Short-delayed-feedback semiconductor lasers

We consider the laser rate equations describing the evolution of a semiconductor laser subject to an optoelectronic feedback. We concentrate on the first Hopf bifurcation induced by a short delay and develop an asymptotic theory where the delayed variable is Taylor expanded. We determine a nearly vertical branch of strongly nonlinear oscillations and derive ordinary differential equations that capture the bifurcation properties of the original delay differential equations. An unexpected result is the need for Taylor expanding the delayed variable up to third order rather than first order. We discuss recent laser experiments where sustained oscillations have been clearly observed with a short-delayed feedback.