Non-Hermitian waves in a continuous periodic model and application to photonic crystals

Abstract

In some non-Hermitian systems, the eigenstates in the bulk are localized at the boundaries of the systems. This is called the non-Hermitian skin effect, and it has been studied mostly in discrete systems. In the present work, we study the non-Hermitian skin effect in a continuous periodic model. In a one-dimensional system, we show that the localization lengths are equal for all the eigenstates. Moreover, the localization length and the eigenspectra in a large system are independent of the types of open boundary conditions. These properties are also found in a non-Hermitian photonic crystal. Such remarkable behaviors in a continuous periodic model can be explained in terms of the non-Bloch band theory. By constructing the generalized Brillouin zone for a complex Bloch wave number, we derive the localization length and the eigenspectra under an open boundary condition. Furthermore we show that the generalized Brillouin zone also has various physical properties, such as bulk-edge correspondence.

14 pages, 6 figures

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• Non-Bloch bands in two-dimensional non-Hermitian systems
• Geometric Origin of Non-Bloch PT Symmetry Breaking
• Photonic corner skin modes
• Hybrid skin-topological effect induced by eight-site cells and arbitrary adjustment of the localization of topological edge states
• Non-Hermitian skin effect induced by Rashba-Dresselhaus spin-orbit coupling
• Non-Bloch band theory for non-Hermitian continuum systems
• Non-Bloch band theory of generalized eigenvalue problems
• Pseudomagnetic suppression of non-Hermitian skin effect
• Role of Topology in Relaxation of One-Dimensional Stochastic Processes
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Non-Hermitian skin effect and lasing of absorbing open-boundary modes in photonic crystals
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Non-Hermitian physics of levitated nanoparticle array
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Exceptional second-order topological insulators
• Optical non-Hermitian skin effect in two-dimensional uniform media
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• Hermitian and non-Hermitian topology in active matter
• Quantum geometrical effects in non-Hermitian systems
• Breakdown of Bulk-Radiation Correspondence in Radiative Photonic Lattices
• Tunable Localisation in Parity-Time-Symmetric Resonator Arrays with Imaginary Gauge Potentials
• Observation of non-Hermitian point gap in photonic crystals
• Algebraic skin effect in two-dimensional non-Hermitian metamaterials