Excitation Mechanisms of Whispering Gallery Modes with Direct Light Scattering

In optics, whispering gallery modes (WGMs) are modes of light that arise in cylindrically symmetric structures. Their intensity profile is strongly confined around the interface of the structure, and their Q-factors are some of the highest ever measured with light. Here, the physical mechanisms governing the coupling of a tangential beam into a WGM of a microsphere are analytically demonstrated. For that, Mie theory and the symmetries of light are made use of. It is demonstrated that the coupling mechanism is not related to any evanescent tunnelling effect. Rather, it is shown that it has to do with the angular momentum matching between the available inner WGMs of the sphere and the angular momentum content of the incident beam. The model is valid for any homogeneous sphere, for any wavelength, and for any incident cylindrically symmetric beam, focused or not. It quantitatively predicts the optical coupling efficiency to the resonator for any tangential position of the incident beam. And it sketches four different regimes of interaction depending on the beam position with respect to the sphere, properly matching experimental resonance spectra observed with free-space laser scattering.