Effect of the frequency detuning on the stability analysis in a ‎semiconductor laser subject to optical injection: Hopf and Routh-Horwitz ‎conditions

Abstract

In this paper, the rate equations for a laser diode subject to an optical injection are studied both ‎analytically and numerically. By determining the Hopf and Routh- Hurwitz conditions, the stability ‎boundaries of the laser system have been studied. The stability diagrams have been discussed in terms ‎of detuning and the injection rate for different values of the linewidth enhancement factor.‎‏ ‏Also, we ‎obtain critical relations for the Hopf points that lead to instability in the laser system. It has also ‎shown that obtained relations depend on four parameters: detuning, linewidth enhancement factor, ‎optical injection strength and pumping current‎.

Keywords

• stability analysis
• semiconductor laser
• hopf point
• routh-horwitz
• frequency detuning
• optical ‎injection