Designing lasing and perfectly absorbing potentials

Abstract

Existence of a spectral singularity (SS) in the spectrum of {a Schrödinger operator with} a non-Hermitian potential requires exact matching of parameters of the potential. We provide a necessary and sufficient condition for a potential to have a SS at a given wavelength. It is shown that potentials with SSs at prescribed wavelengths can be obtained by a simple and effective procedure. In particular, the developed approach allows one to obtain potentials with several SSs and with SSs of the second order, as well as potentials obeying a given symmetry, say, $\PT-$symmetric potentials. Also, the problem can be solved when it is required to obtain a potential obeying a given symmetry, say, $\PT-$symmetric potential. We illustrate all these opportunities with examples. We also describe splitting of a second-order SSs under change of the potential parameters, and discuss possibilities of experimental observation of SSs of different orders.

10 pages, 4 figures

References in corpus (7)

• Coherent Perfect Absorbers: Time-reversed Lasers
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Perfectly absorbing exceptional points and chiral absorbers
• Delta-Function Potential with a Complex Coupling
• Phase transition through the splitting of self-dual spectral singularity in optical potentials
• Three types of discrete energy eigenvalues in complex PT-symmetric scattering potentials
• Linear and nonlinear coherent perfect absorbers on simple layers

Cited by in corpus (11)

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• Fundamental transfer matrix for electromagnetic waves, scattering by a planar collection of point scatterers, and anti-PT-symmetry
• High-order spectral singularity
• A universal form of complex potentials with spectral singularities
• Spectral singularities and tunable slab lasers with 2D material coating
• Robust incoherent perfect absorption
• A universal form of arrays with spectral singularities
• Perfectly absorbed and emitted currents by complex potentials in nonlinear media
• Construction of potentials with multiple spectral singularities
• Scattering by a collection of $\delta$-function point and parallel line defects in two dimensions
• An update on coherent scattering from complex non-PT-symmetric Scarf II potential with new analytic forms