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Physical Review A

Classical phase changes in nonlinear processes and their quantum counterparts

G. S. Agarwal, S. Chaturvedi, K. Tara, Venkatraman Srinivasan

Published Apr 1, 1992• 61 citations
Publisher

Abstract

Quantum-mechanical phase distributions are investigated for some nonlinear optical phenomena which, at a classical level, involve only changes in the phase of the electric field. The phenomena investigated include reflection from a phase-conjugate mirror and propagation through an optical fiber. It is found that, while the peaks of the respective phase distributions exhibit the expected classical behavior, the widths of the phase distributions also undergo substantial changes. The relation between the input and the output phase distributions in the two cases mentioned above is investigated analytically as well as numerically. The results are compared with a phase distribution defined via the Wigner function.

DOI
10.1103/physreva.45.4904

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Quantum-mechanical phase distributions are investigated for some nonlinear optical phenomena which, at a classical level, involve only changes in the phase of the electric field. The phenomena investigated include reflection from a phase-conjugate mirror and propagation through an optical fiber. It is found that, while the peaks of the respective phase distributions exhibit the expected classical behavior, the widths of the phase distributions also undergo substantial changes. The relation between the input and the output phase distributions in the two cases mentioned above is investigated analytically as well as numerically. The results are compared with a phase distribution defined via the Wigner function.
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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.
Most aspects of optical communications can be described in classical terms. Situations involving just a few photons are sometimes exceptions to this rule. The discussion below is an attempt to show that the Wigner quasiclassical treatment of light fields gives a picture close to the true quantum mechanics, applicable not only to linear processes, but also to weak nonlinear phenomena such as are encountered in the propagation of solitons. In effect, the Wigner picture involves treating vacuum zero-point fluctuations as an integral part of the noise field.
Longitudinal spatial effects in the nonlinear medium are analyzed in a model for mirrorless optical bistability due to induced absorption that treats heat conduction, electromagnetic field propagation, and temperature-dependent absorption. We consider two specific cases: the temperature-induced shift of the absorption peak of bound I2 excitons in CdS single crystals and the temperature-induced shrinkage of the band gap in GaAs/GaAlAs quantum-well material. For both cases it is shown that the inhomogeneous spatial distribution of the nonlinear absorption profile along the direction of propagation of the electric field undergoes a first-order-like phase transition commensurate with the transition of the output intensity from one value to another for fixed input intensity. Stability conditions are presented for the steady states of the output intensity as a function of the input intensity for the cases treated. There is a multiplicity of bistability curves, and the stability analysis produced the expected branches of stable solutions.
We review some quantum-phase descriptions of optical fields. We focus on real fields that can be generated in practice in various nonlinear optical processes. Thus, we rather avoid discussions of phase formalisms as such and try to exploit their practical applicability in the description of optical fields. In the description of the phase properties we use two different, though related formalisms: the Pegg-Barnett Hermitian phase formalism and the formalism based on sss-parametrized phase distributions.