Spontaneous-emission-enabled dynamics at the threshold of a directly modulated semiconductor laser

Chaos in semiconductor lasers or other optical systems has been intensively studied in the past two decades. However, modulation around threshold has received much less attention, in particular in gain-modulated semiconductor lasers. In this article, we investigate the bifurcation sequence which appears with pump modulation in the threshold region with a large amplitude and different values of modulation frequency. Modulation around threshold necessarily includes ``below-threshold'' dynamics, which can be effectively displayed only through through a nonlinear visualization of the oscillations. The irregular temporal behaviour is examined at various modulation frequencies and amplitudes, highlighting a possible route to chaos for very large amplitude modulation in the near-threshold region. The addition of the (average) spontaneous emission to the lasing mode enables a coupled dynamics between photons and carriers even below threshold, thus extending the pump range in which the modulation actively modifies the laser behaviour. We also report on the existence of a transition between similar attractors characterized by a temporal transient which depends on the amplitude of the modulation driving the pump.