The high quality electromagnetic oscillations in a dielectric microsphere with multilayer spherical stack

Abstract

We examine the waveguide properties of a spherical stack: a system of optical layers deposited onto the microsphere substrate, with arbitrary ratios between thicknesses of layers and a wavelength of propagating electromagnetic radiation. Frequency dependencies of the reflection coefficient and impedance of the stack are studied. An appropriate matrix formalism is developed to generalize the matrix method well-known for the plane case, into the case of the spherical layer geometry. The material losses and random deviations of thicknesses of layers are taken into account. The quarter-wave length layers are studied in details. Our numerical calculations have revealed the narrow gap of a transparency in a zone of high reflectance of a stack under the suitable parameters. The spectrum of eigenfrequencies of a spherical resonator coating by the dielectric stack has been calculated. It has been found that Q factor electromagnetic oscillations in such a system exponentially grows with increasing number of layers in the stack, but only for eigenfrequencies which are in the zone of high a stack reflection.