International Journal of Theoretical Physics

, Volume 50, Issue 4, pp 1019–1041

\(\mathcal{PT}\)-Symmetric Periodic Optical Potentials


    • Optics Laboratory, School of EngineeringSwiss Federal Institute of Technology Lausanne (EPFL)
  • R. El-Ganainy
    • Department of PhysicsUniversity of Toronto
  • D. N. Christodoulides
    • College of Optics & Photonics-CREOLUniversity of Central Florida
  • Z. H. Musslimani
    • Department of MathematicsFlorida State University

DOI: 10.1007/s10773-010-0625-6

Cite this article as:
Makris, K.G., El-Ganainy, R., Christodoulides, D.N. et al. Int J Theor Phys (2011) 50: 1019. doi:10.1007/s10773-010-0625-6


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 (\(\mathcal{PT}\)) 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 \(\mathcal{PT}\)-symmetry could be physically realized within the framework of classical optics. This proposal has, in turn, stimulated extensive investigations and research studies related to \(\mathcal{PT}\)-symmetric Optics and paved the way for the first experimental observation of \(\mathcal{PT}\)-symmetry breaking in any physical system. In this paper, we present recent results regarding \(\mathcal{PT}\)-symmetric Optics.


\(\mathcal{PT}\)-symmetryNon-Hermitian\(\mathcal{PT}\)-operatorsWave propagationGuided wavesOptical latticesOptical solitonsPeriodic potentialsGain-loss media

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© Springer Science+Business Media, LLC 2011