Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Modern Optics

Optical Bistability and Multistability in the Linear Photorefractive Oscillator Accompanied by a Frequency Shift Due to Grating Motion

T.K. Das, Gopal Chandra Bhar

Published Sep 1, 1993• 2 citations
Publisher

Abstract

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.

DOI
10.1080/09500349314551831

Related papers

Self-oscillation in a photorefractive phase-conjugate mirror with linear absorption I Isotropic four-wave mixing

Nitin C. Kothari, J. A. Tataronis

The effects of linear absorption on the degenerate and nondegenerate self-oscillation conditions of a photorefractive phase-conjugate mirror are explored. In this study, phase-conjugation results from nonlinear mixing of two strong undepleted parallel-polarized counterpropagating pump waves with a probe wave. Numerical results are presented that illustrate that the linear absorption tends to increase the value of the coupling coefficient required for self-oscillation. It is also found that the pump intensity ratio r is almost independent of the linear absorption for positive normalized detuning Δωτ between the probe and the pump frequencies and of the zero phase shift, ϕ, between the gratings and the light interference patterns when the gratings are stationary. For ϕ = ±π/2, the variation of r with respect to absorption is symmetric for positive and negative detunings.

Journal of the Optical Society of America B•Oct 1, 1996•2 citations

Phase conjugate resonators and bistabilities in BaTiO3

Mostafa Dokhanian, Putcha Venkateswarlu, P. Chandra Sekhar

We report our observations of optical bistabilities and hysteresis1 in photorefractive passive phase conjugate resonators with BaTiO3, caused by grating erasure effects between two resonators in three different configurations. Bistable oscillations have been observed between two semilinear oscillators, two ring resonators, and also between a ring and a semilinear resonator. In the experimental arrangement used for bistability studies, a single-mode argon ion laser beam (4880 Å) entered the crystal in a face appropriate for self-pumped phase conjugation. However, the orientation is kept in such a way that no self-pumped phase conjugation is observable if none of the resonators is in operation. In this geometry, bistability and hysteresis were observed in the signal intensity of one resonator as the reflectivity of the variable beam reflector in the second resonator was increased and then decreased in a cycle. Bistability was also seen in the signal intensity of a single resonator as a function of the reflectivity of the external mirror.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations

Bistable phase-conjugate reflectivity controlled by a forward pump beam

Yoshihisa Takayama, Atsushi Okamoto, Mototsugu Takamura +1 more

One of the typical methods to generate the phase-conjugate beam is four-wave mixing with a photorefractive crystal. It is known that the phase-conjugate reflectivity shows the bistability in some cases. Analyzing the temporal property of four-wave mixing, we offer a new method to control the bistable phase-conjugate reflectivity, and we perform an experiment of the bistability control by the method. An equation to obtain the threshold value of the coupling strength for showing the bistability is derived by a steady-state analysis of four-wave mixing, and the temporal property of four-wave mixing is studied with two different initial conditions that are used for letting the phase-conjugate reflectivity R converge to an off state (R=0) or to an on state (R>0). The initial condition for the converging off state is that the forward pump beam is turned off throughout. The condition for the converging on state is that the forward pump beam is turned on in advance, and after enough time passes, it is turned off. In both conditions, the backward pump beam and the probe beam continue to illuminate throughout. Whereas both optical arrangements are equivalent after setting up these initial conditions, each phase-conjugate reflectivity converges to different stationary values, R=0 and R>0. Besides, an experiment is performed and we actually control the bistability by this method. Furthermore, the temporal and the spatial variation of the refractive-index grating in the photorefractive crystal is investigated, and the process of the bistability is explained.

Journal of the Optical Society of America B•Oct 1, 1997•2 citations

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 by photorefractive two-wave mixing

Jianquan Yao, J. Wang

It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.

Annual Meeting Optical Society of America•Jan 1, 1987•0 citations

Self-induced coherent oscillations with photorefractive Bi_12SiO_20 amplifier

Henri J. Rajbenbach, Jean‐Pierre Huignard

We report coherent oscillations due to self-induced moving gratings in photorefractive BSO crystals when recording with an external applied field. Different types of ring and phase-conjugate resonators pumped with low-incident- intensity beams and having short response times are demonstrated. The conditions permitting oscillation and the respective frequencies of the pump and the signal beams in the cavity are analyzed.

Optics Letters•Mar 1, 1985•123 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.
The effects of linear absorption on the degenerate and nondegenerate self-oscillation conditions of a photorefractive phase-conjugate mirror are explored. In this study, phase-conjugation results from nonlinear mixing of two strong undepleted parallel-polarized counterpropagating pump waves with a probe wave. Numerical results are presented that illustrate that the linear absorption tends to increase the value of the coupling coefficient required for self-oscillation. It is also found that the pump intensity ratio r is almost independent of the linear absorption for positive normalized detuning Δωτ between the probe and the pump frequencies and of the zero phase shift, ϕ, between the gratings and the light interference patterns when the gratings are stationary. For ϕ = ±π/2, the variation of r with respect to absorption is symmetric for positive and negative detunings.
We report our observations of optical bistabilities and hysteresis1 in photorefractive passive phase conjugate resonators with BaTiO3, caused by grating erasure effects between two resonators in three different configurations. Bistable oscillations have been observed between two semilinear oscillators, two ring resonators, and also between a ring and a semilinear resonator. In the experimental arrangement used for bistability studies, a single-mode argon ion laser beam (4880 Å) entered the crystal in a face appropriate for self-pumped phase conjugation. However, the orientation is kept in such a way that no self-pumped phase conjugation is observable if none of the resonators is in operation. In this geometry, bistability and hysteresis were observed in the signal intensity of one resonator as the reflectivity of the variable beam reflector in the second resonator was increased and then decreased in a cycle. Bistability was also seen in the signal intensity of a single resonator as a function of the reflectivity of the external mirror.
One of the typical methods to generate the phase-conjugate beam is four-wave mixing with a photorefractive crystal. It is known that the phase-conjugate reflectivity shows the bistability in some cases. Analyzing the temporal property of four-wave mixing, we offer a new method to control the bistable phase-conjugate reflectivity, and we perform an experiment of the bistability control by the method. An equation to obtain the threshold value of the coupling strength for showing the bistability is derived by a steady-state analysis of four-wave mixing, and the temporal property of four-wave mixing is studied with two different initial conditions that are used for letting the phase-conjugate reflectivity R converge to an off state (R=0) or to an on state (R>0). The initial condition for the converging off state is that the forward pump beam is turned off throughout. The condition for the converging on state is that the forward pump beam is turned on in advance, and after enough time passes, it is turned off. In both conditions, the backward pump beam and the probe beam continue to illuminate throughout. Whereas both optical arrangements are equivalent after setting up these initial conditions, each phase-conjugate reflectivity converges to different stationary values, R=0 and R>0. Besides, an experiment is performed and we actually control the bistability by this method. Furthermore, the temporal and the spatial variation of the refractive-index grating in the photorefractive crystal is investigated, and the process of the bistability is explained.
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
It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.