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Journal of the Optical Society of America B

Double phase-conjugate mirror: convection and diffraction

A. A. Zozulya, Mark E. Saffman, Dana Z. Anderson

Published Feb 1, 1995• 11 citations
Publisher

Abstract

Development of scattered radiation in the geometry of a double phase-conjugate mirror is investigated numerically in the framework of a two-dimensional model that accounts for both diffraction and noncollinearity of the interacting beams. The large-scale structure of the scattered beams is found to be distorted because of the convective flow of energy out of the interaction region. We show that the output characteristics of the double phase-conjugate mirror depend strongly on the level of seed radiation in the direction of the scattered beams. The seed radiation may be due to incoherent scattering of the pumping beams inside the medium or to self-broadening of the pumping beams’ spectra because of nonlinear self-interaction.

DOI
10.1364/josab.12.000255

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Development of scattered radiation in the geometry of a double phase-conjugate mirror is investigated numerically in the framework of a two-dimensional model that accounts for both diffraction and noncollinearity of the interacting beams. The large-scale structure of the scattered beams is found to be distorted because of the convective flow of energy out of the interaction region. We show that the output characteristics of the double phase-conjugate mirror depend strongly on the level of seed radiation in the direction of the scattered beams. The seed radiation may be due to incoherent scattering of the pumping beams inside the medium or to self-broadening of the pumping beams’ spectra because of nonlinear self-interaction.
The double phase-conjugate mirror is an oscillator in the framework of the one-dimensional theoretical model previously used for its description. Results of a more consistent two-dimensional approach qualitatively differ from those of a one-dimensional analysis, indicating that the double phase-conjugate mirror is a convective amplifier. The correct physical picture of the scattering development is revealed, and the transverse profiles of scattered beams and the dynamics of nonlinear reflectivity are calculated.
Mutually pumped phase conjugation, a process by which two incident laser beams can mutually pump each other to generate the phase-conjugate replica of the other beam, is studied in a transparent Kerr medium with an electrostrictive nonlinearity. The nonlinear medium acts as a phase-conjugating mirror to both of the incident beams and generates their Stokes-shifted phase-conjugated outputs by the nearly degenerate four-wave mixing process. Our results show that this process will occur only if the coupling strength, defined by the product of the Kerr amplitude gain coefficient, the total input intensity, and the interaction length, is above the threshold value of 2. If the intensity of one of the input beams exceeds the threshold value and the second input beam is weaker than the first, then the weak beam is phase conjugated with a large reflectivity that has a maximum value of the intensity ratio of the strong to the weak input beam. For negligible absorption in the medium, a complete transfer of energy of both the incident beams into the phase-conjugate beams can occur for finite interaction lengths that are only slightly larger than the threshold value. Seeding the oscillation beams tends to lower the phase-conjugate power reflectivities, probably because of increased contribution from the competing two-wave mixing process.
We present theoretical and experimental studies of mutually pumped phase conjugation when a seed beam is injected that is the conjugate of one of the pumping beams. Good agreement exists between the theoretical and the experimental functional dependencies of the conjugate reflectivities on seed-beam intensity. However, the calculated gain is lower than that measured by two-beam coupling by nearly a factor of 2. We found that the seed-to-pump intensity ratio needs to exceed approximately 10−6, greater than 100 times the scattering, before the phase of the grating in the mutually pumped phase conjugator will follow the phase of the seed beam when it is varied by a moving mirror.
Phase-modulation effects in self-diffraction with two pump beams incident on a nonlinear medium were studied theoretically and experimentally. Based on a two-level model and considering the influence of the phase modulation on the phase matching, expressions describing the first-order and second-order scattered intensities were derived. The influences of phase modulation on the pump-intensity dependence and the sample-concentration dependence of the scattered intensities were discussed via numerical calculations. Experiments were performed with tetrahydrofuran solution of 1,4-diethinyl benzene to demonstrate the theoretical results. Some interesting results predicted by the theory, such as the fact that the scattered intensities of the sample with lower concentration can be larger than that with higher concentration at suitable high intensity of the pump, have been observed. \textcopyright{} 1996 The American Physical Society.