Abstract
The local density of states (LDOS) of the electromagnetic field on the surface of an absorbing dielectric microsphere at frequencies of the whispering-gallery modes (WGMs) is evaluated using the dyadic Green tensors of the electric and magnetic fields. In the calculation, the morphology-dependent resonances in the frequency dependence of the Mie coefficients are described analytically in terms of the resonant frequency and the partial quality factors which allow for light radiation and absorption. The Purcell factor of LDOS enhancement by WGMs is calculated to be proportional to the product of the quality factor and the squared ratio of the light wavelength to the sphere diameter. The ultimate values of the electric-field LDOS enhancement are estimated to be of the order of ${10}^{7}$ for a fused-silica microsphere in air. The efficiency of radiation of the resonant spontaneous emission from electric dipoles located near the surface outside of a sphere is determined. The characteristics of a dielectric microsphere are compared with those of other cavities.
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