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Journal Article

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


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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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
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.