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Spectrum engineering in whispering gallery mode resonators

We investigate several possibilities of designing spectrum of a whispering gallery mode resonators to create groups of optical modes with desired free spectral range as well as group velocity dispersion. This will enable efficient resonant nonlinear frequency conversion processes such as hyper-parametric and parametric oscillations, frequency doubling, and electro-optical frequency shifting and modulation. We show that the spectral design can be achieved via a proper modification of the shape of the resonator and via the change of the distribution of the refractive index of the resonator host material.