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Abstract
In this paper a detailed derivation and numerical solutions of CoupledNonlinear Schr¨odinger Equations for pulses of polarized electromagnetic wavesin cylindrical fibers has been reviewed. Our recent work has been compared withsome previous ones and the advantage of our new approach over other methods hasbeen assessed. The novelty of our approach lies is an attempt to proceed withoutloss of information within the frame of basic approximations. In our work we focusedon the multimode The eigen mode definition is based on complete linearizedMaxwell equations and Hondros-Debye boundary conditions, which depend on thegeometry of the dielectric waveguide. We proved both stability and convergencein the L2 space of an explicit finite-difference scheme for the Coupled NonlinearSchr¨odinger Equations and those estimations are used for an implicit scheme. Totest our hypothesis we compare numerical solutions for Manakov system withknown analytical solitonic solutions. We also consider an important example ofthe general system - an evolution of two pulses with different group velocity whichcan serve as a model of pulses interaction in multimode optic fibers. Last case,a nonlinear dispersion of rectangular pulse, exhibits an asymptotic behavior similarto Nonlinear Schr¨odinger Equation solution asymptotics for the rectangularinitial condition. Finally, we compared theoretical results with specially arrangedexperiments employing a photonic crystal fiber.
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
The European Physical Journal-Special Topics
no. 173,
pages 5 - 55,
ISSN: 1951-6355 - Language:
- English
- Publication year:
- 2009
- Bibliographic description:
- Reichel B., Leble S.: Coupled nonlinear Schrödinger equations in optic fibers theory// The European Physical Journal-Special Topics. -Vol. 173, nr. Nr 1, June (2009), s.5-55
- Verified by:
- Gdańsk University of Technology
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