Abstract

We investigated the impact of Kerr nonlinearity and stimulated Raman scattering on the whispering gallery modes of an optical microsphere. When two resonant modes are nonlinearly interacting due to the Kerr effect, a resonant mode undergoes a frequency shift that depends not only on its energy, but also on the energy of the other mode. A mathematical theory is developed taking into account the tensorial nature of the third-order susceptibility and vector nature of whispering gallery modes. The technique is extended to include stimulated Raman scattering, and coupled mode equations are developed to describe the energy transfer between the pump and Stokes waves without ignoring self-phase modulation and cross-phase modulation. The analytical model is found to be in good agreement with the numerical results in situations where the pump depletion is negligible.

© 2016 Optical Society of America

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