Validation of FDTD-2D for high-Q resonances description

TL;DR

This paper evaluates the accuracy of standard FDTD simulations in modeling high-Q whispering-gallery-mode resonances in circular dielectric resonators, comparing results with exact Mie-series solutions for various materials and polarizations.

Contribution

It provides a systematic assessment of FDTD's precision in high-Q resonance modeling, highlighting error characteristics and limitations.

Findings

FDTD accurately predicts resonance frequencies for high-Q WGMs

Errors increase with higher Q-factors and resonator size

Comparison with Mie-series solutions validates FDTD's applicability

Abstract

The objective of the study is to assess the accuracy of a standard FDTD code in description of high-Q resonances such as whispering-gallery-mode (WGM) ones excited in circular dielectric resonators. To achieve the goal, we consider circular resonators excited by line currents and extract the data on FDTD accuracy from comparisons between the FDTD-solution and the exact one obtained by the Mie-series solutions. The near-field and far-field characteristics are studied for resonators of various sizes, made of quartz and silicon. Both E - and H - polarizations are considered. The computational error, i.e. a resonance frequency shift observed for the FDTD solution, is analyzed and compared for several WGMs having different Q-factors.