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 ω0 of the PCM element, independent of the cavity length L, plus half-axial sidebands spaced by Δωax = 2π(c/4L), with phase and amplitude constraints on each pair of upper and lower sidebands.
© 1980 Optical Society of America
Original Manuscript: June 14, 1979
Published: February 15, 1980
Pierre A. Bélanger, Amos Hardy, and A. E. Siegman, "Resonant modes of optical cavities with phase-conjugate mirrors," Appl. Opt. 19, 602-609 (1980)