Nonlinear Dynamics Of An Optically Injected Semiconductor Laser Subject To FBG Feedback

Recently, semiconductor lasers(SLs) have been developed fast as the most important light source in the field of optical communication. Diverse external disturbances such as optical injection, optical feedback, and optoelectronic feedback have been introduced into SLs, and their influences on the nonlinear dynamics of SLs have been widely investigated. Among these external disturbances, optical injection and optical feedback are two commonly adopted schemes. With optical injection, locking and unlocking phenomena in SLs have been extensively studied. With optical feedback, stability, instability and chaos in SLs have been demonstrated. Especially, in many particular application fields requiring narrow linewidth microwave photonic signals or broad bandwidth chaos signals, both the optical injection and optical feedback may be needed to introduce into SLs simultaneously. Compared with the case of SLs subject to only optical injection or optical feedback, the dynamics of SLs subject to both optical injection and optical feedback will be more complicated owing to the mixed effects of optical injection and optical feedback. Therefore, it would be valuable to understand the dynamics of SLs subject to both optical injection and optical feedback. However, most of the researches of nonlinear dynamics of semiconductor lasers subject to optical feedback are usually focused on the case that the optical feedback is provided by a mirror. An optical fiber Bragg grating(FBG) as a wavelength selective filter passive optical device, can also be constituted the external cavity of the semiconductor laser, and provides distributed optical feedback. Although the dynamics of SLs subject to FBG feedback has been studied, the research of nonlinear dynamics of a semiconductor laser subject to FBG optical feedback and optical injection has not been reported.In this paper, the nonlinear dynamical characteristics of a semiconductor laser subject to optical injection and FBG optical feedback are theoretically and experimentally investigated. First, we make the central wavelength of the free-running S-SL locates at the peak reflected wavelength of FBG by adjusting the driving current. Then, the influences of FBG feedback and bandwidth on nonlinear dynamics of a semiconductor laser subject to FBG optical feedback and optical injection are investigated. The results show that, we investigate the nonlinear dynamics of the S-SL subject to only optical injection. Through varying the injection strength and the frequency detuning between a master SL(M-SL) and a slave SL(S-SL), some dynamical states with typical characteristics are recorded and judged, such as injection-locking state(IL), period one state(P1), period two state(P2), multi-period state(MP), and chaos oscillation state(OC). However, if the FBG feedback works, the dynamical characteristics of the optically injected SL are changed. The dynamical state of the S-SL is transferred from a stable state(S) into P1, changed IL and P1 to MP, and evolved P2 into CO. The variations of these dynamical states are further investigated with the introduction of a FBG feedback, and the according results show that these dynamical evolution routes are changed after a FBG feedback is introduced into the S-SL. Finally, through the analysis of time series, power spectrum and spectrum, the mappings of the dynamical states of S-SL in the parameter space of injection strength and frequency detuning under different FBG feedback strengths are obtained. With the increase of the FBG feedback strength, the minimum optical injection strength required for stable injection-locking increases and the minimum injection strengths corresponding to the frequency detuning shifts to negative frequency detuning direction. At the same time, the chaos oscillation(OC) region expends. In addition, we numerical simulate the mappings of the dynamical states of S-SL in the parameter space of injection strength and frequency detuning under certain FBG feedback strength and different FBG bandwidth. With the increase of the FBG bandwidth, the OC region expends, and the dynamical distribution of S-SL in optical injection parameter space has a trend to that of a SL subject to mirror feedback and optical injection.