Bifurcation Analysis On The Semiconductor Laser With Sasturable Abusorber And Delayed Optical Feedback

In recent years, lasers have been applied to many important areas, especially inoptical data storage and light in telecommunications. As a lasing device, the laserdevice has received extensive attention, in which the semiconductor laser device hasmany excellent characteristics, such as small size, light weight, reliable operation,high efficiency and so on. At present, optical fiber communication has become thepredominant mode of large-scale data conversion, and this communication networktakes the semiconductor laser as optical laser source. So the research ofsemiconductor laser device has important theoretical and practical significance.In this paper, we constitute a delayed feedback laser device system based onthe absorber semiconductor laser device model raised by Yamada et al., throughadding optical feedback. With the time delay as the bifurcation parameter, we findthat the system can experience a Hopf bifurcation, which makes the local stability ofthe equilibrium change, by discussing the existence of pure imaginary roots for thecharacteristic equation and transversal condition. First, the bifurcation near the zeroequilibrium is considered. Under certain reasonable assumptions, we linearize thedifferential equation set at the zero equilibrium. By analyzing the distribution of theroots for the characteristic equation, the local stability of the zero equilibrium is got.When all the characteristic roots have negative real parts, the zero equilibrium islocally asymptotically stable; if there is a characteristic root has positive real part,the zero equilibrium becomes instability; especially, when the characteristicequation has a zero real part root, some bifurcation phenomena can be judged (suchas the Hopf bifurcation). Second, utilizing the center manifold theorem and thenormal form method, the system can be simplified well. By calculating theimportant parameters, we can determine the direction and the stability on the centermanifold of bifurcating periodic solutions near the zero equilibrium. Finally, the examples with specific experimental data are given and simulated using themathematical software Matlab, and the corresponding waveforms and phasediagrams are drawn. Simulation results are completely consistent with ourtheoretical results, which states the correctness of our conclusion.