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

Hexagon formation in photorefractive crystals as mirrorless coherent oscillation

Yoshiaki Uesu, A. Ueno, Masataka Kobayashi, S. Odoulov

Published Jul 1, 1998• 4 citations
Publisher

Abstract

The spontaneous appearance of hexagon patterns in photorefractive crystals is treated as mirrorless coherent four-wave mixing oscillation. It is shown experimentally that the system has a well-defined coupling-strength threshold and behaves as other coherent optical oscillators near the threshold. A simple relation for the angle of the hexagon sideband as a function of the distance between the end mirror and the sample is derived and verified experimentally.

DOI
10.1364/josab.15.002065

Related papers

Coherent optical oscillator with periodic zero- π phase modulation

Aleksandr Shumelyuk, A. Hryhorashchuk, Serguey G. Odoulov

The four-wave-mixing coherent optical oscillator is described, which is emitting light wave with regular alternation of its phase between two discrete values zero and $\ensuremath{\pi}$. Such a periodic self-modulation is a consequence of competition of photorefractive gratings formed by movable charge species of two different signs. The period of modulation depends on overthreshold coupling strength and on decay time of slow photorefractive grating. It falls to few seconds range for ${\mathrm{Sn}}_{2}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ crystals at ambient temperature but it can go down to microsecond range for photorefractive semiconductors.

Physical Review A•Aug 22, 2005•18 citations

Exact solution of degenerate four-wave mixing in photorefractive media

Aleksander Błȩdowski, Wieslaw Z. Krolikowski

A novel method for the exact solution of four-wave mixing in photorefractive media is presented. This method allows us to treat exactly the effects of nonequal angles of incidence, different refractive-index modulation of interacting waves, and external incoherent illumination of the photorefractive crystal.

Optics Letters•Feb 1, 1988•17 citations

Oscillation spectra of semilinear photorefractive coherent oscillator with two pump waves

P. Mathey, Serguey G. Odoulov, Daniel Rytz

The transition of the single-frequency oscillation of a semilinear photorefractive coherent oscillator for sufficiently large coupling strengths into two-frequency oscillation is predicted and is observed experimentally. The critical value of coupling strength at which the bifurcation occurs is a function of pump-intensity ratio and cavity losses. For certain combinations of these parameters, the critical coupling strength for spectrum bifurcation becomes smaller than the threshold coupling strength: in these cases double-frequency oscillation appears at the threshold. The supercritical bifurcation in the oscillation spectrum is analogous to the second-order phase transition.

Journal of the Optical Society of America B•Dec 2, 2002•15 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

Fanning and photorefractive self-pumped four-wave mixing geometries

A. A. Zozulya

Results of recent experimental and theoretical investigations on the role of fanning in the operation of several popular photorefractive self-pumped FWM geometries, including the double phase conjugate mirror (DPCM), the ring oscillator, the semilinear mirror, the system of two coupled DPCMs, and the total internal reflection (TIR) mirror, are presented. The results can be divided into two groups. Geometries of the first group (the DPCM and the ring oscillator) have soft excitation thresholds. Geometries of the second group (the semilinear mirror, the system of the two DPCMs and the TIR mirror) have hard excitation thresholds. Geometries of the first group experience a noticeable influence of fanning only when the level of fanning of a single pumping beam passing through a crystal, is high. Geometries of the second group, such as the semilinear mirror, the system of two DPCMs, and the TIR mirror without fanning, are not self-starting.>

IEEE Journal of Quantum Electronics•Jan 1, 1993•28 citations

Generalized derivation of equations for four-wave interaction in photorefractive media

V. Yu. Petrun’kin, Ivan V. Murashko, Elena V. Mokrushina

The emergence of optical waves out of optical noise (fanning) in a photorefractive medium is considered in an unconventional manner, i.e., using the Lorentz lemma and ensemble averaging. The derivation of equations for four-wave interaction in the scheme of a double incoherent phase-conjugate mirror is described in detail. Numerical calculation based on the resulting system of equations provides insight into the effect of noise on the oscillation threshold and makes it possible to discover the “higher threshold” effect in saturation-free noisy materials.

Technical Physics•Aug 1, 2006•0 citations
The spontaneous appearance of hexagon patterns in photorefractive crystals is treated as mirrorless coherent four-wave mixing oscillation. It is shown experimentally that the system has a well-defined coupling-strength threshold and behaves as other coherent optical oscillators near the threshold. A simple relation for the angle of the hexagon sideband as a function of the distance between the end mirror and the sample is derived and verified experimentally.
The four-wave-mixing coherent optical oscillator is described, which is emitting light wave with regular alternation of its phase between two discrete values zero and $\ensuremath{\pi}$. Such a periodic self-modulation is a consequence of competition of photorefractive gratings formed by movable charge species of two different signs. The period of modulation depends on overthreshold coupling strength and on decay time of slow photorefractive grating. It falls to few seconds range for Sn2P2S6{\mathrm{Sn}}_{2}{\mathrm{P}}_{2}{\mathrm{S}}_{6}Sn2​P2​S6​ crystals at ambient temperature but it can go down to microsecond range for photorefractive semiconductors.
The transition of the single-frequency oscillation of a semilinear photorefractive coherent oscillator for sufficiently large coupling strengths into two-frequency oscillation is predicted and is observed experimentally. The critical value of coupling strength at which the bifurcation occurs is a function of pump-intensity ratio and cavity losses. For certain combinations of these parameters, the critical coupling strength for spectrum bifurcation becomes smaller than the threshold coupling strength: in these cases double-frequency oscillation appears at the threshold. The supercritical bifurcation in the oscillation spectrum is analogous to the second-order phase transition.
Results of recent experimental and theoretical investigations on the role of fanning in the operation of several popular photorefractive self-pumped FWM geometries, including the double phase conjugate mirror (DPCM), the ring oscillator, the semilinear mirror, the system of two coupled DPCMs, and the total internal reflection (TIR) mirror, are presented. The results can be divided into two groups. Geometries of the first group (the DPCM and the ring oscillator) have soft excitation thresholds. Geometries of the second group (the semilinear mirror, the system of the two DPCMs and the TIR mirror) have hard excitation thresholds. Geometries of the first group experience a noticeable influence of fanning only when the level of fanning of a single pumping beam passing through a crystal, is high. Geometries of the second group, such as the semilinear mirror, the system of two DPCMs, and the TIR mirror without fanning, are not self-starting.>
The emergence of optical waves out of optical noise (fanning) in a photorefractive medium is considered in an unconventional manner, i.e., using the Lorentz lemma and ensemble averaging. The derivation of equations for four-wave interaction in the scheme of a double incoherent phase-conjugate mirror is described in detail. Numerical calculation based on the resulting system of equations provides insight into the effect of noise on the oscillation threshold and makes it possible to discover the “higher threshold” effect in saturation-free noisy materials.