Nonhermitian transport effects in coupled-resonator optical waveguides

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.

arXiv comment11 pages, 9 figures

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• Linear response theory of open systems with exceptional points
• Bulk and edge-state arcs in non-hermitian coupled-resonator arrays
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• Embedding quantum systems with a non-conserved probability in classical environments
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• Unitary Scattering Protected by Pseudo-Hermiticity
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Tachyonic Dispersion in Coherent Networks
• Helical transport in coupled resonator waveguides
• Quantum quench dynamics in the Luttinger liquid phase of the Hatano-Nelson model
• Non-Quantized Edge Channel Conductance and Zero Conductance Fluctuation in Non-Hermitian Chern Insulators
• Slow approach to adiabaticity in many-body non-Hermitian systems: the Hatano-Nelson Model
• Non-Hermitian interaction of a discrete state with a continuum
• Fundamental issues with light propagation through $\mathcal{P}\mathcal{T}$-symmetric systems
• EP restoration and fast-light edge states in photonic crystal waveguide with glide and time reversal symmetry