Spacing gain and absorption in a simple $\mathcal{P}\mathcal{T}$-symmetric model: spectral singularities and ladders of eigenvalues and resonances

Abstract

We consider a parity-time ($\mathcal{P}\mathcal{T}$-) symmetric waveguide consisting of a localized gain and loss elements separated by a variable distance. The situation is modelled by a Schrödiner operator with localized complex $\mathcal{P}\mathcal{T}$-symmetric potential. Properties of the latter Hamiltonian are considered subject to the change of the gain-to-loss distance. Resonances, spectral singularities and eigenvalues are analyzed in detail and discussed in the context of the associated laser-absorber modes and $\mathcal{P}\mathcal{T}$-symmetry breaking phase transition. Increasing gain-to-loss distance creates new resonances and spectral singularities which do not exist in the waveguide with adjacent gain and loss. In the limit of large gain-to-loss distance, the waveguide features a ladder of resonances which can be transformed to a ladder of complex eigenvalues by means of the change of the gain-and-loss amplitude.

References in corpus (8)

• Coherent Perfect Absorbers: Time-reversed Lasers
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Model of a PT symmetric Bose-Einstein condensate in a delta-functions double well
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• Phase transition through the splitting of self-dual spectral singularity in optical potentials
• New classes of non-parity-time-symmetric optical potentials with all-real spectra and exceptional-point-free phase transition
• Nonlinear currents in a ring-shaped waveguide with balanced gain and dissipation

Cited by in corpus (2)

• Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations
• Construction of potentials with multiple spectral singularities