Test of the FDTD accuracy in the analysis of the scattering resonances associated with high-Q whispering-gallery modes of a circular cylinder

TL;DR

This paper evaluates the accuracy of FDTD simulations in analyzing high-Q whispering-gallery resonances of a circular dielectric cylinder, revealing significant limitations near these resonances compared to exact solutions.

Contribution

It demonstrates the failure of conventional 2D FDTD methods to accurately model high-Q whispering-gallery modes, highlighting the need for improved computational techniques.

Findings

FDTD fails to accurately characterize emission rates near high-Q resonances.

Errors increase with higher Q-factors, up to 10^3.

Comparison with exact solutions shows significant discrepancies.

Abstract

The objective of the paper is the assessment of the accuracy of a conventional FDTD code in the computation of the near and far-field scattering characteristics of a circular dielectric cylinder. We excite the cylinder with an electric or magnetic line current and demonstrate the failure of the two-dimensional FDTD algorithm to characterize accurately the emission rate and the field patterns near high-Q whispering-gallery-mode resonances. This is proven by comparison with the exact series solutions. The computational errors in the emission rate are then studied at the resonances still detectable with FDTD, i.e. having Q-factors up to 10^3.