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

Annual Meeting Optical Society of America

Controlling the frequency shift of a self-pumped phase conjugator

J. P. Jiang, Jack Feinberg

Published Jan 1, 1986• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1986.mee8

Related papers

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

Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity

Mark Cronin‐Golomb, Baruch Fischer, Jeffrey Owen White +1 more

A passive phase conjugate mirror based on four-wave mixing in an optical ring cavity is described. Unlike previously demonstrated passive phase conjugate mirrors it generates only one of its pumping beams by nonlinear optical interactions, the other being provided by feedback of the probe after transmission through the nonlinear medium. The results of a theory yielding phase conjugate reflectivity and oscillation thresholds are presented together with an experimental demonstration of phase conjugation in barium titanate and strontium barium niobate. The device is self-starting by four-wave mixing, and has an oscillation threshold lower than that of other previously demonstrated passive phase conjugate mirrors with similar ease of alignment. The operation of a device which generates nonconjugate oscillation beams is also reported.

Applied Physics Letters•Jun 1, 1983•111 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

Theory of a self-pumped phase conjugator with two coupled interaction regions

Kenneth R. MacDonald, Jack Feinberg

We present a plane-wave analysis of a recently demonstrated self-pumped phase conjugator. This device uses four-wave mixing to produce the phase-conjugate replica of an incident optical wave. All the waves are derived from the single incident wave: there are no externally supplied pumping beams. We consider the case of four-wave mixing in two interaction regions coupled by simple reflection. We calculate the phase-conjugate reflectivity as a function of coupling strength, taking into account imperfect coupling between the two interaction regions, and show that there is a threshold coupling strength below which the reflectivity is zero and above which the reflectivity is multiple valued. We also compute the coupling strength per unit length for a photorefractive crystal of barium titanate.

Journal of the Optical Society of America•May 1, 1983•165 citations

Stabilization of the phase conjugate reflectivity in photorefractive four-wave mixing

Tsutomu Shimura, Atsushi Nakamura, Kazuo Kuroda +2 more

Phase conjugate reflectivity of the photorefractive four-wave mixing system is usually quite unstable and it is serious issue for practical use of these systems. The cause of this instability is mainly combination of the fluctuation of the phases of input signal and pump beams and the slow response time of the photorefractive crystal. When all input beams in the four-wave mixing system are mutually coherent and the phases of the input beams are not stable, four kinds of gratings are compete each other and the phase conjugate output becomes quite unstable. To avoid this problem, we can make one of the pump incoherent to the signal and another pump1. The phase conjugate output is, however, still unstable due to the rewriting of the grating caused by the fluctuation of the phase of the input beams. In this paper, we report our feedback system to stabilize the power of the phase conjugate output from the four-wave mixing system by controlling the phase of the signal beam. In this system, we detect the phase difference between signal and forward pump beam with lock-in amplifier and control the phase of the signal with a piezoelectric mirror to stabilize the phase difference.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 1, 1996•0 citations

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

Kenneth R. MacDonald, Jack Feinberg

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.

Physical Review Letters•Aug 19, 1985•78 citations
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 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.
A passive phase conjugate mirror based on four-wave mixing in an optical ring cavity is described. Unlike previously demonstrated passive phase conjugate mirrors it generates only one of its pumping beams by nonlinear optical interactions, the other being provided by feedback of the probe after transmission through the nonlinear medium. The results of a theory yielding phase conjugate reflectivity and oscillation thresholds are presented together with an experimental demonstration of phase conjugation in barium titanate and strontium barium niobate. The device is self-starting by four-wave mixing, and has an oscillation threshold lower than that of other previously demonstrated passive phase conjugate mirrors with similar ease of alignment. The operation of a device which generates nonconjugate oscillation beams is also reported.
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 a plane-wave analysis of a recently demonstrated self-pumped phase conjugator. This device uses four-wave mixing to produce the phase-conjugate replica of an incident optical wave. All the waves are derived from the single incident wave: there are no externally supplied pumping beams. We consider the case of four-wave mixing in two interaction regions coupled by simple reflection. We calculate the phase-conjugate reflectivity as a function of coupling strength, taking into account imperfect coupling between the two interaction regions, and show that there is a threshold coupling strength below which the reflectivity is zero and above which the reflectivity is multiple valued. We also compute the coupling strength per unit length for a photorefractive crystal of barium titanate.
Phase conjugate reflectivity of the photorefractive four-wave mixing system is usually quite unstable and it is serious issue for practical use of these systems. The cause of this instability is mainly combination of the fluctuation of the phases of input signal and pump beams and the slow response time of the photorefractive crystal. When all input beams in the four-wave mixing system are mutually coherent and the phases of the input beams are not stable, four kinds of gratings are compete each other and the phase conjugate output becomes quite unstable. To avoid this problem, we can make one of the pump incoherent to the signal and another pump1. The phase conjugate output is, however, still unstable due to the rewriting of the grating caused by the fluctuation of the phase of the input beams. In this paper, we report our feedback system to stabilize the power of the phase conjugate output from the four-wave mixing system by controlling the phase of the signal beam. In this system, we detect the phase difference between signal and forward pump beam with lock-in amplifier and control the phase of the signal with a piezoelectric mirror to stabilize the phase difference.
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.