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Acta Optica Sinica

The effect of frequency shift on the stability and mode properties of stimulated scattering phase-conjugate resonators

Jing Liu

Published Jan 1, 1988• 0 citations
OpenAlex

Abstract

The effect of frequency shift on the stability and mode properties of Stimulated Scattering Phaae-Conjugate Resonators (SSPOR) has been studied by introdaoing the generalized self-consistency condition and the Stimulated Scattering Phase-Conjugate Mirror(SSPOM')s transfer matrix that has explicit variable frequency.

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The phase-conjugation operator is investigated in the context of the canonical operator theory of first-order optics, which was introduced in a previous series of articles. The matrix representation of this operator and its action on the generalized modes are derived, elucidating the relation between forward and reversed propagation in this new context. The resulting formalism makes possible the derivation of the eigenmodes of conventional and phase-conjugated resonators with loss or gain. Various resonator properties—confinement, stability, mode biorthogonality, and real or complex character of the spot-size parameter—simply follow from the guiding-ray-label representation.
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.