Exceptional points by coupling of modes with different angular momenta in deformed microdisks: A perturbative analysis

Abstract

Recently, it has been shown numerically and by a semiclassical approach [Phys. Rev. Lett. 120, 093902 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.093902] that second-order exceptional points can appear in the spectrum of weakly deformed microdisk resonators by coupling of optical modes with different angular momentum. Here, we use a perturbation theory for weak boundary deformations to derive an effective non-Hermitian Hamiltonian from which we obtain analytical formulas to describe the formation of second-order exceptional points in such systems. The theory is extended to third-order exceptional points and confirmed by full numerical calculations. © 2018 American Physical Society.