The nonlinear Schrödinger equation (NLSE) describes a vast variety of phenomena in the optics of Kerr media. Being supplied by gain and dissipation it is employed for modeling of open systems [1,2]. Soliton formation described by the NLSE equation and soliton properties depend dramatically on the dimensionality of the system. In particular, in the conservative case, while the one-dimensional cubic NLSE equation with homogeneous coefficients has stable soliton solutions, no stable localized states can exist in two or more dimensions in focusing medium. When homogeneous linear gain and nonlinear dissipation are added to the system, stable stationary localized structures do not exist even in one-dimensional case. Nevertheless, stabilization can be achieved by considering a spatially localized gain.

© 2011 IEEE

PDF Article
More Like This
Optical solitons supported by localized gain in the presence of two-photon absorption

Amit Goyal, Vivek Sharma, and C. N. Kumar
WPo.5 International Conference on Fibre Optics and Photonics (Photonics) 2012

Self-trapping of Necklace Beams in Self-Focusing Kerr Media

Marin Soljačić, Suzanne Sears, and Mordechai Segev
WD7 Nonlinear Guided Waves and Their Applications (NLGW) 1999

Stable dissipative topological solitons in optical parametric oscillators

Stefano Trillo, Marc Haelterman, and Adrian Sheppard
QWG2 Quantum Electronics and Laser Science Conference (QELS) 1997


You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
Login to access OSA Member Subscription