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 Letters

Enhanced Four-Wave Mixing by Use of Frequency-Shifted Optical Waves in Photorefractive BaTi O3

Kenneth R. MacDonald, Jack Feinberg

Published Aug 19, 1985• 78 citations
Publisher

Abstract

We present theory and experiments to show that the efficiency of four-wave mixing in photorefractive materials can be enhanced by use of optical waves of slightly different frequencies. The optimum frequency shift scales inversely with the response time of the material. We show that the \ensuremath{\sim}1-Hz frequency shift previously observed in the output of a self-pumped phase conjugator that used photorefractive BaTi${\mathrm{O}}_{3}$ is the result of this inherent property of four-wave mixing.

DOI
10.1103/physrevlett.55.821

Related papers

Controlling the frequency shift of a self-pumped phase conjugator

J. P. Jiang, Jack Feinberg

When the phase-conjugate replica of an optical beam is generated by traditional four-wave mixing with external pumping beams, the frequency of the phase-conjugate beam is fixed by the frequencies of the three input beams. In self-pumped phase conjugation, there is only one input beam, and the frequency of the output beam is free to roam. In photorefractive materials, this frequency difference between the incident and output beams is typically a few hertz. We present a method for controlling this frequency shift in the self-pumped phase-conjugate mirror that uses a ring configuration1 in photorefractive barium titanate. We show that two-beam coupling of an additional control beam with either of the optical beams already present in the ring cavity can alter the frequency of the phase-conjugate beam. We show that the control beam can alter the nonreciprocal phase shift2 of light propagating around the ring and thereby alter the frequency of the phase-conjugate beam. We also calculate the magnitude and the sign of the expected frequency shift as a function of the intensity, direction, and frequency of this control beam.

Annual Meeting Optical Society of America•Jan 1, 1986•0 citations

Origin of frequency shift and temporal instability in photorefractive self-pumped phase conjugators

Ping Xie, Peng‐Ye Wang, Jian-Hua Dai

The physical origin of frequency shift and dynamic instability in a photorefractive self-pumped phase conjugator is analyzed by use of four-wave mixing and multi-four-wave mixing. We show that the frequency shift and the instability result from the requirement of the maximal energy transfer between the interacting beams. Two examples of numerical results in a cat self-pumped phase conjugator are given, which are in good agreement with previous experimental results. A simple method is proposed to change an unstable phase-conjugate output to a stable one.

Journal of the Optical Society of America B•Jul 1, 2000•0 citations

Spectral response of nearly degenerate four-wave mixing in photorefractive materials

Juan Francisco Lam

A theory of nearly degenerate four-wave mixing in photorefractive materials is presented. We predict the existence of self-oscillation, intensity-dependent bandwidth, and nonlinear phase shift effects. UFDAT;8342.65.Cq, 42.80.Ks

Applied Physics Letters•Jan 15, 1983•21 citations

Phase shifts of photorefractive gratings and phase-conjugate waves

Ian C. McMichael, Pochi Yeh

We present measurements of the two-wave mixing gain as a function of frequency detuning in photorefractive crystals. In many cases, this function is asymmetric, indicating that the phase shift of the photorefractive inde grating with respect to the light interference pattern is not exactly 90 degrees , as is often assumed. In four-wave mixing, the phase of the phase-conjugate wave contains the phase of the pumping and probe waves and a phase shift determined by the interaction taking place in the nonlinear medium. This second term, the phase shift of the phase conjugator, is a function of the type of grating and the phase shift of this grating. The phase shift of the grating obtained from the two-wave mixing measurements compares well with that obtained from four-wave mixing measurements of the phase of the phase conjugator.

Optics Letters•Jan 1, 1987•34 citations

Photorefractive optical phase-sensitive detection

Charles L. Woods, J. Khoury, V. Ryan +1 more

Phase-sensitive detection can be realized optically by using degenerate four-wave mixing in photorefractive materials. Phase-sensitive detectors or lock-in amplifiers use a reference-triggered phase-sensitive mixer followed by a time-integrating low-pass filter. Mixing the two signals gives sum- and difference-frequency outputs, and a low-pass filter extracts the difference frequency. The phase encoded in the photorefractive hologram relative to the reference beam provides the mixing, and the response time of photorefractive material provides the time integration. Correctly modulating only the phase of the reference beam at a period much shorter than the photorefractive response time eliminates the phase-conjugate beam. Then modulating the phase of the signal input beam in the same waveform, but at a slightly different frequency from the reference, produces an oscillating phase-conjugate intensity. When the modulation frequencies of the two beams are phase-locked, a stable phase-conjugate signal is obtained with an intensity determined by the relative phase shift. These optical phase-sensitive detection experiments agree with calculations from dynamic photorefractive theory for the phase-conjugate intensity.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations

Photorefractive phase conjugators

M. D. Ewbank

The demonstration of optical phase conjugation in photorefractive materials has been accomplished by numerous methods, including i) externally-pumped four-wave mixing,1ii) self-pumped (passive) phase conjugation,24iii) stimulated backscattering,5,6and iv) mutually-pumped phase conjugation.7-10Stimulated backscattering and self-pumped phase conjugators have only a single incident beam. On the other hand, externally-pumped four-wave mixing has two auxiliary pumping beams in addition to the incident probe beam. Different still is the cross-conjugation of the two incident beams in mutually pumped phase conjugators. To use these conjugators in a given application, the compatibility between the processes generating the phase-conjugate wave(s) and the application must be considered. The distinguishing features of the different conjugators translate to advantages or disadvantages for certain applications.

Digest on Nonlinear Optics: Materials, Phenomena and Devices•Jan 1, 1990•1 citation
We present theory and experiments to show that the efficiency of four-wave mixing in photorefractive materials can be enhanced by use of optical waves of slightly different frequencies. The optimum frequency shift scales inversely with the response time of the material. We show that the \ensuremath{\sim}1-Hz frequency shift previously observed in the output of a self-pumped phase conjugator that used photorefractive BaTiO3{\mathrm{O}}_{3}O3​ is the result of this inherent property of four-wave mixing.
When the phase-conjugate replica of an optical beam is generated by traditional four-wave mixing with external pumping beams, the frequency of the phase-conjugate beam is fixed by the frequencies of the three input beams. In self-pumped phase conjugation, there is only one input beam, and the frequency of the output beam is free to roam. In photorefractive materials, this frequency difference between the incident and output beams is typically a few hertz. We present a method for controlling this frequency shift in the self-pumped phase-conjugate mirror that uses a ring configuration1 in photorefractive barium titanate. We show that two-beam coupling of an additional control beam with either of the optical beams already present in the ring cavity can alter the frequency of the phase-conjugate beam. We show that the control beam can alter the nonreciprocal phase shift2 of light propagating around the ring and thereby alter the frequency of the phase-conjugate beam. We also calculate the magnitude and the sign of the expected frequency shift as a function of the intensity, direction, and frequency of this control beam.
The physical origin of frequency shift and dynamic instability in a photorefractive self-pumped phase conjugator is analyzed by use of four-wave mixing and multi-four-wave mixing. We show that the frequency shift and the instability result from the requirement of the maximal energy transfer between the interacting beams. Two examples of numerical results in a cat self-pumped phase conjugator are given, which are in good agreement with previous experimental results. A simple method is proposed to change an unstable phase-conjugate output to a stable one.
We present measurements of the two-wave mixing gain as a function of frequency detuning in photorefractive crystals. In many cases, this function is asymmetric, indicating that the phase shift of the photorefractive inde grating with respect to the light interference pattern is not exactly 90 degrees , as is often assumed. In four-wave mixing, the phase of the phase-conjugate wave contains the phase of the pumping and probe waves and a phase shift determined by the interaction taking place in the nonlinear medium. This second term, the phase shift of the phase conjugator, is a function of the type of grating and the phase shift of this grating. The phase shift of the grating obtained from the two-wave mixing measurements compares well with that obtained from four-wave mixing measurements of the phase of the phase conjugator.
Phase-sensitive detection can be realized optically by using degenerate four-wave mixing in photorefractive materials. Phase-sensitive detectors or lock-in amplifiers use a reference-triggered phase-sensitive mixer followed by a time-integrating low-pass filter. Mixing the two signals gives sum- and difference-frequency outputs, and a low-pass filter extracts the difference frequency. The phase encoded in the photorefractive hologram relative to the reference beam provides the mixing, and the response time of photorefractive material provides the time integration. Correctly modulating only the phase of the reference beam at a period much shorter than the photorefractive response time eliminates the phase-conjugate beam. Then modulating the phase of the signal input beam in the same waveform, but at a slightly different frequency from the reference, produces an oscillating phase-conjugate intensity. When the modulation frequencies of the two beams are phase-locked, a stable phase-conjugate signal is obtained with an intensity determined by the relative phase shift. These optical phase-sensitive detection experiments agree with calculations from dynamic photorefractive theory for the phase-conjugate intensity.
The demonstration of optical phase conjugation in photorefractive materials has been accomplished by numerous methods, including i) externally-pumped four-wave mixing,1ii) self-pumped (passive) phase conjugation,24iii) stimulated backscattering,5,6and iv) mutually-pumped phase conjugation.7-10Stimulated backscattering and self-pumped phase conjugators have only a single incident beam. On the other hand, externally-pumped four-wave mixing has two auxiliary pumping beams in addition to the incident probe beam. Different still is the cross-conjugation of the two incident beams in mutually pumped phase conjugators. To use these conjugators in a given application, the compatibility between the processes generating the phase-conjugate wave(s) and the application must be considered. The distinguishing features of the different conjugators translate to advantages or disadvantages for certain applications.