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Journal of the Optical Society of America

Modes of phase-conjugate resonators with bounded mirrors

P. A. Bélanger, C. Paré, Michel Piché

Published May 1, 1983• 14 citations
Publisher

Abstract

The diffraction losses of phase-conjugate resonators with bounded mirrors are shown to depend only on two dimensionless parameters. The hemispherical phase-conjugate resonator is shown to yield a fundamental mode with minimum loss among all phase-conjugate resonators with the same mirror dimensions. Proof is given that the diffraction losses around the phase-conjugate mirror are larger than the diffraction losses around the conventional mirror; hence diffraction coupling is more efficient around the phase-conjugate mirror. Numerical results support these conclusions.

DOI
10.1364/josa.73.000567

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Journal of the Optical Society of America•May 1, 1983•9 citations
The diffraction losses of phase-conjugate resonators with bounded mirrors are shown to depend only on two dimensionless parameters. The hemispherical phase-conjugate resonator is shown to yield a fundamental mode with minimum loss among all phase-conjugate resonators with the same mirror dimensions. Proof is given that the diffraction losses around the phase-conjugate mirror are larger than the diffraction losses around the conventional mirror; hence diffraction coupling is more efficient around the phase-conjugate mirror. Numerical results support these conclusions.
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.