spectrum of a fabry-perot resonant cavity containing an active medium

Spectrum of a Fabry-Perot Resonant CavityContaining an Active Medium

B. F. Hochheimer

A Michelson interferometer has been used to measure the visibility curves for the 6328 A neon emissionline in a 90% He-10% Ne gas mixture in order to determine the effect of an optical cavity upon the lineshape when the medium exhibits a net gain and yet the system is below lasing threshold. An analyticalmodel for the effect of the cavity is proposed and a computer program set up to fit the model to the data.The cavity gain and finesse are used as variable parameters. The same techniques can be applied to alaser and the number of longitudinal lasing modes can be determined; however, in this case the gain andto some extent the finesse are indeterminate.

Introduction

A Michelson interferometer has been used as a high-resolution spectrometer to determine the line shape ofthe 6328 A neon spectral line from a laser cavity whenthe input source power level was set at a point belowlasing threshold. A Brewster-angle helium-neon laseroperating in a hemispherical configuration was used forthe experiments; the light was taken from the sphericalmirror end of the cavity. The view seen by looking intothis end of the cavity through a narrow-band 6328 Ainterference filter is a uniform low-intensity backgroundand a bright central core. When not lasing, this core(see Fig. 1) contains no evidence of structure althoughwhen lasing the TEMoo mode occupies only about one-fourth of the core diameter. When the back (plane)mirror is blocked the core disappears; the core alsoblends into and out of the background when a polarizeris rotated in front of the cavity.

The light from the cavity core passing through theinterference filter was examined with a spectrometer, andit was found that every neon line that did not end on ametastable state was contributing to the core while thelines ending on metastable states or helium lines con-tributed only to the background. As can be seen fromthe spectra (Fig. 2), the 6328 A line is greatly enhancedeven over the other nonmetastable state lines.'

The frequency content of the 6328 A core light wasthen studied with and without the cavity to find theinfluence of the cavity on this light.

An interferometer was used for the spectral studybecause resolution in excess of one million was desired.A Michelson interferometer was chosen over an available

The author is at the Applied Physics Laboratory, The JohnsHopkins University, Silver Spring, Maryland.

Received 14 May 1965.

Fabry-Perot2 interferometer because beat measure-ments, as described by Herriott,3 between the laserlongitudinal modes indicated a lack of long time stabil-ity which would give an almost continuous drift to thelaser modes; this would make time integration with aFabry-Perot impossible. However, this slow wave-length shifting does not affect the Michelson interfero-meter as long as the spectral components maintain theirrelative positions because the fringe scan time is fastwith respect to this slow drift although the total scantime is long. A long time integration is necessarywith either interferometer because of the low light levelinvolved.4 As will be shown later, the individuallongitudinal modes of the cavity have a relatively highintensity (although still low with respect to a laser), butthe total integrated light over the spectral line is lowbecause of the sharpness of these modes.5 Terrien6 hasshown how sensitive the visibility functions measuredwith a Michelson interferometer are to change in lineshapes, and thus how valuable this interferometer is forthis work in spite of some major disadvantages whichwill be apparent later.

TheoryWith a Michelson interferometer the fringe visibility

is defined as

(1)-max - mil

Ima + mil

where I is the intensity of the circular Michelson cosinefringes at maximum and minimum points. The visi-bility, or contrast, can be used to determine spectralline shapes when V is taken as a function of path differ-ence between the beams of the interferometer. It wasshown by Michelson7 8 and Rayleigh9 that the visibilityfunction is the Fourier transform of the line shape. Byrearranging and substituting terms from the formulas

January 1966 / Vol. 5, No. 1 / APPLIED OPTICS 113

where T is the transmission of the medium in the cavity,R the reflectivity of the plates, and T' the transmissionof the plates. When this series is summed, omitting theconstant frequency term e"', then

IT TT' 1 I (1 -TR) 2 1 + [4TR/(1- TR)2 ] sin2 (o/2)}' (6)

where so is the phase difference between the beams and isgiven by

(7)

Fig. 1. View seen looking into the spherical mirror end of ahemispherical laser when the power is reduced to a point below

lasing threshold.

given by Born and Wolf 10 it can be shown that, if thespectral line is symmetrical and has a Doppler shape,

V(L) = L(J AX) (2- 2-)d(AX), (2)

where o is the mean wavelength of the line, AXo is thehalf-width of the line (full width at half-height), AX' isthe distance from the line center, and L is the pathdifference in the interferometer (i.e., twice the distancethe movable mirror is positioned from the point of zeropath difference).

Equation (2) is based on a symmetrical Doppler lineshape and if such is the case then a simple inversion ofthe Fourier integral will yield the line shape. Forexample,' if

( 7rLA~o \ 2

V(L) = e- 1.66lo2) (3)

then(1.66AX' 2

j(X) = joe \ J -, (4)

) V(Lo) is a normalizing function and is the integral ofthe area under the curve of the line shape, this integral isproportional to the spectral line intensity when j istaken as unity.

When the cavity is considered it is necessary to have aline shape different from a Doppler shape and thefollowing derived equation will be used to describe thisline. If the cavity is considered to be a Fabry-Perotinterferometer with an absorptive medium inside, then aderivation similar to that given by Candler" can bemade. A beam of light originating inside of the inter-ferometer is reflected back and forth between the plates,some light leaving at every bounce. The light leaving isthen given by an infinite series:

Itotal = ITT'eiwt + IT1T3R2ei(W1+s) + IT'T5R4eI(-t + 2) +

(5)

a. a.

INC'

where

n = the index of refraction of the medium in this problem itis assumed to be 1,

D = separation of the plates,X = is the wavelength.

In order to sum the series given by Eq. (5) into Eq. (6) itis necessary that the product TR be less than 1. Thisrestricts the use of Eq. (6) to those cases where this istrue. The multiplying terms for the sin2 part areabbreviated as F which is given by

F = 4TR/(1 - TR)2. (8)

Equation (6) times the Doppler line shape will be takenas the frequency spectrum of the cavity. If this is thespectral intensity distribution, the visibility functionis given by

0-~ L1TI ( 1.66XM) 2\

V(L) = 1 ( -TR)2w DAXOw V(Lo) o I + Fsin2 ' a -

),2 /

[27rAX'L ]d" cos (9)

The helium-neon mixture used in the experiment wasobtained from the Matheson Corporation and the neon

IaIL

041"Iso1

.N

X, - co.

pnO. 0.(sN N

(a)

, ,.

a. 0.

M I

(b)

Fig. 2. Spectrum of a helium-neon gas mixture in the vicinityof the 6328 X line: (a) spectra from side of tube; (b) spectra

from resonant cavity.

114 APPLIED OPTICS / Vol. 5, No. 1 / January 1966

,p = 2nD/?,

I

Table I. Definition of Symbols

Term Definition

V Visibility of fringesV(L) Visibility as a function of path differenceV(Lo) Normalization function for the calculated visibility;

it is proportional to the line intensityX0 Mean wavelength, 6.3282 X 10-5 cmAX0 Half-width of line at XoAx' Distance from the line center; this is the integration

variable for V(L)L Path differencej(X) Line intensity as a function of wavelengthT Transmission of active mediumT' Transmission of mirror, 0.003R Mirror reflectivity, 98%D Separation of cavity mirrorsA Neon isotope 20 concentration 90%B Neon isotope 22 concentration 10%a Isotope line separation 1.328 X 10-'° cmK Variable in equation for transmission

Finesse of Fabry-PerotF Variable in cavity line equation, proportional to 52

presumably has the normal isotopes present in neonusually given asl2 : neon 20, 90%; neon 21, 0.27%; andneon 22, 9.73%.

The presence of these isotopes puts fine structure inthe 6328 A line. The distance between the two spectralcomponents from neon 20 and neon 22 is given byBartlett and Gibbons' 2 as 0.332 cm-'. In this problemthe neon 21 was neglected because of the small per-centage normally present. This fine structure destroysthe symmetry of the spectral line and, as shown byRayleigh,9 makes the inversion of the Fourier integralimpossible without the necessary and extremely difficultto obtain phase information about the interferencefringes. However, the visibility function can still becalculated if the line shape is known. This is done asfollowsl:

V(L) = Vc i ± S2| (10)P

where

P = l j(A')d( AX'),

= f j(AX')cos(27rAX'L/Xo2)d(AX'),

= f j(AX')sin(27rAX'L/Xo2)d(AX'),

trations for neon 20 and neon 22, respectively, and 6 isthe neon isotope line separation.

The cavity line shape was assumed to be

-_(1.66AX') 2

TT' |Ae AX0j(AX') = TT' I-eA(1- TR)2 1 + Fsin2 4 7DAX

L XoB

+Be

, 1.66(AX'+b)]2L AX0

(15)1 + Fsin2 47rD(AX' + a)

Note that in the sin2 term the 2 of Eq. (9) has here beenreplaced by a 4 to account for doubling of the number ofpeaks because the actual cavity used was hemisphericaland not a flat plate cavity. 2 This equation describes aspectral line broken up into a number of peaks, thenumber and spacing depend on the parameters.

In order to correlate theory and experiment it wasalso found necessary, as will be seen later, to make somefurther assumptions as to the line shape. The assump-tion used was that T, the transmission of the activemedium, was not a constant independent of wavelength,but instead was a function of the line intensity, that is,

(F/1_.(1.66X'> 2 _ 1.66(A'+ ) 21)T = To + KAe AX0 + Be* j A

(16)

Equation (10) for the visibility function with theaddition of Eqs. (11)-(13), (15), and (16) was program-med for an IBM 7090 computer. Equation (14) wastreated as a special case of Eq. (15). Provision wasmade to treat F as given by Eq. (8) or as a constant.The reason for this is discussed later.

In most cases the following things were calculatedfrom the equations noted above: (1) the line shape it-self, that is, j(AX') (jo = 1); (2) V(Lo) which is theintegral of j(AX') and is proportional to line intensity;(3) ten points on the visibility curve spaced from L = 0to 25 cm; and (4) a visibility curve using only theenvelope of the cavity peaks when cavity computations

(11)

(12)

(13)

where j(AX') is the line shape. It should be noted thathere the integrations are carried out from minus to plusinfinity.

The line shape that was assumed for the noncavityline is

CHOPPER

_ ( 1.66AX) "1.66(AX'+3)

j(AX') = Ae AXo 0 + Be- I I

where A and B are the neon isotope percentage concen- Fig. 3. Michelson interferometer and auxiliary equipment.


(14)

1.00

0.8C

0.60 -

CAVITY

0.20 _ _ _ _ _ _ _ _ _

NON0- ~~~~~~~~CAVITY

10 20D (m)

Fig. 4. Visibility curves: (a) cavity, (b) noncavity.

30

were made. Table I lists the various symbols usedtheir values when they are constants.

ExperimentFigure 3 is a diagram of the experimental arranger

to measure the visibility functions. The resoenergy from the laser cavity is filtered with a Corcolor glass filter and a grating monochromator.light was polarized to remove any complications in Icalculations. It was found necessary to use a mchromator of fairly high resolution and fairly highpersion to prevent the 6334 A neon line from entEthe interferometer. The high dispersion was needEthe entrance slit of the monochromator was madefield stop of the system and was made to be about 2both horizontally and vertically. This was s:enough so that the error due to the finite angular si:the field stop in making a phase errror over the cerMichelson fringe pattern was always less than 1%This correction was therefore neglected. The Ileaving the monochromator was collimated beentering the interferometer, the interfering beams collected with a telescope objective and focused1P21 photomultiplier. The moving mirror ofinterferometer was driven with a small clock mthrough a gear reduction drive at the rate of aboutfringes per minute. The mean position of the mo,mirror was measured with a Simpson Optical CompVernac, the zero position being determined with w

light fringes in the interferometer. This mean positionof the moving mirror could easily be set to 0.01 mm.

The Michelson interferometer itself was constructedwith a precision Hardinge lathe bed as a base, themoving mirror was mounted on a compound rest. Themirrors, dividing plate, and compensating plate were5-cm diam quartz blanks polished to better than 0.1wave on both sides. Less than 1 square cm area ofthese plates was used. The dividing plate was leftunsilvered because the aluminizing, with the polarizedlight from the cavity, caused different amplitude divi-sion of the light at the aluminized surface dependingon whether the division occurred at an air-aluminum ora glass-aluminum surface.'5 With this condition themaximum visibility we could obtain even at zero pathdifference was about 85%. This causes no problems,however, as the visibility curve is normalized to unityat maximum. The aperture stop of the system wasplaced at the last telescope objective helping to elimi-nate stray light. The beam was limited in diameterbefore entering the interferometer so that no overlapfrom unused divider plate or compensator plate reflec-tions occurred.

The calculated resolution for 20 cm path difference,which was used most of the time, is 0.01 A.'6 Whilethis resolution is insufficient to resolve the individualpeaks of the cavity, it permits detection of the peakenvelope curve.6 Greater path differences were avail-able, but accurate alignment of the interferometer be-comes increasingly difficult as the fringe contrast dropsto lower values. The actual alignment of the inter-ferometer was carried out with the aid of a krypton light

i and source in a manner similar to that described by Stroke. 14

An eyepiece at the photomultiplier position was used tocenter cross hairs on the central circular fringes formedwith the krypton lamp. With the eyepiece removed, a

nent Maxwellian view of the last objective showed thenant Twyman-Green localized fringes. The interferometerning was aligned for zero fringes in the field, the cross hairsThis and eyepiece realigned with the krypton lamp, and thenlater the source to be measured centered in the eyepiece with-ono- out touching either interferometer or final telescope.dis-

eringed ase the00 Amallo7e ofitral13,14

light,forevereon athe

otortwotving

ianyhite

-

Z1 lUU I

PLATE CURRENT (milli-omps)50

Fig. 5. Visibility at path difference of 10.2 cm vs plate currentof transmitter for: (a) cavity, (b) noncavity.


0.65

0.55 ' _1 1I

0.45

CAVITY0.35

3 0 0 ~~~0 0 -- 0.25 NON CAVITY,

0.25

Iou 75

0.41

0.20

1.4 AA. 101 0

cm

1.6

2.2 1.-8

0 __ ____ ____ ___ 2.4 2.0

0 1 0 20 30D (cm)

Fig. 6. Computer visibility curves of a noncavity spectral linefor various values of line half-width. Points indicated are

experimental data.

The energy from the cavity was mechanically choppedat 870 cps, amplified with a tuned amplifier, synchro-nously rectified and recorded on a Brown recorder.The linearity of the amplifier-photomultiplier combina-tion was checked with a set of calibrated neutral den-sity filters.

Experimental Data

The visibility curves for the cavity and noncavitylines are shown in Fig. 4. The noncavity data is theaverage of three separate days' measurement where theindividual values do not differ by more than 4%. Thecavity curve is the average of two measurements. Theratio of the intensity from the cavity with the front cav-ity mirror removed to that with the cavity present is 2.1to 1 (noncavity gives larger value). Then, if the back(flat) mirror is blocked, the energy drops by a factor of2.0. Figure 5 shows the measured visibility function atL of 10 cm vs plate current of the transmitter. For thenoncavity case the visibility is constant; however, theline intensity itself increases with plate current. 1 Forthe cavity, on the other hand, the same power changeproduces a marked change in the visibility.

The transmission of the spherical mirror was meas-ured on a Beckman Model DK-1 double-beam spectro-photometer at 6328 A to be 0.003.

Analysis of Data

Noncavity

Figure 6 shows several computed visibility curves andthe measured points for the case of the noncavity data.

From these curves a value of AX0 of 0.02 A was chosen asgiving a good fit between experimental and computeddata. If the line is doppler shaped, its half-widthcan be used to determine the temperature from theformula (see, for example, Tolanskyl 7 ):

= 0.71 X 10-6(T/M)'/2 v(cm-), (17)

where c is the half-width in wavenumbers, v is thefrequency of the line in wavenumbers, T is the absolutetemperature, and M is the molecular (or atomic) weight.

The temperature computed from Eq. (17) for a AX0 of0.02 A is 3950 K. Figure 5 indicates that the tempera-ture is relatively independent of power input.

Cavity

Figure 7 shows visibility curves computed as pre-viously outlined using the AX0 found above; the experi-mental data points are also shown. It can be seen thata K value of 0.017 gives a reasonably good fit to theexperimental data.

If this value of K = 0.017 is assumed to be correctthen the integrated line intensity, V(Lo), should be 0.98times the integrated line intensity for the noncavitydoppler line. This is based on the measured value ofthe ratio of cavity to noncavity intensity. However,the actual theoretical integrated line intensity is 72times the noncavity line intensity, and the measuredratio cannot be obtained for any reasonable K value.This indicates that although the cavity line envelope isknown the mode width has not yet been correctly pre-dicted.

1.01

F F (T, R)

0.8c

0 MEASUREDDATA

0.60

D (m)

Fig. 7. Computed visibility curves of a resonant cavity spectralline for various values of cavity gain where F is a function of

gain. Points indicated are experimental data.


0.40

K = 0.015K = 0.014K = 0.013K = 0.012

0.20

00 10 20 30D (cm)

Fig. 8. Computed visibility curves of a resonant cavity spectralline for various values of cavity gain where F is a constant of

4000. Points indicated are experimental data.

Modified Cavity ComputationsEquation (8) gives the term F as,

F = 4TR/(1 - TR) 2.

4000, that is, F is not treated as a function of K. It isseen from the figure that a K of 0.014 gives a good fitbetween computed and measured data.

If K is held at a constant value (K = 0.014) and F (Fnot a function of K) is varied it is found that the visi-bility curves do not change by measurable amounts.Although the visibility curves do not change, the inte-grated line intensity does change with change in F value.This is shown plotted in Fig. 9. A value of F = 8 X107 fits the integrated line intensity value betweencavity and noncavity data. Using Eq. (18) and thedefinition of , this implies a mode width of approxi-mately 10 kc/sec.

Limitations in this MethodIt has been shown by Terrien0 that the visibility

curves change very fast with small changes in line shape.This can also be seen to be the case from Figs. 6-8 wherethe visibility curve changes rapidly for small changes inthe parameters K. It will now be shown that the visi-bility curves are quite independent of certain otherparameters. This was indicated above when it wassaid that the visibility curve changes little with thevalue of F when K is held constant. The visibilitycurve does not change measurably if the number ofpeaks is halved, if, for example, a flat plate laser wereused, it is immaterial for the visibility curves if 75 Mc/secor 150 Mc/sec spacing is used and only an error of 2 willresult in the integrated intensity values.20 It might beargued that the interferometer does not possess sufficient

109

(8)

Thus, if T is given by Eq. (16), then F is a wavelength-dependent function. It is the value of F which for aFabry-Perot interferometer determines the resolution ofthe interferometer. It is related to the finesse 5: of theinstrument, that is, the ratio of fringe separation to half-width of the ring and is given by 0

5 = r/2 (F)'/'.lo8

(18)

a as defined by Eqs. (8), (16), and (18) is then a functionof the line intensity, that is, a variable dependent onwavelength. This might indeed be the case, but thereare two other possibilities that might be explored. Thefirst possibility is that the value of 5F might be limited bythe quality of the cavity mirrors and also in our case bythe Brewster-angle windows on the gas cell. Chabballhas shown how this limiting , 5d, depends on the type oferror and the magnitude of these errors. Based on thisanalysis a value of of approximately 100 might be areasonable guess, and has been tried in some of thecomputations. On the other hand, the value of 5: (or F)might well be determined by the gain of the tube and bevery large. It is known, for example, that the individ-ual longitudinal laser modes have extremely narrowline-widths,'" that is, the value of 53 for a laser must beextremely large, perhaps 104 or So.2

Figure 8 shows the computed visibility curves forvarious values of K with F held at constant value of

F

107

06 0.

I _ _ I

_ _ _ *1 =<

5

Fig. 9. Computed value of integrated line intensity ratios vs F.The indicated point is that ratio necessary to match the experi-

mental data.


I X . 21 1.5 2

V (L.) non cavityV ( L) cavity

2.5

2.5

CAVITY

1.C _ _ _

Fz 0 03

/ ~ ~~~-~NON C

-0.040 -0.030 -0.020 -0.010 0 0.010 0.020

A (X)

Fig. 10. Noncavity spectral line shape and theof the individual peaks (modes) of the resonant

line.

envelope curvecavity spectral

resolution to discern peaks at the path differences used.The computer was programmed to give visibility curveto 100 cm. At this distance the visibility is down toapproximately 3 X 10-5, an immeasurably small varia-tion with the author's present equipment. In additionto this, the visibility curve of the envelope of these peakswas calculated. Even at 100 cm path differences, thedifference in visibility curves between the envelope andthe individual peaks is only one part in two hundred.This inability of the Michelson interferometer to discernthe individual peaks is why, if K = 0, a match with theexperimental data cannot be made to the calculatedvisibility curves no matter what value of T is chosen, asthen just a doppler-shaped visibility curve results.Thus, the visibility curve can be used to give a goodindication of the envelope of the peaks but does notnecessarily show any fine structure under the envelope.Figure 10 shows the doppler noncavity line shape andthe envelope of the cavity curve for one set of para-meters. It can be seen that the heights of these curvesdiffer by over 104; however, the integrated values of theactual curves (nonenvelope) are about equal, that is, theindividual modes have very high intensity, but thefrequency band width is very narrow so that there isvery little energy present.'

Extension to a Laser

If the light from a laser is viewed with a Fabry-Perotetalon2 the number of longitudinal lasing modes can becounted; this was done here, and the number of lasingmodes was found to be six. The laser was operating inthe TEMoo transverse mode. If the cavity gain doesnot change appreciably when the lasing threshold isexceeded, then Eq. (15) when suitably truncated wouldpredict the lasing spectral distribution. This cannot bethe actual case, however, since the factor TR must beless than 1 for the equation to hold true. Ignoring thispoint, the visibility curves for a laser with 2, 4, 6, 8, and10 peaks were calculated and are shown in Fig. 11 withthe experimental points. There is excellent agreementwith the experimental points and the six-peak computeddata. These data were computed for a K of 0.014 and an

F of 107 (F not a function of K). It was further foundthat if either K or F are varied over wide ranges there isno measurable change in the visibility function. Thus,the visibility function can predict the number of lasingpeaks but not necessarily a gain function.

Conclusions

(1) The 6328 A neon spectral line of a typical laserdischarge is about 0.02 A in width and is dopplershaped.

(2) The effect of enclosing the discharge tube in alaser cavity with the power level below lasing thresholdis to change the line from a doppler shape to one havinga number of very narrow longitudinal modes.

(3) The envelope of the cavity mode structure is nolonger doppler shaped due to the non linear gain intro-duced by the active medium. This gain is a function ofthe original line intensity. 2 '

(4) The longitudinal mode width is about 10 kc/secfor a mirror reflectivity of 0.98 and a medium trans-mission of 0.014 (TR = 0.9937 at the line center).

Discussion

The derivations or explanations that are given herewere formulated on a classical basis. Even from thedata shown it is obvious that this cannot be strictlyvalid. For example, classical optics predicts for acavity of this type that

= RI'/(1 - R) = 0.98r/(1 - 0.98) 140, (19)

while a lower limiting value as indicated by Chabbal,5 = sf z 100 might be even better. However, the dataindicate that 5f is approximately 104. Another example

1.00

4

6

0.0

8

0.60 10NO. OF PEAKS

3

2

0.40

0 MEASUREDDATA

0.20

0 10 20 31D (cm)

Fig. 11. Computed visibility curves for a laser with variousnumbers of excited longitudinal modes. Points indicated are

experimental data.


I

E

30

is in the visibility curves for the cavity, here the shape isprimarily determined by the first term, T'R/(1 - TR) 2 inEq. (15) and to fit the data it was found necessary tomake T a function of the intensity of the radiation. Athird example is the data shown in Fig. 5 where V isplotted as a function of power input for the cavity andnoncavity spectral line. The fact that the noncavityline visibility is constant indicates that the temperatureand, therefore, any classical Boltzmann-type particledistribution is constant. However, the fact that thecavity visibility changes indicates that the distributionof the number of excited atoms in the upper and loweratomic levels of the 6328 A transition is changing.These three examples show the need for a nonclassicalrather than a classical approach for an explanation ofsome of the phenomena associated with placing anactive medium inside a Fabry-Perot resonant cavityeven when the cavity is in a nonlasing condition.

The author wishes to thank Mary Lynam for pro-gramming, Robert Rector for designing and construct-ing the Michelson interferometer, and Robert Hart, J.T. Massey, and A. G. Schulz for their help and advice.

This work was supported by the Bureau of NavalWeapons, Department of the Navy, under a contract.

References

1. J. T. Massey, A. G. Schulz, B. F. Hochheimer, and S. M.Cannon, J. Appl. Phys. 36, 658 (1965).

2. B. F. Hochheimer and J. T. Massey, Appl. Phys. Lab. Tech.Digest 3, 2 (Jan.-Feb. 1964).

3. D. R. Herriott, J. Opt. Soc. Am. 52, 31 (1962).4. P. Jacquinot, J. Phys. Radium 19, 3, 223 (1958).5. L. D. Vilner, S. G. Rautian, and A. S. Kharkin, Opt. i

Spektroskopiya 12, 937 (1962); Opt. Spectry. 12, 240(1962).

6. J. Terrien, "The Visibility of Two Beam Interference, ItsMeasurement and Its Spectroscopic Interpretation", Natl.Physical Lab. Symp. No. 11 on Interferometry (9-11 June1959).

7. A. A. Michelson, Phil. Mag. 31, 338 (1891).8. A. A. Michelson, Phil. Mag. 34, 280 (1892).9. Lord Rayleigh, Phil. Mag. 34, 4 (1892).

10. M. Born and E. Wolf, Principles of Optics (Pergamon, NewYork, 1959), Sec. 7.5.8.

11. C. Candler, Modern Interferometers (Hilger & Watts, London,1959), Chap. 13, Sec. 10.

12. J. H. Bartlett, Jr., and J. J. Gibbons, Jr., Phys. Rev. 44,538 (1933).

13. G. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 45, 112(1955).

14. G. W. Stroke, J. Opt. Soc. Am. 47, 1097 (1957).15. A. F. Turner, in Radiative Transfer from Solid Materials, H.

Blau and H. Fisher, eds. (Macmillan, New York, 1962).16. P. Jacquinot, Rept. Progr. Phys. 23, 267 (1960).17. S. Tolansky, High Resolution Spectroscopy (Pitman, New

York, 1947).18. R. Chabbal, Research on the Best Conditions for using a

Fabry-Perot Photo-Electric Spectrometer, translated by R. B.Jacobi (No. 778, AERE, Harwell, 1958).

19. A. Javan, E. A. Ballik, and W. L. Bond, J. Opt. Soc. Am.52, 96 (1962).

20. A. L. Bloom, "Properties of Laser Resonators GivingUniphase Wave Fronts", Spectra-Physics Laser Tech. Bull.No. 2 (Aug. 1963).

21. V. N. Smiley, Proc. IEEE 51, 120 (1963).

Meetings Calendar continued from page 40

16-18 Natl. Symp. on Microwave Theory & Techniques,Palo Alto, Calif. IEEE, 345 E. 47th St., New York,N.Y. 10017

31-June 3 16th Ann. Mtg. Soc. of Physical Chemistry, ParisGuy Emschwiller, Societ6 de Chimie Physique, 10rue Vauquelin, Paris 5, France

31-June 4 Ann. Mtg. German Soc. of Applied Optics, Bamberg,K. Rosenhauer, Deutsche Gesellschaft fur angewandteOptik, Bundesallee 100, Braunschweig 33, Germany

June13-17 Soc. for Applied Spectroscopy, 5th Natl. Mtg.,

Sheraton-Chicago Hotel, Chicago J. E. Burroughs,Borg-Warner Corp., Wolf and Algonquin Rds., DesPlaines, Ill. 60018

14-16 Internatl. Material Symp., U. of Calif., BerkeleyT. H. Chenoweth, Hearst Mining Bldg., U. of Calif.,Lawrence Radiation Lab., Berkeley, Calif.

20-24 Internatl. Cong. on Crystal Growth K. J. Button,MIT, Natl. Magnet Lab., Cambridge, Mass.

21-23 Conf. on Precision Electromagnetic Measurements,Boulder J. E. Brockman, NBS, Boulder Labs.,Boulder, Colo. 80301

22-24 2nd Rochester Conf. on Coherence and QuantumOptics, U. of Rochester E. Wolf, Dept. of Physics& Astronomy, U. of Rochester, Rochester, N.Y. 14627

26-July 1 ASTM 69th Ann. Mtg. and 17th Materials TestingExhibit, Chalfonte-Haddon Hall, Atlantic City,N.J.

Internatl. Union of Crystallography, 7th Gen.Assembly and Internatl. Cong., Moscow N. V.Belov, c/o Inst. of Crystallography, Acad. of Sciences,Leninskii Prospekt 59, Moscow B-383, U.S.S.R.

20-21 Symp. on Crystal Growth, Moscow N. V. Belov,cdo Inst. of Crystallography, Acad. of Sciences,Leninskii Prospekt 59, Moscow B-33, U.S.S.R.

August7 Symp. on Solar-Terrestrial Physics, Belgrade, Dejan

Bajic, ETAN/URSI, P.O.B. 356, Belgrade, Yugo-slavia

14-19 Internatl. Cong. of Ophthalmology, Munich E.Weigelin, Inst. fur Experimentelle Ophthalmologie,Bonn, Germany

21-24 Symp. on Free Radicals, Ann Arbor, Michigan. R.C. Elderfield, Dept. of Chemistry, Univ. of Michigan,Ann Arbor, Mich.

22-26 SPIE 11th Ann. Tech. Symp., St. Louis SPIE, P.O.Box 288, Redondo Beach, Calif., 90277.

23-30 Internatl. Conf. on Luminescence, Budapest G.Szigeti, Hungarian Academy of Sciences, P.O.B.Ujpest 1, no. 76, Budapest, Hungary

September? Internatl. Conf. on Magnetic Resonance and Relaxa-

tion, Ljubljana R. Blinc, Nuklearni Institut JozefStefan, Ljubljana, Yugoslavia

5-9 Internatl. Conf. on Semiconductor Physics, TokyoG. M. Hatoyama, Sony Research Lab., 174 Fujit-sukacho, Hodogayaku, Yokohama, Japan

9-13 17th Symp. on Molecular Structure and Spectroscopy,Columbus H. H. Nielsen, Dept. of Physics andAstronomy, Ohio State U., Columbus, Ohio

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120 APPLI ED OPTICS / Vol. 5, No. 1 / January 1966

July12-19

spectrum of a fabry-perot resonant cavity containing an active medium

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