Amos Hardy

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.

Eigenmodes of optical resonators with mirrors having Gaussian reflectivity profiles.

A general procedure for calculating all the eigenmodes of optical resonators with mirrors having Gaussian reflectivity profiles is described. The eigenmodes are expanded in terms of the freely propagating Her-mite-Gaussian beams. The expansion enables one to apply well known matrix techniques to this kind of systems. The eigenvalues found determine the eigenfrequencies and the mode discrimination properties of such resonators.

Generalized mode propagation in first-order optical systems with loss or gain

Mode propagation through first-order systems with loss or gain is derived based on a canonical transform theory developed recently. In analogy to quantum theory, creation and annihilation operators are defined for the construction of high-order modes. The evolution of these mode-generation operators through an optical system is shown to describe the propagation of the actual fields that are parameterized by two raylike labels—two guiding rays. The mode-generating operators create a set of generalized modes that may be reduced to the ordinary Her-mite–Gaussian modes only in a lossless system. Many characteristics of these generalized modes are evaluated by operator algebraic manipulations without the need for the explicit form of the actual modes that are shown also to be Hermite–Gaussian but involve complex scaling parameters.

Low-power phase-conjugate interferometry

The operation of Mach-Zehnder and Michelson phase-conjugate interferometers is demonstrated. Phase conjugation is obtained by degenerate four-wave mixing in thin films of eosin. High-visibility fringes are observed both in cw and pulsed modes of operation.

Stability of optical laser resonators with mirrors of gaussian reflectivity profiles, which contain an active medium

Abstract The stability of laser resonators which contain a medium with a gain profile is investigated. Such resonators are unstable when the resonator mirrors are large (infinite aperture approximation), and the gain is lowest on the optical axis and increases with radial distance. It is shown that such resonators have well-defined regions of stability if the mirrors have gaussian reflectivity tapers.

Orthogonality properties of phase conjugate optical resonators

The orthogonality properties of the eigenmodes of general optical resonators which have a phase conjugate mirror at one end are derived. It is shown that essentially these are biorthogonal relations as in conventional resonators, which are satisfied between the set of modes propagating in one direction around the resonator and the adjoint set of modes propagating in the reversed direction.

Structure of the electromagnetic field near the focus of a stigmatic lens

The structure of the electromagnetic field near the focus of a stigmatic lens is investigated by use of the vectorial integral representation and the Fresnel formulas of refraction. The electric and magnetic vectors are calculated in the image space; from these, the energy densities and the Poynting vector are obtained. Numerical results, calculated for the focal plane and illustrated by diagrams, emphasize the departure from scalar theory. At the limit of small angular apertures, the results approach the scalar theory, i.e., the known Airy pattern.

Saturation effects in phase-conjugate lasers

Phase-conjugate lasers with saturable gain medium are analyzed, taking into account the saturation of the reflectivity of the phase-conjugate mirror that is due to pump depletion. It is shown that the behavior of the laser is determined by the extent to which the reflectivity is saturated as compared with the saturation of the gain medium. For weakly saturated phase-conjugate mirrors, the intensities and gain are not much different from those in conventional lasers. For strongly saturated mirrors, the laser behaves more like a single-pass amplifier with output intensity proportional to the pump intensity of the phase-conjugate mirror.

Higher-order modes of phase conjugate resonators

A numerical analysis based on the Prony algorithm was carried out to find the higher-order modes of phase conjugate optical resonators with hard-edged apertures. The mode patterns are nearly Hermite-Gaussians even for unstable resonator configurations. This indicates that there is not a phase conjugate analog of conventional unstable resonators. The eigenvalues and the extent to which the phase fronts match the surface of the conventional mirror were also calculated for a variety of resonator parameters. When there is one limiting aperture in the resonator and all others (including the phase conjugating mirror) can be considered as unbound, the eigenvalues and phase matching parameter are scalable by the ratio g/N, where N is the Fres-nel number of the aperture and g = 1 - L/R as in conventional resonator theory.

Gaussian modes of resonators containing saturable gain medium

The modes of resonators, which consist of mirrors with Gaussian reflectivity profile and contain saturable gain medium, are analyzed by applying ray matrix techniques. A self-consistent equation is obtained which takes into account the mutual effect of the beam on the medium and that of the medium on the beam. The following approach also provides a first-order approximation to the calculation of beam parameters and diffraction losses for the more common lasers with finite (but large) end mirrors.