Fractal Weyl laws for amplified states in PT-symmetric resonators

TL;DR

This paper demonstrates that in PT-symmetric resonators, hierarchical phase-space structures lead to a reduction in strongly amplified states, generalizing fractal Weyl laws and impacting mode competition in laser-absorbers.

Contribution

It introduces a semiclassical mechanism based on phase-space structures that reduces amplified states in PT-symmetric systems, extending fractal Weyl laws to these non-Hermitian resonators.

Findings

Hierarchical phase-space structures suppress amplified states.

Reduction of participating modes in PT-symmetric laser-absorbers.

Generalization of fractal Weyl law for non-Hermitian systems.

Abstract

We find that in nonhermitian PT-symmetric systems (as realized in resonators with balanced absorption and amplification), a mechanism based on quantum-to-classical correspondence reduces the occurrence of strongly amplified states. The reduction arises from semiclassically emerging hierarchical phase-space structures that are associated with the coupling of the amplifying and absorbing regions (forward and backward-trapped sets and their complements), and amounts to a generalization of the fractal Weyl law, earlier proposed for ballistically open systems. In the context of the recently introduced class of PT-symmetric laser-absorbers, this phenomenon reduces the number of states participating in the mode competition.