Chaos in semiconductor lasers or other optical systems have been intensively studied in past two decades. However, the route from period doubling to chaos is still not sufficiently visible, in particular, in gain-modulated semiconductor lasers. In this article we perform a careful investigation of the route to chaos exhibited by directly modulated semiconductor lasers near the threshold region with various values of modulation frequency and amplitude. Gain nonlinearity is included in the simulation of pulse train generation through gain switching, and a new form of phase space representation is introduced to distinctly display period doubling, tripling, quadrupling and chaos. The irregular behaviour is examined at various modulation frequencies and amplitudes, highlighting the possible route to chaos for very large amplitude modulation in the near-threshold region. The existence of deterministic trajectories below the laser threshold is rendered possible by the presence of the (average component of the) spontaneous emission, a point which has not often been explicitly considered. Furthermore, we 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.
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