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This paper theoretically analyzes a hollow cylindrical whispering gallery mode resonator with radially inhomogeneous cladding. We propose an index profile of n(r) = b/r to enhance field penetration towards the resonator core. With such index profile, externally coupled evanescent wave can easily penetrate the resonator cladding without any potential barrier.

Radially graded index whispering gallery mode resonator for penetration enhancement