Optical lattices with exceptional points in the continuum

Abstract

The spectral, dynamical and topological properties of physical systems described by non-Hermitian (including $\mathcal{P}\mathcal{T}$-symmetric) Hamiltonians are deeply modified by the appearance of exceptional points and spectral singularities. Here we show that exceptional points in the continuum can arise in non-Hermitian (yet admitting and entirely real-valued energy spectrum) optical lattices with engineered defects. At an exceptional point, the lattice sustains a bound state with an energy embedded in the spectrum of scattered states, similar to the von-Neumann Wigner bound states in the continuum of Hermitian lattices. However, the dynamical and scattering properties of the bound state at an exceptional point are deeply different from those of ordinary von-Neumann Wigner bound states in an Hermitian system. In particular, the bound state in the continuum at an exceptional point is an unstable state that can secularly grow by an infinitesimal perturbation. Such properties are discussed in details for transport of discretized light in a $\mathcal{P}\mathcal{T}$-symmetric array of coupled optical waveguides, which could provide an experimentally accessible system to observe exceptional points in the continuum.

11 pages, 4 figures, slightly revised revision (corrected misprints in caption of Figs.2 and 4 from published version)

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Cited by in corpus (23)

• Applications of Bound States in the Continuum in Photonics
• Inverse design of third-order Dirac exceptional points in photonic crystals
• Flat bands in lattices with non-Hermitian coupling
• Quasi-bound states in the continuum induced by $\mathcal{P}\mathcal{T}$-symmetry breaking
• Non-Hermitian lattices with a flat band and polynomial power increase
• Enhanced nonlinear frequency conversion and Purcell enhancement at exceptional points
• Observation of supersymmetric scattering in photonic lattices
• Non-Hermitian tight-binding network engineering
• Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry
• Bound state in the continuum by spatially separated ensembles of atoms in a coupled-cavity array
• Exceptional points and their coalescence of PT-symmetric interface states in photonic crystals
• Bound states in the continuum in a two-dimensional PT-symmetric system
• Quantum decay in a topological continuum
• Non-Hermiticity-Induced Wave Confinement and Guiding in Loss-Gain-Loss Three-Layer Systems
• Exceptional points as signatures of dynamical magnetic phase transitions
• Quantum decay and amplification in a non-Hermitian unstable continuum
• Supersymmetric correspondence in spectra on a graph and its line graph: From circuit theory to spoof plasmons on metallic lattices
• Multitude of exceptional points in van der Waals magnets
• Phase Transitions and Virtual Exceptional Points in Quantum Emitters Coupled to Dissipative Baths
• Linear localization of zero modes in weakly coupled non-Hermitian reservoirs
• Invisible surface defects in a tight-binding lattice
• Superoscillatory PT-symmetric potentials
• Non-Hermitian interaction of a discrete state with a continuum