Collection of emission from an oscillating dipole inside a sphere: analytical integration over a circular aperture.

We describe a method for integrating analytically, over a circular aperture, the emission from an oscillating dipole inside a dielectric sphere. The model is useful for investigating fluorescence, Raman, or other emission from molecules inside of spherical particles or droplets. The analysis is performed for two cases: (a) the dipole emits from a fixed orientation, and (b) the dipole emits from all orientations and the collected energy is summed. This second case models the collection of emission from a molecule that is excited repeatedly; after each excitation it rotates to a random orientation before emitting. These results are applicable to single-molecule detection techniques employing microdroplets and to other techniques for characterizing microparticles with luminescence or inelastic scattering.