Eur. Phys. J. D 59, 13-21 (2010)
https://doi.org/10.1140/epjd/e2010-00116-6

Soliton lasers stabilized by coupling to a resonant linear system ^*

¹ SUPA and Department of Physics, University of Strathclyde, 107 Rottenrow East, Glasgow, G4 0NG, United Kingdom
² IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain

Corresponding author: ^a p.v.paulau@gmail.com

Received: 22 December 2009
Revised: 16 March 2010
Published online: 5 May 2010

Abstract

Separation into spectral and nonlinear complex-eigenvalue problems is shown to be an effective and flexible approach to soliton laser models. The simplest such model, a complex Ginzburg-Landau model with cubic nonlinearity, has no stable solitonic solutions. We show that coupling it to a resonant linear system is a simple and general route to stabilization, which encompasses several previous instances in both space- and time-domains. Graphical solution in the complex eigenvalue plane provides valuable insight into the similarities and differences of such models, and into the interpretation of related experiments. It can also be used predictively, to guide analysis, numerics and experiment.