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Applied Physics Letters

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

Mark Cronin‐Golomb, Baruch Fischer, Jeffrey Owen White, Amnon Yariv

Published Jun 1, 1983• 111 citations
Publisher

Abstract

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.

DOI
10.1063/1.93800

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We introduce a semi-self-pumped phase conjugate mirror (PCM) in which one pump is externally injected into a ring resonator while the other is self-induced as in a unidirectional ring resonator. One application is in one-way imaging through optical distortions using a phase conjugate window.1 The original realization of the phase conjugate window was similar to an externally pumped PCM and had the disadvantage of requiring a clean pump beam coherent with the distorted probe. This meant that the clean beam had to bypass the distortion, thus limiting the practical utility of the device. By replacing the externally pumped PCM portion of the device with a semi-self-pumped PCM, the clean beam can be self-induced as an oscillation beam. The second application is as a thresholding phase conjugate mirror which would be useful, for example, in some optical associative memories.2 In the semi-self-pumped phase conjugator, the presence of the externally injected pumping beam suppresses buildup of the self-induced pumping beam until the signal reaches a certain threshold intensity.

Annual Meeting Optical Society of America•Jan 1, 1986•0 citations
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.
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.
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.
The effects of linear absorption on the degenerate and nondegenerate self-oscillation of a photorefractive phase-conjugate mirror under condition of anisotropic four-wave mixing are considered. The phase conjugation results from nonlinear mixing of two strong undepleted orthogonally polarized counterpropagating pump waves with a probe wave. We consider two types of situation for orthogonally polarized pump beams corresponding to two crystal families: one such as the Bi12SiO20 crystal family (sillenite family) and the other such as the BaTiO3 and strontium barium niobate crystal family. In both of these crystal families the degenerate and nondegenerate self-oscillations are shown to occur in the presence of linear absorption, which tends to increase the value of the coupling coefficient required for self-oscillation. Numerical results are presented that exhibit various features of degenerate and nondegenerate self-oscillation in both crystal families for different values of the phase ϕb of the backward grating.
We demonstrate a phase-conjugating mirror that has a continuous-wave power reflectivity much greater than unity (gain ~100). This mirror uses nonresonant degenerate four-wave mixing in a single crystal of barium titanate (BaTiO3). With our mirror we have (1) observed cw self-oscillation in an optical resonator formed by this mirror and a normal mirror, (2) demonstrated a cw oscillator that, in spite of phase-distorting material placed inside the resonator, will always emit a TEM00 mode, and (3) demonstrated an optical image amplifier. This mirror will work at any visible wavelength and with weak (milliwatt or weaker) pump beams.
We demonstrate a phase-conjugating mirror that has a continuous-wave power reflectivity much greater than unity (gain ~100). This mirror uses nonresonant degenerate four-wave mixing in a single crystal of barium titanate (BaTiO3). With our mirror we have (1) observed cw self-oscillation in an optical resonator formed by this mirror and a normal mirror, (2) demonstrated a cw oscillator that, in spite of phase-distorting material placed inside the resonator, will always emit a TEM00 mode, and (3) demonstrated an optical image amplifier. This mirror will work at any visible wavelength and with weak (milliwatt or weaker) pump beams.
We introduce a semi-self-pumped phase conjugate mirror (PCM) in which one pump is externally injected into a ring resonator while the other is self-induced as in a unidirectional ring resonator. One application is in one-way imaging through optical distortions using a phase conjugate window.1 The original realization of the phase conjugate window was similar to an externally pumped PCM and had the disadvantage of requiring a clean pump beam coherent with the distorted probe. This meant that the clean beam had to bypass the distortion, thus limiting the practical utility of the device. By replacing the externally pumped PCM portion of the device with a semi-self-pumped PCM, the clean beam can be self-induced as an oscillation beam. The second application is as a thresholding phase conjugate mirror which would be useful, for example, in some optical associative memories.2 In the semi-self-pumped phase conjugator, the presence of the externally injected pumping beam suppresses buildup of the self-induced pumping beam until the signal reaches a certain threshold intensity.