Geometrical-optics analysis of whispering-gallery modes in the layer of a coated spherical resonator

Schweiger, G. and Weigel, T. and Ostendorf, A.

Volume: 102 Pages:
DOI: 10.1103/PhysRevA.102.053506
Published: 2020

The resonance properties of a layer on the surface of a spherical microresonator are investigated using geometrical optics. The resonance condition for these shell-guided modes is formulated. Shell-guided modes are located in the layer and are bounded by the inner and outer surfaces of the layer. It is shown that the resonance condition depends - similarly to the case of a homogeneous resonator - on the difference of the phase propagation of a ray crossing the layer and the corresponding phase propagation along the associated caustic. It is shown that the layer can support resonances only in a certain thickness range that depends, among other factors, on the resonance order and the wave number. A straightforward explanation is given for these limitations. Comparison with solutions from wave theory shows excellent agreement. A simple analytical solution is presented to calculate the sensitivity of the resonator to the refractive index and the thickness of the layer as well as to the refractive index of the environment. © 2020 American Physical Society.

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