The spectral Fourier–Bessel numerical solver is suitable for obtaining steady state modal properties for resonators and waveguides fitting a cylindrical geometry. The material properties and geometry of the structures are directly responsible for the optical properties of the states obtained. The solver computation domain is extended such that it can be used when the constitutive expressions include the magneto-electric coupling, bi-anisotropic. Full computation expressions required to populate the matrices are included along with three forms of the system matrix constructed from Faraday's and Ampere's curl relations. Two representative numerical computation examples are provided when axial rotation of the structure (Sagnac effect) is present; the resonator state properties of a uniform ring structure supporting whispering-gallery modes and a 6-fold rotationally symmetric deformed ring structure.

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Keywords Bi-anisotropy, Fourier–Bessel, Nano-optic resonators, Optical resonator, Resonator states, Sagnac effect
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Journal Optics Communications
Gauthier, R. (2019). Bi-anisotropic resonators analyzed using Fourier–Bessel numerical formulation; Sagnac effect application. Optics Communications, 435, 413–425. doi:10.1016/j.optcom.2018.11.026