An analysis of waveguide resonator coupling in a microsphere and confocal cavity whispering gallery system

Abstract

There are two kinds of coupling method in an optical-fiber taper coupled to a silica-microsphere whispering gallery mode (WGM) system. One is indirect coupling; another is direct coupling. In the case of indirect coupling, pump light is injected from the side of the micro-cavity. Thus, a ring mode results from the total internal reflection excited by spherical ring standing wave. In the case of direct coupling, pump light is injected from the front of the micro-cavity. Thus, a concentric mode or confocal mode result from the transmission input excited by spherical axial-oscillating standing wave. The ring mode and concentric mode have both been adopted in microsphere cavities. However, the confocal mode has not been reported, either in theory or experiment. In this paper, we adopt a micro-spheroid resonator as the confocal cavity, which can be obtained by exerting a pressure on the microsphere cavity. Thus, the confocal mode is produced in a micro-spheroid resonator. Then we investigate waveguide resonator coupling in a microsphere and confocal cavity WGM system. Finally, we make a detailed analysis of the full width at half maximum (FWHM), ζ, and quality factor, Q, between the indirect coupling and the direct coupling. We find that for the concentric mode, $Q=6.74\times {10}^4$, which is nearly the same as that of the ring mode, Q = 7.2 × 10⁴. For large diameter of injection laser beam, the confocal mode can obtain higher quality factor (Q > 1.202 × 10⁶) than that of the ring mode (Q = 7.2 × 10⁴).

Keywords:

• micro-confocal cavity
• whispering gallery system
• quality factor