Resonant optical pulses on a continuous wave background in two-level active media

TL;DR

This paper derives exact multi-soliton solutions for a two-level active medium with a continuous wave background, revealing new pulse structures like breathers, periodic trains, and rogue waves influenced by the background.

Contribution

It generalizes the inverse scattering transform to Maxwell-Bloch equations, classifying novel soliton solutions on a continuous wave background in active media.

Findings

Derived exact N-soliton solutions on a continuous wave background.

Identified distinct families of soliton solutions including breathers and rogue waves.

Showed the solutions' relation to classical nonlinear Schrödinger equation solutions.

Abstract

We present exact N-soliton optical pulses riding on a continuous-wave (c.w.) beam that propagate through and interact with a two-level active optical medium. Their representation is derived via an appropriate generalization of the inverse scattering transform for the corresponding Maxwell-Bloch equations. We describe the single-soliton solutions in detail and classify them into several distinct families. In addition to the analogues of traveling-wave soliton pulses that arise in the absence of a c.w. beam, we obtain breather-like structures, periodic pulse-trains and rogue-wave-type (i.e., rational) pulses, whose existence is directly due to the presence of the c.w. beam. These soliton solutions are the analogues for Maxwell-Bloch systems of the four classical solution types of the focusing nonlinear Schrodinger equation with non-zero background, although the physical behavior of the corresponding solutions is quite different.