The Effect of Random Surface Inhomogeneities on Microresonator Spectral Properties: Theory and Modeling at Millimeter Wave Range

TL;DR

This paper investigates how random surface inhomogeneities affect the spectral properties of open microresonators, combining theoretical modeling with experimental validation in the millimeter wave range.

Contribution

It introduces a theoretical and experimental framework for understanding the impact of surface inhomogeneities on microresonator spectra, emphasizing the gradient scattering mechanism.

Findings

Gradient scattering dominates non-dissipative losses.

Surface inhomogeneities cause effective mode wave number renormalization.

TM oscillations are less affected by inhomogeneities than TE oscillations.

Abstract

The influence of random surface inhomogeneities on spectral properties of open microresonators is studied both theoretically and experimentally. To solve the equations governing the dynamics of electromagnetic fields the method of eigen-mode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential. We prove theoretically that it is the gradient mechanism of wave-surface scattering which is the highly responsible for non-dissipative loss in the resonator. The influence of side-boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation. To study experimentally the effect of inhomogeneities on the resonator spectrum, the method of modeling in the millimeter wave range is applied. As a model object we use dielectric disc resonator (DDR) fitted with external inhomogeneities randomly arranged at its side boundary. Experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism. It is shown theoretically and confirmed in the experiment that TM oscillations in the DDR are less affected by surface inhomogeneities than TE oscillations with the same azimuth indices. The DDR model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigen-frequencies and the Q-factors of resonance spectral lines to fairly good accuracy. The results of calculations agree well with obtained experimental data.