Theory of Cavity-Mode-Mixing Effects in Internally Scanned Lasers

Abstract

An analysis of cavity-mode-mixing effects is given for a variety of cavity geometries and coupling parameters in the presence of a continuous transverse aperture velocity. The paper represents an extension of the previous work by Fox and Li, and Boyd and Gordon to include the effects of time-dependent changes in the transverse aperture location. The average beam profile in the scanning reference frame is calculated through a continuous reexpansion of the optical field in terms of the set of self-reproducing modes characteristic of the same cavity under static transverse boundary conditions. Results are specifically given for square aperture, plane-parallel, concentric, and confocal geometry for light, plane polarized orthogonally to the scan velocity. The effects of a random variation in the mirror-transmission coefficient are calculated, and it is shown that these effects are largely averaged out in the scanning process. Cavities of the type considered earlier by Pole and Myer and by Beiser are specifically considered. A method of evaluating different real systems with the present calculations is discussed; it is shown that a "push-pull"-type scanning laser should have an inherent scan velocity roughly twice that for the single-ended scanning laser geometry previously considered for the same degree of beam degradation and other cavity parameters. A method is developed for the derivation of self-reproducing confocal modes which arise with stationary, continuously varying aperture transmission functions. The method is specifically applied to a confocal Gaussian gain aperture and to a nonsymmetric confocal gain aperture. It is shown that the odd-symmetry mode of the Gaussian gain aperture dominates over the even-symmetry mode at low-gain coefficients, in opposition to the normal diffraction-limited rectangular-transmission-aperture case. An extension of the scanning problem is given to include the transverse displacement of a continuous gain aperture; it is shown formally that the solution of the continuous-aperture problem goes continuously over to the rectangular-aperture results at low values of the gain. The method is specifically applied to a hypothetical scanning laser employing swept Gaussian and nonsymmetric gain apertures.