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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Introduction To And Applications Of Optical Phase Conjugation

Robert A. Fisher, J. McIver, A.F. Lange, Arthur H. Guenther, A.F. Stewart, G. J. Lapeyre

Published Nov 20, 1985• 0 citations
Publisher

Abstract

Optical phase conjugation is concerned with the use of nonlinear optical effects to precisely reverse the direction of propagation of each plane wave in an arbitrary beam of light. This causes the return beam to exactly retrace the path of the incident beam, leading to many applications of automatic pointing and tracking (even in the presence of an inhomogeneous medium). The main goals of this course are familiarization with how each of the many nonlinear optical effects gives rise to a phase conjugate signal, and understanding and appreciation of the many potential applications for optical phase conjugation. Conjugation techniques involving Kerr-like degenerate four-wave mixing, resonant degenerate four-wave mixing, stimulated Brillouin scattering, photorefractive effects, surface phenomena, and others will be carefully reviewed. Applications of particular importance to this course will include distortion correction, pointing, tracking, laser-resonator design, optical information processing, etc. Throughout the course, key references will be identified for those wishing to pursue any topic more vigorously.

DOI
10.1117/12.976180

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Recent work on phase conjugate resonators and their bistabilities and applications is reviewed. Emphasis is given to resonators involving degenerate four-wave mixing and those involving Brillouin enhanced four-wave mixing.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 1, 1991•0 citations
Optical phase conjugation is concerned with the use of nonlinear optical effects to precisely reverse the direction of propagation of each plane wave in an arbitrary beam of light. This causes the return beam to exactly retrace the path of the incident beam, leading to many applications of automatic pointing and tracking (even in the presence of an inhomogeneous medium). The main goals of this course are familiarization with how each of the many nonlinear optical effects gives rise to a phase conjugate signal, and understanding and appreciation of the many potential applications for optical phase conjugation. Conjugation techniques involving Kerr-like degenerate four-wave mixing, resonant degenerate four-wave mixing, stimulated Brillouin scattering, photorefractive effects, surface phenomena, and others will be carefully reviewed. Applications of particular importance to this course will include distortion correction, pointing, tracking, laser-resonator design, optical information processing, etc. Throughout the course, key references will be identified for those wishing to pursue any topic more vigorously.
Summary form only given. In this tallk I will try to supplement what I learned in the field. Here are the topics to be touched on. The order is not historical, but serves a tutorial purpose. 1. Time reversibility (TR) of optical wave propagation. 2. Mathematical description of TR in terms of complex amplitudes and complex conjugate amplitudes. 3. Static holography by real and conjugate images. 4.Static holography: illumination by counterpropagating reference waves at the recording and reconstruction stages. 5. Dynamic holography/four-wave mixing for phase conjugation (R. Hellwarth, A. Yariv, Yariv-Pepper instability. 6. Delayed and hidden holograms, photon echoes, electro-acoustic echoes. 7. Two-photon coherence, fast nonlinearities and three-wave mixing via X(2) nonlinearity. 8. Yet unrealized: Bragg (periodic domain). Time-domain phase conjugation: reversal of chirp and compensation of the dispersion spread in fibers. 10. Why a laser may (and may not) oscillate at a single transverse mode: discrimination of gain/loss. 11. Phase conjugation via stimulated Brillouin scattering (V.V. Ragulsky; V.V. Shkunov). 12. Brillouin-enhanced four-wave mixing for phase conjugation, ten to the tenth power amplification of the image (G.A. Pasmanik). 13. Photorefractive crystals: nonlinear response at low intensity at a cost of long build-up time. 14. Double phase conjugation 15. Feinberg's cat and cat conjugator.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
Optical phase conjugation (OPC) is a nonlinear optical technique for the generation of phase conjugate waves (PCWs) and their application. For a coherent and monochromatic light wave (signal beam) with a given wavefront shape, one can generate a new light wave with a reversed wavefront shape (with respect to the propagation direction) via nonlinear optical methods. This newly generated optical wave is termed the PCW of the input signal beam. Three major nonlinear optical methods can be employed to generate various PCWs: nonlinear four- or three-wave mixing, backward stimulated scattering, and backward stimulated emission (lasing). PCWs can overcome disturbing and aberration influences from the propagation medium. Therefore, this technique is especially useful in high brightness laser oscillator/amplifier systems, laser aiming and targeting systems, and long-distance and high bit-rate optical fiber communication systems. It also provides an effective approach to achieve lasing or stimulated scattering from a randomly disturbed gain medium.
The generation of phase conjugated replicas of optical signals has been the subject of many theoretical and experimental studies. Phase conjugation of harmonic signals is a byproduct of certain nonlinear processes such as degenerate four- wave mixing and stimulated Brillouin scattering. Although conjugation of steady signals is well established, the possibility and the effectiveness of conjugating unsteady signals remain largely unexplored. When the envelope of an optical signal varies, new physical phenomena in the conjugation process arise. As previously shown,1 dispersion in the conjugation process distorts the phase conjugate replica of a pulsed signal. Distortion appears even if the response of the medium to the applied optical signal is instantaneous.
This thesis describes theoretical and experimental aspects as well as potential applications in the field of coherent optics known as Phase Conjugate Optics (PCO). By utilizing nonlinear optical techniques, real-time or wavefront reversal of an arbitrary incident electromagnetic field can be realized. The nonlinear optical interaction gives rise to what is referred to as the phase conjugate (of the incident monochromatic wave) by performing the operation of complex conjugation upon the incident wave's complex spatial amplitude in real time. This conjugate wave, which is also designated as being a wavefront, has the property of exactly retracing the path of the incident field. The ability of the conjugate wave to correct for inhomogeneous linear and nonlinear (intensity-dependent) aberrations as well as polarization distortions is proved. In particular, the theory of a degenerate four-wave nonlinear optical interaction as providing for the conjugator is presented. The effects of linear and nonlinear losses upon this interaction are discussed. The quantum mechanical origin of the third order nonlinear optical susceptibility responsible for the four-wave mixing process is analyzed for both single and two-photon allowed transitions in an atomic (or molecular) system. The analogies of four-wave mixing with that of real-time holography are discussed. The theory of conjugation via four-wave mixing in optical waveguides is presented. Several of the above characteristics of conjugate fields are verified experimentally where conjugate fields via degenerate four-wave mixing were observed both in the bulk and in waveguide geometries, using carbon disulfide as the nonlinear medium. Amplified time-reversed wavefront generation as well as a mirrorless optical parametric mode of oscillation have been observed, both in agreement with theoretical predictions. Potential applications of PCO are discussed in three different regimes: spatial-frequency, temporal-frequency, and spatial/temporal frequency domains. In the first category, the ability of PCO to correct for image modal dispersion in optical waveguides as well as the use of PCO to perform real-time coherent image processing and nonlinear microscopy is discussed. Temporal-frequency domain applications of PCO to be analyzed include the use of a nearly degenerate four-wave mixing process as a narrowband, wide field-of-view optical filter, capable of an amplified bandpass. The ability of a PCO interaction to renarrow (transform limited) optical pulses which have been temporally spread due to propagation through (group velocity) dispersive channels is analyzed. A potential application of PCO in the field of nonlinear laser spectroscopy is presented. Specifically, the scattering of a probe photon off a two-photon coherent state (created in a three-level atomic system) is shown to yield a conjugate replica. This conjugate replica is capable of providing sub-Doppler width resolution of the two-photon resonance. Further, in the transient regime, the optical free-induction decay of the conjugate wave is capable of yielding detailed spectral features of the three-level system such as the anharmonic contribution to a (nearly) harmonic potential. This technique, performed in the time domain, is known as [alpha]-beat spectroscopy. Finally, a detailed theoretical and experimental study is presented of a laser resonator in which one (or both) of the mirror(s) comprising the optical cavity is replaced by a conjugate mirror (PCM). This novel resonator, which is termed a conjugate resonator (PCR), combines many of the spatial- and temporal-frequency aspects of PCO interactions discussed above. The stability criterion, transverse and longitudinal mode spectra, and the PCR output energy, as well as the frequency locking features of the laser modes to the PCM are discussed.