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

Chinese Physics B

Transverse effects in photorefractive two-wave mixing

Cai Xin, Jinsong Liu, Shenglie Wang, Shi‐Xiong Liu

Published May 1, 2009• 5 citations
Publisher

Abstract

In a biased photorefractive crystal, the process of two one-dimensional waves mixing, i.e., the dynamical evolution of both pump beam and signal beam, is traced by numerically solving the coupled-wave equation. Direct simulations show that the propagation and stability of the two beams are completely determined by the system parameters, such as the external bias field, the intensity and the beam waist of the pump beam. By adjusting these parameters, one can control the state of two Gaussian waves mixing. The numerical results are helpful for performing a two-wave mixing experiment.

DOI
10.1088/1674-1056/18/5/029

Related papers

Photorefractive wave mixing with finite beams

Wieslaw Z. Krolikowski, Mark Cronin‐Golomb

While the interaction of optical beams in photorefractive crystals can often be accurately described in terms of 1-D plane-wave approximation, 2-D models are sometimes more suitable, as suggested by recent work.1 Here we discuss some aspects of photorefractive interaction of finite size optical beams. We have solved the system of partial differential equations governing two- and four-wave mixing numerically by using iterative procedures. Simulations of beam amplification in two-beam coupling show strong beam deformation even without any spatial information imposed on them. Spatially nonuniform energy transfer is responsible for this effect. The pump beam loses energy during propagation and at the end of its passage through the beam intersection region (which was completely inside the crystal) it is strongly depleted and cannot contribute significantly to beam amplification. As the pump beam crosses through the probe, it amplifies most strongly that side of the probe that it meets first. By the time the pump has reached the far side of the probe, it is strongly depleted and less effective at probe amplification. In the case of phase conjugation through four-wave mixing, we found that the conjugate beam is strongly deformed only when the coupling constant is negative (corresponding to deamplification of the probe input beam). For positive coupling constants the output conjugate beam is a good replica of the input probe beam.

Annual Meeting Optical Society of America•Jan 1, 1991•1 citation

Two-wave mixing of time-varying non-plane-wave optical fields in photorefractive materials

L. Boutsikaris, F. Davidson

A theoretical analysis is presented of two-wave mixing in photorefractive materials in which the complex amplitude of a weak signal beam has slowly varying but otherwise arbitrary spatial dependence and arbitrary time variation. The set of coupled partial differential equations that couple the dynamics of the optical fields to the photorefractive medium is solved analytically to give the complex amplitude of the transmitted signal in the undepleted pump regime. The results are compared with known results for the transient two-wave mixing of plane waves.

Applied Optics•Mar 20, 1993•12 citations

Contradirectional two-wave mixing with partially coherent waves in photorefractive crystals

Xianmin Yi, Ken Y. Hsu, Shiuan Huei Lin +1 more

We investigate contradirectional two-wave mixing with partially coherent waves in photorefractive crystals in the nondepleted pump regime. Equations governing the propagation of the self-coherence function and the mutual-coherence function of the signal wave and the pump wave are derived and simulated numerically. Numerical solutions of these equations are in excellent agreement with the experimental measurements.

Optics Letters•Aug 1, 1996•8 citations

Detection of phase-modulated optical signals through two-wave mixing in photorefractive materials

L. Boutsikaris, Fred Davidson

Two-wave mixing in photorefractive crystals has been shown to combine coherently a modulated optical signal beam with a strong pump optical field.’ For a phase-modulated signal beam, the induced index of refraction phase grating inside the crystal yields a coupling of the optical fields of the pump and signal so that subsequent intensity detection results in apparent intensity modulation of the transmitted signal or pump beams. This provides an easy way to detect phase differences between two optical beams. Some of the advantages the above scheme offers over commonly used coherent optical phase detection schemes are: no loss of 3 dB in the signal beam intensity at the 50/50 beam splitter (used to combine signal and local oscillator fields); automatic alignment of the index of refraction grating with the two incident optical wavefronts; insensitivity to slow random changes in the phases of both beams. Experimental results are given, and a new definition for the resulting mixing gain for the phase-modulated beam is introduced, through which optimal conditions for input beam intensity ratios can be found. Applications to coherent homodyne detection are discussed.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Theory of a Photorefractive Resonator

H. Zeghlache, Laurent Dambly, P. Glorieux

A theory of the two-wave mixing in a photorefractive medium placed in a ring cavity is developped following the model first derived by Yariv and Kwong [1]: a steady refractive index involving the photorefractive effect is used as a non-linear source-term (PNL) in the Maxwell equations, and the cavity field is expanded on the transverse cavity modes. In this model we take into account the intensity change of both the pump and resonator beams inside the crystal due to the mutual power exchange: we have developed a multimode model which gives in the long-time limit the z-dependance of the fields (z is the optical axis) for a passage in the crystal, using the expansion in terms of the complete set of the cavity transverse modes. [2]

Nonlinear Dynamics in Optical Systems•Jan 1, 1992•0 citations

Frequency shift in an oscillator with photorefractive gain

Laurent Dambly, H. Zeghlache

A self-consistent theory is used to derive the frequency shift presented by the oscillating mode in a cavity that contains a photorefractive crystal. A long-time-limit theory has been used to get the steady characteristics of the cavity field. The problem of the weak-field approximation is avoided. This approximation is useless in the case studied because the interaction along the crystal is so strong that one has to take in account the intensity exchange occurring inside the material between the pump and oscillating beams (two-wave mixing). We have fully analyzed the influence of the transverse nature of the beams on the intensity exchange in the two-wave mixing situation. In the photorefractive resonator case, the frequency shift of the oscillating beam is expressed in terms of a ratio that presents poles. The dependence on the problem parameters of these poles is studied and a perturbative method is developed; it is based on the smallness of the transverse overlap between the pump and cavity modes. An analytical expression for this frequency shift is obtained.

Physical Review A•Mar 1, 1993•15 citations
In a biased photorefractive crystal, the process of two one-dimensional waves mixing, i.e., the dynamical evolution of both pump beam and signal beam, is traced by numerically solving the coupled-wave equation. Direct simulations show that the propagation and stability of the two beams are completely determined by the system parameters, such as the external bias field, the intensity and the beam waist of the pump beam. By adjusting these parameters, one can control the state of two Gaussian waves mixing. The numerical results are helpful for performing a two-wave mixing experiment.
While the interaction of optical beams in photorefractive crystals can often be accurately described in terms of 1-D plane-wave approximation, 2-D models are sometimes more suitable, as suggested by recent work.1 Here we discuss some aspects of photorefractive interaction of finite size optical beams. We have solved the system of partial differential equations governing two- and four-wave mixing numerically by using iterative procedures. Simulations of beam amplification in two-beam coupling show strong beam deformation even without any spatial information imposed on them. Spatially nonuniform energy transfer is responsible for this effect. The pump beam loses energy during propagation and at the end of its passage through the beam intersection region (which was completely inside the crystal) it is strongly depleted and cannot contribute significantly to beam amplification. As the pump beam crosses through the probe, it amplifies most strongly that side of the probe that it meets first. By the time the pump has reached the far side of the probe, it is strongly depleted and less effective at probe amplification. In the case of phase conjugation through four-wave mixing, we found that the conjugate beam is strongly deformed only when the coupling constant is negative (corresponding to deamplification of the probe input beam). For positive coupling constants the output conjugate beam is a good replica of the input probe beam.
A theoretical analysis is presented of two-wave mixing in photorefractive materials in which the complex amplitude of a weak signal beam has slowly varying but otherwise arbitrary spatial dependence and arbitrary time variation. The set of coupled partial differential equations that couple the dynamics of the optical fields to the photorefractive medium is solved analytically to give the complex amplitude of the transmitted signal in the undepleted pump regime. The results are compared with known results for the transient two-wave mixing of plane waves.
Two-wave mixing in photorefractive crystals has been shown to combine coherently a modulated optical signal beam with a strong pump optical field.’ For a phase-modulated signal beam, the induced index of refraction phase grating inside the crystal yields a coupling of the optical fields of the pump and signal so that subsequent intensity detection results in apparent intensity modulation of the transmitted signal or pump beams. This provides an easy way to detect phase differences between two optical beams. Some of the advantages the above scheme offers over commonly used coherent optical phase detection schemes are: no loss of 3 dB in the signal beam intensity at the 50/50 beam splitter (used to combine signal and local oscillator fields); automatic alignment of the index of refraction grating with the two incident optical wavefronts; insensitivity to slow random changes in the phases of both beams. Experimental results are given, and a new definition for the resulting mixing gain for the phase-modulated beam is introduced, through which optimal conditions for input beam intensity ratios can be found. Applications to coherent homodyne detection are discussed.
A theory of the two-wave mixing in a photorefractive medium placed in a ring cavity is developped following the model first derived by Yariv and Kwong [1]: a steady refractive index involving the photorefractive effect is used as a non-linear source-term (PNL) in the Maxwell equations, and the cavity field is expanded on the transverse cavity modes. In this model we take into account the intensity change of both the pump and resonator beams inside the crystal due to the mutual power exchange: we have developed a multimode model which gives in the long-time limit the z-dependance of the fields (z is the optical axis) for a passage in the crystal, using the expansion in terms of the complete set of the cavity transverse modes. [2]
A self-consistent theory is used to derive the frequency shift presented by the oscillating mode in a cavity that contains a photorefractive crystal. A long-time-limit theory has been used to get the steady characteristics of the cavity field. The problem of the weak-field approximation is avoided. This approximation is useless in the case studied because the interaction along the crystal is so strong that one has to take in account the intensity exchange occurring inside the material between the pump and oscillating beams (two-wave mixing). We have fully analyzed the influence of the transverse nature of the beams on the intensity exchange in the two-wave mixing situation. In the photorefractive resonator case, the frequency shift of the oscillating beam is expressed in terms of a ratio that presents poles. The dependence on the problem parameters of these poles is studied and a perturbative method is developed; it is based on the smallness of the transverse overlap between the pump and cavity modes. An analytical expression for this frequency shift is obtained.