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

Abstract

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.

Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification

“…Nano-optomechanical systems [44,82] as well as multiscale optomechanical crystal structures [45] are also ideal platforms where to implement NH lattice dynamics. Optical systems, such as coupled waveguide arrays [35,83,84] and topolectric circuits [85,86] are also excellent candidate platforms. Our work naturally opens the door to the study of other sources of gain, such as parametric processes [87,88], with applications to the design of novel lattice amplifiers and sensors [51][52][53].…”

“…Moving to OBC, we obtain the singular vectors as eigenvectors of Eq. (35). The mapping from a one-band non-Hermitian model to a Hermitian SSH model in a doubled space allows us to import the Hermitian BBC for the GSSH model; for a rigorous proof see Ref.…”

“…Our ideas are directly relevant for applications to drivendissipative lattice systems where aspects of NH physics (topology, nonreciprocal couplings, NHSE) have already been demonstrated, e.g. in photonic lattices [34,35], topolectric circuits [36][37][38][39][40], mechanical [41,42] and robotic [43] metamaterials. Especially suitable for implementing our ideas are nano-optomechanical lattices [44,45] and superconducting circuit optomechanics [46], where non-reciprocal couplings, gain and loss can be engineered to a high degree.…”

Special exceptional point acting as Dirac point in one dimensional PT -symmetric photonic crystal

“…We theoretically reveal and prove that in the 1DPTSPC, a special EP at the center of the Brillouin zone can also act as a Dirac point. This theory was developed by applying the biorthogonal bases of the non-Hermitian Hamiltonian [55,56] to k • p method [57,58]. By tuning the non-Hermiticity in 1DPTSPC, two linear dispersions can cross at a critical EP, and the corresponding effective Hamiltonian can be cast into a massless Dirac Hamiltonian under biorthogonal bases of the non-Hermitian Hamiltonian; therefore, this point can be called the Dirac point.…”

Coherence onset in PT-symmetric organic microcavities: towards directional propagation of light

“…Under certain conditions, i.e. when gain and loss are balanced, parity-time (PT) symmetry [7,8] is still preserved in NH systems, and has striking implications [9,10]: Optically active photonic structures with well-integrated PT-symmetry may become immune to structural defects and disorder or experience spontaneous symmetry breaking and, in this way, allow to engineer light flow [11,12]. Unidirectional optical elements are required in all-optical components in integrated circuits [13]; they may also pave the road towards a broader vision of invisibility while from inside being still able to see the outside world [14].…”