Quantum noise and mode nonorthogonality in non-Hermitian PT-symmetric optical resonators

PT-symmetric optical resonators combine absorbing regions with active, amplifying regions. The latter are the source of radiation generated via spontaneous and stimulated emission, which embodies quantum noise and can result in lasing. We calculate the frequency-resolved output radiation intensity of such systems and relate it to a suitable measure of excess noise and mode nonorthogonality. The line shape differs depending on whether the emission lines are isolated (as for weakly amplifying, almost-Hermitian systems) or overlapping (as for the almost-degenerate resonances in the vicinity of exceptional points associated with spontaneous PT-symmetry breaking). The calculations are carried out in the scattering input-output formalism, and are illustrated for a quasi-one-dimensional resonator setup. In our derivations, we also consider the more general case of a resonator in which the amplifying and absorbing regions are not related by symmetry.