PIERS ONLINE, VOL. 5, NO. 7, 2009 617 Moving Solitons in a Cavity Soliton Laser K. Mahmoud Aghdami 1 , F. Prati 2 , G. Tissoni 2 , M. Brambilla 3 , and L. A. Lugiato 2 1 Physics Department, Payame Noor University, Mini City, Tehran 19569, Iran 2 INFM-CNR and CNISM, Dipartimento di Fisica e Matematica, Universit`a dell’Insubria, Como, Italy 3 INFM-CNR and CNISM, Dipartimento di Fisica Interateneo, Politecnico di Bari, Italy Abstract— We show that in a cavity soliton laser based on a VCSEL with a saturable absorber the solitons can spontaneously move. A key parameter ruling the dynamical instability is the ratio of the carrier lifetimes in the amplifier and in the absorber. The direction of the spontaneous motion is arbitrary but it can be controlled by injecting a low-intensity guiding beam for a short interval of time. The final velocity of the moving soliton is determined by the parameters of the system. 1. INTRODUCTION Cavity solitons (CSs) are bright intensity peaks over a dark homogeneous background. They typi- cally arise in the coherent field transmitted by nonlinear optical resonators driven by a homogeneous holding beam, and are generated through diffraction-mediated light-matter interaction which leads to field self-localization within the cavity [1]. CSs have been experimentally demonstrated in broad area, driven vertical cavity surface emitting lasers (VCSELs) below and above threshold [2,3]. A radical simplification could be achieved implementing the concept of Cavity Soliton Laser (CSL), i.e., a device generating CS without holding beam. Such a device, in addition to having maximum contrast between the CSs and the homogeneous background, would have tremendous advantages in terms of simplicity, robustness, and compactness, especially if realized in semiconductor-based microresonators. The first theoretical prediction of dissipative optical localized structures (autosolitons) in a laser with a saturable absorber was proposed by Rosanov and co-workers [4] in the limit of fast materials, then it was extended to the case of finite relaxation times by the same group [5], and spontaneous motion of the localized structures was demonstrated [6]. Here, we consider a VCSEL with an absorbing medium integrated in the cavity, taking into account the finite relaxation rates of the material, the saturable dispersion associated with the linewidth enhancement factors [7], and the radiative recombination processes typical of semicon- ductors [8]. Different methods for switching on/off CSs and the dynamical behavior of the laser during the different switching processes have been investigated [9]. The first experimental demonstration of a semiconductor CSL has been achieved recently with an alternative scheme in which a frequency selective feedback element is placed in an external-cavity configuration for the VCSEL [10]. More recently, a saturable absorber based semiconductor CSL has been experimentally realized with two mutually coupled broad-area semiconductor resonators, where one is pumped above transparency and plays the role of the laser, while the other one plays the role of the saturable absorber [11]. In this paper, we investigate the mechanism giving rise to a dynamical instability leading to the spontaneous motion of cavity solitons. A key role is played by the ratio between nonradiative recombination lifetimes in the amplifier and in the absorber. 2. DYNAMICAL EQUATIONS The dynamics of a laser with saturable absorber can be described by the following set of equations ˙ F = £ (1 - iα) D + (1 - iβ) d - 1+ i∇ 2 ⊥ / F (1) ˙ D = b 1 h μ - D ‡ 1+ |F | 2 · - BD 2 i (2) ˙ d = b 2 h -γ - d ‡ 1+ s |F | 2 · - Bd 2 i (3) where F is the slowly varying amplitude of the electric field, D and d are the population variables related to the carrier densities in the active and passive material, respectively. The parameters α