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Morphology-dependent resonances of microspheres sitting upon an index-matched single-mode fiber half-coupler are excited by a tunable 753-nm distributed-feedback laser. Resonance peaks in the scattering spectra and associated dips in the transmission spectra for the TE and TM modes are observed. We present a new model that describes this interaction in terms of the fiber–sphere coupling coefficient and the microsphere’s intrinsic quality factor Q_0. This model enables us to obtain expressions for the finesse and the Q factor of the composite particle–fiber system, the resonance width, and the depth of the dips measured in the transmission spectra. Our model shows that index matching improves the coupling efficiency by more than a factor of 2 compared with that of a non-index-matched system.