Theoretical seminar | 20 November 2024

A cylindrical microresonator with radius variation based on standard optical fiber is a promising platform for generating optical frequency combs with a low repetition rate based on a set of axial modes. Unlike azimuthal modes, axial modes with different quantum numbers have different mode volumes and coupling strengths. In this regard, the Lugiato-Lefever equation, which is typically used to model the nonlinear dynamics of azimuthal modes, is not suitable for describing the nonlinear dynamics of axial modes.

The report will present a theory of the nonlinear dynamics of modes in a cylindrical microresonator with radius variation. The theory shows that the cylindrical geometry of the microresonator leads to large anomalous group velocity dispersion of axial modes, which ensures the existence of soliton solutions regardless of the form of radius variation. The report will also propose a method for optimizing the coupling between the microresonator and the taper to reduce the threshold for Kerr nonlinear effects in experiments and will describe the theory of modulation instability of axial modes. We will demonstrate the generation of soliton solutions with similar parameters in cylindrical microresonators with different forms of radius variation.

Main paper/arXiv, related to the seminar, and other references:

1. A. Y. Kolesnikova, S. V. Suchkov, and I. D. Vatnik, “Frequency comb generation in SNAP fiber resonator based on axial-azimuthal mode interactions,” Opt. Express, vol. 30, no. 7, p. 10588, 2022, doi: 10.1364/oe.450298.
2. A. Y. Kolesnikova and I. D. Vatnik, “Theory of nonlinear whispering-gallery-mode dynamics in surface nanoscale axial photonics microresonators,” Phys. Rev. A, vol. 108, no. 3, pp. 1–8, 2023, doi: 10.1103/PhysRevA.108.033506.
3. A. Y. Kolesnikova and I. D. Vatnik, “Modulation-instability analysis of axial-azimuthal modes in surface nanoscale axial photonic microresonators,” Phys. Rev. A, vol. 109, no. 5, pp. 1–8, 2024, doi: 10.1103/PhysRevA.109.053520.