Studies on the eigenmodes of self-defocusing nonlinear optical systems with PT-symmetric super-Gaussian and k -wavenumber Scarf II potentials.

Abstract

The interaction of the high-intense beam with parity-time (PT) symmetric single and coupled nonlinear optical media, modelled by modi ed nonlinear Schrodinger equation, generates families of localised waves called optical bright and dark solitons, which nd applications in high-speed signal communication, all-optical switching, unidirectional and non-reciprocal light transmission etc. Even though the stationary states and propagation dynamics of optical bright solitons are intensively studied, the existence and dynamics of dark solitons are less explored. In the thesis, we analysed the existence of dark soliton-like solutions, stability, beam propagation and switching dynamics in the PT-symmetric optical systems with self-defocusing nonlinearity. The symmetric real and antisymmetric imaginary components of the PT-symmetric super-Gaussian and k -wavenumber Scarf II well and barrier potentials take the role of refractive index distribution and gain/loss e ects. The real part of these potentials consists of di erent pro les of refractive index from smooth to step-index distributions. The delicate balancing between the e ects of defocusing nonlinearity and PT-symmetric potentials leads to dark soliton form of solution, which is discussed in a single system. The threshold condition of PT phase transition depends on the strength of the nonlinearity and coe cients of real and imaginary potential. The stability of the solution is veri ed using the linear stability analysis and the propagation in the PT regime has also been analysed. The study has been extended to coupled system with equal gain and loss. The power variations of the low and high-frequency modes have been analysed using varia- tional analysis. The switching dynamics of the coupled systems with PT-symmetric potentials are analysed for PT and broken PT phases using nite di erence beam propagation method. The power switching between the channels in the PT regime and power con nement in one of the channels in the broken PT regime are observed. The existence of the dark soliton-like solution has relevance in long-distance energy-e cient communication technology due to its high stability against losses. The switching dynamics in a PT-symmetric coupled system can contribute to the construction of switching devices and optical nanostructures. The power con ne- ment in the broken PT regime has relevance in non-reciprocal and unidirectional signal transmission.