$\mathcal{PT}$ -Symmetric Periodic Optical Potentials

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International Journal of Theoretical Physics, ISSN: 0020-7748, Vol: 50, Issue: 4, Page: 1019-1041

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K. G. Makris; R. El-Ganainy; D. N. Christodoulides; Z. H. Musslimani
Springer Nature
Mathematics; Physics and Astronomy; PT-symmetry; Non-Hermitian; PT-operators; Wave propagation; Guided; waves; Optical lattices; Optical solitons; Periodic potentials; Gain-loss media; NON-HERMITIAN HAMILTONIANS; BLOCH WAVES; PHYSICS; COMPLEX; Physics; Multidisciplinary
article description
In quantum theory, any Hamiltonian describing a physical system is mathematically represented by a self-adjoint linear operator to ensure the reality of the associated observables. In an attempt to extend quantum mechanics into the complex domain, it was realized few years ago that certain non-Hermitian parity-time (PT) symmetric Hamiltonians can exhibit an entirely real spectrum. Much of the reported progress has been remained theoretical, and therefore hasn't led to a viable experimental proposal for which non Hermitian quantum effects could be observed in laboratory experiments. Quite recently however, it was suggested that the concept of PT -symmetry could be physically realized within the framework of classical optics. This proposal has, in turn, stimulated extensive investigations and research studies related to PT -symmetric Optics and paved the way for the first experimental observation of PT -symmetry breaking in any physical system. In this paper, we present recent results regarding PT -symmetric Optics. © 2011 Springer Science+Business Media, LLC.