Generalized theory of optical resonator and waveguide modes and their linear and Kerr nonlinear coupling
Silver JM, Del'Haye P (2022)
Publication Type: Journal article
Publication year: 2022
Journal
Book Volume: 105
Article Number: 023517
Journal Issue: 2
DOI: 10.1103/PhysRevA.105.023517
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.
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APA:
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). https://dx.doi.org/10.1103/PhysRevA.105.023517
MLA:
Silver, Jonathan M., and Pascal Del'Haye. "Generalized theory of optical resonator and waveguide modes and their linear and Kerr nonlinear coupling." Physical Review A 105.2 (2022).
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