Parity-time symmetry in scattering problems

Abstract

The realization that non-Hermitian parity-time (PT) symmetric Hamiltonians can exhibit entirely real spectra has raised considerable interest in the physics and engineering communities. In the context of optics and photonics, in particular, mathematical analogies with quantum mechanical problem have enabled several breakthrough in terms of observing and utilizing PT-symmetry in closed guided-wave systems. On the other hand, less attention has been paid to the scattering behavior of open PT-symmetric systems. In this chapter, we consider canonical PT-symmetric open systems and explore some of the scattering characteristics of coupled waveguide cavity arrangements. In this regard, we show how an open PT-symmetric configuration can be compared to a closed system, and how the scattering properties are related to the spectral properties of the PT-symmetric system and the associated phase transitions. Afterwards, different scattering geometries are explored in one, two and three dimensions. In addition, we review recent investigations on this topic and highlight opportunities for future research.