The Effect of Random Surface Inhomogeneities on Microresonator Spectral   Properties: Theory and Modeling at Millimeter Wave Range
  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. 
E.M. Ganapolskii, Z.E. Eremenko, Yu.V. Tarasov