Motion of dissipative solitons in a laser cavity with a smooth transverse inhomogeneity
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LECULES, OPTICS
Motion of Dissipative Solitons in a Laser Cavity with a Smooth Transverse Inhomogeneity N. N. Rosanov* S. V. Fedorov**, and A. N. Shatsev*** Research Institute for Laser Physics, Vavilov State Optical Institute, St. Petersburg, 199034 Russia St. Petersburg State University of Information Technologies, Mechanics, and Optics, St. Petersburg, 197101 Russia * e-mail: [email protected] ** e-mail: [email protected] *** e-mail: [email protected] Received July 17, 2007
Abstract—The effect of the inhomogeneity gradient in a large-aperture class A laser with a saturable absorber on the transverse motion of dissipative solitons and their clusters in the laser cavity is analytically and numerically studied. A soliton with a nonzero topological charge is found to move rectilinearly in the steady-state regime but in a direction that differs from the direction of the cavity length gradient, which is connected with a nontrivial internal structure of the soliton. The steady-state motion of soliton clusters can be curvilinear, including translational and rotational motions of their center. PACS numbers: 42.65.Tg DOI: 10.1134/S1063776108030060
1. INTRODUCTION Dissipative solitons, i.e., wave objects localized due to the balance between inflow and outflow of energy and/or matter, occur in many nonlinear physical, chemical, and biological systems [1] and are of considerable interest as examples of self-organization. Recently, optical dissipative solitons have been studied more intensively [1, 2], which is connected with a high simplicity and availability of nonlinear optical phenomena and with a high potential for their applications in information technologies. For experiments and applications, the most promising are spatial (transversal two-dimensional) dissipative solitons in large-aperture schemes such as a nonlinear interferometer excited by external radiation [3, 4] and a laser with a saturable absorber [5]. Since the system is translationally invariant under ideal conditions, single solitons possess high (axial) symmetry, are motionless, and can be localized at any point of the aperture. Their motion can be caused by a transverse inhomogeneity of the parameters of the scheme, such as the cavity (interferometer) length, which corresponds to mirror nonparallelism, losses, or gain of an active medium (in laser schemes) and intensity and phase inhomogeneities of an external signal (in nonlinear interferometers), see [2, 6] and references therein. Another reason for the transverse motion, which is present even under conditions of a transverse homogeneity of the system, is an asymmetry of the soliton structure, for example, in asymmetric clusters of cou-
pled dissipative solitons [7–9]. In the general case, these two factors act simultaneously. The effect of inhomogeneities of a system on the transverse localization and motion of dissipative localized structures is important because of the following circumstances, which were initially studied for nonlinear interferometers [7, 10, 11]. It is significant that, as a
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