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Optica Acta International Journal of Optics

Fundamental Modes of Stimulated Scattering Phase-conjugate Resonators

Wang Shaomin, H. Weber

Published Sep 1, 1984• 7 citations
Publisher

Abstract

An equivalent transfer matrix describing the operation of stimulated scattering phase-conjugate mirrors is given. By this matrix the fundamental eigenmodes of a resonator with such a phase-conjugate mirror can be derived. It is shown that this resonator is unconditionally confined, absolutely dynamically stable, and stable against perturbations.

DOI
10.1080/713821617

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Journal of the Optical Society of America•May 1, 1983•14 citations
An equivalent transfer matrix describing the operation of stimulated scattering phase-conjugate mirrors is given. By this matrix the fundamental eigenmodes of a resonator with such a phase-conjugate mirror can be derived. It is shown that this resonator is unconditionally confined, absolutely dynamically stable, and stable against perturbations.
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.
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.