Contents I. Introduction
Lasing characteristics of semiconductor lasers under the influence of external optical feedback (EOFB) have been studied extensively for the past 3 decades [1]–[3]. It has been shown that an EOFB-driven laser, which demonstrates rich nonlinear dynamics, can be a very complex nonlinear system. However, the better understanding of these nonlinear dynamics allows the use of semiconductor lasers with EOFB to generate as well as synchronize chaotic signals for the applications in chaotic system [4]–[7]. Due to the advantages (i.e., low-threshold current, single-longitudinal-mode, low beam divergence, and low production cost) of vertical-cavity surface-emitting lasers (VCSELs) over the conventional facet emitting lasers, researchers have shown great interests to realize chaotic lasing sources by using VCSELs. In fact, synchronizations between two chaotic VCSELs with bidirectional and unidirectional coupling have been demonstrated [8]–[10]. The suitability of VCSELs to chaotic optical communication has also been verified [11], [12]. Unfortunately, the excitation of multiple-transverse-modes inside VCSELs always weakens the synchronization and decoding performances of the chaotic communication system [13], [14].
