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Continuously self-focusing and continuously self-defocusing two-dimensional beams in dissipative media
 

Summary: Continuously self-focusing and continuously self-defocusing two-dimensional beams
in dissipative media
A. Ankiewicz, N. Devine, and N. Akhmediev
Optical Sciences Group, Research School of Physical Sciences and Engineering, Australian National University,
Canberra ACT 0200, Australia
J. M. Soto-Crespo
Instituto de Óptica, CSIC, Serrano 121, 28006 Madrid, Spain
Received 7 January 2008; published 21 March 2008
Using the Lagrangian formalism, with a simple trial function for dissipative optical two-dimensional 2D
soliton beams, we show that there are two disjoint sets of stationary soliton solutions of the complex cubic-
quintic Ginzburg-Landau equation, with concave and convex phase profiles, respectively. These correspond to
continuously self-focusing and continuously self-defocusing types of 2D solitons. Their characteristics are
distinctly different, as the energy for their existence can be generated either at the center or in the outer layers
of the soliton beam. These predictions are corroborated with direct numerical simulations of the Ginzburg-
Landau equation. Regions of existence in the parameter space of these two types of solutions are found and
they are in reasonable agreement with the predictions of the Lagrangian approach. In addition, direct numerical
simulations allow us to find more complicated localized solutions around these regions. These solutions lack
cylindrical symmetry and/or pulsate in time. Examples of the complex behavior of these beams are presented.
DOI: 10.1103/PhysRevA.77.033840 PACS number s : 42.65. k, 47.20.Ky
I. INTRODUCTION

  

Source: Akhmediev, Nail - Research School of Physical Sciences and Engineering, Australian National University
Australian National University, Research School of Physical Sciences and Engineering, Optical Sciences Group

 

Collections: Engineering; Physics