Generalized Theory of Optical Resonator and Waveguide Modes and their Linear 
and Kerr Nonlinear Coupling

Silver, Jonathan M.; Del'Haye, Pascal

doi:10.1103/PhysRevA.105.023517

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Generalized Theory of Optical Resonator and Waveguide Modes and their Linear and Kerr Nonlinear Coupling

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Del'Haye, Pascal
Del'Haye Research Group, Research Groups, Max Planck Institute for the Science of Light, Max Planck Society;
Department of Physics, Friedrich–Alexander University Erlangen–Nuremberg;

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https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.023517
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Citation

Silver, J. M., & Del'Haye, P. (2022). Generalized Theory of Optical Resonator and Waveguide Modes and their Linear and Kerr Nonlinear Coupling. Physical Review A, 105(2): 023517. doi:10.1103/PhysRevA.105.023517.

Cite as: https://hdl.handle.net/21.11116/0000-0009-6646-6

Abstract

We derive a general theory of linear coupling and Kerr nonlinear coupling between modes of dielectric optical resonators from first principles. The treatment is not specific to a particular geometry or choice of mode basis, and can therefore be used as a foundation for describing any phenomenon resulting from any combination of linear coupling, scattering and Kerr nonlinearity, such as bending and surface roughness losses, geometric backscattering, self- and cross-phase modulation, four-wave mixing, third-harmonic generation and Kerr frequency comb generation. The theory is then applied to a translationally symmetric waveguide in order to calculate the evanescent coupling strength to the modes of a microresonator placed nearby, as well as the Kerr self- and cross-phase modulation terms between the modes of the resonator. This is then used to derive a dimensionless equation describing the symmetry-breaking dynamics of two counterpropagating modes of a loop resonator and prove that cross-phase modulation is exactly twice as strong as self-phase modulation only in the case that the two counterpropagating modes are otherwise identical.