Non-Hermitian photonics based on parity–time symmetry

The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of \({\cal PT}\) symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These \({\cal PT}\) symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space. This paper describes the unusual classical and quantum properties of these theories.

Invisibility by metamaterials is of great interest, where optical properties are manipulated in the real permittivity-permeability plane. However, the most effective approach to achieving invisibility in various military applications is to absorb the electromagnetic waves emitted from radar to minimize the corresponding reflection and scattering, such that no signal gets bounced back. Here, we show the experimental realization of chip-scale unidirectional reflectionless optical metamaterials near the spontaneous parity-time symmetry phase transition point where reflection from one side is significantly suppressed. This is enabled by engineering the corresponding optical properties of the designed parity-time metamaterial in the complex dielectric permittivity plane. Numerical simulations and experimental verification consistently exhibit asymmetric reflection with high contrast ratios around a wavelength of of 1,550 nm. The demonstrated unidirectional phenomenon at the corresponding parity-time exceptional point on-a-chip confirms the feasibility of creating complicated on-chip parity-time metamaterials and optical devices based on their properties.

Topology is revolutionizing photonics, bringing with it new theoretical discoveries and a wealth of potential applications. This field was inspired by the discovery of topological insulators, in which interfacial electrons transport without dissipation even in the presence of impurities. Similarly, new optical mirrors of different wave-vector space topologies have been constructed to support new states of light propagating at their interfaces. These novel waveguides allow light to flow around large imperfections without back-reflection. The present review explains the underlying principles and highlights the major findings in photonic crystals, coupled resonators, metamaterials and quasicrystals.