Eigenfrequency Spectrum of Prolate Spheroidal Magneto-optic Cavities

In this work we report on the eigenfrequencies of magnetooptic cavities, their non-degeneration, and their sensitivity, when the cavity deviates from the traditional spherical shape and deforms, due to manufacturing defects, into a prolate spheroid. Since the cavity is statically magnetized due to an external magnetic bias, its permittivity tensor becomes gyroelectric. To solve this problem, we employ a technique based on spheroidal eigenvectors for the expansion of the electromagnetic field in the anisotropic region of the cavity. The eigenfrequencies are obtained by setting system's matrix determinant equal to zero, with the matrix being obtained after the satisfaction of the boundary conditions at the spheroidal surface. Comparisons with a shape-perturbation technique are performed, and numerical results on the eigenfrequency spectrum are given for different aspect ratio magneto-optic cavities.