Through - Federation of American Scientists · Experimental demonstration of phase-conjugate...

Throughthe

Looking Glasswith phase conjugation

“I don’t understand. . .,” said Alice. “It’s dreadfully confusing!”“That’s the effect of living backwards, ” the Queen said kindly: “it

always makes one a little giddy at first-”“Living backwards!” Alice repeated in great

heard of such a thing!”

by Barry J. Feldman, Irving J. Bigio, Robert A. Fisher,

Claude R. Phipps, Jr., David E. Watkins, and Scott J. Thomas

Imagine a mirror that reflects morelight than was incident, that reflects abeam into the same direction regard-less of the mirror’s tilt, that eliminatesimage distortions by causing light

rays to retrace their paths as if runningbackward in time, and that when looked at

At left. A whimsical look at four aspectsof phase-conjugate reflection. These are(clockwise from upper left) backward-traveling wavefronts, light returning toits point of on, time reversal, andrestoration of beam quality.

LOS ALAMOS SCIENCE/Fall 1982

allows the observer to see absolutely nothing.Science fiction, you say? Well, such mirrorshave been the subject of intense investigationboth here at Los Alamos and at otherresearch laboratories around the world. Notonly do they exist, but their practical ap-plications may be far-reaching.

The mirrors we refer to are called phaseconjugators, and they reflect light in a man-ner radically different from conventionalmirrors. Consider a beam of light incident ona conventional mirror (Fig. la). The incom-ing rays can be characterized by a wavevector k pointing along the direction ofpropagation. When a ray is reflected by a

astonishment. “I never

—Lewis Carroll

nent of the wave vector normal to the mirrorsurface, is inverted. Thus a light beam can bearbitrarily redirected by adjusting the orien-tation of the conventional mirror. In con-trast, a phase conjugator (Fig. lb) inverts allcomponents of k and thus causes the wavevector to change sign, that is, to be reversedin direction. In this case, regardless of theorientation of the conjugator, the reflectedbeam exactly retraces the path of the inci-dent beam. Surprising, perhaps, but there ismore.

In addition to propagation direction, acomplete description of a light beam requiresinformation concerning its intensity andphase. The spatial and temporal dependence

3

of a beam’s electric field E are separable, andtypically the spatial component (at an instantin time) is described mathematically as thesum of many plane waves, each with a

information as a function of the spatialcoordinate r. The electric field of an incom-ing beam, E in, can be written as

The ‘intensity of the incoming beam. Iin, is

then given by

After reflection by a phase conjugator of

the outgoing beam, Eout, becomes

Eo u t =

The components of the outgoing beam cor-respond to the components of the incomingbeam, only with the amplitudes replaced bytheir complex conjugates and with the signsof the wave vectors reversed. This simplerelationship between the incident andreflected beams should make it clear why theprocess is called phase-conjugate reflection.

So far we have ignored the temporaldependence of the electric field. To be com-

nent waves must be included in the equationsfor the incident and reflected beams. Takingthese oscillatory factors into account,have

and

The fact that the sign reverses for the kn

we

. r,

4

ConventionalMirror

(a)

PhaseConjugator

(b)

Fig. 1. (a) A conventional mirror reflects light by inverting only the normal component

incidence equals the angle of reflection and allows the direction of the reflected beamto be altered by changing the tilt of the mirror. (b) A phase conjugator reflects light byinverting all components so that the propagation vector changes sign (kout = –kin). Inthis case, regardless of the tilt of the mirror, the reflected light exactly retraces thepath of the incoming beam.

indicates that Eout is propagating opposite tothe direction of E in. Moreover, the complexconjugation of the amplitudes reverses theconstant-phase wavefronts with respect tothe propagation direction (for example, a lag

in phase for E in becomes an advance inphase for E out, and so forth). Regardless ofthe value of the reflectivity, E out can bethought of as having wavefronts that are

everywhere in space coincident with those ofE in but that are traveling backward. It is as iftime had been reversed: the reflected wavereplicates—in reverse—the phase behaviorof the incident wave.

Now we can understand one of the mostimportant implications of this kind of reflec-tion. Consider the situation in which a beampasses through an aberrator, or phase-dis-

Fall 1982/LOS ALAMOS SCIENCE

Through the Looking Glass with phase conjugation

Conventional Reflection: Wave Distorts Further

Incident Wave

Glass II

L

IPlane DistortedWave Wave

Phase-Conjugate Reflection:

Fig. 2. Phase distortion with conventional and phase-conjugatereelection. In both cases the incoming plane wave (left side)encounters a block of glass, and a distorted wave is formedbecause the glass, with a different refractive index, retards thephase of the wave’s central region. Conventional reflection (topright) retains this lag in plume so that the return trip through

torting medium, and then reflects from aphase conjugator (Fig. 2). The aberratorchanges the beam into a distribution givenby E ln that contains information about all of

the phase distortions introduced by the me-dium. The phase conjugator then convertsE in into a new distribution E out (by complex-

Restored ConjugatePlane DistortedWave Wave

the glass doubles the distortion. On the other hand, phase-conjugate rejection (bottom right) changes the lag in phase toan advance in phase so that the return trip removes thedistortion and a plane wave emerges, as if the wave hadtraveled backward in time.

conjugating all amplitudes and by reversing Thus, a high-quality optical beam can beall wave vectors). This reflected beam is ex- double passed through a poor-quality optical

actly programmed so that after passing system with no overall loss in beam quality.

backward through the aberrator it becomes a This double-passing technique can be applied

backward propagating replica of the original to many problems in which a distorting

beam. The emerging beam does not contain medium, such as the turbulent atmosphere or

any evidence that the aberrator existed! a multi-mode optical fiber, would be

LOS ALAMOS SCIENCE/Fall 1982 5

ReturnBeam

Reference Beam

Aberrating Phase ConjugatorMaterial or

Conventional Mirror

Return Beam

Returned byConventional

Mirror

Returned byPhase Conjugator

Fig. 3. Experimental demonstration of phase-conjugate reflec- (middle photograph), whereas phase-conjugate reelection re-tion. An undistorted laser beam (left photograph) is double moves the distortions and only a uniform intensity change ispassed through an aberrating material. Conventional reflec- obvious (right photograph).tion for the return trip results in a highly distorted beam

detrimental to effective beam transport.Figure 3 shows an experimental demon-

stration, with the aberrator pictured in Fig.4, of this amazing feature of phase-conjugatereflection. Only two conditions are required

to insure repair of the distorted beam. First,the phase-distorting aberrator must notundergo any changes during the time it takesfor the beam to strike the phase conjugatorand return; second. the light itself must notaffect the physical properties of the aber-rater.

It should now be clear why, when onelooks at an ideal phase conjugator, one sees“nothing.” All the light impinging on an idealphase conjugator returns exactly on the pathfrom where it came. Light glancing off one’snose, for example, is reflected directly backto one’s nose. not into one’s eyes. The onlylight an observer has a chance of seeing is

6

that reflected off one’s eyeball to the mirrorand back. This is perhaps not quite nothing,but not much either. For those who believethat the eye is the “window to the soul,” thephase conjugator allows the possibility ofsoul searching (patent pending), at least inthe technical sense.

How Does One Make Such aMirror?

In principle, if the phase distortions in abeam of light were known in advance, thenone could design a mirror with a compensat-ing surface to perform as a phase con-jugator. Indeed, this is the principle behindthe field of adaptive optics, in which a mirrorsurface is controlled and modified in such amanner as to reverse the phase front of anincoming beam (Fig. 5). Typically, the ele-

ments used for the shaping of this “rubber”mirror are piezoelectric crystals whoselengths change precisely when the voltagesacross their faces are changed. Such mirrorshave been built, and research on improvingtheir properties is proceeding in a number oflaboratories. However, these mirrors sufferfrom slow response time (about 1 milli-second), imperfect correction due to thefinite spatial resolution of each piezoelectricelement, and expense in the construction andcomputer control of the large number ofpiezoelectric elements generally involved. Incontrast, the phase conjugators discussed inthis article (which invoke nonlinear opticaltechniques) need not suffer from such limita-tions.

NONLINEAR OPTICS. The methods to bediscussed henceforth invoke processes en-



Fig. 4. Is this optical element useful? The distorted sodium chloride window in thispicture was used as an aberrator in the experiment of Fig. 3 to illustrate the healingproperties of phase-conjugate reflection. This technique becomes an attractive optionwhen the quality of key optical components is limited by expense or technicalconsiderations.

“Rubber”Mirror

tirely different from those of the flexiblemirror described above, although the desiredend result, formation of the conjugate wave,is the same. The research carried out at LosAlamos addresses the field that has becomeknown as nonlinear phase conjugation. Inthis approach the processes that generate aphase-conjugate reflection depend upon the


Fig. 5. Adaptive optics. If the phasedistortions of the wavefront of an opticalbeam are known, a mirror surface canbe shaped such that its surface is normalto the wave's propagation vector at everypoint. The reflected beam would then bethe phase conjugate of the incomingbeam because conventional reflectionnormal to the surface reverses the sign ofthe propagation vector.

nonlinear response of matter to an opticalfield. (Generally, the nonlinearity of theresponse attains a useful magnitude only atthe field intensities available from a laserbeam.) There exists a plethora of theseeffects. In general, if a nonlinear responsecauses the refractive index of a medium tochange with optical intensity, then the inter-

ference pattern formed by two or more laserbeams can produce a volumetric index-of-refraction grating in the medium. Suchgratings are the key to the magic of phaseconjugators. But what is a refractive-indexgrating and why is it important?

First, it should be remembered that therefractive index is a relative measure of thespeed of light through a material. As a result,the refractive index appears as a factor in the

of the light in vacuum). The refractive indexthus directly influences the oscillatory factorcontaining the phase information. Anyphysical process that alters the refractiveindex in a region of a material will, in turn,alter the phase of any light passing throughthat region. The trick, of course, is to alterthe refractive index in just the right way sothat the material scatters the light wave intoits conjugate.

To further understand refractive-indexgratings, we turn momentarily to holo-graphy. In fact, the true father of phaseconjugation may well be the person whodeveloped the notion of the hologram, Den-nis Gabor (with help from W. L. Bragg). Wesay this because there are importantsimilarities between holography and opticalphase conjugation. One of the most impor-tant optical phase-conjugation techniques,which will be discussed later, is called de-generate four-wave mixing and is essentiallyreal-time optical holography.

Consider the making of a holographicimage (Fig. 6a). Typically, the light from alaser is split into two plane-wave beams.One, the reference beam, remains un-distorted. The second is reflected diffuselyoff the object, causing the optical phase frontto be distorted. The reference beam and the

distorted beam are then directed from dif-ferent angles onto a photographic film where

they meet to form an interference pattern.All the phase information implicit in theinterference is recorded as a fine pattern ofsilver grains in the developed film emulsion;the interference pattern has been “written”permanently into the film. Later, the patternis “read” by directing at the film from therear an undistorted plane wave (Fig. 6b), Inthis case, the grains of silver act as a gratingand scatter the light to generate a distortedbeam with the same phase relationships ofthe original distorted beam (when viewedfrom the same angle). This scattered beam isseen by the eye as a virtual image of theobject.

The key to holography, of course, is the

7

Reading the Hologram

GrainPatternGrating \

PlaneWave

Object{a) Reconstructed Image

of the Object (b)

Fig. 6. Conventional holography consists of two distinct traveling in the exact opposite direction, reads the hologram by“write” and “read” steps. (a) First, the film is exposed to the scattering off the pattern of grains. Because the variousinterference pattern formed by an undistorted reference beam scattered waves interfere with each other, these grains act as awith a distorted beam reflected off the object. The result, after heterogeneous grating. When viewed at the original angle, thedevelopment of the film, is the hologram, a grain pattern in the phase relationships of the distorted beam will have beenemulsion. (b) A second undistorted reference beam, here reconstructed, creating an image of the object.

pattern formed in the film emulsion. But thisis a permanent grating. What is needed forphase-conjugate reflection is some mediumin which a grating is written and readsimultaneously; that is, the incident distortedbeam generates a grating pattern that im-mediately scatters the reflected beam in theopposite direction with the conjugate phaserelationships of the original. To set up such agrating we invoke nonlinear optics.

The nature and effectiveness of a refrac-

tive-index grating depend strongly on thenonlinear mechanism coupling the light andthe material. Many such mechanisms areavailable. For example, if the opticalwavelength corresponds to an absorptionwavelength in the material, then the ab-sorbed energy will give rise to heating of thematerial and a corresponding modification ofthe refractive index at that wavelength. If theabsorption is bleachable (that is, if the ma-

8

terial becomes more transparent as moreenergy is absorbed), then the index of refrac-tion will change with intensity. However, ifthe material is nominally transparent, thenother effects typical of nonlinear optics (suchas those called stimulated Brillouin scatter-ing, the optical Kerr effect, stimulatedRaman scattering, and multiple-photonabsorption) can be used to produce a refrac-tive-index grating. The material itself can bea solid, liquid, gas, or plasma or more exoticsystems such as liquid crystals, dielectricparticles within a liquid, gaseous bubbles, orbulk plasma within a solid.

In this article we will discuss two types ofnonlinear mechanisms for phase con-jugators: those involving elastic photon scat-tering, in which the conjugating medium isleft essentially unchanged by the process,and those involving inelastic photon scatter-ing, in which the incident photons deposit

some of their energy in the medium. We willtreat an important example of each.

DEGENERATE FOUR-WAVE MIXING. Anexample of an elastic photon-scattering proc-cess in nonlinear optics is degenerate four-wave mixing, the phase-conjugation tech-nique that corresponds to real-time holo-graphy. In this case the light and the materialcouple through a nonlinearity in the ma-terial’s polarizability. When a light beamtravels through a transparent material, itsoscillating electric field generates a cor-responding polarization wave by altering anumber of properties (for example, the aver-age position of the material’s electrons). Atlow intensities the polarization can be takento be directly proportional to the electric field

tion wave oscillates at the same frequency asthe radiation but radiates its energy with a



PhaseConjugator Refractive-Index

Plane Wave El

Fig. 7. In degenerate four-wave mixing the write and read steps of holography takeplace simultaneously. Interference of the intense plane wave El and the distorted waveE3, generates a refractive-index grating in the nonlinear optical material of the phaseconjugator. The intense countetpropagating plane wave E2 immediately scatters offthis grating to form the reflected wave E4 that is the phase conjugate of E3. Becausethe roles of E1, and E2 can be exchanged, a second wave, indistinguishable from E4, isalso produced. The intensity of the reflected wave is a function of the three incidentfields (EI, E2, and E3) and of the material properties of the phase conjugator (such asthe magnitude of its nonlinear optical effect).

time lag that retards the phase of the lightbeam (giving rise to the material’s normalrefractive index). At high enough intensities,however, the polarization becomes nonlinearand can be expressed as

the higher-order terms in this equation causethe polarization wave to have a variety offrequency components that can radiate innew directions and at new frequencies andthat alter the material’s refractive index. Thethird-order term consists of a number ofcomponents, one of which is responsible forthe polarizability changes used to generatethe refractive-index grating in degeneratefour-wave mixing.

in this process three fields of the samefrequency impinge on a transparent or semi-transparent material with a large third-orderpolarizability (Fig. 7). Two of the fields (E1,and E 2) are counterpropagating, high-in-tensity plane waves (a reference field to helpwrite the grating, another to read it), and thethird (E3) is the field one wishes to “reflect,”or phase conjugate. In this environment theinterference of the reference field E l with the


field of interest E 3 generates a refractive-index grating. The other reference field E 2

experiences this bulk grating within the ma-terial and is partially scattered back alongthe direction of E3. We refer to this scatteredwave as E4. However, the roles of E l and E 2

can be interchanged. Thus E 2 and E 3 estab-lish a different refractive-index grating thatpartially scatters E1 back along the direction

two gratings are indistinguishable and bothcontribute to the phase-conjugate field E 4.Here we see that the sequential steps ofnormal holography—the formation of agrating and the subsequent scattering fromit—are, indeed, accomplished simulta-neously. It should be evident from thisdiscussion, however, that in degenerate four-wave mixing E4 is not really a reflection ofE 3 but rather a scattering of E l and E 2.

Is the scattered field the conjugate of theincident field? The phase of a scattered beamis determined by the phase variations withinthe refractive-index gratings. Because of theunique phase relationships between the refer-ence beam and the grating, the scattered fieldE 4 should be proportional to the complexconjugate of E 3. In fact, with the nonlinearpolarization appropriate to degenerate four-

wave mixing, Maxwell’s equations give E4 aseverywhere strictly proportional to the phaseconjugate of E 3. In degenerate four-wavemixing experiments it is crucial that E 1 andE2 approximate plane waves within the inter-action volume and that they be precisely

counterpropagating; otherwise, the scat-tered radiation will not be exactly the con-jugate of E 3.

Although degenerate four-wave mixing isa nonlinear optical effect generated by theinteraction of three fields, the effect is never-theless linear with respect to the field E3 that

is being phase conjugated. This means that asuperposition of E 3 fields will generate acorresponding superposition of E 4 fields.Thus, accurate reconstruction of the originalfield (only propagating in the opposite direc-tion) is possible.

If E1 and E2 are sufficiently intense and E3,is weak, it is conceivable that E4 will be moreintense than E3. Hence the phase-conjugatescattering can actually lead to a “reflec-

This is accomplished, of course, not bygenerating light out of thin air but by scatter-ing light from the intense fields E l and E 2

back into the direction of E 3, giving theappearance of amplification. Alas, energy isalways conserved.

The origins of the concept of nonlinearoptical phase conjugation are somewhat ob-scure owing to confused terminology andvarious incomplete demonstrations. Gener-ally, B. I. Stepanov, E. V. Ivakin, and A. S.Rubanov of the Soviet Union are creditedwith the first demonstration in 1970 ofdistortion correction by degenerate four-wave mixing (similar work by J. P. Woerd-man was nearly concurrent), and there islittle doubt that the early pioneering in thefield was by Soviet researchers. In particular,B. Ya. Zel’dovich, V. I. Popovichev, V. V.Ragul’skii, and F. S. Faizullov stand out asthe first to recognize that nonlinear opticalphase conjugation would also occur viastimulated processes such as our next exam-ple.

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STIMULATED BRILLOUIN SCATTERING.

This technique is an example of an inelasticphoton scattering process. An intense laserbeam is focused into a nearly transparentoptical material where it Brillouin scatters offacoustic phonons (Fig. 8). As a result, thebeam loses energy to the acoustic wave inthe medium and is slightly reduced in fre-quency as it scatters back in the oppositedirection. The high intensity of the focusedlaser beam literally drives the process to highefficiency by stimulating the scattering.Zel’dovich and coworkers were the first todemonstrate that this scattered beam was thephase conjugate of the incident beam. Here’show it works.

Intense optical radiation can interact withtransparent media to produce material-den-sity gradients by an effect called electrostric-tion. Electrostriction refers to the phenome-non in which a dielectric in an electric-fieldgradient experiences a force in the directionof increasing electric field. An analysis ofthis effect shows that the mechanicalpressures in a liquid at the focal volume ofcommonly available lasers can exceed 100atmospheres.

Now consider a strong incoming beam

material that exhibits electrostriction. As-sume that the beam scatters off a soundwave (some acoustic noise always exists; forexample, the laser beam itself can createsuch noise) to travel in the backward direc-tion as E out

natively, assume that the incoming beaminterferes with optical noise. If some of theoptical noise happens to have the frequency

o u t and is propagating opposite to E in, the

two will interfere and produce a movingintensity grating. Because of electrostrictionthe intensity grating generates a sound wave,

where vs is the sound velocity.Thus, there are two concurrent processes

being described here. In one E in interacts

10

IncidentWava

ConjugateWaveE out

Brillouin Scattering

LensMedium

/ /

Focused \Beam Material

DensityGrating

(Sound Wave)

Fig. 8. Backward stimulated Brillouin scattering. The incoming field Ein interacts withan acoustic wave to produce a backward scattered wave Eout and also interacts withEout (through the medium) to produce an acoustic wave. The two processes positivelyreinforce each other only when Eout is the phase conjugate Of Ein.

with a sound wave to produce E out. In theother E in interacts with E out to produce asound wave. For exactly the right set offrequencies and wave vectors, these twoprocesses will reinforce each other bypositive feedback and E out will grow ex-ponentially (until E in is signif icant lydepleted). Exponential growth will be fastestwhen E out is precisely the phase conjugate ofE in, and thus non-phase-conjugate scatteringis suppressed.

The acoustic wave generated in this proc-ess travels in the same direction and, mostimportant, with the right phase fronts toconjugate the incident wave Ein. In essence, a“rubber grating” has been created in theconjugating medium whose scattering planesare always correctly aligned to reflect theconjugate wave.

Of course, the effectiveness of stimulatedBrillouin scattering as a phase conjugatingprocess is also dependent on the phasecoherence of the incident beam, the extent ofits phase disturbances, and the depth of theestablished grating. The details of these de-

pendences are only now beginningappreciated.

Infrared Phase Conjugators

to be

Work on nonlinear optical phase conjuga-tion received a late start in this country, andit wasn’t until the work on this phenomenonin 1976 by R. W. Hellwarth and in 1977 byA. Yariv and D. M. Pepper that phase-conjugation studies began in earnest in theUnited States. Not long thereafter, workbegan at Los Alamos in the laser fusioneffort when it became apparent thatnonlinear optical phase conjugation heldpromise not only for improvement of thebeam quality of large-aperture lasers but alsofor improved target sighting and tracking ofthe tiny fusion pellets. (More will be dis-cussed about applications later.)

Because the Los Alamos candidate in thelaser fusion derby was the carbon dioxide(CO 2) gas laser operating in the infrared at awavelength of 10 micrometers, the challengewas to find efficient nonlinear optical phase-


Experimental Setup

Optically Resonant Cavity

Fig. 9. Reconfiguring the carbon dioxide (CO2) laser cavity for the output coupler places the germanium, a highly nonlinearthe degenerate four-wave inking experiment. (a) The conven- optical material, on the inside of the optically resonant cavitytional C02 laser uses germanium as the substrate for the and thus within the intense, almost perfectly counterpropagat-partially reflective coating on the output coupler. (b) Flipping

.ing fields that constitute the laser cavity’s standing wave.

conjugating materials at this wavelength. InMarch 1978, Ernest Bergmann, Irving Bigio,Barry Feldman, and Robert Fisher suc-cessfully produced the first demonstration ofinfrared optical phase conjugation with aC 02 laser utilizing germanium as thenonlinear material.

Germanium had played an important rolein C02 laser technology for many years. Asan easy to grow, easy to polish, opticallytransparent material in the infrared, it hadlong been used as the substrate material thatis coated with a partially reflecting, partiallytransmitting film to make it into a CO2 lasermirror. Figure 9a shows the material in useas the substrate for a laser “output coupler”


with the reflective coating toward the insideof the laser cavity. This device transmits partof the beam out of the laser and reflects therest back into the optically resonant cavitywhere the counterpropagating beams form astanding wave. Note that the germaniummaterial itself is outside the laser cavity.

With one of those welcome flashes ofrecognition, it was realized that a simplereversal of the output coupler (Fig. 9b)would immediately satisfy many of the re-quirements for degenerate four-wave mixing.This trivial operation placed the germaniumsubstrate, which has a rather large nonlinearoptical coefficient, inside the cavity, where itwas exposed to the high-intensity intracavity

electromagnetic field. Moreover, the twobeams making up the standing wave insidean optical resonator are almost perfectlycounterpropagating plane waves by design;the problems of misaligned and convergingor diverging beams were thus readilyavoided. All that was needed to complete theexperiment was to redirect at an obliqueangle the output of the laser back into theilluminated portion of the germaniumsubstrate (Fig. 10). Lo and behold, phaseconjugation occurred in the germanium. Thereflectivity measured in that first experimentwas only 2 per cent, but the work repre-sented a breakthrough in CO2 laser develop-ment and demonstrated that optical phase

11

Partially

Fig. 10. Degenerate four-wave mixing in the infrared. Here the splitter allows both the original laser output beam and theC02 laser shown in Fig. 9b with counterpropagating fields El reflected conjugate beam to be monitored by infrared-sensitiveand E2 has part of its output directed at an angle back into the detectors. An aberrator can be placed in the beam to check thegermanium to form the field E3. Since this arrangement phase-conjugate properties of the reflected wave. The C02

provides the proper conditions for degenerate four-wave mixing laser has been simplified here for the sake of clarity.(Fig. 7), the phase-conjugate wave E4, is generated. The beam

12 Fall 1982/LOS ALAMOS SCIENCE


Fig. 11. Phase-conjugate reflectivity of germanium as a function of intensity. Highfield intensities in germanium give rise to a high-density electron plasma within thatmaterial. This creates large optical nonlinearities and phase-conjugate reflectivities of200 per cent or greater.

conjugation was both possible and simple toachieve with materials already on hand inmost laboratories involved in research onC O2 lasers.

After these initial experiments, continuedwork on germanium by Claude Phipps andDavid Watkins revealed more surprises fromthis innocent looking material. In a carefullycontrolled experiment with germaniumoutside the laser cavity, they demonstrated,for field intensities of 100 megawatts persquare centimeter and greater, that thephase-conjugate reflectivity increased dra-matically. Apparently, at these high in-


tensities free electrons were generated bymultiple-photon absorption across the 0.6-e l e c t r o n - v o l t i n d i r e c t b a n d g a p o fgermanium. This rapidly gave rise to a high-density electron plasma (2 x 1O1s electronsper cubic centimeter) within the bulkgermanium. Such a highly nonlinear processproduced a dramatic increase in the phase-conjugate reflectivity of the material. Reflec-tivities greater than 200 per cent were dem-onstrated for germanium samples (Fig. 11).

Concurrently, Fisher and Feldman usedthe CO2 gain medium itself as an opticalphase conjugator by using the saturation

properties of the excited CO2 gas mixture to

establish a field-dependent population grat-ing. Because of larger interaction volumesand favorable gain conditions, effectivephase-conjugate reflectivities greater than400 per cent were obtained. At this sametime, Fisher, Feldman, and Bergen Suydamcarried out theoretical work on the pulsecharacteristics of optical phase conjugation.

Further C02 laser research was done byWatkins on a saturable absorber consistingof potassium chloride doped with rheniumtetroxide. This work confirmed many of thetheoretical predictions about phase conjuga-tion by ideal saturable absorbers.

Ultraviolet Phase Conjugators

Throughout 1979 substantial develop-ments in the field continued worldwide forboth the infrared and visible portions of thespectrum; there were, however, no observa-tions of phase conjugation in the ultraviolet.Because of the increasing importance ofultraviolet lasers in photochemical and fu-sion research, Los Alamos researchersfocused their attention on this part of thespectrum. Using pulses of 20-picosecondduration from a Nd:YAG laser whose emis-sion had been quadrupled in frequency toyield light at a wavelength of 266nanometers, Feldman, Fisher, and StanleyShapiro set up the degenerate four-wavemixing experiment shown in Fig. 12. Theincreased complexity (when compared withthe previously described experiment of Figs.9 and 10) was required because great carehad to be taken to insure temporal overlap ofthe very short pulses within the phase-conjugating medium by making the opticalpath lengths of each of the three interactingbeams equal to within about 1 millimeter.

Liquid carbon disulfide (CS2) was one ofthe most attractive conjugator candidatesbecause of its large nonlinear optical coeffi-cient. Although CS2 is strongly absorbing inthe ultraviolet, dilution with hexane pro-duced a “window” between the two strongabsorption peaks centered at 230 and 330

13

Fig. 12. Degenerate four-wave mixing in the ultraviolet. The beams (E1 and E2). Part of the remaining 10 per cent arrives asfrequency-quadrupled output (266-nanometer wavelength) of a E3, at the conjugator from a different angle and is phase-Nd:YAG laser is split so that 90 per cent of the beam is conjugate reflected (E4).directed to the phase conjugator as two counterpropagating

nanometers. The transmission window had per cent and less were observed from the CS2

the remarkable property of being tunable as -hexane mixture and from several othera function of CS2 concentration in hexane materials, these observations represented the(Fig. 13). A 40-per cent (by volume) mixture first demonstration of nonlinear opticalof CS2 in hexane was chosen to optimize the phase conjugation in the ultraviolet and gavenonlinear interaction at 266 nanometers. impetus for further development.Although conjugate reflectivities of only 0.1 Work in the ultraviolet continued at Los

14

Alamos with several other notable achieve-ments. This work was motivated by thedevelopment in the late ’70s of a new class oflasers, the rare-gas halide excimers. The

excimer lasers offered for the first time the

possibility of high-power, high-efficiencyemission at various wavelengths in the ultra-



100

o2 4 0 2 7 0 3 0 0

Wavelength (µm)

violet. Using a high-power spectrally nar-rowed krypton fluoride laser at a wavelengthof 248.6 nanometers, Bigio, MichaelSlatkine, Feldman, and Fisher successfullydemonstrated optical phase conjugation,again based on degenerate four-wave mixingin various liquid solutions. Similar successeswere achieved with a xenon fluoride laser at

351 nanometers using backward stimulatedBrillouin scattering in various organic liquids(Fig.14). In the latter case phase-conjugate

Fig. 13. The transmission spectra ofvarious CS2-hexane solutions. Thetransmission increases, broadens, andshifts as the percentage of CS2 in themixture decreases. These curves are for1-millimeter path lengths through thesample.

reflectivities of over 70 per cent were clearlydemonstrated, In another experiment nearlyphase-conjugate reflectivities of about 30 percent were observed us ing backwardstimulated Raman scattering in liquid nitro-gen. This process is, in essence, the same asstimulated Brillouin scattering except thatrather than coupling with sound waves,energy from the incident beam is depositedinto the vibrational energy levels of thenitrogen molecules. One of the remarkable

features of this experiment, and of stimulatedRaman scattering in general, is the largewavelength shift of the scattered beam withrespect to the incoming beam. In this casethe phase-conjugate beam at 382 nano-meters was visible whereas the incomingbeam at 351 nanometers was not. Thiswavelength shift precisely equals the dif-ference between energy levels of the vibra-tional mode of the nitrogen molecule, arelatively large energy change.

In all cases involving these excimer lasers,whose emission is normally broad in fre-quency, phase conjugation could be ob-served only when the laser was constrainedto operate within a narrow frequencybandwidth. Put simply. a broad range offrequencies results in a “smeared” inter-ference pattern and a nondistinct refractive-index grating that fails to scatter the beamefficiently. The necessary bandwidth reduc-tion was achieved by a process called injec-tion locking in which a much weaker laser atthe same frequency but with a narrowbandwidth controls the laser of interest. Thistechnique was perfected at Los Alamos byBigio and Slatkine. For example, the xenonfluoride laser was successfully injectionlocked using a weak, narrow-bandwidthargon-ion laser operating at a wavelengthcoincident with one of those of the xenonfluoride laser. As little as one watt from theargon-ion laser was sufficient to control the

Fig. 14. In this photograph an ultraviolet light beam from a beam in the cell is due to fluorescence. Part of the phase-xenon fluoride laser passes through the optics from left to right conjugated return beam is diverted by the beam splitter on theand is phase-conjugate reflected by liquid hexane in the cell on left and appears as the spot in the background.the right via stimulated Brillouin scattering. The visible light


Amplifier

Lens

Preamplifier Preamplifier

Imperfect LaserAmplifier System

Fig. 15. Laser fusion systems. The conventional system (top) amplified, phase-conjugate reflected, and further amplified onuses a long chain of laser amplifiers that may gradually its return. Because the phase-conjugate beam exactly retracesintroduce distortions in the beam arriving at the fusion target. its path, the amplified beam automatically hits the tiny fusionIn the phase-conjugate laser fusion system (bottom), a target. In addition, any phase distortions imparted to the beamspatially broad, low-intensity laser illuminates the target. A by the complex amplification system will be removed on thesmall fraction of this illumination is reflected off the fusion return pass.target into the solid angle of the focusing optics and is

output bandwidth of the ten-million-wattxenon fluoride laser.

Applications of Optical PhaseConjugation

Although still in its infancy, the emergingfield of nonlinear phase conjugation showspromise of revolutionizing the design ofoptical systems. As we have already dis-cussed, the phase-conjugate beam has theremarkable property of emerging undistortedon its return pass through a distorting opticalsystem. The advantages of this property foroptical systems such as those involved inlaser fusion, optical-fiber communication,and atmospheric propagation are enormous.Already the application of phase-conjugationtechniques to the large fusion research lasershas resulted in their increased brightness ontarget. Moreover, the use of this technique

(demonstrated in the Soviet Union) results inthe automatic alignment of the beam on the

16

fusion pellets. A schematic of such a phase-conjugating laser fusion system is shown inFig. 15. Light from a low-intensity illumina-tion laser is scattered off a fusion target. Thisillumination beam can be spatially broad andneed not be critically aligned. Some of thescattered radiation is gathered in by a focus-ing system and undergoes amplification as ittravels through the laser amplifiers. At thefar end of the amplifier chain the radiation isreturned by a phase conjugator through thelaser chain for further amplification to ex-ceedingly high intensities. Regardless of theoptical distortions encountered on the firstpass, the phase conjugator automaticallyredirects the beam back to its source, thefusion target. The amplified beam cannotmiss! This technique allows the use of lowerquality optics and eliminates much of theexpense of the alignment systems usuallyrequired.

We now reconsider the scheme in Fig. 15,but this time with the laser and the targetseparated from each other by more than

several hundred miles. Just as in the laser-fusion application of optical phase conjuga-tion, similar aiming procedures could be usedto direct laser light nearly instantaneouslyand accurately over long distances throughthe Earth’s distorting atmosphere. Theseprocedures could be extremely useful forcommunications systems.

Other potential applications of phase con-jugation abound. The use of a phase con-jugator as one of the cavity mirrors of a laserallows automatic cavity alignment and couldlead the way to improved beam quality andstability. In fact, if a tunable laser is used toestablish the counterpropagating beams fordegenerate four-wave mixing, then externalfrequency control of the laser output ispossible.

A phase conjugator has also been used asa fine optical frequency filter. In one of theinjection-locking experiments describedabove, a xenon fluoride laser emitting radia-tion in roughly equal amounts at 351 and353 nanometers was Brillouin scattered from



a variety of liquids. Because of injectionlocking by an argon-ion laser, the bandwidthof the radiation at 351 nanometers wasmuch narrower than that of the 353-nanometer radiation. As a result, only the351-nanometer light could form a distinctgrating and only this radiation was efficientlybackscattered. Thus all radiation but thenarrow-bandwidth phase-conjugate compo-nent at 351 nanometers was filtered out bythe scattering process.

Applications of phase conjugation havealso been proposed in the use of photolithog-raphy. Potentially, the use of short-wavelength ultraviolet radiation should yield

greater resolution and accuracy in the manu-facture of microelectric circuits. However,distortions in the ultraviolet imaging systemshave impeded the success of this application.Even with imperfect optics the unique imag-ing properties of the phase-conjugation proc-ess could result in far greater resolution andaccuracy than heretofore has been possible.

Finally, a theoretical analysis of the quan-tum optical properties of a phase-conjugatedbeam arising from degenerate four-wavemixing indicates that a particular state (theso-called two-photon coherent state) of thisradiation field possesses unique properties.These properties may allow substantial sig-

nal-to-noise improvements in certain light-detection schemes, improvements that wouldbe especially pertinent to such applicationsas the detection of gravity waves.

In conclusion, optical phase conjugation is

a rapidly expanding field that is radicallyaltering the design of optical systems andtheir capabilities. Although not all of the

proposed applications may prove to be moreeffective than other more conventional ap-proaches, there i s l i t t le doubt tha tsome—and indeed many not yet even fore-

seen—will have a major impact on opticalsystems of the future. Much remains to beexplored in this intriguing wonderland. ,

Further Reading

John Auyeung, D. Fekete, David M. Pepper, and Amnon Yariv, “A Theoretical and ExperimentalInvestigation of the Modes of Optical Resonators with Phase-Conjugate Mirrors,” IEEE Journal ofQuantum Electronics QE-15, 1180-1188 (1979).

E. E. Bergmann, I. J. Bigio, B. J. Feldman, and R. A. Fisher, “High-Efficiency Pulsed 10.6 µm Phase-Conjugate Reflection via Degenerate Four-Wave Mixing,” Optics Letters 3, 82 (1978).

I. J. Bigio, B. J. Feldman, R. A. Fisher, and E. E. Bergmann, “High-Efficiency Wavefront Reversal inGermanium and in Inverted CO2 (Review),” Soviet Journal of Quantum Electronics 9, 1365-1369 (1979).

Irving J. Bigio and Michael Slatkine, “Transform-limited-bandwidth Injection Locking of an XeF Laserwith an Ar-ion Laser at 3511 A,” Optics Letters 7, 19-21 (1982).

B. J. Feldman, Robert A. Fisher, and S. L. Shapiro, “Ultraviolet Phase Conjugation,” Optics Letters 6,84-86 (1981).

D. Gabor, “A New Microscopic Principle,” Nature 161, 777-778 (1948).

Concetto R. Giuliano, “Applications of Optical Phase Conjugation,” Physics Today 34, 27-35 (April198 1).

R. W. Hellwarth, “Generation of Time-Reversed Wave Fronts by Nonlinear Refraction,” Journal of theOptical Society of America 67, 1 (1977).

A. A. Ilyukhin, G. V. Peregudov, M. E. Plotkin, E. N. Ragozin, and V. A. Chirkov, “Focusing of a LaserBeam on a Target Using the Effect of Wave-Front Inversion (WFI) Produced as a Result of StimulatedMandel ‘Shtam-Brillouin Scattering (SMBS),” JETP Letters 29, 328-332 (1979).

M. D. Levenson, K. M. Johnson, V. C. Hanchett, and K. Chiang, “Projection Photolithography byWave-Front Conjugation,” Journal of the Optical Society of America 71, 737 (1981).

David M. Pepper, “Nonlinear Optical Phase Conjugation,” Optical Engineering 21, 156-183 (1982).

Michael Slatkine, Irving J. Bigio, B. J. Feldman, and Robert A. Fisher, “Efficient Phase Conjugation ofan Ultraviolet XeF Laser Beam by Stimulated Brillouin Scattering,” Optics Letters 7, 108-110 (1982).

B. I. Stepanov, E. V. Ivakin, and A. S. Rubanov, “Recording Two-Dimensional and Three-DimensionalDynamic Holograms in Transparent Substances,” Soviet Physics Doklady 16,46-48 (1971).

D. E. Watkins, J. F. Figueira, and S. J. Thomas, “Observation of Resonantly Enhanced Degenerate Four-Wave Mixing in Doped Alkali Halides,” Optics Letters 5, 169-171 (1980).

D. E. Watkins, C. R. Phipps, Jr., and S. J. Thomas, “Observation of Amplified Reflection ThroughDegenerate Four-Wave Mixing at CO2 Laser Wavelengths in Germanium,” Optics Letters 6, 76-78(1981).

J. P. Woerdman, “Formation of a Transient Free Carrier Hologram in Si,” Optics Communications 2,212-214 (1970).

Amnon Yariv and David M. Pepper, “Amplified Reflection, Phase Conjugation, and Oscillation inDegenerate Four-Wave Mixing,” Optics Letters 1, 16-18 (1977).

Horace P. Yuen and Jeffrey H. Shapiro, “Generation and Detection of Two-Photon Coherent States inDegenerate Four-Wave Mixing,” Optics Letters 4, 334-336 (1979).

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Connection Between theWave Fronts of the Reflected and Exciting Light in Stimulated Mandel ‘Shtam-Brillouin Scattering,”JETP Letters 15, 109-115 (1972).


AUTHORS

Barry J. Feldman received his Bachelor of Science from Brown University in1965 and his Ph.D. in physics from Massachusetts Institute of Technology in

1971. It was at M. I. T., under the tutelage of Drs. Ali Javan and MichaelFeId, that he first began his love affair with lasers. Upon graduation he came

directly to Los Alamos where for several years he was involved in theoreticalefforts related to laser fusion and laser isotope separation programs. His

work included theoretical studies of laser coherence phenomena, laser pulsepropagation, and Raman scattering. In 1976 he joined the C02 Laser

Research and Applications Group as Associate Group Leader and wasinvolved in the group’s experimental efforts at ultrashort pulse generation,

new laser development, optical phase conjugation, and nonlinear optics in theultraviolet. Currently he has turned his attention to the study of nonlinear

optical phenomena in organic and biological systems.

Irving J, Bigio received his B. S., M. S., and Ph.D. degrees in physics from theUniversity of Michigan in 1969, 1970, and 1974, respectively. His doctoralwork under John Ward and Peter Franken dealt with nonlinear optics, and

he has maintained a broad interest in the field of quantum electronics eversince. He came directly to Los Alamos in April 1974 as a staff member in the

laser isotope separation program and has also worked in the laser fusionprogram. In 1976 he received a Fulbright Senior Scholar Award and spent

the 1976-77 academic year as a visiting professor at the Weizmann Instituteof Science, Rehovot, Israel. During his tenure at the Weizmann Institute, he

taught graduate courses in laser physics and nonlinear optics and helpeddirect graduate student research. Since returning to Los Alamos he has

resumed his research and has taught courses at the University of NewMexico Graduate Center. Currently, he is working on a variety of topics inquantum electronics and has recently taken an interest in the application of

laser techniques and nonlinear optics to the solution of biophysics problems.

Robert A. Fisher received all of his schooling at the University of California,Berkeley, obtaining a B.A. in 1965, an M.A. in 1967, and a Ph.D. in 1971.

He then joined the laser fusion effort at Lawrence Livermore Laboratory andconcurrently taught at the University of California, Davis, before discovering

New Mexico in 1974. While at Los Alamos he has worked in the LaserFusion and Applied Photochemistry divisions. He was vice-chairman of the1981 Gordon Conference on Lasers and Nonlinear Optics, and he served on

the program committees for both the 1982 International Quantum Elec-tronics Conference and the 1981 Annual Meeting of the Optical Society of

America. He is the guest editor of a special issue on optical phaseconjugation of the Journal of the Optical Society of America and is the editor

of the soon-to-be-published Academic Press book entitled Optical PhaseConjugation. His professional interests include nonlinear optics, laser-related

phenomena, optical phase conjugation, and molecular physics.

18 Fall 1982/LOS ALAMOS SCIENCE


AUTHORS

Claude R. Phipps, Jr., has been a staff member at Los Alamos since 1974.He received his B.S. and M.S. in electrical engineering from the Massachu-setts Institute of Technology in 1961 and 1963 and his Ph.D. in electricalengineering (plasma physics) from Stanford University in 1972. His researchinterests have ranged from superconductivity through Thomson scattering inplasmas to nonlinear optics at infrared wavelengths, particularly phaseconjugation. He has also played a significant role in the measurement ofinfrared properties of optical materials. His wife, Lynn, is a commercialartist, and his son, David, is a physics major at Boston University. He is amember of the Society of Photo-Optical Instrumentation Engineers.

David E. Watkins earned his Bachelor of Science in 1975 from New MexicoInstitute of Technology and his Master of Science in 1978 and his Ph.D. in1981 from the University of Washington. He performed the research for hisPh.D. thesis, which involved phase conjugation by degenerate four-wavemixing, at Los Alamos as a graduate research associate. David has workedon high repetition rate CF4 lasers and Raman conversion for the uraniumenrichment program and maintains a strong interest in nonlinear opticalphenomena.

Scott J. Thomas was born in Spruce Pine, North Carolina, on November 18,1934. He joined the U.S. Air Force in 1955 and worked as an aircrafttechnologist in the Strategic Air Command. From 1961 to 1974 he wasemployed by Lawrence Livermore Laboratory in the Laser Fusion Division.He came to Los Alamos in 1974 and worked on laser research anddevelopment for the laser fusion program until 1981. Since then he hasworked in the Applied Photochemistry and Chemistry divisions. He haspublished work on laser-produced plasmas, laser photochemistry, chemicallasers, dye lasers, gas lasers, nonlinear optical studies, and laser damage tooptical surfaces. His present position as a staff member entails work on laserresearch and development.


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