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Optical and Quantum Electronics

Phase-conjugate bistability and multistability in moving-grating operated orthogonally polarized pump four-wave mixing in photorefractives

T. K. Das, Gopal Chandra Bhar

Published Nov 1, 1994• 6 citations
Publisher
DOI
10.1007/bf00305002

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We investigate the bistable and multistable response of the phase conjugate reflectivity (PCR) for the case of a linear photorefractive (PR) oscillator in presence of the moving grating operation. Numerical evaluation of stable multiple solutions of the PCR shows enhancement, bistable, multistable and self-oscillating behaviours with respect to the control parameters like the frequency-shift (Ω) due to grating motion, reflectivities (M 1 and M 2) of cavity mirrors, the coupling strength (of complex gL and real g 0 L values) and the PR phase shift (φPR). If the different branches are assumed to be stable, multistable but isolated branching behaviour with an increased PCR can be predicted. Results are interpreted physically by considering the competitions between (i) the strengths of two moving transmission gratings that arise from A1–A4 (forward oscillating pump-incident) and A2–A3 (backward oscillating pump-phase conjugate) interferences and (ii) the applied frequency detuning that causes the gratings to move and the self-induced cavity detuning that appears when the gratings are stationary. Numerical evidence of the results is presented graphically.

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Bistability control by forward pump beam in photorefractive four-wave mixing

Yoshihisa Takayama, Atsushi Okamoto, Kunihiro Sato

A typical method of generating phase conjugate light using photorefractive crystals is four-wave mixing. It is known that the phase conjugate reflectivity is multivalued in a steady state. In this paper, a time domain response analysis of four-wave mixing is carried out and the method for controlling the bistability of the phase conjugate reflectivity is described. First, a steady-state analysis of the four-wave mixing is carried out and the condition is derived for bistability of the phase conjugate reflectivity. Next, by using two different initial conditions, the time response analysis is carried out for the four-wave mixing. Under one of the conditions, no forward pump beam is incident before and after observation of the bistability for measurement of phase conjugate reflectivity. Under another condition, the forward pump is incident before observation of the bistability. The phase conjugate reflectivity is measured after this pump is cut off when a steady state is reached. For each case, the numerical calculations are carried out. It is shown for the first time that the bistability of the phase conjugate reflectivity can be controlled by the initial condition. Further, the temporal and spatial variations of the diffraction grating generated in the crystal are studied and the process of the phase conjugate reflectivity to exhibit bistability is clarified. © 1998 Scripta Technica, Electron Comm Jpn Pt 2, 81(2): 1–8, 1998

Electronics and Communications in Japan (Part II Electronics)•Feb 1, 1998•0 citations

Optical bistability in photorefractive nearly DFWM using orthogonally polarized pumps: transmission geometry

N Birla, Avinashi Kapoor

Optical bistability based on the theory of photorefractive nearly degenerate four-wave mixing (DFWM) is considered for the case of transmission geometry with orthogonally polarized pump beams. The coupled wave equations are solved to obtain a nonlinear algebraic equation. This equation is being solved iteratively using Muller's method. The effect of different parameters pump ratio (r), probe ratio (q), coupling strength ( Gamma ) and frequency shift ( Omega ) on the phase conjugate reflectivity (PCR) have been investigated and the results are reported.

Journal of Optics•Sep 1, 1995•0 citations
We investigate the bistable and multistable response of the phase conjugate reflectivity (PCR) for the case of a linear photorefractive (PR) oscillator in presence of the moving grating operation. Numerical evaluation of stable multiple solutions of the PCR shows enhancement, bistable, multistable and self-oscillating behaviours with respect to the control parameters like the frequency-shift (Ω) due to grating motion, reflectivities (M 1 and M 2) of cavity mirrors, the coupling strength (of complex gL and real g 0 L values) and the PR phase shift (φPR). If the different branches are assumed to be stable, multistable but isolated branching behaviour with an increased PCR can be predicted. Results are interpreted physically by considering the competitions between (i) the strengths of two moving transmission gratings that arise from A1–A4 (forward oscillating pump-incident) and A2–A3 (backward oscillating pump-phase conjugate) interferences and (ii) the applied frequency detuning that causes the gratings to move and the self-induced cavity detuning that appears when the gratings are stationary. Numerical evidence of the results is presented graphically.
A typical method of generating phase conjugate light using photorefractive crystals is four-wave mixing. It is known that the phase conjugate reflectivity is multivalued in a steady state. In this paper, a time domain response analysis of four-wave mixing is carried out and the method for controlling the bistability of the phase conjugate reflectivity is described. First, a steady-state analysis of the four-wave mixing is carried out and the condition is derived for bistability of the phase conjugate reflectivity. Next, by using two different initial conditions, the time response analysis is carried out for the four-wave mixing. Under one of the conditions, no forward pump beam is incident before and after observation of the bistability for measurement of phase conjugate reflectivity. Under another condition, the forward pump is incident before observation of the bistability. The phase conjugate reflectivity is measured after this pump is cut off when a steady state is reached. For each case, the numerical calculations are carried out. It is shown for the first time that the bistability of the phase conjugate reflectivity can be controlled by the initial condition. Further, the temporal and spatial variations of the diffraction grating generated in the crystal are studied and the process of the phase conjugate reflectivity to exhibit bistability is clarified. © 1998 Scripta Technica, Electron Comm Jpn Pt 2, 81(2): 1–8, 1998
Optical bistability based on the theory of photorefractive nearly degenerate four-wave mixing (DFWM) is considered for the case of transmission geometry with orthogonally polarized pump beams. The coupled wave equations are solved to obtain a nonlinear algebraic equation. This equation is being solved iteratively using Muller's method. The effect of different parameters pump ratio (r), probe ratio (q), coupling strength ( Gamma ) and frequency shift ( Omega ) on the phase conjugate reflectivity (PCR) have been investigated and the results are reported.