| We present an investigation into various aspects of the dynamics of a laser consisting of a semiconductor diode coupled to a long external cavity, with particular emphasis on the role of the external cavity dispersion. We begin by developing a large-signal dynamical model for the diode itself. Employing a multiple scales analysis to simplify the familiar travelling wave phenomenological equations, we find the diode dynamics are accurately described by a time dependent reflection coefficient and one ordinary differential equation for the carrier density. We do not assume that the photon and carrier densities are uniform along the diode, nor need we calculate them explicitly at each point. Instead, we assume that the dynamical time scales of interest are longer than the round trip time within the diode. We apply this model first to the study of large-signal direct modulation of dispersive extended cavity semiconductor lasers, and find an expression for instantaneous frequency from which insight is gained into the role of dispersion. In cases where gain non-uniformity is important, we find significant differences between our results and those of previous models. We also apply our diode model to an investigation of laser stability. Surprisingly, instability had been observed experimentally for chirped fiber grating lasers, depending upon grating orientation. We reproduce this through a linear stability analysis, and find that the field equation resembles the nonlinear Schrödinger equation (NLSE). There is a range of dispersion parameter for which stable operation occurs, analogous to normal dispersion of the usual NLSE, but this range is finite due to non-instantaneous carrier dynamics. Lastly, we develop an alternate formalism for semiconductor diode—again without assuming uniformity or small signals—in order to describe etalon effects in non-dispersive external cavity lasers; we examine both laser stability and dynamics resulting from large-signal current modulation. All reflections are included with the introduction of a single additional feedback parameter, and one extra term in the field equation. In the limit of a single reflection, our field equation reduces to a form of the Lang-Kobayashi equation. |
