Investigation Of Time-delay Signature Suppression In Chaotic Output From Vertical-cavity Surface-emitting Lasers

Vertical-cavity surface-emitting laser (VCSEL) is a new kind of semiconductor laser (SL), and develops fast in the past few decades. Compared with edge-emitting SL, VCSELs own some unique advantages, such as low threshold current, single longitudinal-mode operation and easy large-scale integration into two-dimensional arrays etc. The output of VCSEL can be chaos after introducing external disturbance such as optical feedback, opto-electronic feedback, and optical injection, etc. Complex optical chaos has some important applications in chaotic secure communication and ultra fast random bit generation. Among various methods for generating optical chaos, the scheme based on a VCSEL under optical feedback is usually adopted due to simple configuration and easy to generate high-dimension chaos. But in an external cavity feedback VCSEL system, time-delay signature (TDS) of the chaos output is obvious due to optical round trip in the external cavity generally. The TDS reduces the randomness of chaotic signal. For fast random bit generation, the TDS of the chaotic signal will induce recurrence feature and then affect the statistical performance of the generated random bit sequences. For chaotic secure communication, the TDS inevitably provides an available clue to the encryption attackers, who may reconstruction of the chaotic system based on the TDS identification. Therefore, the security of the chaotic encryption may be partly compromise. Hence, it is necessary to develop some strategies to suppress the TDS of chaotic signal.In this paper, based on spin-filp model (SFM), by means of self-correlation function (SF) and permutation entropy (PE), we investigated the TDS in mutually coupled VCSELs and fiber Bragg grating feedback VCSEL system. The results show that, in the mutually coupled VCSELs system, the coupling strength and the frequency detuning between the two mutually coupled VCSELs are the crucial factors for TDS suppression. Under suitable coupling strength and frequency detuning, the TDS of two polarization components from each VCSEL can be suppressed simultaneously. Besides, the TDS behaves the similar evolution trend, when the two VCSELs possess mismatched inner parameters within a relatively small range. In fiber Bragg grating (FBG) feedback VCSEL system, the FBG provides distributed feedback along its length and the TDS of chaos output from a FBG feedback VCSEL is more effectively suppressed compared with that output from a mirror feedback VCSEL. Through detailed simulation, the optical feedback rate and the FBG coupling coefficient are the key factor of TDS suppression in FBG feedback VCSEL system. The TDS evolution map in the parameter space of optical feedback rate and FBG coupling coefficient is plotted and the optimal parameter region of TDS suppression has been determined.