Effect of the Goos–Hänchen shift on the geometrical-optics model for spherical-cavity mode spacing

In the geometrical-optics framework, the internal fields near morphology-dependent resonances (MDR) of dielectric spheres are represented by rays undergoing total internal reflection at the sphere surface. The round-trip path length of rays circumnavigating the sphere is used to compute the mode spacing of MDR’s. The Goos–Hänchen shift of the total internally reflected rays at the sphere surface is included in the ray picture to explain the qualitative behavior of the MDR frequency spacing in the Lorentz-Mie formalism for the entire size-parameter (circumference/wavelength) range. The MDR’s are characterized by a radial distance rm′. A connection between the ray picture and the Mie theory is established, based on rm′.