| With the rapid development of information technology, people have increasing requirements on high transmission speed of information with high security. In recent years, chaotic secure communication based on semiconductor lasers (SLs) becomes one of the focus of research due to its huge application prospect. Generally, SLs can output complex chaos under external disturbance (such as external delay feedback), but the chaos of such system usually contains obvious time-delay signature (TDS), accompanied with the introducing external delay feedback structure. These TDS could provide the break clues that can be utilized to reconstruct the chaotic carrier by the encryption attackers, making the security of chaotic communication system being threatened. Therefore, it is important to investigate the TDS in SLs based chaos system. Currently, most of studies on SLs chaos system focus on the intensity part of the light field (namely intensity time-delay signature, I-TDS). In fact, the light field of SLs output contains two parts:the intensity and the phase. In recent years, the new researches have shown that even the I-TDS of chaos is suppressed, the time-delay signature of phase (namely phase time-delay signature, P-TDS) could still keep obvious. Thus, it provides another possibility clue for the encryption attackers. For the P-TDS problem, related researches are currently focused on the DFB-laser based chaos system. But the rapid development of the vertical-cavity surface-emitting lasers (VCSELs) offers another choice. Compared with DFB-laser, VCSELs have series unique advantages such as low threshold current, high-coupling efficiency to optical fiber, etc. Currently, there are few reports focused on the P-TDS of VCSELs based chaos system. Therefore, analysis of the P-TDS problem of VCSELs based chaos system is important for acquisition of new low TDS optical chaos source and developing high safety performance chaotic secure communication system.In this work, based on spin-flip model, the P-TDS features of mutually-coupled VCSELs system and the TDS and chaos bandwidth (BW) features of master-slave VCSELs system have been investigated systematically. Firstly, for the mutually-coupled VCSELs system, by adopting the self-correlation function (SF) and the permutation entropy (PE) methods, we analyzed systematically the affection of coupling strength, frequency detuning on the P-TDS features, and with the I-TDS compared. The results show that:the chaos P-TDS could be obvious in spite of the I-TDS being very weak in the weaker coupling strength condition. While, under appropriate coupling strength value, the P-TDS and I-TDS could be suppressed simultaneously. Moreover, with deeper investigation of the relationship of frequency detuning and TDS, the optimal parameters range was determined for the simultaneous generation of four-channel chaos signals, whose P-TDS and I-TDS are all suppressed effectively. Next, for the master-slave VCSELs system, the dynamic characteristic was analyzed numerically. Besides, we investigated the influences of injection strength, frequency detuning between master VCSEL (M-VCSEL) and slave VCSEL (S-VCSEL) and external feedback strength of M-VCSEL on the TDS (both I-TDS and P-TDS) and chaos BW. The results show that, under appropriate injection strength and frequency detuning, both I-TDS and P-TDS of two polarized components (named as X-PC and Y-PC) can be suppressed simultaneously. Further analyzing the influence of injection strength on the chaos BW, it is found that the bandwidths in two polarized components can exceed 30 GHz in the large negative frequency detuning region. Combining with the TDS and BW features of chaotic output, the chaotic signals with wide BW and low TDS can be obtained by selecting the appropriate injection parameters. In addition, the reasonable external feedback strength of M-VCSEL contributes to the high-quality chaotic output of the system under the certain injection strength condition. |
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