Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at Real Energies
TLDR
This work identifies spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width and shows that a waveguide modeled using such a potential operates like a resonator at the frequencies of spectral singularity.Abstract:
Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a waveguide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential and demonstrate the above resonance phenomenon for a certain electromagnetic waveguide.read more
Citations
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Observation of parity–time symmetry in optics
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Non-Hermitian photonics based on parity-time symmetry
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References
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Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
TL;DR: The condition of self-adjointness as discussed by the authors ensures that the eigenvalues of a Hamiltonian are real and bounded below, replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive.
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Complex extension of quantum mechanics
TL;DR: If PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed symmetry C of the Hamiltonian, and this work is not in conflict with conventional quantum mechanics but is rather a complex generalization of it.
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Beam dynamics in PT symmetric optical lattices.
TL;DR: In this paper, parity-time symmetric periodic potentials are investigated in detail for both one-and two-dimensional lattice geometries, and it is shown that PT periodic structures can exhibit unique characteristics stemming from the nonorthogonality of the associated Floquet-Bloch modes.
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Optical solitons in PT periodic potentials
TL;DR: In this paper, the effect of nonlinearity on beam dynamics in parity-time (PT) symmetric potentials was investigated and a novel class of one-and two-dimensional nonlinear self-trapped modes were shown to be stable over a wide range of potential parameters.