Physics Letters A 314 (2003) 44–50 www.elsevier.com/locate/pla Complicated basins in external-cavity semiconductor lasers Awadhesh Prasad a,∗ , Ying-Cheng Lai a,b , Athanasios Gavrielides c , Vassilios Kovanis c a Department of Mathematics and SSERC, Arizona State University, Tempe, AZ 85287, USA b Departments of Electrical Engineering and Physics, Arizona State University, Tempe, AZ 85287, USA c Nonlinear Optics Center, Air Force Research Laboratory, DELO, Kirtland AFB, New Mexico, NM 87117, USA Received 26 November 2002; received in revised form 24 March 2003; accepted 23 May 2003 Communicated by A.P. Fordy Abstract We demonstrate that complicated basins of attraction can occur in time-delay coupled, external-cavity semiconductor lasers. In particular, we find that there can be multiple coexisting attractors associated with low-frequency fluctuations in the laser power output, and prediction of the asymptotic attractor for specific initial conditions is practically impossible.  2003 Elsevier B.V. All rights reserved. PACS: 05.45.-a; 42.65.Sf; 42.55.Px Keywords: Nonlinear dynamics; Optical chaos; Semiconductor lasers There has been a continuous interest in the basin structure in nonlinear dynamical systems since the pi- oneering works in the early eighties [1–5]. A reason for such an interest concerns the predictability of as- ymptotic attractors when initial conditions are chosen in the vicinity of basin boundaries. Smooth boundaries are simple sets whose dimensions are one less than that of the phase space. For these boundaries, an im- provement in the precision to specify the initial con- ditions results in an equal amount of improvement in the predictability of the asymptotic attractor. Fractal basins are open (e.g., contain open areas in two di- mensions) but their boundaries contain fractal, chaotic * Corresponding author. E-mail address: awadhesh@enpc589.eas.asu.edu (A. Prasad). invariant sets [1]. Typically, the dimension of a fractal basin boundary is a fraction less than the phase-space dimension. As a consequence, a more precise specifi- cation of the initial conditions often results in a much smaller improvement in the probability to predict the attractor correctly. Riddled basins contain no open sets (e.g., no open area in two dimensions) and have di- mensions close to that of the phase space [6–11]. For riddled basins, a vast reduction in the uncertainty to specify the initial conditions results in hardly any im- provement in ability to predict the final attractor. Be- cause of this serious physical consequence, the phe- nomenon of riddling has received quite a lot of recent attention [6–12]. Complicated basin structures such as fractal and riddled basins are important because they can occur in physical systems [2–5,7,8]. The purpose of this Letter 0375-9601/03/$ – see front matter  2003 Elsevier B.V. All rights reserved. doi:10.1016/S0375-9601(03)00880-6