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# Stability Analysis And Hopf Bifurcation Of Semiconductor Laser With Optical Feedback

Posted on:2007-07-11Degree:MasterType:Thesis
Country:ChinaCandidate:H M WangFull Text:PDF
GTID:2178360212467235Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
Since the first semiconductor laser was invented, it has greatly promoted the development of science and technology, and is considered as one of the greatest inventions in the 20th century. The application of semiconductor laser covers the whole field of optoelectronics, and has been the core technology of optoelectronics.The optical feedback is an important factor which can influent semicon-ductor laser with external cavity. In most applications, people care about stabilities when the optical feedback exists and effect when feedback or other parameters change. In this issue, the L-K equation is taken into account. One equilibrium point of L-K equation is discussed, because it is the only equilibrium point that exists in external cavity mode. It has little relation with parameters, and it is easy to control. The stability of this system is discussed regarding the delay as a parameter. Also, the bifurcation set is given, and the existence of Hopf bifurcation is proved. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation are exhibited. Furthermore, corresponding numerical simulation is carried out using Matlab, and the result is coincident with our theoretical analisis.As former researches have limited to numerical simulation, we discuss the L-K equation theoretically for the first time and have found the relationship of some parameters and the stability. Using our conclusions, we can control the stability or chaos of lasers. So it is very valuable to the research of the optical feedback of semiconductor laser with optical feedback.
Keywords/Search Tags:Semiconductor laser, Time delay, Stability, Hopf bifurcation
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