Exceptional points in optics and photonics

Abstract

Exceptional points are branch point singularities in the parameter space of a system at which two or more eigenvalues, and their corresponding eigenvectors, coalesce and become degenerate. Such peculiar degeneracies are distinct features of non-Hermitian systems, which do not obey conservation laws because they exchange energy with the surrounding environment. Non-Hermiticity has been of great interest in recent years, particularly in connection with the quantum mechanical notion of parity-time symmetry, after the realization that Hamiltonians satisfying this special symmetry can exhibit entirely real spectra. These concepts have become of particular interest in photonics because optical gain and loss can be integrated and controlled with high resolution in nanoscale structures, realizing an ideal playground for non-Hermitian physics, parity-time symmetry, and exceptional points. As we control dissipation and amplification in a nanophotonic system, the emergence of exceptional point singularities dramatically alters their overall response, leading to a range of exotic optical functionalities associated with abrupt phase transitions in the eigenvalue spectrum. These concepts enable ultrasensitive measurements, superior manipulation of the modal content of multimode lasers, and adiabatic control of topological energy transfer for mode and polarization conversion. Non-Hermitian degeneracies have also been exploited in exotic laser systems, new nonlinear optics schemes, and exotic scattering features in open systems. Here we review the opportunities offered by exceptional point physics in photonics, discuss recent developments in theoretical and experimental research based on photonic exceptional points, and examine future opportunities in this area from basic science to applied technology.

Tunable Open‐Access Microcavities for Solid‐State Quantum Photonics and Polaritonics

“…Around the EP, the non‐Hermitian Hamiltonian can result in avoided level crossing of eigenvalues and bifurcation of widths (lifetimes), as well as a variation of the phase rigidity of the eigenfunctions. While the observation of EP and related physical processes have been reported in different systems including microwave cavities, open QDs, single‐electron transistors, and atomic assembles, its application in photonics has also been explored in recent years . Particularly, the experimental investigation of the non‐Hermitian nature and observation of EP in exciton‐polaritons were reported by Gao et al.…”

“…While the observation of EP and related physical processes have been reported in different systems including microwave cavities, open QDs, single-electron transistors, and atomic assembles, [80] its application in photonics has also been explored in recent years. [14,81] Particularly, the experimental investigation of the non-Hermitian nature and observation of EP in exciton-polaritons were reported by Gao et al in 2015 in an optical-induced billiard potential designed on a monolithic microcavity. [82] It is thereby expected that the free design of photonic potentials with strong confinement enabled by the open-access microcavity would help to further explore the exciton-polaritons as a dissipative open system.…”

Unambiguous scattering matrix for non-Hermitian systems

“…(b) Temporal profiles of transmitted intensity for ε ′′ just below and above the lasing threshold near the EP (1) . The inset shows the curve for ε ′′ = 13.8 on the longer scale.Eqs (8). and(9)represent 4 equations for 4 unknown elements of the scattering matrix.…”

Neuromorphic Functions of Light in Parity‐Time‐Symmetric Systems

“…[17] Non-Hermitian photonics [18][19][20] inspired by parity-time (PT) symmetry [21] has rejuvenated the utilization of nonlinear wave channels for photonic [22][23][24] or microwave [25] functionalities. Early studies have mostly focused on linear wave phenomena near the exceptional point (EP), [20,26] such as asymmetric [27] and sensitive [28] excitations, unidirectional invisibility, [29] enhanced spin, [30,31] or orbital angular momentum, [32] and asymmetric modal conversion, [33] which have been demonstrated in waveguides, [27,33] fibers, [29] metamaterials, [30,31] and resonators. Due to the design flexibility of photonic platforms and the Schrödingerlike paraxial wave equation for light, photonic structures have been employed as a testbed for examining wave phenomena in PT-symmetric systems.…”

“…Due to the design flexibility of photonic platforms and the Schrödingerlike paraxial wave equation for light, photonic structures have been employed as a testbed for examining wave phenomena in PT-symmetric systems. The effects of nonlinear wave channels near the EP [26] have been studied for nonreciprocal transparency from directional resonator excitations, [22,23] robust power transfer using gain saturation, [25] and dynamical encircling for polarization conversion which is robust to nonlinear effects. [28,32] Recently, a research focus in this field has been extended to the interpretation of nonlinear wave phenomena.…”