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Journal of the Optical Society of America

Generalized mode theory of conventional and phase-conjugate resonators

Moshe Nazarathy, Amos A. Hardy, Joseph Shamir

Published May 1, 1983• 9 citations
Publisher

Abstract

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.

DOI
10.1364/josa.73.000576

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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.
We have developed a theory for nondegenerate oscillations in optical resonators containing an intracavity phase-conjugate element. The phase-conjugate element consists of a nonlinear transparent medium that is pumped externally by a pair of counterpropagating laser beams of the same frequency and intensity. Phase conjugation of an input beam of slightly different frequency occurs because of nondegenerate four-wave mixing. The theory takes into account linear absorption (or gain) in the medium and is applied to study the threshold behavior of phase-conjugate oscillators. For the special case of no conventional mirrors, the phase-conjugate oscillator reduces to an ordinary phase-conjugate mirror, and our general formulation yields the results of previous studies. Our analysis shows that the parametric gain required for oscillation increases (or decreases) as a result of linear absorption (or gain) in the medium, and oscillation can occur at a frequency different from that of the pump beams in the presence of large linear gain (or loss). The effects of linear absorption (or gain) on the filter operation are also examined.