Construction of non-PT-symmetric complex potentials with all-real spectra

Abstract

We review recent work on the generalization of PT symmetry. We show that, in addition to PT-symmetric complex potentials, there are also large classes of non-PT-symmetric complex potentials which also feature all-real spectra. In addition, some classes of these non-PT-symmetric potentials allow phase transitions which do or do not go through exceptional points. These non-PT-symmetric potentials are constructed by a variety of methods, such as the symmetry and supersymmetry methods and the soliton theory. A generalization of PT symmetry in multi-dimensions is also reviewed.

22 pages, 6 figures

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• Stable localized modes in asymmetric waveguides with gain and loss
• Families of stationary modes in complex potentials
• 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