Resonant wavelengths of whispering gallery modes in dispersive materials

In this work we compute the resonant wavelengths of whispering gallery modes for bulk-fused silica microspheres taking into consideration the material chromatic dispersion. This is done by following two approaches: solving the exact characteristic equation and solving the nonlinear equations that result from the asymptotic approximations for a wavelength-dependent refractive index. Similar results with both methods are obtained with differences below 1%. Nevertheless, important differences are found between the resonant wavelengths computed for a non-dispersive and a dispersive material. We compute the free spectral range and the quality factor, and make a comparison between the variable index and the constant index cases. Our results show that the quality factor is unaffected by chromatic dispersion. However, there are differences of significant relevance in the case of the free spectral range. Our work could be useful as a pathway for designing microspheres for different applications.