Computing resonant modes of circular cylindrical resonators by vertical mode expansions

Area of Science:

• Computational electromagnetics and nanophotonics.
• Development of numerical methods for optical resonator analysis.

Background:

• Subwavelength cylindrical resonators are crucial components in diverse photonic applications.
• Circular cylindrical resonators are particularly significant in nanophotonics due to ease of fabrication and tunable resonance effects.
• Accurate computation of resonant modes is essential for designing and optimizing these structures.

Purpose of the Study:

• To develop an efficient and robust numerical method for computing resonant modes of circular cylinders.
• To handle multilayered cylinders and those embedded in layered backgrounds.
• To analyze both dielectric and metallic nanocylinders.

Main Methods:

• Reduction of the 3D eigenvalue problem to 1D problems using field expansions in vertical modes.
• Application of the Chebyshev pseudospectral method for computing 1D modes and discretizing the eigenvalue problem.
• Development of a novel iterative scheme for reliably solving 1D nonlinear eigenvalue problems.

Main Results:

• The developed method accurately computes resonant modes for multilayered and embedded circular cylinders.
• Resonant modes for metallic cylinders are calculated using analytical models for dielectric functions.
• The method is validated against existing numerical results and applied to explore high-Q resonances in dielectric cylinders and analyze gold nanocylinders.

Conclusions:

• The proposed numerical method offers an efficient and robust approach for analyzing resonant modes in various cylindrical resonator configurations.
• This technique facilitates the exploration and design of nanophotonic devices utilizing subwavelength resonators.
• The study provides valuable insights into the behavior of dielectric and metallic nanocylinders.