Slow-light solitons: Influence of relaxation

¹  Department of Physics, University of Jyväskylä - PO Box 35, FIN-40351, Jyväskylä, Finland
²  St Petersburg University of Information Technologies, Mechanics and Optics - Kronwerkskii ave. 49, 197101, St Petersburg, Russia
³  Physics Department, McGill University - 3600 rue University, Montreal, Quebec, H3A 2T8 Canada
⁴  Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory Los Alamos, NM 87545, USA

Corresponding authors: andrei.rybin@phys.jyu.fi vadeiko@physics.mcgill.ca arb@lanl.gov

Received: 6 August 2007
Accepted: 15 December 2007

Abstract

We have applied the transformation of the slow-light equations to the Liouville theory that we developed in our previous work, to study the influence of relaxation on the soliton dynamics. We solved the problem of the soliton dynamics in the presence of relaxation and found that the spontaneous emission from the upper atomic level is strongly suppressed. Our solution proves that the spatial shape of the soliton is well preserved even if the relaxation time is much shorter than the soliton time length. This fact is of great importance for applications of the slow-light soliton concept in optical information processing. We also demonstrate that relaxation plays a role of resistance to the soliton motion and slows the soliton down even if the controlling field is constant.