Using numerical modeling, we observe surprisingly high coupling efficiencies (up to 0.1) between spatially separated spherical cavities with strongly detuned whispering gallery modes. We show that the coupling arises from resonance between a discrete energy eigenstate in the sphere containing the source of light and a continuum of "quasi"-whispering gallery modes with noncircular shape and reduced quality factors in the sphere receiving the electromagnetic energy. Such coupling effects may make possible broad spectral transmission effects in coupled resonator optical waveguides, previously thought to be excluded in a real system with significant size disorder.
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