arXiv subjects

B. Reichel

Publications and source records attributed to B. Reichel.

3 recordsLinked to original sources

arXiv2006

On convergence and stability of a numerical scheme of coupled nonlinear Schr\"{o}dinger equations

We consider numerical solution of Coupled Nonlinear Schr\"{o}dinger Equation. We prove stability and convergence in the $L_2$ space for an explicit scheme which estimations is used for implicit scheme and compare both method. As a test we compare numerical solutions of Manakov system with known analytical solitonic solutions and as example of general system - evolution of two impulses with different group velocity (model of pulses interaction in optic fibers). Last example, a rectangular pulse evolution, shows asymptotic behavior typical for Nonlinear Schr\"{o}dinger Equation asymptotics with the same initial condition.

math.NA↗

arXiv2006

Mode interaction in multi-mode optical fibers with Kerr effect

We generalize the projection to orthogonal function basis (including polarization modes) method for nonlinear (Kerr medium) fiber and use this method in a case of two-mode waveguide. We consider orthogonal Bessel functions basis that fit the choice of cylindrical geometry of a fiber. The coupled nonlinear Schrödinger equations (CNLS) are derived. Analytic expressions and numerical results for coupling coefficients are given; the fiber parameters dependence is illustrated by plots.

physics.optics↗

arXiv2005

Polarization mode interaction equations in optical fibers with Kerr effect

We derive coupled nonlinear Schrödinger equation (CNLSE) for arbitrary polarized light propagation in a single-mode fiber. We introduce a basis of transverse eigen modes with the appropriate projecting hence solutions depend on the waveguide geometry. Considering a weak nonlinearity which is connected with Kerr effect, we give explicit expressions for nonlinear constants via integrals of Bessel functions. We compare numerical results for the nonlinear constant extracted from experimental observations of a soliton for the nonlinear Schrödinger equation (NLSE) (single-mode one). The method of projecting we use allows a direct generalization to multi-mode fiber case.

physics.optics↗