Optical soliton cooling with polynomial law of nonlinear refractive index
- PDF / 222,862 Bytes
- 4 Pages / 595.276 x 790.866 pts Page_size
- 95 Downloads / 214 Views
RESEARCH ARTICLE
Optical soliton cooling with polynomial law of nonlinear refractive index Anjan Biswas1,2,3
Received: 27 June 2020 / Accepted: 4 August 2020 Ó The Optical Society of India 2020
Abstract The aim of this work is to produce the effect of optical soliton cooling with polynomial law of nonlinear refractive index. This is achieved by the aid of soliton perturbation theory. In this context, both Hamiltonian and non-Hamiltonian type, including non-local type, perturbation effects are considered. Keywords Quasimonochromaticity Soliton perturbation Polynomial law
Introduction Advances in optical soliton dynamics have reached far and beyond and its progress is beyond measure! There are a wide variety of aspects in soliton dynamics that has been touched upon during the past few decades. These include soliton perturbation theory, establishment of conservation laws, addressing highly dispersive solitons, numerical studies with short pulses by Laplace substitution, Bragg gratings, application of semi-inverse variational principle and implementing variational iteration method and several others [1–14]. It is quite noteworthy that research results on optical soliton cooling are few and far
& Anjan Biswas [email protected] 1
Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762–4900, USA
2
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3
Department of Applied Mathematics, National Research Nuclear University, 31, Kashirskoe Shosse, Moscow, Russian Federation 115409
between [1, 4, 5, 7]. In the past, this effect was introduced with optical Gaussons and for solitons with Kerr law, power law, parabolic law, dual-power law and quadratic– cubic law [4, 5, 7]. The current paper thus is bridging the gap by addressing soliton cooling effect with polynomial law of nonlinear refractive index that is occasionally referred to as cubic–quintic–septic law. The perturbation terms considered to study the adiabatic soliton dynamics are of Hamiltonian as well as non-Hamiltonian types that also include non-local kind. The details are sketched in the rest of the paper after a quick re-visitation to the governing nonlinear Schro¨dinger’s equation (NLSE) along with its conservation laws. Governing model The governing nonlinear Schro¨dinger’s equation with polynomial law of nonlinearity, in its dimensionless form, is written as [3, 8]: iqt þ aqxx þ b1 jqj2 þb2 jqj4 þb3 jqj6 q ¼ 0: ð1Þ Here, the dependent variable q(x, t) is a complex-valued function with x and t being the spatial and temporal coordinates, respectively. The coefficient of a is chromatic dispersion, while the last three terms, the coefficients of bj for j ¼ 1; 2; 3, are from self-phase modulation (SPM) effect that stems from nonlinear refractive index of the fiber. The first term is temporal evolution. The coefficients of dispersion and nonlinear terms are all real-valued constants, pffiffiffiffiffiffiffi while i ¼ 1. This form of nonlinearity has not been much studied. Some preliminary result
Data Loading...
