Non-Hermitian photonic lattices: tutorial

Abstract

Non-Hermitian photonic lattices combine the peculiar consequences of energy non-conservation with the physics of bandstructures, giving rise to a variety of exotic properties not found in conventional materials or photonic metamaterials. In this tutorial, we introduce the key concepts in the design and implementation of non-Hermitian photonic lattices, including the general features of non-Hermitian lattice Hamiltonians and their bandstructures, the role of non-Hermitian lattice symmetries, and the topological chracterization of non-Hermitian bandstructures. We survey several important non-Hermitian lattice designs, as well as the photonics platforms on which they can be realized. Finally, we discuss the possibilities for future developments in the field.

Strong coupling of metamaterials with cavity photons: toward non-Hermitian optics

“…Certain non-Hermitian Hamiltonians, particularly those that respect parity-time (PT) symmetry, can also yield real eigenvalues [ 67 ]. The exploration of non-Hermitian Hamiltonians has experienced a substantial surge over the past decade, and novel concepts exploiting non-Hermiticity have been introduced to a plethora of quantum and classic systems, such as atoms, mechanical systems as well as optical ones [ 68 ], [ 69 ], [ 70 ], [ 71 ], [ 72 ].…”

Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

“…Non‐Hermitian (NH) physics is an emergent field of research that has important implications both for quantum and classical physics. [ 1–6 ] A systematic study of this field started with the cornerstone works by Bender and Boettcher on Hamiltonian systems preserving the combination of parity and time‐reversal ($$\mathcal {PT}$$) symmetry, ensuring a real spectrum. [ 7,8 ] At the moment, model Hamiltonian systems respecting $$\mathcal {PT}$$ symmetry are considered excellent models for describing dissipative systems with balanced gain and loss in an effective way.…”

Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal

“…Topological phases, localization and novel phase transitions in non-Hermitian systems with periodic or aperiodic order have recently sparked a great interest in a wide variety of physical systems, ranging from condensed matter physics to cold atoms and classical systems (see e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13] and references therein). Non-interacting particles in crystalline systems described by an effective non-Hermitian Hamiltonian display a variety of exotic physical effects, such as a non-trivial point-gap topology, the non-Hermitian skin effect, the breakdown of the bulkboundary correspondence based on Bloch band topological invariants, and a variety of dynamical and transport signatures .…”