Instability in optical injection locking semiconductors lasers using multiparametric bifurcation analysis.

In this paper, we investigate bifurcations of equilibria and transients by using modified rate equations of semiconductor lasers (SCLs) subjected to optical injection. An analytical study is performed to demonstrate some two-parameter bifurcations, inter alia, Bogdanov-Takens and Gavrilov-Guckenheimer bifurcations. A detailed numerical study based on the multiparametric bifurcation method and using 3D-plots and projections reveal a rich locking dynamics of SCLs. In this way, a so-called zero frequency detuning well is highlighted in the vicinity of a Hopf bifurcation confining minimal states of the larger Lyapunov exponent in injection locking curves. Three-parameter bifurcation curves mainly underscore cusp bifurcation and resizing of its multi-equilibrium region by the specific control parameter defined in this model. The bursting phenomenon observed in the transient regime is discussed by using various numerical approaches wherefrom another quantifying method tapping into two-parameter bifurcation analysis is proposed. Thereafter, metastable chaos dynamics supported by spiraling relaxation oscillations is also investigated as well as planar saddle-node bifurcations with three homoclinic orbits for high positive and negative detunings. At last, zero α-factor effects contribute to drastically shrink the unlocking region of SCLs, twofold increase in Hopf bifurcation along with evidencing of complex chaotic sine-shaped and folded torus-shaped attractors.