Applications of Non-hermitian Optical Pulses

Abstract

The purpose of this paper is to review a interessan method for the generation of nonlinear optical pulses solutions and present an analytical proof of this method, not yet existing in the literature. We explore a new class of solutions of Nonlinear Schrödinger-like Equation (NLS) that represent profiles of optical beams propagating in waveguides. This solutions have several application properties such as prapagation without dispersion and almost no loss energy. This class of solutions that we explore are characterized by parity-time (PT) symmetric potentials. This approach is based on non-Hermitian Hamiltonians that can exhibit entirely real spectra provided they respect paritytime (PT) symmetrie. These solutions establish a deep relationship between the nonlinear electrodynamics and quantum mechanics. We analyzed the potential applications of such solutions in design to the optical fiber sensors, optical networks and crystals which can act as natural selectors optical band. This paper is divided as follows: in Section 1 we present the basis of our research and highlight the technological applications of the method revised in this paper on the recognition, selection and processing of optical signals that the method model. Section 2 provides a brief description of nonlinear Schrödinger equation (NLS) governing the dynamics of nonlinear optical pulses. Section 3 presents the concept of non-Hermitian optical systems and the concept of PT symmetry at which such systems are based and discuss some of these optical systems applications. In Section 4 we present a review of new class of non-Hermitian solutions to a non-linear optical beam and a review of method for generating new non-Hermitian systems from existing ones and also discuss some original applications of the method reviewed here. Section 5 presents the conclusions and comments, section 6 references and the appendix section presents a rigorous proof of the method, that has not been done in the literature.