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

Physical Review A

Feedback-controlled photorefractive two-beam coupling

Vladimir P. Kamenov, Klaus H. Ringhofer, Boris I. Sturman, Jaime Frejlich

Published Oct 1, 1997• 22 citations
Publisher

Abstract

We show that a certain phase feedback between output and input changes dramatically the characteristics of photorefractive two-beam coupling. The diffraction efficiency of the dynamic phase grating, $\ensuremath{\eta}$, reaches 1 or 0 (depending on the feedback sign) within a finite time for a wide range of experimental parameters. The spatial-temporal behavior of the wave amplitudes is strongly nonlinear and the grating fringes for $\ensuremath{\eta}=1$ or $0$ are bended but not tilted. The theory elucidates a number of empirical observations and reveals the great potential of active stabilization for applications.

DOI
10.1103/physreva.56.r2541

Related papers

Shaping of photorefractive two-wave coupling by fast phase modulation

Klaus H. Ringhofer, Vladimir P. Kamenov, Boris I. Sturman +1 more

Using the distinctive features of the photorefractive nonlinearity, we derive a general self-consistent set of equations to describe two-wave coupling in the presence of fast and arbitrary strong-phase modulation. By considering a number of important particular cases, we show that phase modulation is a powerful and useful tool for shaping the characteristics of two-wave coupling such as the value of the energy exchange, the diffraction efficiency of the recorded grating, and the structure of the grating fringes. Finally, we analyze the role of the phase modulation in the active stabilization of wave coupling by means of an electronically introduced phase feedback.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Feb 1, 2000•17 citations

The geometry underlying photorefractive two-beam coupling

Valeria Damiao, Dana Z. Anderson

We cast the theory of photorefractive two-beam coupling in geometrical terms and derive a closed form solution to the problem of two-beam coupling with time-dependent fields that evolve in such a way as to give rise to a stationary index of a refraction grating. The geometrical approach treats the optical field amplitudes in terms of vectors whose spatial dynamics is governed by a Hamiltonian. A density matrix formed from the optical fieldvectors is shown to have particularly simple dynamics. We derive a formula for a transfer matrix that accommodates complex coupling coefficients and that can be used to calculate the instantaneous output of the photorefractive grating given any input. The geometrical picture of photorefractive two-beam coupling is pedagogically developed through several specific examples.

Journal of Optics A Pure and Applied Optics•Oct 27, 2003•1 citation

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

Dynamic bistability of an optical ring circuit having photorefractive gain, loss, and a photorefractive feedback coupling element: theory

David D. Crouch, Anno Hermanns, Dana Z. Anderson

We discuss the properties of an optical circuit with gain and loss provided by two-beam coupling in a photorefractive medium and with a photorefractive element as a programmable mirror to provide feedback. As with an ordinary ring resonator having photorefractive gain and loss the circuit can exhibit reversible or irreversible bistability and self-pulsing. In the limit that the feedback element has a response that is slow compared to the gain and loss, its behavior is much like the conventional case. However, whereas a conventional ring resonator has a well-defined detuning characteristic dependent on the round trip length, in the present circuit a fast photorefractive element continually compensates for changes in the round trip path length. The bistability and self-pulsing characteristics are strongly affected by the relative time constants of the three photorefractive media and by the relative magnitudes of the small signal gain and loss. In particular, the on state of the ring has a memory time determined by the time constant of the feedback element.

Annual Meeting Optical Society of America•Jan 1, 1989•0 citations

Multistability by Two Counterpropagating Waves in Photorefractive Media

Wang Jian, Yao Jianquan

It has been shown that two-wave coupling in photorefractive media may result in energy transference between the two waves without phase crosstalk. The model might be used to show optical bistability with the feedback of one of the output beams into the input of the other beam.

Photorefractive Effects, Materials, and Devices•Jan 1, 1987•1 citation

Two-wave coupling under fast phase modulation

Klaus H. Ringhofer, Vladimir P. Kamenov, Boris I. Sturman +2 more

Using the distinctive features of the photorefractive nonlinearity, we solve exactly the problem of the influence of an arbitrary (in strength and shape) fast phase modulation on 2W-coupling. We show that the fast modulation is a useful tool for shaping the characteristics of wave coupling, such as the value of the energy exchange and the diffraction efficiency of the recorded grating.

Photorefractive Effects, Materials, and Devices•Jan 1, 1999•0 citations
We show that a certain phase feedback between output and input changes dramatically the characteristics of photorefractive two-beam coupling. The diffraction efficiency of the dynamic phase grating, \ensuremathη\ensuremath{\eta}\ensuremathη, reaches 1 or 0 (depending on the feedback sign) within a finite time for a wide range of experimental parameters. The spatial-temporal behavior of the wave amplitudes is strongly nonlinear and the grating fringes for \ensuremathη=1\ensuremath{\eta}=1\ensuremathη=1 or 000 are bended but not tilted. The theory elucidates a number of empirical observations and reveals the great potential of active stabilization for applications.
Using the distinctive features of the photorefractive nonlinearity, we derive a general self-consistent set of equations to describe two-wave coupling in the presence of fast and arbitrary strong-phase modulation. By considering a number of important particular cases, we show that phase modulation is a powerful and useful tool for shaping the characteristics of two-wave coupling such as the value of the energy exchange, the diffraction efficiency of the recorded grating, and the structure of the grating fringes. Finally, we analyze the role of the phase modulation in the active stabilization of wave coupling by means of an electronically introduced phase feedback.
We cast the theory of photorefractive two-beam coupling in geometrical terms and derive a closed form solution to the problem of two-beam coupling with time-dependent fields that evolve in such a way as to give rise to a stationary index of a refraction grating. The geometrical approach treats the optical field amplitudes in terms of vectors whose spatial dynamics is governed by a Hamiltonian. A density matrix formed from the optical fieldvectors is shown to have particularly simple dynamics. We derive a formula for a transfer matrix that accommodates complex coupling coefficients and that can be used to calculate the instantaneous output of the photorefractive grating given any input. The geometrical picture of photorefractive two-beam coupling is pedagogically developed through several specific examples.
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.
We discuss the properties of an optical circuit with gain and loss provided by two-beam coupling in a photorefractive medium and with a photorefractive element as a programmable mirror to provide feedback. As with an ordinary ring resonator having photorefractive gain and loss the circuit can exhibit reversible or irreversible bistability and self-pulsing. In the limit that the feedback element has a response that is slow compared to the gain and loss, its behavior is much like the conventional case. However, whereas a conventional ring resonator has a well-defined detuning characteristic dependent on the round trip length, in the present circuit a fast photorefractive element continually compensates for changes in the round trip path length. The bistability and self-pulsing characteristics are strongly affected by the relative time constants of the three photorefractive media and by the relative magnitudes of the small signal gain and loss. In particular, the on state of the ring has a memory time determined by the time constant of the feedback element.