Topological physics of non-Hermitian optics and photonics: a review.

The notion of non-Hermitian optics and photonics rooted in quantum mechanics and photonic systems has recently attracted considerable attention ushering in tremendous progress on theoretical foundations and photonic applications, benefiting from the flexibility of photonic platforms. In this review, we first introduce the non-Hermitian topological physics from the symmetry of matrices and complex energy spectra to the characteristics of Jordan normal forms, exceptional points, biorthogonal eigenvectors, Bloch/non-Bloch band theories, topological invariants and topological classifications. We further review diverse non-Hermitian system branches ranging from classical optics, quantum photonics to disordered systems, nonlinear dynamics and optomechanics according to various physical equivalences and experimental implementations. In particular, we include cold atoms in optical lattices in quantum photonics due to their operability at quantum regimes. Finally, we summarize recent progress and limitations in this emerging field, giving an outlook on possible future research directions in theoretical frameworks and engineering aspects. [ABSTRACT FROM AUTHOR]