Bifurcations of relaxation oscillations in an optically injected diode laser

A diode laser subject to optical injection is known to perform relaxation oscillations for certain values of amplitude and detuning of the input signal. To describe this, an averaged amplitude-phase equation was derived and studied by means of simulation by de Jagher er al. Here we analyse this model with tools from bifurcation theory. This allows us to give explicit formulae for the relevant bifurcations. In this way we find all regions of different dynamical behaviour of the injected laser when the amplitude of the relaxation oscillations is small. We show that the injected laser can exhibit motion on a torus, the stability of which depends on the linewidth-enhancement factor alpha. The disappearance of this torus goes along with chaotic dynamics. The validity of the present model is discussed.