Abstract

After realizing the counterintuitive fact that $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians can exhibit entirely real spectra, intense studies have been devoted to extend the framework of quantum mechanics into the complex domain [1]. Quite recently however, the concept of $\mathcal{P}\mathcal{T}$-symmetry was introduced [2] and experimentally observed [3,4] in the framework of classical Optics. In this paper, we examine the peculiar properties of $\mathcal{P}\mathcal{T}$-optical lattices and their potential applications as a new class of synthetic metamaterials. In particular, we investigate the complex linear and nonlinear beam dynamics close to the exceptional point of a $\mathcal{P}\mathcal{T}$-lattice, the absence of anomalous diffraction, negative refraction due to non-hermiticity and the effect of Kerr nonlinearity on power oscillations.

© 2013 IEEE