PT-symmetry and Transparency

TL;DR

This paper explores the unique properties of PT-symmetric potentials, showing they cannot achieve perfect absorption without lasing and can act as transparent emitters across all energies, revealing novel optical behaviors.

Contribution

It demonstrates that PT-symmetric potentials inherently prevent Coherent Perfect Absorption without lasing and can function as perfect emitters, introducing the concept of Transparency in such systems.

Findings

PT-symmetric potentials do not allow CPA without lasing at any energy.

Eigenvalues of the scattering matrix can be unitary in unbroken PT-symmetry regimes.

Potential becomes a coherent perfect emitter for all energies.

Abstract

It is known that the perfect absorption of two identical waves incident on a complex potential from left and right can occur at a fixed real energy and that the time-reversed setting of this system would act as a laser at threshold at the same energy. Here, we argue and show that PT-symmetric potentials are exceptional in this regard which do not allow Coherent Perfect Absorption without lasing as the modulus of the determinant of the $S$-matrix, $|\det S|$, becomes 1, for all positive energies. Next we show that in the parametric regimes where the PT-symmetry is unbroken, the eigenvalues, $s_\pm$ of $S$, can become unitary (uni-modular) for all energies. Then the potential becomes coherent perfect emitter on both sides for any energy of coherent injection. We call this property Transparency.