Fakhroddin Nazari - Faculty of Engineering, Amol University of Special Modern Technologies, Amol, Iran

In optics, such complex PT-symmetric configurations can be realized within the framework of the paraxial theory of diffraction by concerning symmetric index guiding and an antisymmetric gain/loss profile, that is, * ( ) ( ) nx nx  (n: the refractive index)instead of complex potentials in the pure quantum mechanics v (x ) v *(x ) . In other words, the index and gain guiding in such configurations must be judiciously realized and electric field envelope along these systems obeys a normalized complex Schrödinger equation. Given the fact that complex (here, PT) arrangements may provide an additional degree of freedom in synthesizing novel optical structures and materials. It would be of great interest to study their optical behavior and characteristics. One fundamental aspect associated with PT components. Unlike Hermitian systems, these Eigen modes are no longer orthogonal. Instead, the basis is now skewed. This, in turn, has important implications for optical-beam dynamics including a non-reciprocal response and power oscillations. For a conventional Hermitian system (Not complex system), any superposition of the two Eigen-modes leads to reciprocal wave propagation. This situation changes when the coupled (complex) system involves a gain/loss dipole. More interestingly, light propagation is now obviously non-reciprocal. Moreover, It is investigated the unusual features of complex (here, PT) systems so that it can be termed such double refraction, power oscillation, band merging and non-reciprocity.

Complex system, Light propagation, Symmetric potential.