1726 J. Opt. Soc. Am. B/Vol. 9, No. 9/September 1992

Phase conjugation by stimulated photorefractive scatteringusing a retroreflected seeding beam

Ruth Ann Mullen, Deborah J. Vickers,* Linda West, and David M. Pepper

Hughes Research Laboratories, 3011 Malibu Canyon Road, Malibu, California 90265

Received April 8, 1991; revised manuscript received December 17, 1991

The threshold for self-pumped optical phase conjugation by means of backward stimulated photorefractive scat-tering has been dramatically lowered by inserting a retroreflecting screen into the path of the beam after thebeam leaves a BaTiO3 crystal. Stable ref lectivities of as much as -60% and good phase-conjugate fidelity havebeen demonstrated in a crystal that has too low a gain-length product to exhibit unseeded backward stimulatedscattering. Precise control of the threshold for stimulated scattering is demonstrated by adjusting the seed in-tensity. Reflectivity and fidelity are experimentally characterized at 515 nm as a function of the following pa-rameters: pump and seed intensities, crystal angle with respect to the incident beam direction, crystalinteraction length, crystal-lens separation, and aberration strength. Operation at 633, 730-800, and 839 nmis demonstrated also.

1. INTRODUCTION

Self-pumped phase conjugation by means of stimulatedscattering processes has been the topic of intense researchand advanced technology development dating back to thepioneering investigations begun in 1972 by Zel'dovich andco-workers,' in which stimulated Brillouin scattering wasused as the nonlinear process. Since that time the inves-tigation of wave-front reversal has continued2 for othertypes of stimulated scattering processes, such as Ramanand Rayleigh-wing scattering, with solids, liquids, andgases in bulk and waveguide geometries. Recently, back-ward stimulated photorefractive scattering was seen toproduce phase-conjugate waves34 in some particularlyhigh-gain crystals. Here we present, for the first time toour knowledge, a backseeding technique that dramaticallylowers the gain-length product threshold requirement forbackward stimulated photorefractive scattering, makingit possible for the process to occur in crystals that wouldnot exhibit this effect in the absence of the seed. Thismethod, that of using a retroreflecting screen in conjunc-tion with a photorefractive crystal of BaTiO3, produces ahigh-fidelity phase-conjugate wave and lends itself to asimple and effective means for controlling the conjugationthreshold. Temporally stable phase-conjugate reflectivi-ties of as much as 60% have been observed, leading to thepossibility of practical devices and applications.5

Since stimulated photorefractive scattering builds upfrom noise, the required gain threshold can, in principle,be reduced by injecting noise in the backward direction(Fig. 1); this technique is referred to as a seeded process.This approach was used with some success in stimulatedBrillouin scattering interactions,6'7 with the trade-off be-ing print-through of the injected beam, which can degradethe fidelity of the conjugate wave. In that study, a secondstimulated Brillouin scattering cell was required for gen-eration of the required Stokes-shifted seed beam. Sincethe Stokes shift in the photorefractive interaction hasbeen measured to be negligibly small (<1 Hz in Ref. 3 and

<0.1 Hz in Ref. 4) and may equal zero, scattered un-shifted photons are able to provide the necessary seed.

Previous observations of phase conjugation by backwardstimulated photorefractive scattering in BaTiO3 have beenrare because most available crystals have too low a back-ward gain, are too short, or contain too few optically scat-tering defects to exhibit an above-threshold gain-lengthproduct. In the first observation of backward stimulatedphotorefractive scattering phase conjugation, by Changand Hellwarth,3 a 5.2 mm X 6.3 mm X 6.7 mm crystalgrown commercially from a top-seeded solution of TiO2and BaO was used, and reflectivities of -10% were re-ported. Mamaev and Shkunov4 reported backward stimu-lated photorefractive scattering phase conjugation with a0.7-mm-thick, high-trap-density, butterfly-wing plateletsample of BaTiO 3 grown by slow cooling of a BaTiO 3-and-KF solution. In these demonstrations, the nature of theseed was internal either to the crystal3 4 or to the glasswall of the cuvette containing the crystal and the index-matching oil.3

Seeded backward gratings may have played a role in theobservations8 of unstable and chaotic self-pumped phaseconjugation in BaTiO3 crystals coated on both c faces withperfectly diffuse white paint in one experiment and withsilver paint in another.

Here we describe a detailed experimental investigationof backseeded stimulated photorefractive scattering phaseconjugation with a simple, yet controllable, external seed.The seed beam is generated by placing a retroreflectingscreen downstream from the exit face of the crystal. Thescreen accurately and efficiently redirects the exitingbeam back into the crystal, producing a higher-intensityseed than would be generated by internal crystal defectsalone. The retroreflected seed overlaps more preciselywith the forward-going beam than would light scatteredfrom randomly arranged defects inside the bulk of thecrystal. The excellent retroreflecting properties of arrayssuch as these have led them to be referred to as pseudo-conjugators.9 At the same time, since adjacent retrore-

0740-3224/92/091726-09$05.00 © 1992 Optical Society of America

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Vol. 9, No. 9/September 1992/J. Opt. Soc. Am. B 1727

(a)

(b)

(c)

(g)

Fig. 1. Physical mechanisms for (a)-(c), forward and (d)-(g)backward stimulated photorefractive scattering when (a)-(f) theseed is intrinsic to the crystal and g, when a retroreflecting arrayis used to backinject a strong seed into the crystal from the out-side. (a) Fresnel refraction and anisotropic light scattering offcrystal inhomogeneities. (b) Formation of photorefractive grat-ings for forward scattering; gratings oriented as shown havehigher two-wave mixing gain coefficients than differentlyoriented gratings. (c) Forward stimulated photorefractive scat-tering, or beam fanning. (d) Anisotropic light scattering offcrystal inhomogeneities. (e) Formation of a high-gain photore-fractive grating for backward scattering. (f) Formation of ahigh-reflectivity phase-conjugate wave when the gain-lengthproduct is above threshold. (g) Backinjection of a seed beam by aretroreflecting array external to the crystal reduces the gain-length product requirement for backward stimulated photorefrac-tive scattering.

flecting elements in these screens have arbitrary phaserelationships relative to one another, the seed generatedby these arrays advantageously contains more spatial noise.These and other properties, such as their high ref lectivi-ties, insensitivity to tilt, large fields of view, and the goodpolarization preservation of the lenslet-array screens, re-sult in a robust and easy-to-use system.

Using this system, we find that the conjugation thresh-old can be easily controlled and that the phase-conjugatefidelity is good. Another key result of our study is thatcrystals having too low a gain-length product to exhibitbackward stimulated photorefractive scattering in the ab-sence of the external seed can readily be made to operateabove threshold in the presence of the seed.

2. THEORETICAL BACKGROUND

While a detailed theoretical treatment of backward stimu-lated photorefractive scattering including the important

effects of pump depletion and transverse spatiotemporalbeam dynamics has not yet been developed, a qualitativedescription of the effect is presented in Fig. 1. Thisfigure illustrates the distinctions between forward andbackward stimulated photorefractive scattering and dif-ferentiates between backward stimulated photorefractivescattering that is seeded by optical inhomogeneities in thecrystal bulk3 and that seeded by an external retroreflector.

Figures 1(a)-1(c) illustrate the evolution of forwardstimulated photorefractive scattering (beam fanning"),which occurs first, and Figs. 1(d)-1(g) illustrate the evolu-tion of backward stimulated photorefractive scattering inboth the absence [Figs. 1(d)-1(f)] and the presence[Fig. 1(g)] of an externally back-injected seed. InFigs. 1(a)-1(c) the beam enters the crystal by ordinary(linear) Fresnel refraction [Fig. 1(a)] before bending to-ward the c axis by forward stimulated photorefractivescattering. This bending occurs as the result of two-beam coupling between the forward-going pump beam andlight scattered isotropically from crystal inhomogeneitieseither in the bulk of the crystal, as shown in Figs. 1(b) and1(c), or at the crystal's surface owing to imperfect polish-ing. For crystals in which the dominant charge carriersare holes, the beam bends in the direction of the positivec axis.

Figures 1(d)-1(f) illustrate the subsequent evolution ofoptical phase conjugation by backward stimulated pho-torefractive scattering without any external seed. Again,crystal inhomogeneities scatter the incoming pump-beamlight in all directions [Fig. 1(d)]. Light that is scatteredbackward and overlaps well with the forward-going pumpbeam forms an intensity interference pattern that writesa photorefractive grating in the index of refraction. Thisgrating is automatically aligned to diffract still more lightin the backward direction [Fig. 1(e)]. The two-beam cou-pling gain for this small-period grating is positive in thedirection opposite that of the +c axis'0"2 ; hence the scat-tered light is amplified in the backward direction. Thisincreases the modulation depth of the index-of-refractiongrating until diffractive scattering from this grating isgreater than the isotropic scattering from the initiatingcrystal inhomogeneities. This is the threshold for back-ward stimulated photorefractive scattering phase conjuga-tion. As the grating modulation depth continues toincrease [Fig. 1(f)], high phase-conjugate ref lectivities oc-cur in the steady state.

Here we show that crystals with gain-length productsbelow the stimulated photorefractive scattering thresholdrequirement can be made to exhibit stimulated photore-fractive scattering when a backinjected seed beam[Fig. 1(g)] is used to lower the threshold.

Excellent theoretical treatments of backward stimu-lated photorefractive scattering, but without pump deple-tion and without full consideration of the transverse beamprofile dynamics, were performed by other authors. 4 "3 '5

Chang and Hellwarth3 were the first to point out the closeanalogy between backward stimulated photorefractivescattering and backward stimulated Brillouin scattering.Mamaev and Shkunov's4,14 experiments and theory high-lighted two important distinctions between backwardstimulated photorefractive scattering and backward stimu-lated Brillouin scattering: (1) that photorefractive risetimes, unlike Brillouin rise times, are inversely dependent

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1728 J. Opt. Soc. Am. B/Vol. 9, No. 9/September 1992

on the local optical intensity and (2) that photorefractivetwo-wave mixing gains are independent of intensity forintensities higher than the equivalent dark intensity. Fora recent theoretical treatment of the time evolution ofbackward stimulated photorefractive scattering, the readeris referred to a paper by Valley5 that presents numericalsimulations of several important features of the back-seeded experiments to be described below. It is hopedthat the experimental results described below will stimu-late future theoretical investigations to include both pumpdepletion and the complete transverse beam dynamics.

3. EXPERIMENTAL APPARATUS

The effectiveness of using a retroreflecting array as theseed to lower the threshold for backward SPS was demon-strated with the experimental apparatus shown in Fig. 2.The argon-ion laser was isolated from the experiment, andits intensity was controlled with a half-wave plate and apolarizing beam splitter. The polarization was rotated tobe in the plane of the crystal's c axis (horizontal, or p po-larized). Optical powers incident upon the crystal rangedfrom 30 to 100 mW with incident beam diameters rangingfrom a few hundred micrometers to 5 mm. Initially, andfor the top-view photographs described below, no spatialfilter or beam expander (collimating spatial filter shownin Fig. 2) was used; in this case the single-longitudinal-mode 515-nm argon-ion laser beam contained enoughhigh-order spatial modes to produce high reflectivity andstable seeded stimulated photorefractive scattering with-out any additional aberrators.

The beam expander, spatial filter, and aberrator wereinserted for measurement of the image resolution and thefidelity of the power through the pinhole. The crystalwas grown at Hughes Research Laboratories and was a50-parts-in-10 6 BaTiO3 Co sample' 6 of dimensions9.2 mm X 6.4 mm X 5.9 mm, with its longest dimensionalong the c axis. The crystal was immersed in index-matching fluid (n = 1.57, compared with n - 2.4 forBaTiO3 and n = 1.5 for the glass wall of the cuvette) andoriented as shown in Figs. 2 and 3. The experimentswere performed with a lenslet-array retroreflectingscreen manufactured by 3M, special-effects projectionscreen 7615, which has a retroreflective accuracy' 7 of-1/2°. Several other retroreflecting arrays, of both the

lenslet-array (3M 7610, 3M Scotchlite 510-10, and 3MScotchlite 3290) and the corner-cube-array (ReflexiteAC/1000P, AC/1OO0M, and AC/1000) varieties, demon-strated similar performances as seeds for backward stim-ulated photorefractive scattering.

The performance of the stimulated photorefractive scat-tering conjugator seeded by the retroreflecting screen wascompared with backward stimulated photorefractive scat-tering in the same crystal seeded by a Lambertian (per-fectly diffuse) scatterer by replacing the retroreflectingscreen with a screen painted with barium sulfate.

The amplitude or image fidelity of the phase-conjugatebeam was evaluated by inserting a U.S. Air Force resolu-tion chart into the expanded beam path with the setupshown in Fig. 2. The phase-conjugate image of this chartwas photographed after the beam transmitted through thechart had double-passed an aberrator by reflection fromthe phase-conjugate mirror. The photographs (repro-

duced in Fig. 4) were taken with a camera placed at theimage plane of lens L2 in Fig. 2 (the pinhole and the detec-tor shown in the figure were removed).

Fidelity measurements were made by choosing a pinholediameter large enough to capture approximately half ofthe incident laser power. Our best quantitative referencefor how our measured fidelities compare with the perfectphase-conjugate fidelity associated with an incident planewave, no aberrator, and a perfectly flat mirror was ob-tained by replacing the phase-conjugate mirror with a flatmirror (positioned either just upsteam from lens L orprecisely at the focus of L,) and using the resulting powerthrough the pinhole as a reference (see Fig. 6 below andthe accompanying text).

The effect of seed attenuation was parameterized byplacing neutral-density filters between the crystal and theretroreflecting screen. To measure the effect of crystalinteraction length on phase-conjugate reflectivities andfidelities, we moved the crystal transversely to the inci-dent beam direction in the plane of the table.

For parameterization of the effect of the lens-crystalseparation on the phase-conjugate reflectivity, the crystalwas positioned over a wide range of crystal-lens separa-tions on both sides of lens L,'s focal point.

Two different aberrators were used in these experi-ments. The initial experiments involving resolutioncharts were performed with a relatively mild aberrator, aglass slide that had been etched in hydrofluoric acid.When sampled with a 1-cm-diameter beam, this aberratorresulted in a 1.3-times-diffraction-limited beam, as mea-sured at the focus of lens L2 shown in Fig. 2. We foundthat the fidelity of the stimulated photorefractive scatter-ing conjugator was sufficiently high that a more severeaberrator was a better test of its performance. The restof our experiments were performed with a 3.7-times-diffraction-limited aberrator.

4. OPERATION AT 515 nm, BEAM ENTERINGAN a FACEIn this section we present our main experimental resultsand relevant physical interpretations.

CUVElTE MIRROR

Fig. 2. Experimental apparatus: L, lens of focal length fi; L 2,lens of focal length f2; A/2, half-wave plate; PBS, polarizing beamsplitter; AFRC, U.S. Air Force resolution chart; N D, neutral-density. The laser is polarized in the plane of the c axis.

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Vol. 9, No. 9/September 1992/J. Opt. Soc. Am. B 1729

C,)

0

(a)

Un0

Cn

C,(

F-

Fig. 3. Time-series photographs of the beam path insidea BaTiO3:Co crystal: (a) before, (b) during, and (c) after thebuildup of a steady-state seeded stimulated photorefractive scat-tering phase-conjugate reflectivity of -60%. In a there was noexternal seed and no backward stimulated photorefractive scat-tering. The seed in (b) and (c) was a special-effects projectionscreen, 3M 7615. The beam enters the crystal's a face. Thelens-crystal separation is 10 cm. The laser beam was neitherexpanded nor spatially filtered. f = 20 cm.

A. Spatial and Temporal Beam Dynamics Inside theCrystalThe complex temporal and spatial dynamics undergone bythe pump beam in forming the phase-conjugate wave areillustrated in Fig. 3 with three top-view negative photo-

graphs of the beam trajectory before, during, and afterthe buildup of backseeded stimulated photorefractive scat-tering. In Fig. 3(a) the retroreflecting array is blockedby an absorbing (black) screen. In this case there is nobackinjected seed and no backward stimulated photo-refractive scattering. The beam refracts into an a faceof the crystal, fans" sharply toward the c axis (by for-ward stimulated Brillouin scattering 0 ), and exits a c faceof the crystal as shown; there is no backward stimulatedphotorefractive scattering under these circumstances. InFig. 3(b) a 3M 7615 retroreflector array is positioned tointercept the transmitted beam. The transmitted beam isthus injected directly backward into the crystal, closelyretracing the path of the forward-going beam and dra-matically lowering the threshold for backward stimulatedphotorefractive scattering. Within seconds the phase-conjugate signal begins to build up.. Figure 3(b) is aphotograph of the beam trajectory during the buildup ofthe backward stimulated photorefractive scattering.Pump depletion is clearly evident in this photograph.The intensity of light striking the back surface of thecrystal is clearly much less than that at the entrance sur-face. Once the reflectivity has built up to its steady-statevalue (in this case -60%o), the beam trajectory [Fig. 3(c)]looks considerably different from that in its transientstate. The beam has formed into a relatively intense fila-ment, perhaps indicating that self-waveguiding of somesort may be occurring.

This sequence of photographs demonstrates that thedominant charge carriers are holes for both the large-period gratings (which cause forward stimulated photore-fractive scattering or beam fanning) and the small-periodgratings (which cause the backward stimulated photo-refractive scattering phase conjugation). The positivec axis of the crystal, marked in Fig. 3a, points in the samedirection as the individual dipole moments in each unitcell of the crystal lattice, i.e., toward the crystal face thatis connected to the negative terminal of the dc power sup-ply during poling. This definition is consistent with thatof Feinberg et al.' 2

Figure 3(a) shows that the beam fans, by means of for-ward stimulated photorefractive scattering, in the direc-tion of the positive c axis. This is because the two-wavemixing gain for large-period gratings is positive in thisdirection whenever carriers are holes.'2

The direction of positive gain, for crystals with a singledominant charge carrier over all grating periods, is deter-mined by the dot product of the pump- and the probe-beam polarizations. Hence, if the dominant chargecarrier does not change sign with grating period, thesmall-period gratings formed by counterpropagatingbeams have positive gains in a direction opposite that ofthe large-period gratings formed by copropagating beams.Since the phase-conjugate waves propagate toward thenegative c axis in Fig. 3, the dominant charge carriers forthe small-period gratings are also holes. Detailed mea-surements of forward two-wave mixing gains as a func-tion of grating period in this crystal, presented by Rytzet al.,'6 are consistent with these results.

B. Resolution of Phase-Conjugate ImageThe high fidelity of seeded stimulated photorefractivescattering phase conjugation is demonstrated in Fig. 4 bycomparing the images of aberrated U.S. Air Force resolu-

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1730 J. Opt. Soc. Am. B/Vol. 9, No. 9/September 1992

tion charts after phase conjugation by the seeded stimu-lated photorefractive scattering conjugator. In Figs. 4(a)and 4(b) the seed is produced with the 3M 7615 screen;the image in Fig. 4(a) was formed by the conjugator with-out the aberrator in the system, while the image in 4(b)has been double-passed through the aberrator. The reso-lution in both these cases is comparable, -5.7 linepairs/mm, and is probably limited by the finite apertureof the crystal.

Using a diffuse (Lambertian) scatterer as the seed andpositioning the crystal 44 cm downstream from the lens,we obtained comparable spatial resolution [Fig. 4(c)] butpoor image uniformity and a much lower steady-state re-

flectivity of -8%. Higher, but unstable, reflectivitieswere obtained with other crystal-lens separations (un-stable reflectivities as high as 28% were obtained for acrystal-lens separation of 52 cm).

The severity of the aberrator is evident from Fig. 4(d),in which the seeded stimulated photorefractive scatteringconjugator is replaced by an ordinary mirror.

C. Reflectivity and Fidelity ParameterizationIn this subsection, measurements of the dependence ofphase-conjugate reflectivities and fidelities on relevantdevice operating parameters are presented. Reflectivityis defined as the ratio of the phase-conjugate power to the

(a) (b)

(C) (d)Fig. 4. Fidelity of seeded stimulated photorefractive scattering phase conjugation, demonstrated by comparing the images of the U.S. AirForce resolution chart after phase conjugation by the stimulated photorefractive scattering conjugator seeded by the retroreflectingscreen (a) without and (b) with a fixed aberrator. Improved performance of the conjugator seeded by the retroreflecting screen comparedwith (c) performance when the conjugator is seeded by a perfectly diffuse scatterer is also evident. The severity of the aberrator isevident from (d), in which the seeded stimulated photorefractive scattering conjugator is replaced by an ordinary mirror. The lens-crystal separation is 35 cm. f = 50 cm.

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Vol. 9, No. 9/September 1992/J. Opt. Soc. Am. B 1731

SEED / PUMP INTENSITY RATIOI . . .I I . .0 0.003 0.006 0.009 0.120

SEED INTENSITY / EQUIVALENT DARK INTENSITYA0 30 60

0 0.2 0.4 0.6 0.8NEUTRAL-DENSITY FILTER TRANSMISSION

50

0

Fig. 5. Observation of threshold in phase-conjugate reflectivityand fidelity as a function of seed intensity. f = 25 cm andf2 = 50 cm. The beam diameter at the crystal's entrance face is-0.3 cm. The pinhole diameter is 50 /um.

power reflected by an ordinary mirror in the absence ofany aberrators. The fractional power through a pinholewas used as a measure of the conjugator's relative fidelity.The reflectivity and the fidelity were positively correlatedas a function of all the experimental parameters testedexcept pump power.

1. Seed AttenuationA sharp threshold is observed in our measurements of re-flectivity and fidelity as a function of the seed attenu-ation. In Fig. 5 reflectivity and fidelity are plotted asfunctions of the strength of the seed. The abscissa of thisfigure gives the double-pass transmission value of the neu-tral-density filters used for the measurements (recall theapparatus of Fig. 2). The horizontal axes at the topboundary of this plot show our best order-of-magnitudeestimate of the seed strength in normalized, dimension-less units of the equivalent dark intensity, as well as theseed/pump intensity ratios corresponding to the variousneutral-density filter values. (A 13.7% retroreflector re-flectivity was measured, the absorption and the Fresneltransmission factor experienced by a beam on either entryto or exit from the middle of crystal was 33%, the totalpower transmitted through the crystal's c face in the ab-sence of the retroreflector was 5.7 mW, and the areas ofboth the forward- and the backward-going beams at thecrystal's exit face just before the onset of backward stimu-lated photorefractive scattering was estimated to beapproximately 2.5 ± 1 mm for these measurements).Noting that the threshold occurred for a double-passneutral-density filter transmission of 5%, we estimate theratio of the forward-going pump intensity to the backwardseed intensity I, inside the crystal to be 1.3 X 103 for thesemeasurements. The crystal's equivalent dark intensity,Id, of 80 W/cm', was obtained in a separate experimentthat measured the backward two-wave mixing gain in thiscrystal as a function of pump power, for s-polarized lightand a pump-to-probe intensity ratio of 10'. The ratio ofthe forward-going pump intensity inside the crystal to thecrystal's equivalent dark intensity is estimated to havebeen 4.3 X 103 just before the onset of backseeded stimu-lated photorefractive scattering. Thus I - 3 d as the

conjugate beam starts to form under the described experi-mental conditions. From Fig. 3 it is clear that, by thetime the phase-conjugate wave has reached its final high-fidelity steady-state value, pump depletion has resulted infurther reduction of the pump and the seed intensities, asmay have been required for the high-fidelity performancedemonstrated with the resolution-chart photographs inFig. 4.

The fact that the steady-state phase-conjugate fidelityremains high for high seed and pump intensities (relativeto the crystal's equivalent dark intensity) is contrary tothe undepleted-pump result of Ref. 15; no evidence ofprint-through is observed. Pump depletion, fanning, andother transverse beam dynamics evidently improve thephase-conjugate fidelity over that predicted by currenttheoretical models by lowering the intensity of the pumpand the seed beams at the back end of the crystal.

The data in Fig. 5 demonstrate that the seeded stimu-lated photorefractive scattering thresholds can be sensi-tively controlled by adjusting the attenuation between thecrystal and the seeding screen. Other possible meansfor controlling seeded stimulated photorefractive scatter-ing thresholds include adjustments of the phase of thelight between the crystal and the screen and incoherenterasure.4 "8

2. Pump PowerMeasurements of the phase-conjugate reflectivity andrelative fidelity (defined above) are plotted as functions ofpump power for a fixed incident beam diameter in Fig. 6.These data demonstrate two important features of ourconjugator. First, while the reflectivity increases withincreasing pump power over this range, the fidelity is anearly constant function of pump power in this experi-ment. Second, this conjugator has good fidelity. Nor-malizing the relative fidelities to that of an ordinarymirror in the absence of an aberrator gives absolute fidel-ities greater than unity. Similarly defined absolute fidel-ity measurements greater than unity were previouslyreported in stimulated Brillouin scattering experiments 9

and were ascribed to pump-beam spatial filtering.20'2 '

3. Distance between Lens and CrystalFor fixed incident pump power the reflectivity was inde-pendent of the distance between the lens and the crystal

500

>0 oW LJ-

100

90

80

70

60

50

40

30

20

10

200

Uv Z

100 o.- _IW

0 4 8 12 16 20 24

INCIDENT POWER (mW)

Fig. 6. Effect of pump power on reflectivity and fidelity for anunaberrated beam. The crystal is positioned 5 cm upstreamfrom the len's focus, where the incident beam diameter is-0.4 cm. f = 50 cm and f2 = 10 cm. The pinhole diameter is100 Im.

I 1I I I I I I I I

DASHED LINE CORRESPONDSTO THE PERFECT FIDELI7Y OFAN ORDINARYMIRROR

FIDELITY

RANGE FOR REFLECTIIYBACKWARD -SPSTHRESHOLD

I I I t oo

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1732 J. Opt. Soc. Am. B/Vol. 9, No. 9/September 1992

except when the crystal was positioned extremely close tothe focal plane of lens L1. At that point instabilities inthe phase-conjugate wave occurred. The instabilities oc-curred over a wider range of positions on both sides of thefocus for an unaberrated beam ( 3-cm range for instabili-ties) than for a 3.7X aberrated beam (1-cm range forinstabilities).

This observation, that an aberrator can eliminate phase-conjugate instabilities, highlights the importance of spa-tial inhomogeneities in stimulated scattering.

4. Beam Interaction LengthThe reflectivity and the fidelity were both found to belargely independent of the crystal's stimulated photore-fractive scattering interaction length, which could bevaried from 3.5 to 6.5 mm by horizontal translation of thecrystal through the beam in the plane of the table.

5. Position and Orientation of ScreenNo dependence of the phase-conjugate reflectivity on ei-ther the screen's angular orientation or the screen-crystalseparation was observed. The broad angular tolerance ofthe screen in this application arises from its ±40° field ofview.'7 The conjugator's insensitivity to screen-crystalseparations varying from 1 to 10 cm results from the half-degree retroreflective accuracy of the screen 7 and fromthe long coherence length (several meters) of the laser.

D. Performance without Index-Matching FluidWhile the most stable, highest reflectivities were obtainedwhen the crystal was immersed in index-matching fluid,seeded stimulated photorefractive scattering phase conju-gation was also observed with the crystal in air. The re-flectivity was less stable in air because reflections frominternal crystal surfaces tended to compete with the seedinjected by the retroreflector array. In air it was diffi-cult to avoid the formation of the internal-loop conjugatorconfiguration discovered by Feinberg,22 and the beamtrajectory tended to change in time as a result of thecompetition between the externally seeded stimulatedphotorefractive scattering and the internal loops. A high-index prism placed in contact with the crystal to spoil theinternal reflections effectively eliminated competitionfrom the internal loop under some circumstances, but themost stable performance, over the widest range of crystalorientations and positions, was achieved with the crystalimmersed in index-matching fluid.

The advantages of using the externally back-seeded con-jugator as compared with the internal-loop conjugator arediscussed in Section 7.

5. OPERATION WITH THE BEAMENTERING THE c FACEMost of our experiments were performed with the laserbeam entering an a face of the crystal, as shown inFigs. 1-3. Figure 7 is a top-view photograph of the beamtrajectory during backseeded stimulated photorefractivescattering phase conjugation with the beam entering thecrystal's c face. To the best of our knowledge, this wasthe first time backward stimulated photorefractive scat-tering was observed to occur either with the beam enter-ing a c face or with the beam propagating so close to the caxis inside the crystal. The reflectivity tended to belower and less stable in this geometry than when the beam

entered the a face of the crystal. There is less beam fan-ning when the beam enters the c face than when it entersthe a face (compare Figs. 3 and 7). The sharp beam fan-ning that occurs when the beam enters the crystal's a face[Fig. 3(a)] causes considerable crossing over and conse-quent interference between the different spatial modes (orspecklons, or pixels) of the incoming laser beam. Fanningalso causes the incoming beam to tend to break up intofilaments, as is also evident in Fig. 3. Both of these phe-nomena (filamentation and cross talk) play importantroles in the selective growth of the phase-conjugate waveat the expense of the nonconjugate noise waves. Hencemore beam fanning leads to higher ref lectivities and bet-ter stability. An excellent description of the role of fila-mentation and cross talk in stimulated Brillouin scatter-ing processes is given by Zel'dovich et al.2

6. RED AND INFRARED OPERATIONWhile most of our experiments were performed at 515 nm,we also demonstrated that backseeded stimulated pho-torefractive scattering functions at the 633-nm He-Neline, over the 730-800-nm Ti: sapphire range, and at839 nm with a GaAs diode laser.

Ref lectivities of 30-40% were obtained at 633 nm withan unfocused 5-mW He-Ne laser (having an -1-cm coher-ence length) and the same BaTiO3: Co crystal used for allthe 515-nm experiments described above.

The observation of stable reflectivities at 839 nm wasmade with a crystal grown by Sanders and Associates,boule cut 120G. Extensive efforts to make the Sanderscrystal operate at 839 nm with the internal-loop geometrywere unsuccessful. The seeded stimulated photorefrac-tive scattering configuration, by contrast, worked easilywith this crystal on the first attempt. A steady-state re-flectivity of -5% was obtained after an 1-h exposure(5 mW of optical power). The reflectivity decayed to -leof its initial value an hour after the seed was blocked.

Fig. 7. Top-view photograph of beam trajectory during back-seeded stimulated photorefractive scattering phase conjugationwith the pump beam entering a c face of the crystal.

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Vol. 9, No. 9/September 1992/J. Opt. Soc. Am. B 1733

At 750 nm we made a side-by-side comparison of thebuildup times for the seeded stimulated photorefractivescattering and the internal-loop conjugators. For the in-cidence angles used at this wavelength we noted that thecrystal could generate phase-conjugate signals from eitherthe total-internal-reflection conjugator or the externallyseeded stimulated photorefractive scattering conjugator,depending on whether the retroreflecting array wasblocked or unblocked, respectively. Before each measure-ment an expanded multiline argon-ion laser of -0.3 W/cm2

was used to erase all gratings by uniformly illuminatingthe crystal for 5 min. The externally seeded conjugatorwas seen to build up 3.3 times faster than the internalloop conjugator for the same incident pump intensities.(The crystal was immersed in oil in both cases.)

7. DISCUSSION

The experiments described above, in conjunction with afew additional measurements described below, raise im-portant questions that are suggestive of interesting areasfor future research.

In what sorts of applications would a backseeded stimu-lated photorefractive scattering conjugator be preferableto an internal-loop conjugator2 2? Clearly, any applica-tions requiring either sensitive threshold control or thecapability of modulating the threshold would benefit fromthe device characteristics discussed in relation to Fig. 5.Furthermore, while the demonstrated reflectivities andphase-conjugate fidelities of the backseeded stimulatedphotorefractive scattering conjugator and the internal-loop conjugator are comparable, the seeded stimulatedphotorefractive scattering conjugator offers the followingthree potential practical advantages: faster response,suitability for operation in mosaic arrays, and scalability.

Why is the backseeded stimulated photorefractive scat-tering conjugator expected to exhibit faster response ratesthan the internal-loop conjugators? This is because thegratings that form the backward stimulated photorefrac-tive scattering conjugators are the small-period, reflectiongratings. The internal-loop conjugators, by contrast, arethought to rely heavily on the larger-period transmissiongratings. In BaTiO3 , measurements2 2 3 have shown thatthe small-period gratings respond 10-50 times faster2 3

than the large-period gratings. Such a grating-period de-pendence of photorefractive response rates is associatedwith the fact that Debye screening plays almost no role inphotorefractive charge transport in short-diffusion-lengthphotorefractive materials 2 4 such as BaTiO 3.

Will these conjugators be useful in laser beam scalingapplications25 26 ? For any applications that involve scalingthese devices to accommodate large-area, high-powerbeams, a key issue is whether the threshold conditions forthese conjugators are associated with the incident pumppower (as for bulk stimulated Brillouin scattering conjuga-tors) or the incident intensity (as for stimulated Brillouinscattering in waveguides). In a simple attempt to answerthis question we repeated our measurement of the pump-power dependence of phase-conjugate reflectivity (Fig. 6)at an incident intensity level five times higher by movingthe crystal closer to lens Ll's focal plane. Doing this, wenoted that, to within our ±25% experimental accuracyin determining the power threshold, the power thresholdwas not changed in spite of the 500% variation in incident

intensity. While these data suggest a tendency for back-seeded stimulated photorefractive scattering, like bulkbackward stimulated Brillouin scattering, to exhibita pump-power threshold, further experiments shouldbe done.

Is it possible to improve the phase-conjugate reflectivityof the backward stimulated photorefractive scatteringconjugator by using longer crystals? We think not, sincewe noted little or no change in the phase-conjugate reflec-tivity as the crystal interaction length was shortened byalmost a factor of 2 (by a lateral translation of the crystalin the beam, Subsection 4.C). Extremely short crystalswould certainly be expected to exhibit lower reflectivities.Crystals with dimensions comparable with an absorptionlength may be optimal.

How does the backseeded stimulated photorefractivescattering conjugator's field of view compare with that ofthe internal-loop conjugator? Feinberg27 demonstratedthat an internal-loop conjugator pumped by a strong pumpbeam at a fixed angle of incidence exhibits a field of viewof .165° for the conjugation of a separate weak probebeam entering the crystal over this wide angular range.In our experiments, we noted that the backseeded stimu-lated photorefractive scattering conjugator exhibited thesame high reflectivities for pump beams entering thecrystal over a 350 range of angles; the angle was limited inour simple experiment by the finite aperture of the crystalrelative to the 2-3-mm beam diameter. Experiments todetermine the limits of this field of view and to measurethe field of view for a separate weak probe beam wouldprovide an interesting comparison between the back-seeded stimulated photorefractive scattering and theinternal-loop conjugators.

Minden et al.5 used an electro-optically modulated back-seeded stimulated photorefractive scattering conjugatorin BaTiO3 to demonstrate phase-conjugate retromodulationand coherent detection through water at carrier frequen-cies above 750 MHz. For lower-bandwidth retromodula-tor applications, one could modulate the intensity or thephase of the seed beam instead of modulating the crystalelectro-optically, thus eliminating both the need to fabri-cate electrodes on the crystal and the danger of acciden-tally depoling the crystal (as can happen, for example, ifthe modulated electrical signal is at any time wrongly ori-ented with respect to the crystal's c axis).

The single, larger interaction region of the seeded stimu-lated photorefractive scattering conjugator should facili-tate the use of this conjugator for the coherent coupling ofmultiple beams, an application requiring that the multiplebeams accurately overlap in the nonlinear interaction re-gion. Furthermore, since the seeded stimulated photore-fractive scattering conjugator involves no internal loops orinternal reflections, it should exhibit a higher damagethreshold than the internal-loop geometry.

Finally, the fact that the seed is injected externallyshould facilitate efforts to understand the detailed dynam-ics of the process, since the properties of the seed can beprecisely measured and controlled.

8. CONCLUSION

A new seeding technique using retroreflecting screenshas been developed for phase conjugation by meansof stimulated photorefractive scattering. This simple

Mullen et al.

1734 J. Opt. Soc. Am. B/Vol. 9, No. 9/September 1992

technique enhances the practicality of using stimulatedphotorefractive scattering conjugators in a wide range ofpotential applications at wavelengths ranging from theblue-green to the near infrared. An experimental studyof this seeded stimulated photorefractive scattering con-jugator was performed at 515 nm as a function of thefollowing parameters: crystal orientation, lens-crystalseparation, beam interaction length, incident pump power(for two different beam diameters), seed attenuation,crystal-screen separation, and screen orientation. Op-eration of the externally seeded stimulated photorefrac-tive scattering conjugator at 633, 730-800, and 839 nmhas been demonstrated. The improved performance ofthe retroreflective-array seeds over perfectly diffuseseeds is ascribed to the fact that the retroreflective seedredirects the transmitted light closely back onto itself.This action results in greatly improved overlap of the seedwith the forward-going filaments inside the crystal.

Detailed observations of the dependence of this conjuga-tor's reflectivity and fidelity as a function of the incidentand backinjected powers have been reported. Interestingfuture experiments include the characterization of phase-conjugate fidelity as a function of aberration strength anda systematic characterization of conjugator responsetimes. The relative performance of differently dopedcrystal samples and the use of incoherent illumination ofthe crystal in order to adjust its equivalent dark inten-sity4' 8 should be investigated. The threshold controldemonstrated by adjusting the strength of the back-injected seed (Fig. 5) suggests interesting device applica-tions as well as the following interesting questions forfuture research: Over how many orders of magnitudedoes the threshold control extend? How does the mea-sured threshold vary from variously doped crystals, eachhaving different material gain coefficients and differentequivalent dark intensities? How would the thresholdlevel vary as a function of incoherent crystal illumination?

ACKNOWLEDGMENTS

We thank J. F Lam, D. Rytz, and G. C. Valley for manyhelpful technical discussions, D. Rytz and B. A. Wechslerfor the BaTiO3 : Co sample, J. 0. White for helping us withthe diode laser demonstration at 839 nm, and C. C. Nelsonfor expert technical assistance. This research was sup-ported by the U.S. Office of Naval Research under con-tract N00014-87-C-0122, by General Motors ResearchLaboratories, and by Hughes Aircraft Company internalresearch and development funds. D. J. Vickers acknowl-edges the support of the General Motors FellowshipProgram.

*Permanent address, General Motors Research Labora-tory, Warren, Michigan 48090.

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