Theory of large-signal direct modulation of extended cavity semiconductor lasers with dispersive loss

We present a model of coupled semiconductor diode-dispersive extended cavity lasers that describes arbitrarily large current modulation, does not assume uniform photon and carrier densities within the semiconductor diode gain medium, and is simple to implement numerically. In particular, we look at the fiber grating laser, an example of such a coupled system that has been studied as a possible optical communications source. We find simple expressions for the instantaneous frequency and intensity in terms of a few parameters characterizing the dispersion, allowing for the design of the system to minimize chirp. From these expressions we also recover Kazarinov and Henry's adiabatic chirp formula in the limit of slow modulation and Petermann's dynamical chirp formula in the limit of uniform carrier and photon densities. We show that in typical cases, where nonuniformity is important, the instantaneous frequency modulation is quantitatively and qualitatively different than is predicted by previous models.