Eigenmodes of spherical dielectric cavities: coupling of internal and external rays

Eigenmodes of spherical dielectric cavities are investigated within the fra mework of geometrical optics. A model for the coupling of internal and exte rnal rays is presented. Approximate expressions for the expansion coefficie nts of Mie theory are derived. Formulas for the modulus and the phase are g iven. The systematic behavior of the phase angle is investigated. All expre ssions are explicit equations and may be used to calculate the expansion co efficients as a function of order l or size parameter x. All features of th e presented results are understandable in terms of light rays. A plane inte rface analog is presented. The so-called resonance regime (Lambda/n < x < L ambda), where n is the relative refractive index and Lambda = l + 1/2, is c onsidered especially. An implicit equation for these resonance positions is rederived, and explicit relations for their strengths and widths are given . All findings are in agreement with results derived from Mie theory. (C) 1 999 Optical Society of America [S0740-3232(99)00804-2].