2018/03/30 by Kathleen McGarvey-Lechable, Pablo Bianucci · 11 citations
Engineering · Physics and Astronomy · #Advanced Fiber Laser Technologies #Bloch wave #Condensed matter physics #Coupling coefficient of resonators #Degenerate energy levels #Dispersion relation #Floquet theory #Optics #Photonic and Optical Devices #Photonic crystal #Photorefractive and Nonlinear Optics #Physics #Quantum mechanics #Rayleigh scattering #Resonance (particle physics) #Resonator #physics.optics
paper · pdf · doi:10.1103/physrevb.97.214204
published in Physical review. B./Physical review. B 97(21) (American Physical Society)
arxiv created 2018/03/30 · openalex publication_date 2018/06/19 · arxiv updated 2018/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Modal coupling between frequency-degenerate resonances of an optical ring resonator is a commonly observed phenomenon that results in adverse mode splitting. Traditionally, this coupling is attributed to Rayleigh scattering of a propagating electromagnetic wave into its associated degenerate counterpropagating mode from small perturbations to the dielectric material of the resonator. We have chosen to reframe the problem of intracavity Rayleigh scattering by considering the optical ring resonator as an infinitely long, one-dimensional photonic crystal (PhC) that possesses a lattice constant equal to the perimeter of the ring. Through application of Bloch-Floquet theory, we show that modal coupling between degenerate resonances of a ring can effectively be described as the formation of photonic frequency bands in the dispersion relation of the resonator. We additionally demonstrate that the Bragg planes of the PhC lattice coincide with the phase matching conditions for constructive interference in the ring. Finally, we show that the magnitude of frequency splitting of a particular resonance is proportional to its associated coefficient in the Fourier expansion of the ring's periodic dielectric function. The fine control of the mode splitting that can be obtained in this way provides a straightforward way to obtain ring resonances with anomalous dispersion in arbitrary wavelength ranges.