Optical spectral singularities as zero-width resonance frequencies of a Fabry-Perot resonator

Abstract

Spectral singularities are spectral points of non-Hermitian Hamiltonians with the real energies, that annihilate the completeness of the eigenfunctions. The complex $\mathcal{P}\mathcal{T}$-symmetric potentials with real spectrum have such Hamiltonians. It was identified that the spectral singularities of complex potentials such as an optical gain medium correspond to zero-width resonance modes of the reflected and transmitted beams from the medium. We show that a Fabry-Perot resonator with a gain medium under inclined incident beam exhibits spectral singularities that are measurable by changing the incident angle of the beam to the resonator. The results are realized by theory and simulations.