We report a theoretical and experimental study of coupling between a whispering-gallery-mode (WGM) microdisk resonator and a fiber taper which exchange energies at two distinct regions. We observe an oscillatory behavior in the coupling strength as a function of the distance between the two coupling regions when a fiber taper is moved laterally above the resonator at fixed vertical distance. This oscillation is clearly seen in the linewidth of the resonance as well as in the on-resonance transmission. A theoretical model considering for two-point coupling successfully explains the experimental observations as being a result of the interference between the light fields coupled into and out of the resonator at two distinct regions and the light transmitted through the waveguide. Critical coupling in two-region coupling is a collective result of the coupling at two different coupling regions, and does not require critical coupling at both or at any one of the two coupling regions. This relaxes the conditions for achieving critical coupling in waveguide-resonator systems. The discovery of this previously unnoticed oscillatory behavior in two-region coupling between a WGM resonator and a waveguide will benefit both fundamental studies and practical applications based on WGM resonators.
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