REPORT SSD-TR-90-29 L'

SA •. - ;EROSPACE REPORT NO.

AD-A230 183

Degenerate Four-Wave Mixing of CW HF Laser Bear sin HF Absorption Cell

Prepared by

H. MIRELS, J. G. COFFER, J. M. BERNARD, and R. A. CHODZKOAerophysics LaboratoryLaboratory Operations

DTIC..-:' '-- ,E.,ZTEDEC 20 1990 6 August 1990

Prepared for

SPACE SYSTEMS DIVSIONAIR FORCE SYSTEMS COMMAND

Los Angeles Air Force BaseRO. Box 92960

Los Angeles, CA 90009-2960

Development Group

THE AEROSPACE CORPORATION,-'El Segundo, California

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This report was submitted by The Aerospace Corporation, El Segundo, CA90245-4691, under Contract No. F04701-88-C-0089 with the Space Systems Division, P 0.Box 9296, Los Angeles, CA 90009-2960. It was reviewed and approved for The AerospaceCorporation by R. W Fillers, Director, Aerophysics Laboratory. Captain Rafael Rivierewas the Air Force project officer for the Mission-Oriented Investigation and Experimenta-tion (MOTE) program.

This report has been reviewed by the Public Affairs Office (PAS) and is releasable tothe National Technical Information Service (NTIS). At NTIS, it will be available to the gen-eral public, including foreign nationals.

This technical report has been reviewed and is approved for publication. Publicationof this report does not constitute Ai" Force approval of lihe report's findings or conclusions.It is published only for the exchange and stimulation of ideas.

,

RAIfAEL RIVIERE, CAPT USAF JQATHAN M. EMMES, MAJ, USAFMOlE Project Officer MOlE Program ManagerSSD/CNL AFSTC/WCO OL-AB

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11 TITLE (Include Security Classification)

DEGENERATE FOUR-WAVE MIXING OF CW HF LASER BEAMS IN HF ABSORPTION CELL

12 PERSONAL AUTHOR(S) Mirels, Harold; Coffer, John G.; Bernard. Jay M.; and Chodzko, Richard A.

13a TYPE OF REPORT 13b TIME COVERED 14. DATE OF REPORT fYea, Month, Day) 15 PAGE COUNT

FROM TO 1990 August 6 4716 SUPPLEMENTARY NOTATION

17 COSATI CODES 18 %3. JECT TERMS (Continue on reverse if necessary and identify by block number)

FIELD GROUP SUB-GROUP cw'hydrogen fluoride laser Degenerate four-wave mixing

I IF1ABTATNonlinear ohaetics.gaio

19 ABSTRACT (Continue on reverse if necessary and identify by block number)Phase conjugation of a cw hydrogen fluoride (HF) laser beam has been investigated experimentally andtheoretically using resonant degenerate four-wave mixing (DFWM) in an HF gas absorption cell. A single-line single-mode HF laser. operating on 1;(8), P1(9), or Pl(10transitions, provided total (forward plusbackward) pump beam intensities of 130, (0, and 400 W/,gm respectively, in the HF absorption cel. Aprobe beam intensity of the order of 10 W/O't was also provided. Conjugate reflection of the probe beamwas investigated as a function of gas cell pressure and as a function of frequency detuning from line center.The variation of reflectivity with gas cell pressure at fixed laser beam intensity indicated a peak reflectivityof the order of &,-4 at pressures from 2 to 4 Torr. Measurement of conjugate beam intensity, as a functionof frequency detuning from line center, provided a signal with a full width at half maximum (FWHM) ofabout 30 MHz. The latter is of the order of the homogeneous width, for HF at the test pressure, and maybe compared to the Doppler width i(a = 300 MHz for the medium. An analytical model is presentedwhich provides theoretical estimate. for the variation of reflectivity with pressure. Effects of diffusion, ther-mal conduction, pump depletion, a rid a nonuniform (Gaussian) profile are considered. Theoretical esti-mates for peak reflectivity a wit experiments to within a factor of about 2.

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CONTENTS

I. INTRODUCTION ...................................................... 5

1I . THEORY ............................................................ 7

A. Homogeneous Medium ............................................ 8

B. Inhomogeneous Medium .......................................... 11

C. Pressure Variation Effect in Limit 62 << 1 .................... 12

D. Pump Depletion ................................................ 17

E. Gaussian Profile .............................................. 17

F. Thermal Grating ............................................... 19

III. EXPERIMENTAL APPARATUS AND PROCEDURE .............................. 21

IV. EXPERIMENTAL RESULTS .............................................. 25

A. Detuning Effect ............................................... 25

B. Pressure Variation Effect ..................................... 26

V. CONCLUDING REMARKS ................................................ 31

REFERENCES ............................................................. 33

APPENDIXES ............................................................. A-I

A. SYMBOLS ....................................................... A-I

B. MOLECULAR DATA FOR HF ......................................... B-I

C. DEGENERATE FOUR-WAVE MIXING THEORY ............................ C-I

D. DIFFUSION EFFECT .............................................. D-I

E. THERMAL GRATING .............................. ................ E-I

j Usti f cl tin-------------

/KC I -- - -- .

1 i;jOtlgd IJ I.Y ... .. . ..... ... ..

\. b , :6:,

fI

FIGURES

1. Geometry for DFWM ................................................. 7

2. Grating Formation and Readout in DFWM ............................. 8

3. Variation of Reflectivity with Intensity .......................... 10

•4. Variatio-i of Reflectivity witli Detuning 6 at Fixed It/I ......... 10t s......

5. Variation of Line Center Reflectivity with Pressure ............... 15

6. Comparison of Line Center Reflectivities As ociated with Uniform

and with Gaussian Beam Profiles in Limits a0 L << 1 ................ 20

7. Experimental Apparatus ............................................ 22

8. Effect of Detuning on Conjugate Signal Intensity .................. 25

9. Variation of Line Center Reflectivity with Pressure forFixed Average Intensity It ........................................ 26

TABLES

1. Absorption Coefficient and Saturation Intensity for HF PI(J)Transitions ....................................................... 13

2. Maxima Associated with Variation of Reflectivity with Pressurefor Inhomogeneously Broadened Medium .............................. 16

3. Comparison of Theory and Experiment for pm and (RD)m,p ............ 29

I. INTRODUCTION

Phase conjugation of a cw HF chemical laser beam is of interest for

aberration correction in systems that employ these lasers. Studies of

phase conjulgation of an HF chemical laser beam by means of stimulaLed

Briliouin scattering (SBS) are reported in Refs. 1 and 2. A difficulty

with the SBS approach to HF laser phase conjugation is the need for

megawatt power levels in order to achieve threshold.3 In addition, the

frequency of the conjugate beam is Doppler shifted from the incident

beam. These limitations can be circumvented by employing degenerate four-

wave mixing (DFWM) (e.g., Refs. 4-7). A theoretical study of the

application of DFWM for phase conjugation of a pulsed, multiline HF

chemical laser by use of a homogeneously broadened saturable gain medium is

reported in Ref. 8.

The use of DFWM for phase conjugation of a cw HF chemical laser beam

is investigated analytically and experimentally in this report. Analytic

expressions are deduced for DFWM reflection coefficients associated with a

saturable absorber. Effects of diffusion, heat conduction, pump depletion,

and a Gaussian profile are considered. The experimental study employs a

single-line, single-longitudinal mode ow HF laser operating at 1-10 W and a

gaseous HF absorption cell operating at nominal pressures of 1-10 Torr.

Experimental values of reflection coefficient are reported as a function of

frequency detuning from line center and absorption cell pressure.

Symbols are defined in Appendix A. Spectroscopic and chemical rate

data for HF are given in Appendix B.

5

II. THEORY

The DFWM process is illustrated in Fig. 1. Here, If I b , Ip and Ic

denote the intensity of the forward pump, backward pump, probe, and

conjugate vas, rcspect-ively. The waves are assumed to have the same

frequency and to interact in a saturable medium. The forward and backward

pump waves are required to be phase conjugates. This is easily achieved by

the use of counter-propagating plane waves from a single laser source. The

angle between I and If is denoted 8 and is assumed small in this study.

p If

If I k

-NONLIN

EAR

MEDIUM

P L

Fig. 1. Geometry for DFWM.

The physical basis for the generation of Ic is illustrated in Fig.

2. The interaction between waves Ip and If creates a stationary sinusoidal

interference pattern of wavelength X = A/[2 sin(0/2)] which interactsPfwith the saturable medium to form a sinusoidal variation in medium

susceptibility. The latter scatters the incident beam Ib to form Ic , which

can be shown to be the phase conjugate of Ip. Similarly, Ip and Ib form a

grating of wavelength A = /[2 cos(6/2)] which scatters If to add

7

xpt = X/[2 sin(0l2)]

0 0 0

-lhtXpb X/[2 cos(0/2)] I

Ip .P b Ic

(a) FORMATION (b) READOUT

Fig. 2. Grating Formation and Readout in D.M.

coherently to the phase conjugate I c . For small 6, the gratings XAf and

Apb are termed "wide" and "narrow," respectively.

In the following sections, we sumarize expressions for the reflectiv-

ity R - Ic/I p for both homogeneously and inhomogeneously broadened

saturable media. To simplify the expressions, we assume If = I b , Ip, e <<

and 02 << I. Beam intensity is assumed to be uniform in the tran -

verse direction. The effects of a Gaussian intensity profile, diffusion,

heat conduction, and pump depletion are also considered.

A. HOMOGENEOUS MEDIUM

Reflectivity expressions for a homogeneously broadened saturable

,in the limit pc << fb and 62 << I, are given in Appendix C.

Whten pump depletion effects are negligible and If = I b , the reflectivity

is, from Eq. (C-9b),

62) R - (It/Is)2 [1 + O(aEL)])(1)

(cEL)2 [1 + 2(It/I)] 3

where a term of order aL is neglected and

it f if + Ib (2a)

I = I0(1 + 62) (2b)

6 = (V-VO)/(AVh/2) (2c)

Here, Is is a suitable line center (6 = 0) saturation intensity, Av is the5 hhomogeneous width, u is the length over which the four waves interact,

Eand O is the line center small-signal electric-field absorption

0 Ecoefficient. Expressions for Is , a0 and Avh are given in Appendix B. The

variation of (1 + 6 2)R/(a L)2 with It/Is is indicated in Fig. 3. The

reflectivity has a maximum value given by

27(0 + 62) Rm 'I = 1 (3)(aEL)

2

which occurs at an intensity

It/ s = 1 (4)ts

The variation of R/(ctEL)2 with the detuning parameter 6, for fixed00

It/I , sis indicated in Fig. 4. For each curve, the intensity is a maximum

at 6 = 0. The half width at half maximum (HWHM) of these curves equals

0.51 in the limit It/1 0 0 and increases with increase in It/I.

9

1.0

"0.8 -

'Cj

>: 0.4-

uj0.2U-j

01 2 3 4 5INTENSITY, It/Is

Fig. 3.Variation of Reflectivity with Intensity.

Eq. (1), Et0L (K 1.

1.0 1 1

0.9- 4 .0

0.4,

LU

0.1

*0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

DETUNING, 6

Fig. It. Variation of Reflectivity with Detuning 6 at Fixed

1/0. E

10

B. INHOMOGEAEOUS MEDIUM

The anatysis of degenerate four-wave mixing in an inhomogeneously

broadened medium is complicated by the need to consider particle thermal

velocity dis-ribution-,. It is expected that only particles with velocity

near zero (i.e., within the homogeneous width abost line cer.ter) will be

resonant with all rour wave.-, thereby contributing to the interaction. It

is also expected that the interaction will be similar to thar. for a homo-

gen ously broadened medium with a like number of resonant particles. It

has therefore been suggested 4 that the reflectivity R in an inhomogeneously

broadened mediuim be computed from expressions deduced for a homogenously

broadened medium using appropri ite inhomogeneous medium values for .0 and

is . However, the effect of particle diffusion on reflectivity must be

considered. 'I. - latter is evaluated in Appendix D.

Let RD and R denote estimates for reflectivity which include and ex-

clude, respectively, the effect of diffusion. The results of Appendix D

ind icate

R2 2D 112 + 112 ](:s

I + -rDk 1 + TDkpf Ipb

where the terms involving kpf and kpb represent the contributions of the

wide and narrow gratings, respectively. For an inhomogeneously broadened

medium (i.e., Av h/Av d << 1) and 02 << 1, Eq. (5) becomes

D -1 + 0()2 (6a)

1 + tDk pf

In this limit, the narrow grating is washed out. The wide grating is fully

effective when TDk 2 << I. In this limit RD/R = 1/4. For an inhomogen-pf E

eously broadened medium, 0'- << and a0L << 1, Eqs. (1) and (6a) 'ndicate

R (It/12 i + o(aEL)]. ...- 1 12)] 1 2 (6b)

E 2 [1 2I/) 3 1 2 ~( 0 L)I + Dkpf

Equiat ion (6b) i: mpi i cable to the present experimental study.

11

C. PRE SSRE S VA, IA&' LON LI'FECT IN LIMIT 62 << 1

The variation of reflectivity with cell pressure is of interEst. We

issum,. I- << I. For the present ca-c of a hydrogen fluoride gas at

prossires- oF order 110 Torr, the pressure dependence of 0 arid I can be

ex~rcss:-as

A = p a (7a)

o a2

0 -S'3 K P'- (Tb)

::.,v r~o~cs -o11 pres:re. Theoretical estimates for k and ks are

de. in Appen(ijv B and are listed in Table 1. We write Is/it and u"L inst 0the form

lol =4(plci) (8a)

EL c(p/e (8b)c0

2' t 1/2(8c)

c = k L1 (8d)c1

Sustitstion into Eq. (6b) yields, for 62 << 1,

216R D 27(p/c1 )8 L1 + O(c)]

- -- 2---2- (9a)c [2(p/c 1 ) 2-+ 1]3 L(P/C 1 )2 + B]2

where B is independnt of pressure and is given by

B -p 2 D k /Cl2 (9b)pf 1

12

Table 1. Absorption Coefficient and Sat ration Int-nskty for

HF PI(J) Transitions. k = /p, k I /pax 0 s 3

T J k 3

(K) W

(cm-Torr)

300 7 0.07943 78.52

300 8 0.01897 74.60

300 9 0.00364 71.14

300 10 0.00056 68.03

400 7 0.15308 52.49

400 8 0.05643 49.87

400 9 0.01702 47.55

400 10 0.00436 45.47

500 7 0.21055 38.40

500 8 0.09567 36.49

500 9 0.03786 34.79

500 10 0.01310 33.27

600 7 0.23437 29.75

600 8 0.12508 28.27

600 9 0.05932 26.96

600 10 0.02509 25.78

13

Equation (9a) provid&.3 the variation of RD with pressure and is plotted in

Fig. 5a. The reflectivity RD has a maximum at

p 2 2 1/2(-1h) = (1/2)[1 + B + (1 + lOB + B2) / ] (10a)

whicn, for small and large B, becomes, respectively,

(Pm/ci = 1 + 3B - 6 32 + O(B3 ) (lOb)

= B11 + (3/B) + 0(1/B 2 )] (10c)

The reflectivity maximum is denoted (RD)m, p and is obtained by substitution

of Eq. (10) into Eq. (9). For small and large B,

216 (RD)m ,p . I - 2B + O (B2 ) (11a)

2C

27 B + 0(-I)] (11b)3--2B 2B-B

Equations (8a) and (lob) indicate that at the maximum point, 1/1 0

(1/4)[1 + O(B)]. This result differs from Eq. (3b) due to the variation

of E with p.

Corresponding values of B, pm/cl, (RD)m,p/c2 and (TDk2f =

m2 pfB/(pm/c1) 2 are given in Table 2. These permit theoretical estimates of pm

and (RD)m,p for given values of It , ka, ks , and L. Conversely, c,

ci, k and k- can be deduced from experimental observation of pm and

(RD)m,p for given I. and L. The procedure is most accurate when B << 1.

14

1.0-

B = 0.0

CNJ(J 0.8 --0.2cc- 0.5 c << 1

c 0.6

o..0~0.4-LLJ

LU0.2-

0.00 2 4

PRESSURE, p/c1

(a)

1.0-c = 0.01

* 0.8 0.1- -0.2

.-00.3

0.00

0 .4 -' .Lu

LM"0.2-

0.0 1.0 2.0 3.0 4.0 5.0

PRESSURE, p/c1(b)

Fig. 5. Variation of Line Center Reflectivity with Pressure. (a) Effect ofdiffusion for case where narrow grating is fully washed out and c<< 1, Eq. (9). (b) Effect of pump depletion for case wherediffusion effects are negligible. The degree of pump depletion ischaracterized by the value of the parameter c. Appendix C.

15

Table 2. Maxima Associated with Variation of Reflectivity with Pressurefor Inhomo3geneou,'sly ' Broadened Medium and lf(O) = Ib(L), Ip, C

I f,, , - << 1, - << 1.

(a) Eft'ect of Diffusion As:iuming Negligible Pump Depletion(c<I) and Complete Narrow Grating Washout (t Dkpb >> 1).See Eqs. (9) and (10) and Fig. 5a.

PM C'Pm 16(R D) m, p (rDk 2.m?13(

c2 ft~ ~mcl p

0.000 1.000 1.000 0.0000.100 1.122 0.844 0.0790.200 I.213 0.739 0.1360.300 1.289 0.662 0.1810.400 1.355 o.602 0.2180.500 1.414 0.553 0.2500.600 1.468 0.512 0.278

0.700 1.519 0.478 0.3030.800 1.566 0.448 0.3260.900 1.611 0.423 0.3471.000 1.653 0.400 0.3662.000 2.000 0.263 0.5003.000 2.272 0.198 0.5814.000 2.505 0.159 0.6375.000 2.713 0.133 0.6796.000 2.902 0.115 0.7127.000 3.079 0.101 0.7398.000 3.244 0.090 0.7609.000 3.400 0.081 0.77910.000 3.548 0.074 0.794

(b) Effect or Pump Depletion Assuming Negligible Diffusion.

See Appendix C and Fig. 5b.

Pm 54R , p

0.000 1.000 1.000

0.010 0.985 0.9800.100 0.878 0.8300.200 0.799 0.7110.300 0.7142 0.6230.500 0.662 0.14970.600 0.632 O.4511.000 0.547 0.3253.00() 0.380 0.121

16

In this limit

c = [216(RD ) mp]1/2 (12a)

c1 = Pm (12b)

k [216 (RD ) mp]1 2 /(p mL) (12c)

ks sks = 41t/P 2 (12d)

D. PUMP DEPLETION

In the previous sections it was assumed that the pump beam intensity

did not vary along the optical path. This assumption is consistent with

the assumption ctEL << 1. With increase in aEL, pump depletion, due to

absorption, must be considered. A computation procedure which incorporates

pump depletion is outlined in Appendix C. The variation of reflectivity

with pressure, at fixed-incident pump beam intensity, is indicated in Fig.

5b. Diffusion and detuning effects are neglected. The magnitude of the

pump depletion effect is characterized by the parameter c, which is relatedto aEL. Pump depletion is seen to reduce 54 / 2 and Pm/C. These

maxima are tabulated versus c in Table 2b.

E. GAUSSIAN PROFILE

It has been assumed that each of the beams participating in the DFWM

process has a uniform intensity profile. We now assume that each beam has

a Gaussian profile with a beam waist w. Reflectivity is estimated. We

assume a homogeneously broadened medium and neglect diffusion and detuning.

The Gaussian profiles are expressed

Ic Ip I t -2 (r/w)2

-= P - - =e (13)Ic,O Ip,O It,O

17

where r is the transverse radius, and subscript zero denotes the centerline

value. Let Pt-= Pf + Pb denote the net pump beam power. The latter is

related to It, 0 by

P t I t 'ot t2 (14a)2 2

1TW

I t (14b)

Equation (14b) defines an average net pump intensity denoted I We now

assume that the grating wavelengths Apf and Xpb are small compared with

w. The DFWM process at each radius r may then be assumed to be the same as

that for corresponding uniform beams. The average reflection

coefficient R is then

p f RIpr dr- 0R - (15)

P f I r dr0 p

which can be evaluated using Eq. (1) and Eq. (13). For 62 << 1, the result

can be expressed in the forms

=1 [In(I + 4a) 48(I+68)] (16a)(E L)2 =

_____ '4(+8)0

R 1 [in(1+4) 4 2(+60)i (16b)c 2 64B 2 (1+40)2

where I 2I t c1a 1 (16c)

Equation (16a) gives the variation of R with It at constant p, while Eq.

(16b) gives the variation of R with p at constant It" These may be

compared with the corresponding expressions for a uniform intensity

profile, namely

18

R 3 (17a)(aL)2 1 + 2) 3

andR (17b)c (1 + 26)

where = It/Is* Equations (16) and (17) are plotted in Fig. 6. Equations

(16a) and (16b) have maxima at

27R m27m - = 0.8278 (18a)(a EL) 2

I = 1.106 (18b)

and

54 = - 0.9412 (19a)2

C

Pm/Cl 1.147 (19b)

The right-hand sides of Eqs. (18) and (19) equal I for the corresponding

case of a uniform profile. Thus, the difference between the uniform and

Gaussian beam is relatively small (i.e., of the order of 10 to 20% in the

vicinity of the maximum reflectivity point), provided It is evaluated in

accord with Eq. (14). The symbols RD and RD are used interchangeably in

subsequent sect ions.

F. THERMAL GRATING

Thermal gratings are discussed in Appendix E. It is concluded that

thermal grating effects are negligible in the present study. However, the

increase in mean temperature along the optical axis, due to energy

absorption, affects mean fluid properties such as k and ks (e.g., Table 1)

and thereby affects reflectivity.

19

1.0 -I0UNIFORM PROFILE (R vs I /Is)'

S0.8- "' .8 I" " /GAUSSIAN PROFILE-

0.6

S0.4LUIU-LU 0.2

I0.00 2 4 6 8

(a).o-~~ -_,/ 0

cli 0.8- GAUSSIAN PROFILE

0 '"UNIFORM PROFILE- 0.6

i0.4LU

LU

0.2

0.00 1 2 3 4

PRESSURE, p/c1(b)

Fig. 6. Comparison of Line Center Reflectivities associated with Uniformand with Gaussian Beam Profiles in Limit a0 L << 1. (a) Reflectiv-ity versus intensity. (b) Reflectivity versus pressure.

20

Il[. EXPERIMENTAL APPARATUS AND PROCEDURE

A diagram of the apparatus used in the present experiment is shown in

Fig. 7. A low-power single-line cw HF laser provided two counter-propagat-

ing pump beams and an off-axis probe beam within a 10-cm-long HF absorption

cell. The HF laser had a stable cavity which produced a TEMoo Gaussian

beam in a single longitudinal mode. Power levels up to about 10 W were

obtained on P1 (8), PI(9), and P1 (10) transitions. The Gaussian beam was

focused with a concave mirror (MI) such that the forward pump beam, the

backward pump beam, and the probe beam were all simultaneously focused in

the center of the absorption cell. The interaction distance for the three

beams was greater than the 10-cm absorption cell length. The angle between

the probe beam and the forward pump was approximately I deg to provide good

overlap of the beams and avoid washout of the wide grating. The Gaussian

beam waist (radius) in the cell was 0.55 mm. The phase conjugate return

signal was measured with detector D1, a LN2-cooled HgCdTe detector.

The concave mirror of the HF laser stable-resonator was mounted on a

piezoelectric-driven translation stage (Burleigh Inch Worm) so that the

laser frequency for each PI(J) transition could be adjusted by varying the

cavity length. During the phase conjugation reflectivity measurements, the

frequency of the laser was continuously varied over a 300-MHz range using

the Inch Worm driver. The 300-MHz range corresponds to the free spectral

range of the resonator cavity and is approximately equal to the Doppler

width of the HF absorption line at 300 K. Laser frequency was monitored

with a scanning confocal interferometer using the 1% reflected beam from

beamsplitter BS 0.

A chopper was used on the probe beam so that a lock-in amplifier could

discriminate the small reflected-conjugate signal from scattered cw light

and other noise sources. Beam blocks were inserted in the optical path of

the probe and pump beams to verify that the observed signal was produced by

the interaction of all three beams within the absorbing HF medium. A

removable retroreflector and some removable neutral-density filters were

21

L

0 _w - - -- _ _

LWINDOW CL d WINDOWGAUSSIANPROFILE(all beams) L = 10 cm PHF = 1 - 10 Torr

d = 1.0cm T = 3000 Kw = 0.55 mm0 = 0.017 rad

(a) CELL GEOMETRY

DiCOOLED Fr-"HgCdTe TO0DETECTOR COPR LOCK-IN

REMOVABLE_ . r BEAM AMPLIFIER DIGITALFII TERS *. DUMP OSCILLOSCOPE

PHASECONJUGATE

S 2/-PROBE

CHOPPER --- - - BEAM

S 3 ABSORPTION REMOV,,,, REMOVABLE

CELL PSEUDO-

v A HF GAS CONJUGATE

CONFOCAL TO RETROREFLECTOR

HeNe LASER 0 INTERFEROMETER VACUUM

DETECTO Vi ]PZT LENGTH L H 0

ADJUSTMENT OSCILLOSCOPE

SINGLELINE,SINGLE FREQUENCY (b) ARRANGEMENT

CW HF LASER

Fig. 7. Experimental Apparatus. (a) Cell geometry, (b) Arrangement.

22

used to position the detector at the location of the conjugate return beam,

to calibrate the reflectivity measurement, and to establish reflected

signal-to-noise ratio. Signal-to-noise ratios as high as 60 were

measured. The ratio of reflected signal on line-center to background off

line-center was usually about 5 to 1. In most cases, the difference

between these two signals was used to evaluate the reflected signal when

calculating conjugate reflectivity.

23

IV. EXPERIMENTAL RESULTS

A. DETUNING EFFECT

The variation of conjugate intensity with detuning v-v0 .3 indicated

in Fig. 8. For the present case, the Doppler and homogeneous widths are

Ad 300 - 106 Hz and A h X 106 Hz, respectively. It is seen that

the FWHM (full width at half maximum) of the conjugate signal is of' the

order of Avh. This is expected from physical reasoning because only

particles within the frequency range Avh about line center are resonant

with the three input beams If, Ib , and Ip. These results also support the

present use of a homogeneous theory (with appropriate absorption and

saturation coefficients) to model DFWM in an inhomogeneously broadened

medium.

LLJ

CDI.O

= ,UCD

L_

C/ L 3.0 -

-150 0 +150

-150 0 +150

LASER FREQUENCY DEVIATIONFROM LINE CENTER, MHz

Fig. 8. Effect of Detuning on Conjugate Signal Intensity.

25

B. PRESSURE VARIATION EFFECT

The variation of line Center (6 0 O) reflection coefficient RD with

pressure p is given in Fig. 9 for three transitions P1(8), P1 (9), and

P1 (10) with pump intensities It = 130, CO0, and 400 W/cm2 , respectively.

The maximum reflectivity (RD)ip is of the order of 10- 4 and occurs at

pressures pm from 2 to 4 Torr. The experimental values of (RD)m,p and pm,

deduced from Figs. 9a to 9c, are listed in Table 3c.

Figure 9 include theoretical estimates for the variation of RD with

p. Thesc were obtained using Eq. (9a) with an analytical estimate f-r B

and 4ith arbitrary choices for c and c I . The latter were chosen so that

the experimental and theoretical curves were in agreement at the maximum

point. The shapes of the theoretical and experimental curves are in

approlximat- agreement.

I XPLRIMENIAL DAIA

J=8L]CI - 130 Wlcm

2

X Pm = 16 fou

2 -- 1'4 x (0D6.p 25 -

>_-

/-THEORY, [E (9a)El 0241c = 0277uC-) I=

Lij c 128

,W, 0al:

00 1 2 3 4 5 6

CELL PRESSURE p, Torr(a)

Fig. 9. Variation of Line Center Reflectivity with Cell Pressure for FixedAverage Intensity I Experimental data denoted by squares.

t.Theoretical curves are based on Eq. (9a) using values of c and c I

chosen to match experimental values of [Rn) and pm. (a) Tran-sition P1(8), intensity I t = 130 W/cl . "b5 Transition PI(),intensit I = 600 W/cm . (c) Transition P1 (10), intensity It =400 W/cm

26

5 XF'[RIM[NIAL DATA

CcC

CD E0 20

oc1 2 4 5 36

CELPESUEpIrL(b)

1 _. 0 0X[TET[DT

J = TO

1= 400 Wjcmn2

pm =3 5 Torr

~1.2 THEORY. [0 (9a)

cc: 0

0.010 1 2 3 4 5 6

CELL PRESSURE P, Torr(c)

Fig. 9 (ccncluded)

27

Tanle 3 represents an attempt to compute (RD)m,p and pm from purely

analytical considerations. Table 3a contains estimates for k , ks , C, C1

and B. The latter are based on a temperature T = 300 K and thereby neglect

laser heating. The estimates for (RD)mp and pm in Table 3a are based on

Eq. (9a) and take diffusion into account. Table 3b corrects these

estimates for Gaissian profile and pump depletion effects. The correed

theory in Table 3b agrees with the experiment to within a factor of about

2, except for the value of (RD)m,p for the case J = 10. The poor agreement

for this case is probably due to the present neglect of the induced

temperature rise. (Note, from Table 1 , that the variation of k with T is

greatest for the J = 10 case.)

Tnermocouple measurements near the optical axis indicate temperature

increases of the order 50-100 K due to absorption of laser radiation. The

latter measurements were made by R. M. Kurtz. Further study is needed of

the magnitude of the temperature rise and its effect on reflectivity.

28

a E

Q) - ?-)CE I (\ I L

oc Nx) N t,- c\00

CN m

Q)

CC)Q N f -0-

m CL (a. C AJ

C)Qo LC l

C) -. C 'J C

0 ~ C 0.C ~ C) -

C'D tI a) 000

0 cj " C a

C)) -Lr)

C) -j

Q)) -4 E Lr t-E-1*~~~~1 -C~>, 0 0-'0j.

--T 0~--C C-1 C;CIL 0 0N n

C) 4-- Q0) mx. R'Z -0 C

rt' Q ) 03'oI~ ~00 >)OC) C) CjC -

.0 '- 0 CIO CTW-C--~~~~~ CD 00C -. 'ir)~C

U) w 0 4- -- -r . 04A-) C) C)

>10 0 U) LC ) E0* 70%

0- 0\ C)C) cD,0o C 0' LC)

(D'I ~ ~ ~ ~ ~ U 0k ) 0 0 C E ~ tlL C

00- r100 0) 01) 0 C

V. CONCLUDING REMARKS

The present study may be viewed as a first attempt to investigate

phase conjugation of a cw HF laser beam by use of an HF absorption cell.

Emphasis has been placed on the variation of reflectivity with pressure.

The theoretical development included consideration of diffusion, thermal

conduction, pump depletior and Gaussian profile effects. Further study is

needed, particularly with regard to temperature effects and conjugation

fidelity.

31

REFERENCES

1. Duignan, M. T., Feldman, B. J., Gibson, N. D., and Whitney, W. T.,"Stimulated Brillouin Scattering of Multiline Hydrogen Fluoride LaserRadiation," SPIE Vol 874, 1988, p. 25.

2. Koop, C. G., "Stimulated Brillouin Scattering at 2.9 t," Inter-national Conference on Lasers '88, Harvey's Resort Hotel, Lake Tahoe,Nevada, December 4-9, 1988.

3. Shen, Y. R., The Principles of NoiiLnear Optics, John Wiley & Sons,1984, pp. 187-192.

4. Abrams, R. L. et al., "Phase Conjugation and High-Resolution Spectros-copy by Resonant Degenerate Four-Wave Mixing," in R. A. Fisher, Opti-cal Phase Conjugation, Academic Press, 1983, pp. 211-284.

5. Eaintjes, J. F., Nonlinear Optical Parametric Processes in Liquids andGases, Academic Press, 1984, pp. 377-392.

6. Brown, W. P., "Absorption and Depletion Effects on Degenerate Four-Wave Mixing in Inhomogeneously Broadened Absorbers," J. Opt. Soc. Am.,Vol. 73, No. 5, May 1983, pp. 629-634.

7. Gruneisen, M. T., Gaeta, A. L., and Boyd, R. W., "Exact Theory ofPump-Wave Propagation and its Effect on Degenerate Four-Wave Mixing inSaturable-Absorbing Media," J. Opt. Soc. Am. B, Vol. 2, No. 7, July1985, pp. 1117-1121.

8. Galushkin, M. G., Nikitin V. Yu, and Oraevskii, A. N., "Phase Conjuga-tion of an Optical Wave in the Case of Degenerate Four-Wave Inter-action in an Amplifying Medium of a Chemical HF Laser," Soy. J.Quantum Electron. 18 '1), January 1988, p. 87.

9. Mire! , H., "Inhomogeneous iroacening Effects in cw Chemical Lasers,"AIAA J., Vol. 17, No. 5, May 1979, p. 478.

10. Mirels, H., "Effects of Translational and Rotational Nonequilibrium oncw Chemical Laser Performance," Appl. Opt., Vol. 27, No. 1, 1 January1988, p. 89.

11. Svehla, R. A., "Estimated Viscosities and Thermal Conductivities ofGases at High Temperatures," NASA Technical Report, R-132, 1962.

12. Zel'dovich, B. Ya., Pilipetsky, N. F., and Shkunov, V.V., "Principlesof Phase Conjugation," Springer-Verlag, Berlin, 1985, pp. 176-184.

33

13. Caro, R. G., and Gower, M. C., "Phase Conjugation by Degenerate FourWave Mixing in Absorbing Media," IEEE J. Quantum Electron., Vol. QE-18, No. 9, September 1987, p. 1376.

34

APPENDIX A

SYMBOLS

B parameter characterizing diffusion effect, Eq. (9b)

c k Lc1

ci 2(1 t/k )/2

D diffusion coefficient Eq. (D-i)

k wave number of incident waves

kij wave number associated with Ei + c. waves

k absorption coefficient parameter, Eq. (7a)

ks saturation intensity parameter, Eq. (7b)

I intensity

It sum of pump wave intensities, If + IbIS, I0 saturation intensity, Eq. (2b)

L length of cell

PI(J) P-branch transition from v = 0, J to v = 1, J-1

Pt net power in Gaussian profile pump waves, Pf + Pb

p cell pressure

r transverse radius

R reflection coefficient in absence of diffusion, Ic/I p

RD reflection coefficient in presence of diffusion, Ic/I p

(RD)m,p reflectivity maximum associated with pressure variation, Eq. (11)

T temperature

w Gaussian profile beam waist, Eq. (13)

a electric field absorption coefficient at low powerEa E line center value of a6 detuning, (v-v )/(h/2)

E. iith electric field, Eq. (C-2a)

a angle between Ip and If

A wavelength of incident waves

ij wavelength associated with ci and e. waves

v frequency of incident waves, s

A-I

V 0 line center frequency of resonant absorber

AVd Doppler width (FWHM)

AVh homogeneous width (FWHM) of resonant absorber, Eq. (B-2)

Subscripts

T lifetime of upper level

W frequency of incident waves, rad/s

6 detuning parameter, Eq. (2c)

f,b,p,c refers to forward pump, backward pump, probe,and conjugatewaves, respectively.

i refers to ith wave

j refers to jth wave

ij refers to combination of ith and jth waves

m associated with maximum point

Superscript

(-) vector quantity or average value

A-2

APPENDIX B

MOLECULAR DATA FOR HF

Notation: Dimensions used herein are PHF (Torr), T(K), A(cm), E (cm-1)

,J(s- ) k (cm- Torr-) k (W cm-2 Torr- 2 ), I (W cm

- 2)

cv.s s

Doppler Width (FWHM):

AV d ---0-- (B-1)

where A is in centimeters.

Homogeneous Width (FWHM):

Avh 1.5 x 107 (300)112 H (B-2)h T - PHF

Equation (B-2) is based on a mean value for HF-HF collisions.9

Absorption Coefficient:9

E 2.13 x 10 1 (1 + v - O.01v)(1 + O.063J)J0 T3 / 2 exp[J(J + 1)TR/fT- (B-3a)

S[n v - n v+e 2JTR/Ti

where TR = 30.16 K for HF. Equation (B-3a) assumes an inhomogeneously

broadened medium in the limit Av h/Av d << 1 and applies for laser P-branch

transitions

v, J + v + 1, J-1 (B-3b)

B-I

where v,J denote the vibrational and rotational energy level of the

absorbing particle. An alternate notation for the P-branch transition is

Pv (J). -The quantities nv and nv I denote number density, in moles/cm3 ,

of particles in the lower and upper vibrational level, respectively. At

room temperature, under nonlasing conditions, nv+i/n v << I and Eq. (B-3a)

becomes

atE 6 + - 3 +O03)

k - 0 3.42 x 10 (1 v 0.01v3W + O.063J)J (B-3c)ot - / expT-CY+ifT[(-c

PHF T5 / 2 R

where the equation of state nv = 1.603 - 10-5 PHF/T has been used. Values

of k are listed in Table 1.

Wavelength for PI(J) Transition:

10 4A = 2.7441; 2.7826; 2.8231; 2.8657 (B-4)

J = 7; 8; 9; 10

Saturation Intensity:

A definition of saturation intensity, consistent with Eq. (D-1), is

i0 1 2 (B-5a)s - sPHF

5 t(O/E vJ

where I0 is line center saturation intensity, T is mean particle collisions

time (i.e., upper level lifetime), and

(Q) _ 3.79 x 1013 J(1 + 0.063J)(1 + v - 0.01v 3 ) cm2

vJ T2Avh (2J + 1) j-

B-2

is the cross section for photon absorption.1 Substitution into Eq. (B-5a)

indicates, by Use of Eq. (B-11),

k= 52.79. (2J + 1), (300/T) 1.14 3(-

JO1 + 0.063J)(1 + v - 0.01v3)(-c

Values of ksare listed in Table 1.

Gas Properties:

Density

p = 1.069 x 10- 6 PHF(300/T) g/cm3 (B-6)

Index of refraction

n-i1 = 5.0 x 10-7 P HF(300/T) (B-7a)

An *, 9B72

A T = (-1) 1. 0 P HF (300/T) (-b

Specific heats

cp= 1.146 J/(g-K) (B-Ba)

Y = c I c v= 1.4 (B-8b)

Mean particle spread v and sound speed a

1/2 A-vd11i2)'2 (-V=[8/(Y7T)] a = vd(7n)B-a

= 5.64 x 10 4(/0) 12 cm/s (B-9b)

Mean free path

B-3

4.17 x 10-3 T 1.4-_ 20 (-) cm (B-10)

0.499 pv PHF

Mean collision time

Z 740 1-8 (T0.9

v PHF T0 *9 s (B-11)

Comparison of Eqs. (B-2) and (B-11) indicates AVhT = 3.5. The latter

expression equals 1 for a simple billiard ball model.

Transport properties :11

Viscosity

4 T 0.9 _1.25 x 10- 3 cms (B-12)

Thermal conductivity

k 2.64 104 0.9 j (B-13)

T 00) cm-s-K

Diffusion coefficient

D - 1.33P 1.56 x 10 2 (T/300) 1" 9 cm2. .56. (B-114)P PHF s

Grating washout parameter for 02 << 1,

2 168 T 2.8 2.8 4 2 (B-15)TDkf p 2 3 0.017 A

PHF

B-4

APPENDIX C

DEGENERATE FOUR-WAVE MIXING THEORY

Expressions are derived that define reflection coefficients associated

with four-wave mixing in a homogeneously broadened medium. The

configuration of Fig. 1 is assumed with e2 << I and Ip c << If, b Pump

depletion effects are included.

The electric susceptibility of a homogeneously broadened medium is

x - 2i(I - i6) a(C-a)X = - k f _+ VTfs- C- a

where

6 (V - VO)/[Ah/2] (C-Ib)

= /(0 + 6 ) (C-ic)0

I0(1 + 62) (C-id)

E.Here a0 is the low-power electric-field absorption coefficient evaluated at

0 0line center, Is is saturation intensiti, and I is the line centerS S

saturation intensity [e.g., Eq. (B-5a)]. Other symbols are defined in

Appendix A.

Components of the electric field are expressed in the form

= ie + c.c.] (C-2a)

where

Ei /E s A AizWe-ik'z (C-2b)

C-1

and Es (21s/cc)1 1 2 is the electric field associated with the saturation

intensity Is . The net local intensity I is then

2I E 1 * - z (C-3a)lv i = A.A.e ij (-aTs sT- ijF i Aj e

where

k.. k- . (C-3b)ij 1 j

IkijI =- k ij =27r/Xij (C-3c)

Here i and j each take on the values f, b, p, and c. For i j, Eq. (C-3)

defines interference terms. The wavelengths of the wide and narrow

gratings in Fig. 2 are then, respectively,

pf - k ______

A kf 2 sin (-0/2) (C-14a)pi

pb k (C-4b)

A k = 2cos Ce /2pb

Substitution of Eqs. (C-la) and (C-3a) into the electromagnetic wave

equation yields, 4- 7 for Epc << Ef,b,

dAfdz f - fAf

(C-5a)dz f f

dAb bA (C-5b)

dA bdzp - pA + KA

(C-5c)dz p p (C5c

dA ,d-- a mpA c - KA p (C-5d)

C-2

where

1 A 2 A 2

Ot ~ l-W [I + - (I - f- b- -)~f,b (1i) q 2A 2qf,b

2+2

cc (Ot - ot + OP 3PH PI

2A A)

q3

[q + 2(A 2 + A2 + A2 A2) 1/2

22

The boundary conditions at z = 0 and z =L are

Af (0) =GIVEN A P(0) = GIVEN (C-6a)

A b(L) = GIVEN A (LM) = 0 (C-6b)

Equations (C-5c) and (C-5d) can be combined to yield an expression for the

ratio r(z) 7A c/Ap , namely,

djr t K -* r2 -adz ~pr (C-a

r(L) =0 (C-7b)

where r (0) defines the reflection coefficient. Equation (C-7) is now inte-

grated for the cases of zero and nonzero pump depletion.

C-3

(a) Zero Pump Depletion (aL << 1)

If pump depletion effects are neglected, the coefficients in Eq. (7a)

are independent of z and Eq. (7a) can be integrated to yield

R Ir(O)l2 pR +w cot w(C1,(C

where

W2 _ a 2 (C-8b)

Note that R = Ic(O)/Ip(O) is the intensity reflection coefficient for the

four-wave mixing process. In the limit aL << 1, which is consistent with

the neglect of pump depletion, Eq. (Sa) becomes

= JKLJ 2 [I + O(cIpRL)] (C-9a)

or, equivalently,

(I /s )2 ( - d 2 ) [I + O(pR L)](1 + 2 R t 22 (C-9b)

(a0 L)2 [ + 2 (It/I S ) + (It/I )2d2 ]3

where It = If + Iby and d = if - Ibl/It. The case d = 0, apRL - E L is

considered in Eq. (1).

(b) Nonzero Pump Depletion [EaL = 0(l)]

In the case of nonzero pump depletion, it is con .--nient to write Eqs.

(C-5a) and (C-5b) in the form

d(If/I S ) If

dz = -2cfR I (C-10a)

S

C-Li

d(Ib /1 b (C-b)

dz bR ClS

where

If(O)/I s = GIVEN (C-10c)

Ib(L)/I s = GIVEN (C-10d)

Here afR and abR are the real parts of af and a b respectively. The re-

flectivity r(O) is found by integrating Eqs. (C-7) and (C-l0) in the inter-

val 0 S z L. The latter is a two-point boundary value problem which can

be reduced to a one-point boundary value problem by evaluating If(L)/Is

analytically and integrating from z = L to z = a. When If(O) = Ib(L), the

analytic solution for If(L)/I s is found from (e.g., Ref. 7)

D _[I + ED2 + 2(0 + K)]112

DI [2(1 + K)]1/2

where

K = S - (D2 + 2S + 1)1/2

S = [Ib(L) + If(L)]/Is

D = [Ib(L) - If(L)]/I s

Equation (C-11) applies for gain as well as absorption. Numerical results

for the variation of R with pressure, for a fixed pump intensity, are given

in Fig. 5b. Pump depletion effects increase with increase in the parameterE.

c, which is related to a L. Maxima, from Fig. 5b, are listed in Table 2b.

C-5

APPENDIX D

DIFFUSION EFFECT

Particle diffusion reduces the effectiveness of the gratings induced

by the four-wave mixing process.1 2 The diffusion effect is estimated

herein.

We first consider a homogeneously broadened medium. Let nI and n2

denote particle number density in the lower and upper laser energy

levels. For weak saturation, n2 << n1 , the variation of n2 with time is

given by

3n2 n2 n1 IE12 V2=- - + - + (D-1)at T r

s

where -r is n2 particle lifetime and D is the diffusion coefficient. For

the case of multiple electric fields given by Eq. (C-3a), the steady state

solution of Eq. (D-1) is,

1 A.A.n2 1 . 2 -ik.z (D-2)1 i j 1 + k ij

Each term in Eq. (D-2), for i j, corresponds to an interference

grating. The effect of diffusion is to reduce the amplitude of each2 -1

grating by the factor (1 + TDk. j)_. The reflectivity coefficient R given

in Eq. (C-8a) is the result of two gratings with amplitudes proportional

to AfAp and AbAp, respectively. Let R and RD denote estimates of

reflectivity which exclude and include the effect of diffusion,

respectively. It follows that

RD ( 1/ 2 1/2 2)2 (D-3)

1 + 1 Dk 2 + TDk 2pf pb

where the terms involving kpf and kpb correspond to the wide and narrow

gratings, respectively, in Fig. 2.

D-1

Equations (D-1) and (D-3) apply to an inhomogeneously broadened medium

for cases where 6 < 1 (i.e., for cases where the laser radiation interacts

with particles which have low thermal velocity.) In these cases, T is the

mean particle collision time. It can be shown from expressions in Appendix2 2

B that TDk - (AVd/ vh) . It follows that22

2 AVd2tDkpf - () (2 sin (D-4a)

AVh 22

2 Aos 2 2

rDkPb Avh ( cos (D-'4b)

For an inhomogeneously broadened medium, Avh << V d the narrow grating is

always washed out (i.e., Dkb >> 1). The wide grating will be fully2 py

effective (i.e., -rDk f << 1) when

(OAvd/AVh)2 << 1 (D-5)

In the latter case, the right-hand side of Eq. (D-3) is equal to 1/4.

Equation (D-5) indicates the need for small e when AVd /A h is large.

D-2

APPENDIX E

THERMAL GRATING

In the present experiment, laser energy continuously heats the absorb-

ing medium. After an initial transient, an elevated steady-state tempera-

ture distribution is established along the optical axis. This steady state

temperature has an average value such that heat loss by radial conduction

and by convection equals the energy input. The increase in average temper-

ature, due to laser heating, appears to be of the order of 100 K in the

present experiments. In addition, there are small periodic variations in

temperature associated with each of the standing waves established by the

four-wave mixing process. The corresponding refractive index variations

constitute thermal gratings which are similar to the saturation-induced

gratings discussed in Appendix C. The reflectivity associated with the

thermal gratings is deduced herein.

The net heat addition per unit volume, per unit time, due to laser

radiation, is given byS.. i2tI - oI s A A A.Aie ij-z (E-1)

3i j iJ

The equation for conservation of energy becomes

is * i -iki3. z - T kT2 TI " = PC - + q - 2 (E-2)

where q is the local energy loss per unit volume, per unit time, due to

radial conduction and convection, and kT is the thermal conductivity coef-

ficient. Under steady state conditions, the solution of Eq. (E-2) is, for

i j,

q tI5 A2 - 2a I. (E-3a)a i L

and for i j

E-1

I A.A. -AT.. s i j e j (E-3b)

1j k k2

T ij

The average temperature along the optical axis is the value for which rad-

ial conduction and convection permit Eq. (E-3a) to be satisfied. The quan-

tity AT.. in Eq. (E-3b) is the temperature perturbation associated withl the

grating defined by k..y j

Denote the local index of refraction by n = no + An where An denotes

the perturbation due to AT. The electric susceptibility is then2

X =n 2-1

- (n2 _ 1) + 2n0 A z AT.. (E-4)

Substitution into the wave equation yields

dA * (E-5a)

dz c

dAc -KA (E-5b)

dz pwhe re

2

2ikv An I /2 (1+ (E-5c)k k2 AT (Iflb) b i k b (f

T pf

Note that /k 2 = tan2(0/2) so that this term (i.e., contribution of thepf pb

narrow grating) can be neglected in Eq. (E-5c). Comparison with Eqs. (C-5)

and (C-8) indicates that the reflectivity associated with the thermal grat-

ing is

Rth = tan2 I L (E-6)

Thermal gratings induced by a pulsed laser, with pulse length T and neglig-

ible conduction, have been investigated. 13 The present results agree with

those in Ref. 13 if (k k2 )1 is replaced by t/pc in Eq. (E-5c). ThisT pb p

equivalence can be deduced directly from Eq. (E-2).

E-2

Evaluation of Eq. (E-6) for typical conditions of the present experi-

ment indicates Rt' - 10 . The reflectivity associated with saturation is

of order R - 10 - . Hence, thermal gratings play no role in the present

experiment. However, the increase in mean temperature along the optical

axis does affect fluid property values and thereby affects the performance

of the saturation gratings.

E-3

LABORATORY OPERATIONS

The Aerospace Corporation functions as an "architect-engineer" for national securityprojects, specializing in advanced military space systems. Providing research support, thecorporation's Laboratory Operations conducts experimeatal and theoretical investigations thatfocus on the application of scientific and technical advances to such systems. Vital to the successof these investigations is the technical staff's wide-ranging expertise and its ability to stay currentwith new developments. This expertise is enhanced by a research program aimed at dealing withthe many problems associated with rapidly evolving space systems. Contributing their capabilitiesto the research effort are these individual laboratories:

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