Ultrashort opposite directed pulses dynamics

TL;DR

This paper develops a method to model ultrashort pulse propagation in isotropic media, deriving a system of equations for opposite directed pulses and analyzing their interactions, extending the Short Pulse Equations.

Contribution

It introduces a transformation method for Maxwell's equations that captures bidirectional pulse dynamics, generalizing existing unidirectional models.

Findings

Derived a system of equations for opposite directed ultrashort pulses.

Showed how the generalized Short Pulse Equations emerge from the model.

Analyzed the interaction effects of counter-propagating pulses.

Abstract

In this article we consider one dimensional model of an ultra short pulse propagation in isotropic dispersionless media taking into account a nonlinearity of the third order. We introduce a method for Maxwell's equations transformation based on a complete set of projecting operators. The operators generally correspond wave dispersion branches. As a simplest result of the method application we derive a system of equations describing dynamics of ultrashort pulses of opposite directions of propagation. We show that in such way the generalized Short Pulse Equations of Shafer and Wayne is obtained if the only directed wave is initialized. The effects of the unidirectional pulses interaction are traced.