AN EXPERIMENTAL STUDY OF FREQUENCY
MODULATION OF THE LASER BY THE
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
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
TABLE OF CONTENTS
LIST OF ILLUSTRATIONS
II PHYSICAL PRINCIPLES
Stimulated Emission of Radiation
The Zeeman Effect
Fundamentals of Frequency Modulation
Methods of Frequency Modulation
Details of Frequency Modulation by the
III THE ZEEMAN EFFECT FREQUENCY MODULATED LASER
The Light Beam Transmitter
Discharge Tube Configuration
IV THE EXPERIMENTAL STUDY
Details of the Experiment
The Receiver System
V MEASUREMENTS AND RESULTS
VI SUIMARY AID CONCLUSIONS
LIST OF REFERENCES
LIST OF ILLUSTRATIONS
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-
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
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
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
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
Since the time of the mathematical description of the
laser, or optical maser, by A. L. Schawlcu and C. H. To-.nes
, 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-
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
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.
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
Stimulated Emission of Radiation
Schawlow and Townes  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
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
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
!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
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,
For gm equal to gn,
Also, umn -
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 ,
Comparing this with the Planck radiation formula,
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:
Amn = 2 h Bn .
low the energy lost in the spontaneous m-n transitions may
be calculated relative to the energy added to um by
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
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.
HeI213) + Ne(CS i He1'5) + l:e(3s2)
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
en rj c-'
ti H- 0% CA\ CO %0
c Nj rr r- -1 C Hi
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.
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.,
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
A laser with external mirrors and Brewster-angle windows
is shown on the next page in Figure 3. Brewster-angle win-
dows  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 . 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
I I Is
3 T :
become complicated. In their paper, Statz, Paananen, and
Foster  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.  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
based on j-1 coupling rather than L-S coupling will then
The net magnetic moment u is the vector sum of the
orbital magnetic si of all v electrons of an atom.
u0- [ -() 1i + E
= ( ) (L + 2S)
Ir m -
6- e J + )
where J = L + S
U (J + ) B.
2 m -
From a consideration of the vector quantities and their
various rates of processing, the following equations are
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.)
W= 7 m g r"
where g has the value of the quantity in large brackets in
the proceeding equation.
The energy differences become
Em 2 m bm "Jm and
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.
0 I 0
-- i 0
o~ n o+
Figure 5. Energy Levels
of the Zeeman
II Ii a
and Spectral Lines
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
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  for a carrier of amplitude A and a signal
frequency of the form B sin wst, the frequency modulated
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
Phase modulation is similar to frequency modulation
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
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
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 . 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
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
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 , 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
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
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,
M H u e
The frequency difference between the a and i rays is Civen
by the following equation
F = GpfD/h.
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-
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
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.
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.
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
>- oJ o
C'S cii LO
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
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.
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
the topic "frequency pulling." Mirror reflectance, which
determines the Q of the optical cavity, also affects fre-
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
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.
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 -)
AB AB -B
0 1 + jQB( 19.
The total gain is
A = AAAB = AAAB WA B 20
0 0 1+jQA(U -U) 1+jQB(B- -)
The imaginary component vanishes at the system resonant
S WA i 0B
J(QA(Zc ) + QB( =)) 0
(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,
0 + WA "O + "B 23.
Q C ) -Q s 24.
A .0 A Be 0 B17
which is the same as equation 17.
In their article, Gordon, Zeiger, and Townez 
gave the following expression for frequency pulling for a
He-:e laser, analogous to equation 24:
B B 25.
= 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 . 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
",_ 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
125 cm. focal length, separated to 128 cm., that a point 2
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)
vgE = AvC + C
C ( + ca+a c
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
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.
1.28 _1.28 2.56fi
n = l e 3"lOs
S 3xl08 3108
n + 1 = ----
f f = 3108 = 117 l106 cps
The approximate response of the cavity is shown below.
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
1000 mcps. Using the latter figure, AvB = 109. For
H = 10 gauss and g = 1.3,
c = 22.214.171.1240h0'10
= 1.82 107cps
The frequency separation is
S- VC 1.e82x1071.17i10 = 210 cps.
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.
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  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
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..
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
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 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:  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.
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
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'
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-
angle windows, and have an inside diameter of six milli-
meters. Ilo difficulties were experienced in obtaining
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 .
I: y o
modified from equipment already in the laboratory.
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 ,-.
0 C, > >
E-, r-. 0'--
solenoid produced an axial magnetic field with less than
110 per cent variation of field strength over the length of
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
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
Tne LT-11 laser was u-ed first with an exciter of low
L. .. -o a-
--[ -- ^ ^ ^ 5
*" I I
; p (
(U / l
o \ n
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
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.
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
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-
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..
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.
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
Beam 2eam Beam
(a) (b) (c)
Figure 15. Magnetic Field Beam
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
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.
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),
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-
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,
11. W. R. Bennett, Jr., "Hole Burning Effect in a He-Ne
Optical Maser," Ph.sical Review, Vol. 126, April, 1962,
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 ,
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
December 18, 1965
Dean, College of Engineering
Dean, Craduate School
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