Corrected perturbation theory for transverse-electric whispering-gallery modes in deformed microdisks

The perturbation theory by Ge et al. [Phys. Rev. A 87, 023833 (2013)] for transverse-electric polarized modes in weakly deformed microdisks omits terms related to the variation of the normal derivative of the magnetic field along the boundary. Here, we show that these terms are necessary to accurately describe microdisks with a strongly winding boundary. In particular, it is demonstrated that the corrected perturbation theory allows one to describe the counterintuitive phenomenon of Q-factor enhancement due to weak boundary deformation. We discuss in detail the microflower cavity and the limacon cavity. Good agreement of the corrected perturbation theory with full numerical results is observed.