Resonant modes of optical cavities with phase-conjugate mirrors

The lowest-order self-consistent Gaussian transverse modes are derived, also the resonant frequencies of an optical resonator formed by conventional paraxial optical components plus a phase-conjugate mirror (PCM) on one end. The conventional optical elements are described by an over-all ABCD matrix. Cavities with purely real elements (no aperturing) have a continuous set of self-reproducing Gaussian modes described by a semicircular locus in the 1/q plane for one round trip; all Gaussian beams are self-reproducing after two round trips. Complex ABCD matrices, such as are produced by Gaussian aperturing in the cavity, lead to unique self-consistent perturbation-stable Gaussian modes. The resonant frequency spectrum of a PCM cavity consists of a central resonance at the driving frequency omega(0) of the PCM element, independent of the cavity length L, plus half-axial sidebands spaced by Deltaomega(ax) = 2pi(c/4L), with phase and amplitude constraints on each pair of upper and lower sidebands.