Modes in spherical-mirror resonators. dominant mode calculations in output-coupled infinite strip mirror resonators

Abstract

PART I This work is the examination of a cavity mode approach to the mode structure of a laser. Solutions of the vector wave equation for electromagnetic fields in and between perfectly conducting oblate spheroidal cavities are examined for the case of wavelengths much less than cavity dimensions. These solutions are the field modes in Fabry-Perot type resonators with equal-radius concave spherical mirrors, or with concave-convex spherical mirrors, when the parameters of the oblate spheroids are chosen so that the radii of curvature and spacing on the axis of rotation match those of the resonator mirrors. Expressions for the transverse and longitudinal mode structures are derived. The eigenvalue equations are written, and are solved for the case of the two lowest order modes. Part II This work is the numerical calculation of the steady state lowest order even and odd symmetry electromagnetic field patterns at the mirrors of the multimode resonator formed by two plane-parallel infinite strip mirrors, modified for output coupling by central strips of zero reflectivity. The equation solved is the scalar Huyghens-Fresnel integral equation (a transverse electromagnetic wave approximation to the vector integral equation, valid when the wavelength is much less than the cavity dimensions) relating the fields at the two mirrors, converted to an eigenvalue equation, and approximated for calculations by a matrix eigenvalue equation. The mode structure, power loss and phase shift per transit, and output coupling are discussed.