We consider the propagation of electromagnetic pulses in isotropic media taking a third-order nonlinearityinto account. We develop a method for transforming Maxwell's equations based on a complete set ofprojection operators corresponding to wave-dispersion branches (in a waveguide or in matter) with thepropagation direction taken into account. The most important result of applying the method is a systemof equations describing the one-dimensional dynamics of pulses propagating in opposite directions withoutaccounting for dispersion. We derive the corresponding self-action equations. We thus introduce dispersionin the media and show how the operators change. We obtain generalized Sch¨afer-Wayne short-pulseequations accounting for both propagation directions. In the three-dimensional problem, we focus onoptic fibers with dispersive matter, deriving and numerically solving equations of the waveguide-modeinteraction. We discuss the effects of the interaction of unidirectional pulses. For the coupled nonlinearSchr¨odinger equations, we discuss a concept of numeric integrability and apply the developed calculationschemes.
Authors
Additional information
- DOI
- Digital Object Identifier link open in new tab 10.1007/s11232-011-0079-x
- Category
- Publikacja w czasopiśmie
- Type
- artykuł w czasopiśmie wyróżnionym w JCR
- Language
- angielski
- Publication year
- 2011
