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.

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.…”

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 ].…”

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 .…”