## 1 Introduction  
Rogue waves or freak waves are extreme events in the ocean which are characterized by the emergence of large waves from an otherwise tranquil background [1; 2; 3]. The unexpectedly large displacements of the sea surface pose threats to maritime activities and offshore structures. Intensive research efforts are conducted to understand the physics of rogue wave and to develop measures to predict or detect such waves [4; 5]. Although rogue waves originate from the context of water waves [1; 2; 3; 6; 7; 8; 9], these studies have been extended to other physical contexts like optical fibers [10; 11; 12] and Bose-Einstein condensates [13]. Moreover, it has been demonstrated that optical rogue waves are related to supercontinuum generation [10; 11]. The high repetition rate of optical experiments is an advantage in the study of these rare events. For hydrodynamic surface waves, the nonlinear Schrodinger (NLS) equation governs the slow evolution of a weakly nonlinear wave packet [2]. The NLS equation can also describe the dynamics of temporal pulses in an optical fiber [10]. The Peregrine breather of the NLS equation is localized in both space and time, and is a widely utilized model for rogue waves [14; 15]. This solution is only nonsingular in the focusing regime unless higher order terms are considered [16]. When there are two or more wave trains present, the governing model is then the system of coupled nonlinear Schrodinger equations [17; 18]. The special case where all the coefficients of cubic nonlinearities are identical is known as the Manakov system. In optics, the Manakov equations provide an analytical account on the propagation of two optical beams in a photorefractive medium [19]. Moreover, when polarization effects are taken into account, the evolution of slowly varying, mutually perpendicular electric fields along an optical fiber with birefringence can be described by a system of coupled NLS equations too [20]. Another relevant example in optical physics is the issue of data communication using multi-mode fibers. Spatial multiplexing can relieve the capacity constraints of single-mode fibers. Random coupling of degenerate or quasi-degenerate modes for multi-mode fibers in the nonlinear propagation regime can then lead to generalized Manakov equations with many components [21]. Subsequently, transmissions in multi-mode fibers exhibiting rapidly varying birefringence will also give rise to Manakov equations upon averaging [22], and intermodal modulation instabilities for coupled Schrodinger systems can be analyzed [23]. Finally, the Manakov system is also a useful model in the dynamics of cold atomic species studied in Bose-Einstein condensates [13; 24]. Theoretically, the Manakov equations are obtained by considering the evolution of slowly varying electric fields in temporal or spatial waveguides. For temporal waveguides, group velocity dispersion is balanced by Kerr (cubic) nonlinearity. Rogue waves of the two-component Manakov system in the focusing regime have been studied intensively [25; 26; 27]. In contrast to the single component case, rogue wave modes had been discovered for the coupled NLS equations in the defocusing regime [28; 29; 30; 31] with group velocity mismatch between the two components. This scenario is closely related to new ranges of modulation instability in the defocusing regime. Theoretically, baseband instability is associated with the unstable behavior of disturbances in the low frequency regime. Remarkably these theoretical studies are amply supported by experimental efforts. Indeed, wavelength-division-multiplexed systems have been extended in the laboratory setting beyond the soliton formation regime, or more precisely to baseband and passband regimes for polarization modulation instabilities and the existence of rogue wave modes of the Manakov equations [32]. In another multi-component investigation, optical dark rogue waves are demonstrated by a suitable injection of two colliding and modulated pump beams with orthogonal states of polarization [33].