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Open subwavelength cylindrical resonators of finite height are widely used invarious photonics applications. Circular cylindrical resonators areparticularly important in nanophotonics, since they are relatively easy tofabricate and can be designed to exhibit different resonance effects. In thispaper, an efficient and robust numerical method is developed for computingresonant modes of circular cylinders which may have a few layers and may beembedded in a layered background. The resonant modes are complex-frequencyoutgoing solutions of the Maxwell's equations with no sources or incidentwaves. The method uses field expansions in one-dimensional (1D) ``vertical''modes to reduce the original three-dimensional eigenvalue problem to 1Dproblems, and uses Chebyshev pseudospectral method to compute the 1D modes andset up the discretized eigenvalue problem. In addition, a new iterative schemeis developed so that the 1D nonlinear eigenvalue problems can be reliablysolved. For metallic cylinders, the resonant modes are calculated based onanalytic models for the dielectric functions of metals. The method is validatedby comparisons with existing numerical results, and it is also used to exploresubwavelength dielectric cylinders with high-$Q$ resonances and analyze goldnanocylinders.

Computing resonant modes of circular cylindrical resonators by vertical mode expansions