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 the Optical Society of America B

Degenerate parametric amplification in photorefractive media: theoretical analysis

Henrik C. Pedersen, Per Michael Johansen

Published Mar 1, 1996• 4 citations
Publisher

Abstract

We present for the first time, to our knowledge, a theoretical analysis of the nonlinear dynamic space-charge field buildup when a photorefractive medium is exposed simultaneously to two running gratings. It is shown that the two gratings are nonlinearly coupled, hence, for an appropriate choice of parameters, the two gratings interact, causing one grating to be amplified at the expense of the other. This process is referred to as degenerate parametric amplification. In principle an infinite amplification is possible because, even in cases for which no signal grating (i.e., the one to be amplified) is externally seeded into the crystal, a finite signal-grating amplitude is obtained after relaxation of the amplification process.

DOI
10.1364/josab.13.000590

Related papers

Parametric oscillation in photorefractive media

Henrik C. Pedersen, Per Michael Johansen

We present an analysis of what is called parametric oscillation in photorefractive media. It is shown theoretically that when a running grating and a constant electric field are applied to a photorefractive medium it is possible for two secondary gratings to grow spontaneously. These theoretical predictions are subsequently verified experimentally in the crystal Bi12SiO20, and excellent qualitative agreement is obtained. In previous subharmonic experiments, only grating vectors K/2, K/3, and K /4 were observed. Now, however, a whole continuum of grating vectors has been observed. Thus subharmonic generation in photorefractive materials is simply a special case of parametric oscillation in which the two secondary gratings are identical.

Journal of the Optical Society of America B•Jun 1, 1995•24 citations

Observation of Nondegenerate Photorefractive Parametric Amplification

Henrik C. Pedersen, Per Michael Johansen

We report on the first experimental observation of so-called nondegenerate photorefractive parametric amplification. We show that due to this effect it is possible for a weakly modulated photoinduced grating to be parametrically amplified via nonlinear interaction with a strongly modulated photoinduced grating.

Physical Review Letters•May 27, 1996•10 citations

Parametric coherent oscillation with feedback via an orthogonally polarized wave

P. Jullien, Pierre Lompré, P. Mathey +2 more

Coherent light amplification with photorefractive crystals may be a consequence of several frequency degenerate (or nearly degenerate) processes of nonlinear wave mixing : It appears for two- beam coupling in the crystals with diffusion-driven charge transport [1] or transport via circular photovoltaic currents [2].

Photorefractive Effects, Materials, and Devices•Jan 1, 1999•0 citations

Signal-to-pump ratio dependence of buildup and decay rates in photorefractive nonlinear two-beam coupling

Moshe Horowitz, Ron Daisy, Baruch Fischer

The buildup and the decay of photorefractive two-beam coupling are experimentally demonstrated to be strongly dependent on the intensity ratio of the two beams (signal-to-pump ratio). The experiment, done with a BaTiO3 crystal, shows good agreement with the theory of two-beam coupling in the depleted-pump regime. The deviation of the response behavior from the small-signal regime is seen for ratios as small as ∼10−5. These results are significant for applications of two-beam coupling as gain media, especially for the elimination of amplified noise (fanning).

Journal of the Optical Society of America B•Sep 1, 1992•18 citations

Nonlinear dynamics of two-wave coupling process

M.R. Sayeh, Azad Z. Siahmakoun

We present a closed-form solution for the two-wave coupling process, resulting in a solution with an interesting part, the arbitrary function Lambda(t), not being considered in the previous works. In the photorefractive medium, it has been shown that a moving grating will produce a phase shift in the coupling constant. To our knowledge, this has not been derived directly from the grating dynamic equations. We will also show that the temporal dynamics does not have any asymptotically stable equilibrium points of an exponential form. As an example, we have developed resonance conditions resulting in a new expression for the frequency detuning of a resonator with a photorefractive gain medium.

Optics Express•Jan 1, 2004•3 citations

Simultaneous phase-sensitive parametric amplification and up-conversion of an optical image

A. S. Chirkin, E. V. Makeev

We develop for the first time a quantum theory of simultaneous amplification and frequency up-conversion of optical images in two coupled three-wave processes. The theory developed takes into account the diffraction effect and the difference of the group velocities of the interacting waves. Due to the degenerate parametric process involved in the nonlinear optical interactions, the up-conversion also possesses phase sensitivity. As a result, the statistical characteristics of the amplified image and the converted one depend on the phase relation between the signal and the pump waves. It is shown that at the output of the nonlinear crystal the signal-to-noise ratios for the amplified image and the converted one may be same as those for the initial image, i.e. transformation of the optical image may be 'noiseless'.

Journal of Optics B Quantum and Semiclassical Optics•Nov 4, 2005•12 citations
We present for the first time, to our knowledge, a theoretical analysis of the nonlinear dynamic space-charge field buildup when a photorefractive medium is exposed simultaneously to two running gratings. It is shown that the two gratings are nonlinearly coupled, hence, for an appropriate choice of parameters, the two gratings interact, causing one grating to be amplified at the expense of the other. This process is referred to as degenerate parametric amplification. In principle an infinite amplification is possible because, even in cases for which no signal grating (i.e., the one to be amplified) is externally seeded into the crystal, a finite signal-grating amplitude is obtained after relaxation of the amplification process.
We present an analysis of what is called parametric oscillation in photorefractive media. It is shown theoretically that when a running grating and a constant electric field are applied to a photorefractive medium it is possible for two secondary gratings to grow spontaneously. These theoretical predictions are subsequently verified experimentally in the crystal Bi12SiO20, and excellent qualitative agreement is obtained. In previous subharmonic experiments, only grating vectors K/2, K/3, and K /4 were observed. Now, however, a whole continuum of grating vectors has been observed. Thus subharmonic generation in photorefractive materials is simply a special case of parametric oscillation in which the two secondary gratings are identical.
The buildup and the decay of photorefractive two-beam coupling are experimentally demonstrated to be strongly dependent on the intensity ratio of the two beams (signal-to-pump ratio). The experiment, done with a BaTiO3 crystal, shows good agreement with the theory of two-beam coupling in the depleted-pump regime. The deviation of the response behavior from the small-signal regime is seen for ratios as small as ∼10−5. These results are significant for applications of two-beam coupling as gain media, especially for the elimination of amplified noise (fanning).
We present a closed-form solution for the two-wave coupling process, resulting in a solution with an interesting part, the arbitrary function Lambda(t), not being considered in the previous works. In the photorefractive medium, it has been shown that a moving grating will produce a phase shift in the coupling constant. To our knowledge, this has not been derived directly from the grating dynamic equations. We will also show that the temporal dynamics does not have any asymptotically stable equilibrium points of an exponential form. As an example, we have developed resonance conditions resulting in a new expression for the frequency detuning of a resonator with a photorefractive gain medium.
We develop for the first time a quantum theory of simultaneous amplification and frequency up-conversion of optical images in two coupled three-wave processes. The theory developed takes into account the diffraction effect and the difference of the group velocities of the interacting waves. Due to the degenerate parametric process involved in the nonlinear optical interactions, the up-conversion also possesses phase sensitivity. As a result, the statistical characteristics of the amplified image and the converted one depend on the phase relation between the signal and the pump waves. It is shown that at the output of the nonlinear crystal the signal-to-noise ratios for the amplified image and the converted one may be same as those for the initial image, i.e. transformation of the optical image may be 'noiseless'.