin u>_t) C p 5 = A sin (u> t + m B sin w„ t) c p s where *_ = to t. To relate phase modulation to frequency c c modulation, the parenthetical part of the above equation is differentiated with respect to time to obtain d/dt, or frequency, to compare with equation 10. — (u>_t + m_ B sin to t) = u + m B tocos to_t dt c p s c p s s If, before the modulation took place, the signal were integrated, it would be of the form /B sin to t dt = — B cos u-t. ; s w s s Replacing the signal with its integral in the derivative above, -£ (a) t in B — cos to t) = (io + irr B sin to„t). 11. dtcp^s scp s Equation 11 now has the same form as the parenthetical part of equation 10. Therefore, given a phase modulation device, frequency modulation will result if the signal is first integrated. Since a frequency modulated signal may be obtained, several means of phase modulation will be discussed. In applying the laser to communications work, information must be put on the beam of light using either amplitude or frequency modulation. Here, amplitude modulation includes most forms of pulse modulation and frequency modulation includes phase modulation. Only frequency modulation will be

PAGE 27

20 considered here. Methods of Frequency Modulation There are at least four methods of frequency modulating the laser beam. The first, the subject of this paper, employs the Zeeman effect. This method will be discussed in greater detail in the next section. The second uses an electromechanical transducer to vary the position of one of the high reflectance mirrors [7]. This gives a Doppler shift to the light reflected and a change of optical cavity frequency. This motion is Z = Z q + k B sin oj s t 12 . where k is the transducer coefficient, Z is the mirror separation, and B sin u, s t is the signal. For a constant mirror displacement Z = Z n + a o there will be a change in the cavity frequency, but no Doppler shift. The result of changing the optical cavity frequency is discussed in Chapter III. The third method makes use of an electro-optic material, that is, a material in which the velocity of light In the z direction is a function of the voltage applied in the y direction. Two such materials, which are crystalline, are ammonium dihydrogen phosphate, ADP, and potassium dihydrogen phosphate, KDP. This method involves placing one of these crystals in the optical cavity [8]. This changes the

PAGE 28

21 velocity of light in the cavity, giving a Doppler shift to the light frequency and a change of optical cavity frequency. The fourth method uses the ADP or KDP crystal outside the optical system, where the output beam will pass through it [9]» This gives only a Doppler shift to the light frequency, but has the advantage of no added item within the optical system of the laser oscillator, which could cause diffraction or attenuation of the beam, possibly stopping oscillation. Details of Frequency Modulation by the Zeeman Effect Unlike the second, third and fourth methods just listed, the first method of frequency modulation by the Zeeman effect is achieved directly — phase modulation by Doppler shift is not an intermediate process. From the discussion of the Zeeman effect, the following equations are obtained: W = E m E m n and AW = AE^ AE„ = ± ^=CgJVI Tm g n M T „) m n 2 m m Jm e n Jn' A quantum selection rule states that M T = M, + 1, M_ , Jn Jm ' Jm' Mj m 1. The o spectral lines are due to Mj not equal to M Jm . Assuming that g m equals g n and M Jn equals Mj 1, then iW I TT s " S »H B

PAGE 29

22 The frequency difference between the a and it rays Is given by the following equation F = g^B/ft. Finally f/B = g 1.4 mcps . 14. where f is the difference between the it ray frequency and the a ray frequency, B is the magnetic field strength, g Is the Lande-g factor, p„ is the magnetic moment component in the direction of the applied H field, and h is Planck's constant. This assumes that g = g T+1 • From both experiment and theory, the Lande*-g factor is known to be approximately 1.3 for transitions of Interest in this work. For the general case, which produces the external magnetic field, let the coil be excited by a current which is I(t) Z + I sin u t 15. s s where I is a constant or bias current and I s sin w t is the signal. With a proportionality constant k' relating the current I(t) to the flux density B(t), the frequency expression becomes f = 1.3(1.4) k» (I + I sin u t) mcps. 16. -) With I equal to zero, the center frequency of the light beam will be the same as the frequency for zero magnetic field. Figure 7 is a plot of the beam frequencies for a certain input*

PAGE 30

f(t)t I(t) i=0 23 I_ sin ai t b S Figure 7. Spectral Lines as a Function of Current With circular polarizers it may be possible to separate the i a and the o beam components. Otherwise the signal may be lost or may be recoverable only with a large second harmonic component. With I greater than |l s sin w s t | the center frequencies will be shifted away from the zero field frequency. Figure 8 is a plot of the beam frequencies. f(t) Kt) i=0 I n + I_ sin u_t Figure 8. Spectral Lines as a Function of Current The beam components now have a definite separation and may lend themselves to considerably simpler detection techniques. In Figures 7 and 8, the ir component is included, although, under certain conditions to be described, it will not be in the output beam.

PAGE 31

Ill THE ZEEMAN EFFECT FREQUENCY MODULATED LASER The physical principles pertinent to the laser which is frequency modulated using the Zeeman effect have been discussed. Certain operational peculiarities appear when a magnetic field is applied to a laser. These will now be discussed with emphasis on the helium-neon laser operating at 6328 A with external mirrors and Brewster-angle windows on the discharge tube. Several experiments performed by others, which are concerned with the Zeeman effect and some of the peculiarities will be discussed also. Finally, a means of receiving the light signal will be described. A transmitter consisting of a laser with its modulator and a receiver are needed for a one-way communication system, The simplified system shown in Figure 9 on the next page is similar to the actual system which was constructed for this experiment, described in the next chapter. The simplified system is reminiscent of the system employing a reflex klystron in the transmitter, where signal voltage is merely applied to the klystron reflector and a frequency modulated signal is obtained. The Light Beam Transmitter The laser with the magnet is the essential part of 24

PAGE 32

25 D, 3 s o -p o IX, P. h o -p o o; -p OJ Q M *-i

PAGE 33

26 the transmitter. The transmitter performance is affected by the discharge tube configuration, the optical configuration, and by "frequency pulling." These three factors will now be discussed. Discharge Tube Configuration The discharge tube may have the mirrors built in, or it may be constructed for use with external mirrors. In either case, there are windows at each end of the tube through which the beam passes. These windows must be optically flat if the wave front is to be undistorted. As discussed in the chapter on physical principles, Brewster-angle windows are commonly used for the external mirror configuration, since they permit the electrical field vector to pass through in one polarization without reflection. This means that the beam which builds up within the cavity is linearly polarized; so, also, is the output beam. If internal mirrors are used, the windows are usually perpendicular to the axis to avoid a polarizing effect. An axial magnetic field applied to a laser will split the energy levels as shown in Figure 5 on page 17. Based on the calculations in the section on the Zeeman effect, the Lande-g factors for the initial and final states are assumed to be 1.3. The spectral line simplicity (but not the spacing) of the normal Zeeman effect will be observed. If the laser has internal mirrors and perpendicular windows, the axial field will cause the output beam to split and be

PAGE 34

27 made up of two components, the o + and a" circularly polarized rays. As the ir ray does not exist in the axial direction, there will be no stimulation for the transition which produces the it ray. An axial magnetic field applied to a laser with external mirrors and Brewster-angle windows will produce the o and o~ circularly polarized beams within the discharge tube. On passing through the Brewster-angle windows, the electric vector perpendicular to the plane of incidence is partially reflected, and the emerging beam is elliptically polarized. With no laser excitation, the perpendicular field component would be lost rapidly in the optical cavity. With laser excitation, the loss for the perpendicular component due to window reflection is large enough to prevent laser oscillation in this field component. The contribution to the perpendicular field component per pass will be small, resulting in an output made up of two linearly polarized beams, one at the o + frequency and one at the cr~ frequency. Mirror Configuration The mirror configuration presents no special problems beyond those already discussed in the chapter on physical principles . in operating a laser with an axial magnetic field. This statement is made with regard to mirror shape — confocal, hemispherical, etc., and the mirror location, whether inside or outside the discharge tube. Mirror separation does present certain problems which will be discussed next under

PAGE 35

28 the topic "frequency pulling." Mirror reflectance, which determines the Q of the optical cavity, also affects frequency pulling. Frequency Pulling Frequency pulling is a familiar phenomenon. In the case of two mechanical oscillators moderately to strongly coupled without buffering, when one is tuned rather closely to the frequency of the other, the two will tend to lock and oscillate at one frequency. A strongly tuned cavity will pull the frequency of a microwave oscillator if the two are tuned near the same frequency. The laser, with two resonant systems, exhibits frequency pulling also. The two systems are: the assembly of excited neon atoms, which are radicating by stimulated emission; and the optical cavity, which will support an integral or half-integral number of wave lengths. If two similar resonant systems, A and B, with quality factors Q. and Q , tuned to slightly different frequencies f . and f , are coupled together, the combined resonant frequency, f , will be approximately (f A + f B >/2. If Q A and Q B are not similar, then for Q A greater than Q £ , f Q will be Closer to f. than to f_. A first approximation can be made A B by letting the "willingness to change frequency" be Inversely proportional to the Q or Q (f f ) -(f f ) Q 17. y A VI 6 A ; * b' h B

PAGE 36

29 This is similar to the resultant gain of two tuned amplifiers whose individual gains are A. A A An ui u A , ft A B ~ A B^ *B x + JQbC~ — ) i9. The total gain is A t = A A A B = A A A The imaginary component vanishes at the system resonant frequency: or JCQaC^T "et) + Q B te " Tr)) ^ ^0: »a )( V % ) . _ Q C V u> B )U Q + Mb ) ^ 3 A u B WgWQ For w. approximately equal to u B , W A W " W B W 22. and Then u + u A e w + W B 23. V V V " Q B U 0V 2k * which is the same as equation 17.

PAGE 37

30 In their article, Gordon, Zeiger, and Townes [10] gave the following expression for frequency pulling for a He-Ne laser, analogous to equation 2*J: VAVn Av £ 25. v Q v c Av, or v = V B +C V V B~ v B Av B )/(Av B + Av C ) 26 ' where v„ is the output frequency, v Q is the neon transition frequency, Av D is the half-width of the emission line of neon, v~ is the cavity resonant frequency, and Av c is the half-width of the cavity modes. This equation has also been derived by Bennett [11]. For example, if the cavity is initially tuned to the center of the neon line (v c = v B ) , the second term on the right will be zero. If now the cavity is tuned to a higher frequency, the amount of the frequency increase will not be v v„, but rather t > AV 3 (V C~ V B> Uv c + Av 3 ) * The nominal frequency of the neon transition and Its bandwidth or line-width are constants. The cavity frequency is a function of the mirror separation, and the cavity Q is a function of the mirror reflectance. The neon bandwidth is approximately 1000 mcps, due mainly to Doppler broadening. At these wavelengths the cavity has a resonant point every 120 mcps for 125 cm. mirror separation. It was shown in Figure 2. on page 11 that for confocal mirrors of

PAGE 38

31 125 cm. focal length, separated to 128 cm., that a point 2 o mm. from the center of one mirror is 750 A closer to the other mirror center than Is the center of this mirror. This is a very large operational lattltude. The mirror reflectance is such that one per cent of the energy is lost per pass, giving Q of approximately 100. This is a bandwidth of 1.2 mcps, or a line half -width of 0.6 mcps. Frequency pulling may be calculated using these values; it may be more accurately calculated using known values for the particular equipment. The large operational lattitude mentioned above offers. some relief from pulling, but only at the expense of having the beam wander about on the mirror. This is unlikely because the mirrors are focused. Usually different modes occupy different parts of the mirror. Consequently, a large expected shift In frequency due to the Zeeman effect in the presence of a magnetic field becomes, in actuality, a small shift, due to the frequency pulling of the cavity. The frequency pulling expected in the laser used in this experimental study will now be calculated. Beginning with the equation for frequency pulling, 25 , the frequency difference between the o + and a" beams will be calculated. (v B Av c + Av B v c ) Uvb + Ave) Let Avg = Avp + e

PAGE 39

32 m [( V £)AV C + AV B V C ] V ° (A V Av c ) eAv = v P + where v Q Is beam frequency, v B is neon line center frequency, Av B is neon line width, v c is cavity center frequency, and Av c is cavity bandwidth. Since the cavity remains tuned to the zero magnetic field beam frequency, e is the frequency shift produced by the Zeeman effect, or the frequency difference between the a + and tt beams. Due to frequency pulling, however, the expected observed difference is eAv~ '0 Av n + Av, The bandwidth Av Q of the optical cavity may be determined by considering the Q c , or quality factor, and the resonant frequency increments of the cavity. = energy stored ^c energy dissipated P er cycle Dielectric mirrors of reflectance R will reflect R per eent of the E vector of the light ( and consequently R per cent of the H vector) and transmit (100 R) per cent. Power is proportional to the square of the magnitude of the E vector. The expression for Q c may be written as (100 R) 2 where R is given in percentage. With 99 per cent reflectance mirrors, Q Q is (99/1) 2 or approximately 10".

PAGE 40

33 The resonant frequency increments may be determined by the number of integral or half-integral standing waves the cavity will support. Let n be the number of half wavelengths supported in the cavity, \ x the wavelength, and f x the corresponding frequency. The n + 1 will represent the number of half wavelengths supported in the cavity for a slightly different frequency, and f 2 the corresponding frequency. The mirror separation used is 1.28 meters. Then 1.28 1.28 2.56fi n = x i 3xlQ8 3xl0 8 2f; i n + 1 2.56f 2 3*10 8 f . f , = 3xl ° 8 = 117 * 10 6 cps 1 2 2.56 The approximate response of the cavity is shown below. Ability to Support Standing Waves Av 117 mcps Figure 10. Response of Cavity Based on the calculated Q c and the axial mode separation, Av c is 117*10 6 /Q C , or 11,700 cps. Doppler broadening of the neon line amounts to 500 to

PAGE 41

34 1000 mcps. Using the latter figure, av q 10 9 . For H = 10 gauss and g = 1.3» e 1.4*1.3*10*10 6 = 1.82*10 7 cps The frequency separation is v n . v c = 1.82»10 7 «1. 17*10" = 210 cps . C 10 9 +1.17«10The calculated frequency separation between the o + and °~ beams is 420 cps, using a Doppler broadening of 10 00 mcps, and 840 cps, for a Doppler broadening of 500 mcps. Magnetic field intensities from to 70 gauss were used in the experiments so that the audio range would be covered. Four Experiments Three experiments have been described in the literature in which frequency pulling is studied. In two of these, the Zeeman effect is studied. Each of the first three experiments to be described was performed with the heliumo neon laser operating on the 11,522 A line, the laser being equipped with internal plane mirrors. Bennett [11] described an experiment where frequency pulling is measured. Approximate expressions to account for this pulling were derived. He did not deal with frequency shifts and consequent pulling due to the Zeeman effect, but with pulling due to the cavity, the gaseous medium in the cavity, and

PAGE 42

35 the population levels of the excited gas. The second, by Statz, Paananen, and Koster [5], was an experiment to determine the Zeeman effect. They used a linear polarizer to convert the circularly polarized waves to linearly polarized waves of varying amplitude which were then detected with an infrared phototube. The output with the earth's magnetic field parallel to the laser tube was 1050 cps, indicating that the o + and o" rays were rotating in opposite directions at the rate of 525 revolutions per second. Assuming the field to be 0.5 gauss, they calculated a rotation of 300 rps. With an imposed field of one gauss, they calculated a rotation of 610 rps and measured 625 rps. Culshaw, Kennelaud, and Lopez [12] measured the Zeeman effect superimposed on the 120 mcps beat note detected between oscillations in adjacent cavity modes. They inserted a Nicol prism to polarize the output wave and detected it with an infrared phototube. Both a 4 gauss perpendicular field and a 30 gauss axial field were used in the experiment. With the 30 gauss field, a modulation of 80 kcps was measured; a modulation of 130 kcps was calculated. This calculation included frequency pulling. These results compare favorably with those of Statz, et al.[5]. The last experiment to be discussed, performed by Kiss [13], deals with the Zeeman effect in the CaF^.Dy 2 * solid state laser. This laser is photon exicted or light pumped and is operated at 27°K. The optical cavity consists of

PAGE 43

36 high reflectance mirrors deposited on the ends of crystals, which are spherical. Small magnetic fields up to 80 gauss and large fields of 10,000 gauss were used. The results were as follows: the o + , ir, and a" beam components were observed in the axial direction. A separation of the axial components of 150,000 mcps was observed with the use of a 10,000 gauss magnetic field. Using small fields, frequency modulation was obtained with cavities having a low Q and amplitude modulation with cavities having a high Q. The magnet system used homogenous and inhomogenous fields. The Receiver The frequency modulation receiver used in the present experiments employs a photomultiplier tube for the first detector stage. This tube is sensitive to instantaneous variations in incident light [10, 11, 12, 14] such as the beat or difference frequency between the o rays. The output signal from the photomultiplier is amplified, then demodulated in an f-m detector to ottain the original signal. Caddes and McMurtry [15] discuss photodetectors, giving a conversion equation as follows: I = P H£. "o r light LT where ?]_^o. ht is average light input power, n is quantum efficiency of the photon-electron conversion, e is electron charge, h is Planck's constant and v is light frequency.

PAGE 44

37 The magnitude of the output current is proportional to the square of the input light vector. For an input consisting of the o + and o~ beams, I = k(A cos w t + B cos w t) 2 A 2 cos 2 o) 1 t + 2AB cos u l t cos w t + B 2 cos 2 u> t A 2 cos 2 u 1 t + B 2 cos 2 u 2 t + AB(cosC" 1 + w 2 )t + COs(u 1 U>2)t ) where k is a constant of proportionality, A is the magnitude of the E vector of o + , u 1 is the frequency of o + , B is the magnitude of the E vector of o~, and u> 2 is the frequency of a ~. If o + and o" differ by a few hundred to a few thousand cycles per second, the difference in frequency will occur in the audio range. Let there be two axial modes of oscillation, identified as Beam 1 and Beam 2. For Beam 1, containing o* and o~ t separated 117 mcps from Beam 2, o 2 and o 2# I Q = k(A 1 cos u 11 t + B x cos w 12 t + A 2 cos <»> 21 t + B 2 cos u 22 t) where k is a constant of proportionality, k l and u ll are magnitude and frequency of E vector of o l , B l and u 12 of a ~, A 2 and u 21 of o 2 , and B 2 and u 22 of a". The o + and o" separations will be approximately the same for Beams 1 and 2. If this separation is in the audio range of frequencies, then I Q will contain this audio frequency, the 117 mcps frequency, and sidebands separated from the 117 mcps component by the audio frequency. If

PAGE 45

38 57 («u «i2 ) = *a where f. is an audio frequency, then I contains f , 117 A * A mcps, 117,000,000 * f cps, and others. The signal in frequency modulated form is contained In f .

PAGE 46

IV THE EXPERIMENTAL STUDY The experimental study was conducted from July, 1963, to June, 1965. At that time, there were no gas lasers in the College of Engineering. Part of the time was spent building associated laser equipment, building laser discharge tubes, and making mirrors. The associated equipment will be discussed under Details of the Experiment. Several laser discharge tubes were built. These consisted of Pyrex tubes, usually thirty-six inches long and six to eight millimeters inside diameter, supported on end pieces. The end pieces were metal cups or fittings with windows, mounted on a sturdy base. A fitting at one end of the tube had a connection to the vacuum pump and the gas-filling apparatus. Several means of sealing the windows and the tube to the end pieces were used at different times, Including vacuum wax, O-rings, and tin-indium glass to metal solder. These sealing systems allowed the tube, but not the end pieces, to be baked out. Some plane mirrors were made on flat glass substrates using aluminum, and later, silver. The high reflectivity of magnesium made it attractive as a mirror coating, but the vacuum obtained in the evaporator used was inadequate for 39

PAGE 47

40 giving good quality mirrors. The magnesium gettered the atmosphere of the bell jar, and the deposition was a combination of magnesium oxide and magnesium salts. At this point, multiple dielectric mirrors of confocal design were purchased from Optics Technology, Inc. These mirrors were fitted to the laboratory laser and a number of unsuccessful attempts to obtain laser action were made. The gas filling apparatus consisted of a helium tank, a neon flask, a mercury manometer built for the laboratory, valves, and a thermocouple gauge. After evacuation, the laser tubes were filled with neon and then with helium to a final pressure of 0.5 torr to 1.0 torr. The gas composition was varied from pure neon to one part neon to ten parts helium. Windows perpendicular to the axis and Brewsterangle windows were tried. No evidence of laser action was observed with these tubes. It is believed that the lack of laser action may be attributed to windows which were barely of laser quality, to outgasslng of the tube, and to impurities in the gases (which were not of spectroscopic grade). In the last stage of this work, the windows were checked in the optical cavity of an operating laser and found to be below laser quality. Two commercially assembled laser tubes, PEK LT-11 and LT-12 were obtained and mounted on a previously constructed base. The PEK LT-11 and LT-12 have the gas mixture of helium and neon sealed in, are forty-seven inches over the Brewster-

PAGE 48

41 angle windows, and have an inside diameter of six millimeters. No difficulties were experienced in obtaining laser action. For later experiments, another laser discharge tube was built in the laboratory. This laser discharge tube was constructed with internal mirrors and windows normal to the beam. Mirror mounts were constructed which employed bellows to allow for mirror alignment adjustments. The Optics Technology mirrors were placed in the bellows mount with tinindium solder. A connection was provided in one mount for the gas-filling apparatus linkage. A drawing of the basic unit appears on the next page in Figure 11. The evacuation and back-filling equipment represents another change from the original experiments. A laser mixture of helium and neon, premixed in a one to seven ratio was obtained from the Linde Company. Evacuation to 10" 6 torr (10~ 7 torr at the pump) used first a mechanical pump and then an ion pump, followed by heat gun bakeout of tubulation and discharge tube, but not mirror mounts. Then, gas was admitted through a leak valve into the tube to a pressure of about one torr. Laser action was easily obtained over a range of pressures near one torr. Details of the Experiment The large quantity of support equipment necessary for a laser experiment was in part built for the experiment and

PAGE 49

42 u W CO h o U h C P c H D9 cti CQ U 3 •H

PAGE 50

43 modified from equipment already in the laboratory. Excitation System This system consists of a radio-frequency exciter, matching network, and excitation electrodes, as shown in Figure 12. The exciter includes a 14.4 mcps driver and an amplifier. The amplifier uses three 807 tubes connected in parallel •• and has independently variable plate and screen grid power supplies. The system operates in a shielded design to minimize radiation. The amplifier is loop-coupled to a tank circuit in which the capacitance is made up largely of the capacitance in the electrode structure mounted on the laser tube. Several structures were tried; the final design consists of alternate ground and high voltage electrodes wrapped partly around the tube and connected to the longitudinal ground or high voltage buss. The busses are separated by ceramic spacers and the whole structure is hung from the tube. There are five high-voltage electrodes and six ground electrodes. The Modulation System Several modulation magnets were constructed for the experiment in order that the direction of the externally applied magnetic field through the laser might be varied. The LT-11 tube was fitted with a solenoid three inches in diameter, forty inches long, and wound with two forty-turn windings. Calculations and measurements showed that this

PAGE 51

nn u

PAGE 52

45 -p a > OH 31A Eh Plh W t~-

PAGE 53

kS solenoid produced an axial magnetic field with less than *10 per cent variation of field strength over the length of the discharge. For the LT-12 tube, a pair of rectangular coils about two and one half inches by forty inches, each having a total of eighty turns were constructed. These were placed one on each side of the tube with about three inches separation and connected so that the fields produced were in the same direction. Measurements showed a variation in this transverse field of less than *8 per cent. The rectangular coils described above were used with the internal mirror laser. At the field strengths necessary for observing the Zeeman effect, the coils heated rapidly. A similar set of rectangular coils three and one-half inches by forty inches were built, each having approximately 2500 turns. These were placed one on each side of the discharge tube with two and one-half inches separation. Measurements again indicated a variation in transverse field strength of less than *8 per cent. The Receiver System The optical portion of the receiver consists of two first-surface glass dielectric reflectors (reflection taking place at the air-glass boundary) set at the polarizing angle, and a photomultlplier tube. The reflectors remove the component of light which has the E vector in the plane of incidence, this being the it component. The o components

PAGE 54

»7 are transmitted. The photomultiplier cathode is a square law detector which has all the original, sum, and difference frequencies in its output. Due to the low-pass nature of the electron multiplier section of the tube, the electrical output is made up solely of the lower difference frequencies. The output frequencies include the axial mode beat frequencies in the 115 to 125 mcps spectrum, recoverable with a conventional receiver which tunes to this range, the frequency difference between the o + and a" rays in the audio range when a magnetic field is applied, and the beat frequencies between the transverse modes in the audio range if more than one exists. The f-m receiver used consisted of a wide-band amplifier 0-20 mcps, driving a monostable vibrator. The multivibrator output passed through a diode gate and into a low pass filter. The filter output drives an audio type amplifier and speaker. This is a type of frequency counter in which the output voltage varies as the input frequency which controls the repetition rate of the multivibrator. The wideband amplifier and multivibrator used are part of the circuitry of a Tektronix Model 5^1 oscilliscope. The receiver diagram is shown in Figure 13 on page ^8 and the low-pass filter schematic and response curve in Figure Ik on page k$. Preliminary Tests The LT-11 laser was used first with an exciter of low

PAGE 55

h8 s > CO u > •H o o (U « m rH (1) •rt

PAGE 56

49 to Q " — A" 1 — "* o o in H O o HH 'WV^-" I C o o. to K T5 C a o p CD S-.
PAGE 57

50 power. It provided sufficient excitation for single transverse mode lasing at 50 to 60 watts and multiple transverse mode lasing at 70 to 80 watts. With ambient dust in the air, the beam intensity was observed to be much greater in the cavity than outside the cavity. This is normal, since the reflectivity quoted for the mirrors was 99.5 per cent. The transmission was probably 0.2 per cent. The ratio of reflection to transmission was probably 500 to 1. Tolerance of mirror alignment was next observed. With 80 watts excitation, lasing was maintained over a range of one-half turn of the adjusting screw. This corresponds to a total angular movement of the mirror of one-third degree or a deviation from alignment center of ten minutes. At the same time, another beam with brightness of from 10 to 50 per cent of the main beam was observed. This beam reflected from the Brewster-angle window at an angle apparently equal to the angle of incidence. The spot size, observed on the ceiling, indicated that this was a reflected beam and not just light scattering from imperfections or dust on the window. The intensity of the beam transmitted through the mirror is approximately 0.2 per cent of that of the Internal beam. Therefore, the reflected beam is from 0.02 per cent to 0.1 per cent of the intensity of the beam within the cavity. This indicates that the beam, without a magnetic field, is essentially linearly polarized; the reflection may come from a slight deviation from linear polarization In the

PAGE 58

'51 discharge tube, slight non-parallelism of the Brewsterangle windows, or from slight angular displacement of the polarization by the confocal mirrors. A large glass cylinder with glass ends was filled with benzene to see if the beam could be observed as it passed through. The benzene did not diffuse the beam. It could be observed if a diffusing material were suspended in the benzene. Tap water gave no results either. The beam was visible as it passed through a jar filled with smoke. A photographic slide was made on Kodachrome II film. The beam intensity was measured with a light meter, the diaphragm and shutter speed were set and the picture taken. The result was a completely over-exposed spot in the center of an otherwise black slide. The fact that the camera diaphragm opening has no effect on the intensity of light incident on the film was overlooked; over-exposure could have been avoided only by increasing the shutter speed.

PAGE 59

V MEASUREMENTS AND RESULTS The first experiments were made with the LT-11 laser tube and the axial field solenoid. When several transverse modes were present, the beat frequencies between them were detected in the audio range. Decreasing of the exciter power and realignment of the mirrors returned the system to single transverse mode operation and the beat frequency output ceased. The axial transverse mode beats were detected at 117 mcps using a narrow band all-frequency receiver. With increased exciter power, the multiple transverse mode beats appeared as modulation on the axial mode beats. Next the magnetic field was applied in the range of to 70 gauss. The beat frequency between the o and o~ rays could not be found. Calculations for frequency pulling were made, indicating that an output should be observable in the 10 to 20 gauss range. However, the Zeeman effect did not go entirely unnoticed. A beam disturbance detected electrically as an impulse was observed each time the magnetic field was applied or removed. This is possibly caused by a change in v B due to the Zeeman effect which resulted in sufficient detuning to cause one of the axial modes to cease or begin to oscillate. Under conditions of low exciter power and slight mirror misalignment, lasing would occur only if the magnetic 52

PAGE 60

53 field were present, again possibly due to a change in v_ due to the Zeeman effect. Due to the effect of the Brewster-angle windows, the beam remained linearly polarized throughout the range of the magnetic fields used. This was determined using double dielectric reflectors of the type mentioned in the discussion on the receiver system mounted at each end of the laser in the paths of the output beams. The LT-12 tube was next used with transverse magnetic field coils. With no magnetic field applied, the results of the experiments for the transverse mode beats and the axial mode beats were the same as those obtained with the LT-11 tube. The transverse magnetic field was applied successively in two directions, first to pass the a rays through the Brewster-angle windows unreflected, and second to pass the n ray unreflected. In each experiment, the Zeeman effect was. not observed. Electrical impulses in the output were obtained upon sudden application or removal of the field, but the beat frequency between the o + and -a" rays with the field applied was not detected with field strengths up to 50 gauss. The internal mirror laser described on page Ul was used next, noting that careful attention to good vacuum techniques was necessary to assure reliable operation. The transverse mode beat frequencies again could be obtained and removed by exciter power control and mirror adjust-

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54 ment. The axial mode beats were obtained at 121 mcps, the change due to a reduced mirror separation. The Zeeman effect was observed with field strengths of 50 to 70 gauss. The need for higher magnetic fields was anticipated due to the nature of the laser, the Q of the cavity should be greater than that of the earlier systems as this system does not contain Brewster-angle windows* The Zeeman splitting did not run smoothly up from gauss, but appeared suddenly in the 400 to 800 cps range with about 50 gauss applied. The Zeeman effect was obtained with single transverse mode laser operation. The frequency output, or amount of splitting, depends both on the strength of the applied field and the exciter power level. This splitting dependency has been reported by Statz, et al.[5]. With a field level of 60 gauss and a low exciter level, a splitting of the line of 100 cps was obtained and used as a carrier frequency. The field was then modulated over a range of 20 to 200 cps. The frequency modulated signal was detected over this same range of signal frequencies using the receiver. The inductance of the transverse magnetic coils and the lov/-pass characteristics of the receiver filter precluded the use of higher modulation frequencies. It is interesting to note that photomultiplier alignment was not critical for detection of the Zeeman effect. Parallelism between the beam and a vector normal to the photocathode of within 2 to 3 degrees was adequate.

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VI SUMMARY AND CONCLUSIONS At the beginning of this experimental research, use of only the LT-11 laser tube and axial field solenoid was planned. The negative results obtained in. this experiment and later with the LT-12 laser experiments made it necessary to enlarge the scope of this experimental study twice to achieve positive results. The conclusions based on the LT11 and the LT-12 laser tubes will be given first. At no time was a signal detected which would indicate frequency modulation by means of the Zeeman effect with the external mirror lasers. The three measurements concerned the different orientations between beam polarization, E, and the magnetic field H f . These are shown below in Figure 15. * E Beam I E H^. Beam *E Bf Beam Sf (a) (b) (c) Figure 15. Magnetic Field Beam Orientation Polarizations 55

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56 The first measurement was made according to Figure 15(a). The Zeeman effect indicates that the beam will contain the o + and a" rays which will be circularly polarized in opposite directions. The optical cavity contains two Brewster-angle windows which: are thought to prevent amplification of a circularly polarized wave. This was found to be the case. No beam was found with the electric vector perpendicular to the plane of incidence. Prohibition of circular polarization may prevent the frequency shift due to the Zeeman effect. The second measurement was made according to Figure 15 (b). Here, the beam should contain the o+ and o" components plane polarized in the plane of incidence. Again, no signal was found, apparently because of the strong effects of the plane polarization, or perhaps because of much greater frequency pulling that that believed to be present. The third measurement was made according to Figure 15(c). There, the beam should contain only the * component. Again, no a components were detected. The axial modes, spaced every 117 mcps, were detected. With more intense beams, which permitted laser operation in several transverse modes, audio frequency whistles and squeals were detected. These frequency differences between transverse modes are due to slight path length differences. It appears that the detector does operate properly. Based on these observations and on the four experiments

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57 in the section on the Zeeman effect frequency modulated laser, it is concluded that this laser structure with external mirrors and Brewster-angle windows cannot be frequency modulated using the Zeeman effect with magnetic fields from to 50 gauss* The Zeeman effect may be observed in spontaneous emission provided that the a rays can reach the detector. In laser operation, the neon atom radiates downward from a higher energy level which is metastable. If the a rays are discriminated against by the optical structure, specifically the Brewster-angle windows, there will not be enough gain to support laser action in the a ray mode. Then there will be no o rays to stimulate emission from those metastable atoms with Utt ? 0. The internal mirror laser does not contain any strong polarizer in the form of a Brewster-angle window. Outside the optical cavity, windows are used which are normal to the beam so that there is no polarizing influence there. The only polarizer which may be present, excluding the magnetic field, is a mirror imperfection, and this is not large. The Zeeman effect was observed repeatedly using the internal mirror laser and transverse magnetic fields in the range of 50 to 70 gauss with a a frequency differences of approximately 1000 cps. The magnetic field strength was modulated directly with the signal. The signal was recovered from the frequency modulated light beam using the receiver.

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58 It is noted that from the results of the frequency pulling equations, the Zeeman effect will be small, even in a laser cavity which will support circular polarization. Therefore the range of carrier frequencies and useful modulation frequencies will be small for easily achieved magnetic field strengths. Additionally, at a sufficiently high field strength, the o + and o~ lines may jump to the next axial mode, establishing an upper limit to the useful modulating frequency. By shortening the length of the optical cavity, the axial mode frequencies are raised. Frequency modulation by the Zeeman effect does offer several important advantages. First, it is simple and economical. The magnet structure is simple, and modulating the magnetic current produces frequency modulation of the carrier, which is the difference between the a and a" rays. The system is less sensitive to vibration than a moving mirror system, and does not contain ADP or KDP crystals, which are expensive and which require high driving voltage. The polarizer may be mounted on the laser in the output beam path to lessen the alignment problem between transmitter and receiver. Since both the o + and a rays are transmitted, the receiver photomultiplier tube functions as the first detector of a superheterodyne receiver with the carrier and the local oscillator signals both coming from the transmitter. In the experiment, the corresponding Intermediate frequency is centered at 1000 cps. With this

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59 system, there is no need for a second laser to function as a local oscillator, eliminating what has been, up to now, a significant stability problem. Elimination of the second laser is an added economic factor. From this research, it is concluded that frequency modulation by means of the Zeeman effect is practical only for narrow bandwidth applications, but offers significant advantages in that area. These advantages are simplicity and low cost of the modulator magnet, simple modulator electronics and receiver design which is no more complicated than f-m receivers at radio frequencies. As the modulator magnet does not come in contact with the discharge tube or optical system, the way is left open for combining this system with other systems. Further, the Zeeman effect is not. only influenced by the Q of the optical cavity, but also by the nature of the polarizers within the cavity.

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LIST OP REFERENCES 1. A.L. Schawlow and C. H. Townes, "Infrared and Optical Masers," Physical Review , Vol. 112, December, 1958. p. mo. * 2. W. W. Rigrod, H. Kogelnik, D. J. Brangaccio, and D. R. Herriot, "Gaseous Optical Maser with External Concave Mirrors," Journal of Applied Physics, Vol. 33. February, 1962, pp. ~Jk '3-7^. ' * 3. A. L. Bloom, "Properties of Laser Resonators Giving Uniphase Wave Fronts," Laser Technical Bulletin No. 2. Spectra-Physics, Inc., Mountain View, California. 4. Gerhard Herzberg, Atomic Spectra and Atomic Structure. Dover Publications, New York, 19171 5. H. Statz, R. Paananen, and G. F. Koster, "Zeeman Effect in Gaseous Helium-Neon Optical Maser," Journal of Applied Physics , Vol. 33, February, 1962, pp. 7^7^. 6. T. L. Martin, Jr., Electronic Circuits . Prentice Hall. Inc., Englewood Cliffs, 1955. 7. P. Rabinowitz, J. LaTourette and G. Gould, "AFC Optical Heterodyne Detector," Proceedin gs of the IRE. Vol. 50 July, 1962, pp. 1686-87T ' 8. F. S. Barnes, "On Modulation of Optical Masers," Proceedings of the IRE, Vol. 50, January, I963, pp. iVf^" 153. 9. C. J. Peters, "Gigacycle Bandwidth Coherent Light Traveling-Wave Phase Modulator," Proceedings of the IEEE, Vol. 51, January, 1963, pp. 1^7-153. 10. J. P. Gordon, H. J. Zeiger and C. H. Townes, "The MaserNew Type of Microwave Amplifier, Frequency Standard and Spectrometer " Physica l Review , Vol. 99, August, 1955. pp. 1264-1274. * ' 11. W. R. Bennett, Jr., "Hole Burning Effect in a He-Ne Optical Maser," Physical Review , Vol. 126, April, 1962. pp. 580-593 60

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61 12. W. Culshaw, J. Kannelaud, and F. Lopez, "Zeeman Effect in the Helium-Neon Planar Laser," Physical Review , Vol. 128, November, 1962, pp. 1747-1748. 13. Z. J. Kiss, "Zeeman Tuning of the CaF :Dy Optical Maser," [Paper presented at the Microwave Research Institute Symposium on Optical Masers, Polytechnic Institute of Brooklyn, April, 1963.] 14. P. A. Lindsay, S. F. Paik, K. D. Gilbert and S. A. Rooney, "Optical Mixing in Phototubes," Proceedings of the IRE, Vol. 50, November, 1962, pp. 2380-2381. 15. D. E. Caddes and B. J. McMurtry, "Evaluating Light Demodulators," Electronics , Vol. 37, April, 1964, pp. 54-61.

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BIOGRAPHICAL SKETCH Rhett Truesdale George, Jr., was born on May 2, 1933, in Columbia, South Carolina. In June, 1951, he was graduated from Boys' High School in Anderson, South Carolina. In June, 1955, he received the degree of Bachelor of Science in Electrical Engineering from Duke University. He received the degree of Master of Science in Engineering from the University of Florida in 1956. From 1957 to 1961 and during the fall of 1962, he taught Electrical Engineering at Duke University. In the Fall of 1961, he enrolled in the Graduate School of the University of Florida and has pursued his work toward the degree of Doctor of Philosophy until the present time. From 196l to 1963, he worked as a graduate assistant on the Ford Foundation program in the Department of Electrical Engineering. From September ,1963 » to August, 1964, he was on the Duke University advanced degree program for faculty. From September, 1964, to the present time, he has been teaching Electrical Engineering at Duke University. Rhett Truesdale George, Jr., is married to the former Joanna Marie Huffer. He is a member of Sigma Xi, Phi Beta Kappa, Tau Beta Pi, Eta Kappa Nu, and Omicron Delta Kappa. 62

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This dissertation was prepared under the direction of the chairman of the candidate's supervisory committee and has been approved by all members of the committee. It was submitted to the Dean of the College of Engineering and to the Graduate Council, and was approved as partial fulfillment of the requirements for the degree of Doctor of Philosophy. December 18, 1965 Sc~ /zi

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