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Physical Review A

Phase conjugation by four-wave mixing of statistical beams

G. Lera, Manuel Nieto‐Vesperinas

Published Jun 1, 1990• 7 citations
Publisher

Abstract

A study of the influence of the spatial structure and statistics of the pump beams in the phase-conjugation process is made, showing that the reflectivity varies along the phase-conjugation mirror when the phase factor in the coupling equations that describe the process is not constant. The mutual coherence function of the generated field is calculated from the mutual reflectivity of the mirror for two commonly used statistics for the partially coherent pump beams. Finally, the influence of diffractional effects is also analyzed, showing that, in general, the fidelity of the process is degraded.

DOI
10.1103/physreva.41.6400

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A study of the influence of the spatial structure and statistics of the pump beams in the phase-conjugation process is made, showing that the reflectivity varies along the phase-conjugation mirror when the phase factor in the coupling equations that describe the process is not constant. The mutual coherence function of the generated field is calculated from the mutual reflectivity of the mirror for two commonly used statistics for the partially coherent pump beams. Finally, the influence of diffractional effects is also analyzed, showing that, in general, the fidelity of the process is degraded.
Phase-conjugate beam fidelity is studied in degenerate four-wave mixing with spatially varying pump beams. The theory includes long-cell-length (or high-gain) effects, diffraction, and nonlinear phase variation, focusing of the probe beam, and, finally, losses. Relatively simple algebraic expressions for the reflectivity are given that cover the cases of collinear or near-collinear beam geometries. An easily calculated parameter is defined that characterizes phase-conjugate fidelity and is applied to study focusing effects. It is shown that focusing effects may be useful in greatly reducing the principal distortion of the phase-conjugate beam over a considerable range of variation of beam parameters.
We investigate the effect of beam temporal coherence on four-wave mixing via transmission gratings in photorefractive media. We take into account the propagation of mutual coherence and self-coherence in space and the evolution of mutual coherence and self-coherence with time. Analytical solutions for nondepleted-pump cases and numerical results for general cases are obtained. We find that the mutual coherence of the signal beam and the pump beam can be enhanced or reduced, depending on the coupling constant and the beam ratio of the signal beam and the pump beam. A decrease of the initial mutual coherence can lead to a lower phase-conjugate reflectivity in the nondepleted-pump case. Even with low initial mutual coherence, high phase-conjugate reflectivity can still be obtained in the case with pump depletion. As a result of the shift of the grating profile, partial coherence can lead to an enhancement of the phase-conjugate reflectivity when the signal–pump-beam ratio is small. We also found that when the initial value of the phase-conjugate beam is zero, the phase-conjugate beam and the pump beam are in phase during propagation. Results for beam intensity and mutual coherence are presented and discussed to provide an insight into four-wave mixing with partially temporally coherent waves.
An experimental investigation was made of the influence of the state of optically polished surfaces of various materials on the scattering coefficient which governs the power of the intrinsic noise of phase-conjugate mirrors based on a degenerate four-wave interaction. The angular dependence of this coefficient was also investigated. The noise power of a phase-conjugate mirror made of InAs, operating at the optimal pump wave intensities 1— 2 MW cm -2 , may be reduced to ~2 × 10 -7 W per one spatial mode of the radiation to be phase-conjugated. This was achieved by increasing the angle between the axes of the signal and the pump beams up to ~1 rad without a significant reduction of the reflection efficiency, which can be ~500%.
Nondegenerate four-wave mixing on the j=0\ensuremath{\rightarrow}j=1 transition, in a ``V '' system, using orthogonal, circularly polarized pump beams is used to study theoretically the generation of the phase-conjugate signals. The efficiency of generation of the conjugate wave is studied as a function of the various system parameters such as pump-probe detuning, Zeeman splitting, pump-atom detuning, collisional parameters, and the intensities of the pump beams. The origin of the various resonances in the reflectivity is explained. For weak pump fields, some resonances are shown to have subnatural linewidths. In the degenerate case, the reflectivity as a function of pump-atom detuning has, in contrast to a two-level system, a doublet structure for moderate absorption-length parameters and field strengths. The reflectivity is shown to have additional resonances due to pump imbalance. The phase-conjugate signal is also shown to exhibit the pressure-induced extra resonances.