Theoretical and computational studies of solitons in inhomogeneous optical fibers

摘要

In this work solitons in inhomogeneous optical fibers is studied both numerically and analytically Spatial variation of index of refraction is considered as our source of inhomogeneity Optical solitons can be described by nonlinear Schr?dinger (NLS) equation Due to inherent existence of integrals of motion in the NLS system the solitons can propagate without changing their shapes Soliton communication heavily relies on this latter nature of NLS system The envelope soliton is preserved due to balance between the nonlinear drive (Kerr effect) and the dispersion effect of optical fiber For our numerical simulation finite difference methods (the leapfrog scheme) is employed with Dirichlet boundary conditions For the inhomogeneous optical fibers it is demonstrated that the widths of optical solitons can be controlled so as to prevent unwanted overlapping of the soliton tails (the overlapping of solitons leads to the interaction of solitons) When the index of refraction “n” is reduced spatially along the optical fiber (and thus the permeability “ε”) dispersion effect is reduced which makes the soliton to be localized On top of the numerical analysis the homogeneous NLS equation can be solved by inverse scattering method (ISM) which was initially applied for Korteweg–de Vries (KdV) equation To recapitulate ISM the process of solving KdV equation is presented (which for real values) then for NLS (which is for the complex values A 2×2 matrix equation is required) Finally a variable transformation (B?cklund transformation or Darboux transformation as in Cole-Hopf transformation for Burgers equation) is applied to incorporate inhomogeneity coefficients multiplied to the dispersion term of the NLS equation We compare the analytical solutions with the simulation results

獎項日期	2018 6月 26
原文	English
監督員	Yasutaro Nishimura (Supervisor)