Nonhermitian transport effects in coupled-resonator optical waveguides

TL;DR

This paper investigates how non-hermitian effects in asymmetric, leaky coupled-resonator optical waveguides lead to complex band structures, exceptional points, and deviations in wave packet velocities, revealing new transport phenomena.

Contribution

It introduces a comprehensive analysis of non-hermitian transport effects in open, asymmetric CROWs, highlighting the role of exceptional points and non-orthogonal eigenmodes.

Findings

Complex band structures with real and complex branches

Presence of exceptional points where eigenmodes coalesce

Non-hermitian corrections significantly affect group velocity near exceptional points

Abstract

Coupled-resonator optical waveguides (CROWs) are known to have interesting and useful dispersion properties. Here, we study the transport in these waveguides in the general case where each resonator is open and asymmetric, i.e., is leaky and possesses no mirror-reflection symmetry. Each individual resonator then exhibits asymmetric backscattering between clockwise and counterclockwise propagating waves, which in combination with the losses induces non-orthogonal eigenmodes. In a chain of such resonators, the coupling between the resonators induces an additional source of non-hermiticity, and a complex band structure arises. We show that in this situation the group velocity of wave packets differs from the velocity associated with the probability density flux, with the difference arising from a non-hermitian correction to the Hellmann-Feynman theorem. Exploring these features numerically in a realistic scenario, we find that the complex band structure comprises almost-real branches and complex branches, which are joined by exceptional points, i.e., nonhermitian degeneracies at which not only the frequencies and decay rates coalesce but also the eigenmodes themselves. The non-hermitian corrections to the group velocity are largest in the regions around the exceptional points.