Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies

TL;DR

This paper explores spectral singularities in complex scattering potentials, showing they cause infinite reflection and transmission at real energies, and demonstrates their implications in wave guide resonances through a specific PT-symmetric example.

Contribution

It identifies spectral singularities as real-energy resonances with infinite coefficients and connects them to physical wave guide resonances, providing a concrete PT-symmetric potential example.

Findings

Spectral singularities correspond to infinite reflection and transmission coefficients.

Wave guides modeled with such potentials act as resonators at spectral singularity frequencies.

The PT-symmetric barrier potential exhibits spectral singularities leading to resonance phenomena.

Abstract

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a wave guide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential and demonstrate the above resonance phenomenon for a certain electromagnetic wave guide.