Results and Discussions Regarding the SL-EUDOI-PMOF proposed in this paper, the external optical feedback cavity for the slave laser contains a phase modulator driven by pseudo-random signals, and this would conceal the time-delay eigenpeaks and the TDS generated by the time-delay information of the injected laser and the feedback laser. Thus, the TDS is effectively suppressed. The numerical results show that the TDS of the chaotic laser output from the system is effectively suppressed by optimizing parameter values in the selected parameter value ranges, namely, the time-delay eigenvalue β is smaller than 0.2 [Fig. 2(b) and Figs. 3-7]. Besides, the minimum value of β is close to 0.06 (Fig. 4 and Figs. 6-7). In the proposed SL-EUDOI-PMOF, an external optical feedback cavity is equipped for the master laser, and chaotic laser can thus be output and further injected into the slave laser through two paths. The interference between the injected chaotic laser in the two paths enlarges the intensity of the laser injected into the slave laser, ultimately broadening the BW of the chaotic laser output from the slave laser. The numerical results reveal that the BW is effectively widened under the parameters enabling effective suppression of the TDS, and the maximum value of the 3-dB BW of the chaotic laser obtained is about 20 GHz [Fig. 9(c2) and Fig. 10].

As class-B lasers, distributed feedback semiconductor lasers (DFB-SLs) can output chaotic laser under external disturbances, such as external optical injection and optoelectronic feedback, and the bandwidth is up to GHz. Therefore, DFB-SLs are widely applied in many fields, such as secure communication and physical entropy sources for generating random physical numbers. However, the chaotic laser output from DFB-SLs has weak periodicity and time-delay signature (TDS) due to optical feedback and optical injection. This would reduce the quality of the random numbers generated with chaotic laser sources and restrict the applications of chaotic laser. In addition, the bandwidth (BW) of the chaotic laser determines the transmission rate of secure communication. For the above reasons, the TDS and BW are two important parameters that affect chaotic laser's applications and are often used to characterize the chaotic characteristics of chaotic laser. This paper presents a semiconductor laser system with external unidirectional dual-path optical injection and phase-modulated optical feedback (SL-EUDOI-PMOF) and investigates its effectiveness in suppressing the TDS and broadening the BW of chaotic laser. The results of this paper are significant for achieving information confidentiality and high-speed transmission in chaotic laser-based secure communication.

This paper presents a scheme of semiconductor lasers. Specifically, a DFB-SL with an external-cavity optical feedback is used as the master laser, while a DFB-SL with the PMOF is taken as the slave laser. Subsequently, the chaotic laser output from the master laser is injected into the slave laser through two paths. The SL-EUDOI-PMOF is thereby obtained. Then, the influences of parameters, including the external optical injection coefficients and the feedback coefficients, on the TDS of the chaotic laser output from the SL-EUDOI-PMOF are numerically investigated. The time-delay eigenvalue β is defined as the maximum value of the time-delay eigenpeaks in the autocorrelation function curve of the chaotic laser. When β<0.2, the TDS is suppressed. Furthermore, the BW of the chaotic laser is examined under the parameters enabling effective suppression of the TDS.

This paper proposes the SL-EUDOI-PMOF system for suppressing the TDS and broadening the BW of chaotic laser. For this purpose, the influences of the system's parameters on the TDS are numerically investigated, and the results are physically analyzed. The results show that in the selected parameter value ranges, the time-delay eigenvalue β decreases first and then increases as the feedback coefficient Km or the pumping factor of the master laser increases. The value of β decreases as the feedback coefficient Ks or the two injection coefficients increase. Moreover, the value of β increases first and then decreases with an increasing frequency detuning, and it decreases first, then varies in a gentle manner, and rises slightly higher afterwards with the increase in the pumping factor of the slave laser. The optimal parameter value ranges for suppressing the TDS effectively are obtained accordingly. Then, the BW is investigated under the parameters enabling effective suppression of the TDS, and the result is physically analyzed. The analysis results show that the value of the BW increases rapidly first and then decreases slowly as the feedback coefficient Km or the pumping factor of the slave laser increases. It increases with an increasing injection coefficient K2 or an increasing feedback coefficient Ks. The value of the BW increases first and then varies gently as the pumping factor of the master laser rises, and it increases gradually first and then decreases rapidly with an increasing frequency detuning. The maximum value of the 3-dB BW of the chaotic laser obtained is about 20 GHz.