IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 2, FEBRUARY 2003 197 Topologically Multicharged and Multihumped Rotating Solitons in Wide-Aperture Lasers With a Saturable Absorber Sergey V. Fedorov, Nikolay N. Rosanov, Anatoly N. Shatsev, Nikolay A. Veretenov, and Andrei G. Vladimirov Invited Paper Abstract—We present results of a semianalytical and numerical study of transverse two-dimensional stationary and oscillating soli- tons in a wide-aperture laser with a saturable absorber and fast nonlinearity of both gain and absorption. We determine the sta- bility conditions and bifurcations of axially symmetric solitons with screw wavefront dislocations of different order. We demonstrate the existence of asymmetric rotating laser solitons with different numbers of intensity maxima. Index Terms—Lasers, nonlinear optics, optical bistability, op- tical solitons. I. INTRODUCTION D ISSIPATIVE optical solitons are self-organized light beams created by hard (threshold-type) excitation in nonlinear optical media or schemes with a balance between optical energy losses and gain. The requirement of energy balance results in a discrete spectrum of the main parameters of dissipative solitons, as distinct from the continuous spectrum of more familiar conservative optical solitons, e.g., in fibers with a nonlinear refractive index [1]–[3]. This important difference is interesting not only from a fundamental standpoint. The robustness of the dissipative optical solitons and the suppres- sion of noise due to the threshold character of their excitation open up perspectives of their possible applications in optical information processing. There are a number of optical schemes in which dissipative solitons exist. The dissipative optical solitons were first found theoretically in wide-aperture nonlinear driven interferome- ters [4], [5]. Experimentally, they were first demonstrated in a liquid-crystal valve scheme with spatial filtering in the feedback [6], [7]. Another example of such “driven” schemes in which dissipative solitons exist is a single-mirror feedback system Manuscript received June 4, 2002; revised October 21, 2002. This work was supported by the Russian Foundation for Basic Research under Grant 02-02- 81045. S. V. Fedorov, N. N. Rosanov, and A. N. Shatsev are with the Theo- retical Department, Research Institute for Laser Physics, St. Petersburg 199034, Russia (e-mail: sfedorov@sf3997.spb.edu; rosanov@ilphs.pb.su; shatsev@ilph.spb.su). N. A. Veretenov and A. G. Vladimirov are with the Physics Faculty, St. Petersburg State University, St. Petersburg 198904, Russia (e-mail: werna@mailru.com; andreu@sp1254.spb.edu). Digital Object Identifier 10.1109/JQE.2002.807212 containing a cell with Na vapor [8]. There are also schemes without the external signal, such as wide-aperture lasers with a saturable absorber. Laser solitons in such schemes were predicted in [9], [10] (see also [11]). Subsequent theoretical and experimental studies of dissipative optical solitons are summarized in a number of recent reviews [12]–[20]. Both “driven” (passive) and “laser” schemes are especially promising for applications when based on semiconductor microcavities with multiple quantum wells or dots [21], [22]. The main difference between dissipative solitons in passive and active schemes is the following. Stationary solitons in driven schemes have the frequency of the external signal and are phase-matched with it, whereas the frequency of a stationary laser soliton is the unknown eigenvalue of the problem, and its phase is arbitrary. Note also that feedback is not a prerequisite for the existence of the laser soliton. Localized structures described by equations similar to laser equations can be created in a continuous medium, planar waveguide, or fiber with nonlinear gain and absorption. Therefore, the term cavity soliton is not appropriate here. As a consequence, laser solitons are extremely diverse. (For a review of features of one-, two-, and three-dimensional (1-, 2-, and 3-D) laser solitons, see [20].) Also highly diversified are the scenarios of laser soliton stability loss and generation of new structures. Our aim is to present a systematic semianalytical and numer- ical study of the stability and bifurcations of transversely 2-D solitons characterized by different topological charges (local- ized vortices of different order) in a wide-aperture laser with an intracavitary nonlinear absorber. We also demonstrate the exis- tence of rotating asymmetric “multihumped” solitons with dif- ferent numbers of intensity maxima. In Section II, we describe the laser model, present the governing equation, and discuss its symmetries. In Section III, we study stationary localized structures with axially symmetric intensity distribution, including localized vortices of different order. We analyze their stability with respect to small pertur- bations. In Section IV, we present the results of numerical solutions of the governing equation. We describe the bifurca- tions of the symmetric laser vortices, the appearance of new types of laser solitons, asymmetric and nonstationary ones, and hysteresis phenomena in which all these types of solitons 0018-9197/03$17.00 © 2003 IEEE