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.
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.
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.
Four wave mixing, a third-order optical parametric process, is the nonlinear optical process in which four waves interact with each other through the third-order optical nonlinearity. In this process, three waves form a nonlinear polarization at the frequency of the fourth wave. An important application of degenerate four wave mixing is the generation of phase conjugate wave or simply the phase conjugation. The phase conjugate wave has the same wavefront as the incident wave; however, it propagates backward. The phase conjugation is equivalent to the time reversal. Straightforward application of the time reversal is the correction of phase aberration. Suppose that, the incident wave propagates in the nonuniform medium, such as a laser amplifier, where the temperature is fluctuated by intense pumping. Then, the incident wave suffers severe phase aberration during the propagation and the transmitted wave is then reflected by the phase conjugate mirror and goes back into the same nonuniform medium.
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.
Part I of this thesis describes the theoretical and experimental aspects of a new area in coherent optics known as phase conjugate optics. By using nonlinear optical mixing techniques, the complex conjugate of an arbitrary incident monochromatic wave can be generated. In particular, the theory of the degenerate four-wave mixing technique is presented. Experimental observation of phase conjugate wave front generation in a liquid crystal material (MBBA) is described. The ability of the conjugate wave front to correct for phase aberration is demonstrated. The quantum mechanical origin of the nonlinear third order susceptibility responsible for the four-wave mixing process is illustrated in an atomic system. Because of a finite memory time of such an atomic system, the electromagnetic waves taking part in the mixing process need not occur simultaneously. The applications of the phase conjugation process to real-time information processing and the characteristics of a phase conjugate resonator are discussed in detail. The ability of an optical fiber to confine the propagation of electromagnetic waves over a long distance and within a small cross sectional area implies that large optical intensities can be maintained over a long " interaction length even at moderate incident optical power. Part II of this thesis describes some third order nonlinear optical phenomena that have been observed under this condition. Especially, phase conjugation by degenerate four-wave mixing in a fiber has been shown to require significantly less pumping power. The theoretical and experimental studies of four-wave mixing in a liquid-filled fiber are presented. Extensive experimental efforts have been devoted over the last few years to the study of stimulated Raman scattering and the oscillation of the Stokes radiation inside fibers. A detailed theoretical treatment will be given here to describe these effects. The analysis shows that pump depletion due to the nonlinear process is very important in describing the stimulated Raman scattering in low loss fibers and is the dominant saturation effect in a fiber Raman oscillator. Finally, the implications of nonlinear optical phenomena to fiber optic communication will be mentioned.
Various aspects of optical phase conjugation are discussed: the properties of the conjugate wave, its potential applications, the basic conjugation methods, and a brief history of the question. The theory for phase conjugation in stimulated scattering is set forth in detail. The basic experimental results on this conjugation method are also discussed in detail. Phase conjugation occurs because that configuration of the back-scattered field which has the conjugate wavefront is amplified to the greatest extent (at a doubled gain) in the intense speckle-inhomogeneous conjugate wave in a medium in which stimulated scattering occurs. Because of the large overall amplification in stimulated scattering, all the other, uncorrelated, configurations of the spontaneously scattered nucleating waves are amplified by a factor of 107 less and are discriminated against. The intervals of values of the various parameters in which the conjugate configuration (the specklon) exists are discussed theoretically, as is the effect of nonlinear selection and saturation on phase conjugation in stimulated scattering. There is a review of experimental results on the first observation of the effect, on the measurement of the angular structure of the uncorrelated waves and of the extent to which they are discriminated against, on the phase fluctuations of the conjugate wave, on the conjugation of subthreshold and depolarized radiation, and on phase conjugation in stimulated scattering in focused beams and for other scattered-wave amplification mechanisms.
Optical phase conjugation is a process that leads to the correction of wavefront distortions under conditions such that a beam of light passes twice in opposite directions through an aberrating optical medium. Analogously, the state of polarization of an optical beam can become aberrated, (for example, by passing through a stressed optical component), and these polarization aberrations can be removed by the process of polarization conjugation. In polarization conjugation, the polarization unit vector of the incident wave is replaced by its complex conjugate in the generated wave.