Volume 121, Number 2, January 2018
|Number of page(s)||7|
|Published online||13 March 2018|
Resonant optical pulses on a continuous-wave background in two-level active media
1 Department of Mathematics, State University of New York at Buffalo - Buffalo, NY 14260, USA
2 Department of Physics, State University of New York at Buffalo - Buffalo, NY 14260, USA
3 Department of Mathematical Sciences, Rensselaer Polytechnic Institute - Troy, NY 12180, USA
4 Department of Mathematics, University of Arizona - Tucson, AZ 85721, USA
Received: 18 January 2018
Accepted: 17 February 2018
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 Schrödinger equation with non-zero background, although the physical behavior of the corresponding solutions is quite different.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 05.45.Yv – Solitons / 02.30.Ik – Integrable systems
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