Spacing gain and absorption in a simple -symmetric model: spectral singularities and ladders of eigenvalues and resonances
arXiv:1908.06383 · doi:10.1088/1751-8121/ab40ec
Abstract
We consider a parity-time (-) 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 -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 -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.
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