We present a new dynamical model for a directly modulated semiconductor diode, applicable to systems in which the dynamical time scales of interest are longer than the round-trip time of light in the diode. Employing a multiple scales analysis to simplify the familiar phenomenological equations, we find that the dynamical response of the diode can be described by time-dependent reflection and transmission coefficients for the electric field and one ordinary differential equation for the integrated carrier density. We do not assume that the photon and carrier densities are uniform along the diode and do not need to calculate them explicitly at each point. Additionally, we need not restrict ourselves to only a small-signal response. We justify the multiple scales analysis for parameters corresponding to typical structures through a comparison of the numerical solution of our results and a direct numerical integration of the original phenomenological equations.
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