Generalized theory of optical resonator and waveguide modes and their linear and Kerr nonlinear coupling

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