170 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT December

tion it appears to us that an overall accuracy of 0.1 ,uscould be achieved.

ACKNOWLEDGMENT

This experiment could not have been carried outwithout the cooperation of many agencies, both govern-ment and private, in the U.S. and U. K. Foremost was theBell Telephone Laboratories of the American Tele-phone and Telegraph Company. Not only was Telstarmade available but the engineers at Andover providedthe necessary circuits, suggestions for carrying out theexperiment and operated some of the equipment duringthe passes. Particularly the authors wish to thank P.Wickliffe and Dr. A. J. Giger who were in charge of theAndover station during the tests. T. Thompson suppliedtechnical assistance and aided in the photography. AtWashington, Dr. J. Siry of NASA provided the satelliteephemerides, H. F. Hastings of NRL advised on theelectronics, and Dr. R. G. Hall assisted at the NavalObservatory. We are very grateful for the loan of equip-ment, on short notice, to the Pickard and Burns Com-pany, Sulzer Laboratories, and Horman Associates.

In the U. K. the authors are indebted to the PostOffice Engineering Department for the facilities andassistance provided at Goonhilly and in the planning

stages of the experiment. In addition, the authorswould like to thank the operations controller during theexperiment, R. W. White and the staff at Goonhilly;also J. S. T\lcClements who was responsible for syn-chronizing the station clock with MISF. We are gratefulto the Astronomer Royal for permission to use the re-sults obtained at the Royal Greenwich Observatory.C. R. Cordwell and R. W. Donaldson assisted in themeasurements by the National Physical Laboratory;these were undertaken as part of the research programof the Laboratory and are published by permission ofthe Director.

REFERENCES[1] Essen, L., The international co-ordination of time signals and

standard frequency transmissions, Nature, vol 187, 1960, p 452.[2] Reder, F. H., M. R. Winkler, and C. Bickart, Results of a long-

range clock synchronization experiment, Proc. IRE, vol 49,Jun 1961, pp 1028-1032.

[3] Doherty, R. H., G. Hefley, and R. F. Linfield, Timing potentialsof Loran-C, Proc. IRE, vol 49, Nov 1961, pp 1659-1673.

[4] Markowitz, W., Time measurement in the microsecond regionl,Engineer's Digest, vol 135, 1962, pp 9-16.

[5] Jakes, W. C., Participation of Bell Telephone Laboratories inProject Echo, Bell System Tech. J., vol 40, 1961, p 975.

[6] The Telstar experiment, Ibid., vol 42, 1963, p 739.[7] Taylor, F. J. D., Equipment and testing facilities at the experi-

mental satellite ground station, Goonhilly Downs, Cornwall,Post Office Elec. Engineers J., vol 55, 1962, p 105.

Frequency Stabilization of the He-Ne Maser

KOICHI SHIMODA

Abstract-A bright and monochromatic radiation from an opticalmaser can be used as a stable standard of wavelength, when planemirrors in the maser are automatically controlled so that the oscilla-tion frequency can be kept very close to the center of the atomicline. The separation of mirrors is modulated at a low frequency witha small amplitude. The fundamental-, the second-harmonic, and thethird-harmonic components of the modulation frequency in the lightoutput give correction signals for the tilt of mirrors, the power levelof excitation, and the separation of mirrors.

The photobeat between two independently-stabilized masers of1.15 microns filled with NeO and Ne22, respectively, has been ob-served. The observed fluctuation of beat frequencies shows aGaussian distribution, and no systematic frequency drift has beenfound. It is found that the frequency of each maser stays withinseveral parts in 1010 and the resettability is just as good. Some diffi-culties with stray magnetic field from magnetostriction coils andwith earth magnetic field are found.

Preliminary experiments on pressure shift and its effect on the

Manuscript received June 23, 1964; revised September 22, 1964.The work reported in this paper was supported by the National Aero-nautics and Space Administration.

The author is with the Dept. of Physics, University of Tokyo,Tokyo, Japan. He was formerly with the Physics Dept., Massa-chusetts Institute of Technology, Cambridge, Mass.

stabilized maser are discussed. The theory has been developed, andthe frequency deviations as functions of the gas pressure and of theamplitude of modulation have been calculated.

I. INTRODUCTION

THE STABILITY of frequency and wavelength ofan optical maser is mainly determined by thestability of the Fabry-Perot resonator. In a free-

running oscillator a high degree of frequency stabilitycan be achieved only under special laboratory conditionswhich provide excellent thermal and acoustical isola-tions [1]. Long-termi stability and resettability arequite poor.

After consideration of various possible methods of ob-taining good long-term stability and resettability, anautomatic tuning system using a small-amplitude vibra-tion of mirrors in the maser was investigated and tested.Although a similar but simpler method has been inde-

pendently investigated by Rowley and Wilson [2 ], themethod reported in this paper affords more accuratestabilization. Not only the separation of plane-parallel

1964 Shimoda: Stabilizat

mirrors in the maser but also the angle of tilt and theintensity of excitation are automatically controlled.The normal sample of neon is a mixture of the isotopes

Ne20 and Ne22 so that the output power vs. length char-acteristic of the maser is asymmetric with respect tothe line center [3]. If an enriched isotope of either Ne20or Ne22 is used, a fairly symmetric characteristic can beobserved. However, because the mirrors cannot stayexactly parallel while the separation is varied, and be-cause effects of unwanted isotopes and other impuritiespresent some frequency shifts, the shape of the outputcharacteristic is not completely symmetric with respectto the center. Then the apparent center frequencychanges with mirror alignment and with the intensity ofexcitation.

In order to stabilize the frequency of oscillation of anoptical maser with a high degree of accuracy, therefore,the tilt angles of the mirrors and the excitation powermust be controlled. An optical maser with external mir-rors is not appropriate for frequency stabilization be-cause the optical path-length between the window andthe mirror changes greatly with the pressure, tempera-ture, and humidity of air in the ordinary condition.

In the experiment reported in this paper, the separa-tion and angles of the internal mirrors are controlled bymagnetostriction effect [4]. The excitation is controlledby the grid bias of the RF power amplifier.

II. PRINCIPLE OF OPERATIONA fairly complete analysis of the principle of stabiliza-

tion will appear elsewhere [5 ]. Only a brief descriptionof the principle is given here.The frequency of the maser can be continuously tuned

by varying the separation of mirrors. However, varyingthe length is generally accompanied by a slight, unde-sirable tilt of the mirrors. The misalignment of planemirrors results in the increase of the resonator loss, andhence increases the threshold value of excess populationNth. The effect of such misalignment as a result oflength tuning can be taken into account by allowing Nthto become a function of the frequency deviation which isdenoted by x=(v-v0)//Av, where v0 is the center fre-quency of the line and Aiv= 1/XV2kT M is a measureof the Doppler width.

After some modifications on the theory of an opticalmaser by Lamb [6], the intensity of oscillation can beexpressed by

N -Nth (X) exy(x) = A2ar-l

1+ B1 + a2x2

where N is the excess population of the maser level inthe absence of oscillation, a is the ratio of Av to thenatural width of the transition, and B represents theratio of probability of hard collisions and spontaneousdecay to that of total perturbations iucluding soft colli-sions.

on of tie-Ne Maser 171

Equation (1) is valid for the oscillation on a singlemode. In the presence of hyperfine structure or isotopeshift, the amplitude of maser oscillation cannot be givenby a simple expression. Nuclear spins of Ne20 and Ne22are both zero, so that the hyperfine structure is absentin the spectra of these atoms.By substituting a parameter

a/b2 = a-

1 + B

2 B

v'J

(1) can be rewritten in the form

YO 1 - F(x)ee ± a2x2)1 -F 1 + b2.c2k

(2)

(3)

where F(x) =Nth(x) N and F F(0). The intensity ofoscillation presents a dip [3], [,] near x=0 when theexcitation is not weak. If the eXcitation is reduced sothat (NINth) -1 < (a2 --b2)-1, the power dip disappearsand the output power shows a single mgximum nearx = 0. In the case when (N/N h)-1 = (a2-b2)-l, theoutput characteristic shows a flat-top behavior.The frequency corresponding -o the power minimum

or maximum given by y'(x) = 0 i, not a stable standardof frequency because it changes considerably with thetilt of mirrors and with the power of excitation. It isfound that a more stable standard of frequency will beobtained if the maser is so contreled as to satisfy y =y"=y"' =O.Error signals for the frequency stabilization are found

in the following way. When the separation of mirrors ismodulated sinusoidally with a small amplitude, varia-tion of the maser output cons sts of harmonic com-ponents which sensitively change with the tuning. Theoutput signal from a photomultiplier at the fundamen-tal frequency of modulation is u1sed to control the angleof tilt; the second harmonic component is used to controlthe power of excitation to make cS flat-top characteristic;and the third harmonic is used to control the separationof mirrors.When the frequency of the maser is sinusoidally modu-

lated with an amplitu(de xi (rek.tive to AP'), the centerfrequency of the stabilized maser is calculated to be-come [5 ]

6X12zy1- 224(1- F)Ay3 -18x,2Ay3 -xjyoF`x0 (4)24(12x3yo- 24x1Ay2

where Ay,, AY2, and Ay3 are sma l residual values of thefundamental, the second harmonic, and the third har-monic components in the output of the maser, respec-tively.

III. EXPERIMENTAiL RESULTSThe automatic tuning system described in Section II

has been tested with two similar masers of 50-cm length.Each maser has been equipped wvith four invar rods andthree sets of coils to allow tuning in the separation Z,

_N 7 I_ T 7 1l 7 7 x , -

tio

172 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT December

and the tilt angles X and Y, of mirrors by magnetostric-tive effect.The separation between the mirrors is modulated

nearly sinsuoisdally at f = 71 c/s by a driving currentthrough the Z coil. Because of some asymmetric con-struction of the maser, the modulation of mirrors alongthe Z direction is accompanied by a small modulation oftilt in the Y direction.Then an error signal for the tilt in the Y direction is

obtained from the output of the lf =71 c/s amplifier,while an error signal for the separation is found at theoutput of the 3F= 213 c/s amplifier. An error signal ofthe tilt in the X direction may be obtained by applyinga small modulation at another frequency at 30 c/s. TheRF power for excitation is controlled by the output ofthe 2 F= 142 c/s amplifier.

In a single-mode oscillation with a flat-top character-istic the power level is of the order of 10-6 watts. Whena type 7102 photomultiplier with a total anode voltageof 1000 volts is used to detect the 1.15-micron output,the value of yo across the 200-kilohm load is about 0.1volt. The minimum error signals which are necessaryto drive servomotors at frequencies lf and 3f are

Ayy1= 2 X 10 volts and Ay3 = 1 X 10-6 volts, respectively.The amplitude of frequency modulation employed is

10-15 Mlc/s, that is, xi=2-3X10-2. In a typical casethe maser is filled with 1.0 torr He and 0.1 torr Ne, forwhich the coefficients in (1) and (3) are about a = 15,B = 0.4, and b2= 158.When the excitation is adjusted so that y" =0, the

value of NthIN is close to 1 and

1-F =1

a2- b2 + 1= 1.5 X 10-2

When one maser (A) was filled with Ne22 of about 99per cent isotopic purity and the other (B) was filledwith Ne22 having a few per cent Ne20, a photobeat at afew megacycles was observed. The frequency of themaser B (Ne22+a few per cent Ne20) was found to belower. This is evidently the effect of frequency shiftdue to Ne20 which has a transition at a lower frequencyby 260 Mc/s than Ne22. The frequency of the beat wasmeasured by an electronic counter and recorded forseveral hours.The distribution of the frequency differences between

the two masers has been found to show a Gaussian dis-tribution. Two typical results for the total pressure inmaser B of either 1.78 torr or 0.85 torr with a He-to-Neratio of 7 to 1 are shown in Fig. 1. The average value ofthe beat for PB= 1.78 torr is 1.34 Mc/s with a standarddeviation of 0.35 Mc/s; and the average for PB= 0.85torr is 5.15 Mlc/s with a standard deviation of 0.59 Mc/s.The total pressure in the other maser was PA= 1.1 torrwith a He-to-Ne ratio of 10 to 1.

l00 + t= l.78

50

(5)0

Since F(x) is a slowly varying function, we take F'|<10-3 and IF"'| <10-4. Substitution of these valuesinto (4) gives the frequency shift relative to Az'=5001\Ic/s to be IxOI <3.3X10-5 when x1=3X10-2. Thenthe calculated fractional error in frequency becomes

0 1 2 3 4 5BEAT FREQUENCY

P =0.85

6 7 MC

Fig. 1. The distribution of the observed beat frequencies betweentwo masers filled with He+Ne22. The oscillation frequency of thereference maser is higher because of its greater isotropic purity.The total pressure in the other maser was changed from 1.78 torrto 0.85 torr with a He-to-Ne ratio of 7 to 1.

6

< 6.3 X 10-11vm

(6)

This seems to be a plausible limit of accuracy, whichwould be sufficient for most precision measurementssuch as in long-distance interferometry.The experimental evaluation of the frequency stabil-

ity and resettability were performed by the observationof a photobeat between two stabilized masers. Onemaser was filled with Ne20 and the other with Ne22. Theisotopic purity of these samples was better than 99 per

cent. When both masers were modulated with nearlythe same amplitudes and phases, the photobeat was

observed by a spectrum analyzer at a frequency of about260 Mc/s.

In the intermittent operation of the stabilization sys-

tems for a period of a few weeks the beat appeared re-

producibly within + 1 AIc/s range on the scope of thespectrum analyzer. No systematic drift in frequencywNas found.

The values of a, b, and yo are functions of gas pres-sure. Moreover, the experimental setup of the feedbacksystem was somewhat different for each maser. If thetwo masers at PA=1.1 torr and PB=1.78 torr are as-sumed to have had the same stability, the fluctuation infrequency of each maser should be 9 X 10-10. However,because one was more stable than the other it showed afluctuation in frequency of about 6 X 10-10.The results in Fig. 1 also show an evident shift in

frequency with gas pressure. The frequency of the 1.15-micron oscillation at a He-to-Ne ratio of 7 to 1 isfound to increase by 4.1 Mc/s torr.

IV. EFFECT OF STRAY MAGNETIC FIELD

However, the value of pressure shift discussed in Sec-tion III may not be very accurate because of some com-plicated effect from a weak magnetic field. The leakagefield from magnetostriction coils was of the order ofone oersted around the discharge tube. Thus the re-

1964 Shimoda: Stabilizat

sultant field with the earth magnetic field was quite in-homogeneous and variable with magnetostriction tun-ing. This produced unwanted variations in the outputof the photomultiplier and shifted the apparent fre-quency of the line.The amount of frequency shift due to stray magnetic

field was difficult to measure, but it was estimated tobe approximately + 1 Mc/s in this experiment. Thevalue of pressure shift described in Section III wasmeasured with masers which were equipped with thinpermalloy cylinders around the discharge tube, but theshield was not quite satisfactory.

Each mode of the optical resonator is degenerate inthe absence of a magnetic field. The magnetic nonre-ciprocal character of the medium in the resonator liftsthis degeneracy and the maser oscillation appears as acoupling of the two modes. This coupling gives an el-liptic polarization in the output of the maser and pro-duces rotation of the axis of polarization in most cases.In a strong homogeneous magnetic field (of larger thana few oersteds), the maser oscillates at two differentfrequencies, but in a weak inhomogeneous field it oscil-lates on a superposition of the two modes. Analysis ofthe frequency shift in an inhomogeneous field is not pos-sible. A feasible means of reducing the error in frequencyshift caused by a magnetic field is to insert a glass plateat a Brewster angle inside the resonator so that it canreject one of the two modes.

V. HIGHER ORDER DERIVATIVES ANDDISTORTED M1ODULATION

The calculated frequency deviation given by (4) be-comes smaller as the amplitude of modulation xi in-creases. This is true as long as xi is so small that higherorder derivatives of y with respect to x can be neglected.When xi is large and higher order derivatives are takeninto consideration, the distortion in modulation becomesimportant.The frequency modulation of the maser may be ex-

pressed by

x = xO + xl(cosct + 82 cos 2wt + 83 cos 3wt + ) (7)

The output of the maser is written in the form

y = yo+ ylcos oI +y2cos2s+y3coS3ct + (8)

if phase shift in the oscillation characteristic of themaser is negligible. When the maser is controlled sothat yi, Y2, and Y3 take small values-Ay,, Ay2, and Ay3,respectively the frequency deviation relative to theDoppler width can be obtained after somewhat lengthycalculation from (4), (7), and (8). The result can be ex-pressed to the first orders of /yi in the form

F"' Ay1 + (462 + 654)Ay2 -3Y324a2 4a2yox1

1-F

2 2(62 64)zAy2 AY3}a12y0X13axyl l

X1 X13(2+ 4) 8 (62+264)+ -

2 8(1 -F)(9)

[ion of He-Ne Maser

where terms of Aylb6 and Ay36, are omitted since theyare much smaller than Ay, and Ay:;. In (9) terms having63, 65, and higher order distortions do not appear. Thelast two terms have come from d4yldx4 which has beenapproximated by

d4y

dx4_--24a2(a2 -b2)yo

24a2yo

1 - F(10)

Terms due to d5yldx5 are much smaller in magnitudewhen x1< 6 X 20-2.

Experimental values are a(-=15, b=12.6, 1-F=1.5X10-2, F",t I<to--4, YO= O. volt, Ay,| =2X10-5

volts, AY2| =I ' I0 X 1t(0- volts, and |y3 t1X10-6volts. Then the frequency deviat.on is calculated from(9) as a function of the amplitude of modulation xi. Theupper two curves in Fig. 2 are the calculated deviationfor 621 = 1.0 per cent and 641 =0 2 per cent; the middletwo are for 621 =0.5 per cent ard 641 =-0.1 per cent;and the lower two are for 1621 -0.2 per cent and 1641=0.04 per cent. These curves show that the stabilitywill be nearly optimum w ith a mod ulation of xi = 3 X 10-2,which is consistent with the experimental result.

300kC

z

~2002

a100LU

10-

8-

ay21= IX /104V!y21 = 2x10-5V

S- 1%

2- 82i 0270

lII I

1l 2 3 4 5s lo-2-x

Fig. 2. Theoretical frequency deviations of the stabilized maserfilled with 1.0 torr He and 0.1 torr Ne. (See text for the parame-ters used.) The fourth harmonic distortion is assumed to be1641 = 0.2 1621.

It was very difficult to measur( accurately the distor-tion in maser frequency modulation. Therefore, har-monic coinponents in the driving current through themagnetostriction coils of the maser were measured toallow rough estimates of the amiount of distortion inmodulation. These values varied considerably with thedc bias and with the amplitude ol modulation, and werefound to be

62 =0.4 , 1.5 X 10-2

63 =1 2 X 10-2

641 _ 2 X 10-3

51 _ 1 X 10-3

From these values of distortion it may be concludedthat the calculated deviation in frequency agrees in itsorder of magnitude with the observed fluctuation.

It may be noted that the theoretical estimate given

173

4

0

174 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

by (9) and by Fig. 2 represents the maximum deviation.Thus the experimental fluctuation is somewhat largerthan the theoretical estimate. This discrepancy may bedue to rapid changes in the power supply and to themechanical and acoustic disturbances which cannot becontrolled by the feedback system with a time constantof the order of one second.

VI. EFFECT OF GAS PRESSURE ON STABILIZATION

The parameters A, a, and B in (1) change with thepressures of helium and neon in the maser. The power

dip becomes sharper and deeper as the pressure de-creases. This means that the values of a and B decreasewith the pressure. One might expect, therefore, that thestability would be better at a lower pressure. However,the actual stability is worse at a lower pressure, as can

be seen from Fig. 1.The reason for the decline in stability as pressure is

reduced can be understood by the rapid decrease of theoutput power. The output power of the maser at thecenter frequency can be given by

voV

PQ= E=4Qext

3VOV h I 1-F

4Qext PTIJ 1 + B

where , is the dipole matrix element, E is the opticalelectric field, V is the effective volume of the optical reso-

nator, r' is the lifetime determined by hard and softcollisions, and Qext is the Q value of the output couplinggiven by

2rv0X stored energyQext = loss due to coupling

The parameters in (1) are rewritten [3] by

a= 27rT'Av B= T'lr (12)

and the output of the maser can be expressed by

12 1-F I1-FxT) 1 + B aa2(1 + B)

For a maser tube of about 7 mm ID filled with a

helium-to-neon ratio of 10 to 1, the parameters a andB are found to decrease with pressure [3], [8] as givenapproximately by

1- = 0.0230 + 0.0396pa B

= 1 + 1.4p (13)

where p is the total pressure in torr. The output voltageof the photomultiplier used in the experiment is 0.1volt when y" = 0 at p =1.1 torr, so that

1-F 2.1 X 103

Yo 2.1 + 10 a2( + B)= a4B (14)

Substitution of (13) and (14) into (9) gives the fre-quency stability as a function of the gas pressure. Thestability for a different ratio of helium and neon may becalculated from the parameters of cross sections experi-

mentally obtained by Szoke [8 ]. These calculationsshow that the stability is improved when the pressureis increased.

VII. CONCLUSIONExperimental and theoretical results described here

show that a He-Ne maser of 1.15 microns can be stabil-ized within several parts in 1010. Although it appearsthat greater stability can be obtained at a higher pres-sure, the threshold value of excitation increases withpressure and the oscillation becomes difficult. The pres-sure shift will be large when the pressure is high, and itvaries with a change of gas pressure with time due tooutgassing and cleanup. The magnitude of pressureshift may also change with the temperature. Further-more, the presence of small amounts of impurities inthe gas may distort the line shape and may shift theapparent center of the line. This systematic shift issmaller at a lower pressure.The optimum pressure for the greatest stability

cannot be determined at present for lack of sufficientexperimental results, but the pressure of 1.0 torr He and0.1 torr Ne may not be far from the optimum condition.

Noises in the amplifiier and the starting voltage ofthe servomotor are not the limiting factors in the pres-ent values of residual error signals. If the pickup ofelectrical and magnetic disturbances in the photomulti-plier and amplifiers is reduced, Ayi will be smaller thanthe value used in this paper. The sensitivity in detec-tion is limited chiefly by the poor quantum efficiencyof the photocathode at a wavelength of 1.15 microns. Ifa maser at a shorter wavelength is used, the quantunmefficiency will be two orders of magnitude larger, andhence the frequency deviation will be two orders of mag-nitude smaller in an ideal case.

ACKNOWLEDGMENT

The author is greatly indebted to Prof. A. Javan andDr. A. Sz6ke for their contributions and assistance inevery stage of this study. He would also like to expresshis gratitude to R. H. Addison, R. W. Solomon, andE. T. Leonard for their assistance in the experimentalwork.

REFERENCES[1] Jaseja, T. S., A. Javan, and C. H. Townes, Frequency stability

of He-Ne masers and measurement of length, Phys. Rev. Lett.,vol 10, Mar 1963, pp 165-167.

[2] Rowley, W. R. C., and D. C. Wilson, Wave-length stabilizationof an optical maser, Nature, vol 200, Nov 1963, pp 745-747.

[31 Szoke, A., and A. Javan, Isotope shift and saturation behaviorof the 1.15-,u transition of Ne, Phys. Rev. Lett., vol 10, June 1963,pp 521-524.

[4] Bennett, W. R., Jr., and P. J. Kindlmann, Magnetostrictivelytuned optical maser, Rev. Sci. Instr., vol 33, Jun 1962, pp 601-605.

[5] Shimoda, K., and A. Javan, Stabilization of the He-Ne maser onthe atomic line center, J. Appl. Phys., vol 36, Mar 1965.

[6] Lamb, W. E., Theory of an optical maser, Phys. Rev., vol 134,Jun 1964, pp A 1429-1450.

[7] McFarlane, R. A., W. R. Bennett, Jr., and WV. E. Lamb, Jr.,Single mode tuning dip in the power output of an He-Ne opticalmaser, Appl. Phys. Lett., vol 2, May 1963, pp 189-191.

[8] Szoke, A., Line shapes of the 1.15-,u Ne transition, Bull. Am.Phys. Soc., ser. II, vol 9, Jan 1964, p 65.