Electromagnetic eigenoscillations and fields in a dielectric microsphere with multilayer spherical stack

摘要

We analyze numerically the spectrum of the eigenfrequencies and the electromagnetic eigenfields distribution in the spherical microsphere coated by the multilayered dielectric spherical stack in the optical frequency range. The general eigenfrequency equation is derived. The eigenfrequencies values are calculated versus the number of layers in the stack. We have found what Q factor can reach the large values for the eigenfrequency in the range of strong reflectivity of the stack (stop band). The eigenfrequencies laying beyond the stop band are unstable with respect to changing the number of layers, and such frequencies have low Q factors. The eigenfrequencies inside stop band are stable and their Q factors exponentially increase with the growth of the number of layers in stack until the saturation because of an influence of material losses in layers. The explicit calculation of the radial distribution of the electromagnetic eigenfields confirms that the energy of field is concentrated in the deepest part of the layered system. The confinement of the energy of optical eigenoscillations takes place in such states. The field amplitudes of oscillations decrease exponentially with a removal from the center of resonator up to external boundary. Therefore, the influence of the nonlinearity must be most substantial in the central part of the dielectric microsphere. We analyze several representative geometries: a dielectric sphere, a metallic sphere with the deposited stack on both of them.