Pseudo-Hermitian Hamiltonians Generating Waveguide Mode Evolution

TL;DR

This paper investigates pseudo-Hermitian Hamiltonians derived from transfer matrices in waveguides, revealing eigenvalue transitions and symmetry properties relevant to waveguide mode evolution.

Contribution

It demonstrates how non-Hermitian Hamiltonians in waveguides exhibit pseudo-Hermiticity and symmetry-induced eigenvalue transitions, expanding understanding of waveguide mode dynamics.

Findings

Eigenvalue transitions between real, imaginary, and complex pairs

Identification of pseudo-Hermitian and anti-PT symmetry properties

Simple models illustrating symmetry-breaking phenomena

Abstract

We study the properties of Hamiltonians defined as the generators of transfer matrices in quasi- one-dimensional waveguides. For single- or multi-mode waveguides obeying flux conservation and time-reversal invariance, the Hamiltonians defined in this way are non-Hermitian, but satisfy symmetry properties that have previously been identified in the literature as "pseudo Hermiticity" and "anti-PT symmetry". We show how simple one-channel and two-channel models exhibit transitions between real, imaginary, and complex eigenvalue pairs.