A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

Recent advancements in computational inverse-design approaches—algorithmic
techniques for discovering optical structures based on desired functional characteristics …

Recently, exceptional points, a degeneracy of open wave systems, have been observed in
photonics, acoustics, and electronics. They have mainly been realized as a degeneracy of …

Non-Hermitian optics is a burgeoning field at the intersection of quantum physics,
electrodynamics, and nanophotonics. It provides a new perspective of the role of gain and …

In the past few years, concepts from non-Hermitian (NH) physics, originally developed within
the context of quantum field theories, have been successfully deployed over a wide range of …

Capital to topological insulators, the bulk-boundary correspondence ties a topological
invariant computed from the bulk (extended) states with those at the boundary, which are …

Exceptional points (EPs) are special spectral degeneracies of non-Hermitian Hamiltonians
that govern the dynamics of open systems. At an EP, two or more eigenvalues, and the …

The ideas of topology have found tremendous success in closed physical systems, but even
richer properties exist in the more general open or dissipative framework. We theoretically …

In this Review, the theory and applications of optical micro‐and nano‐resonators are
presented from the underlying concept of their natural resonances, the so‐called quasi …

Singularities of open systems, known as exceptional points (EPs), have been shown to
exhibit increased sensitivities, but the observation of EPs has so far been limited to …