Ray interpretation of multipole fields in spherical dielectric cavities

Abstract

We present a caustic model of morphology-dependent resonances based on geometrical optics, which describes the electromagnetic field in cylinders or spheres by families of ray congruences. A ray congruence in this model is basically a family of rays that osculate in phase on a common circle, the caustic. The circumference of this circle is in the plane case an integer multiple of the wavelength. This integer number corresponds to the mode number in the multipole expansion. In the spherical case two families of caustics exist. The mode numbers l, m of the multipole expansion for spherical particles define the corresponding radii of the caustics of the two ray families. The localization principle follows in this model simply by conservation of angular momentum. The condition for narrow modes caused by total internal reflection and the leaking of these modes is explained. The excitation of narrow resonances can also be explained in a straightforward manner by requiring that rays propagating from the caustic to the surface couple in phase to the caustic after reflection. Comparison with the exact solution shows excellent agreement.