Transfer matrix analysis of the spectral properties of complex distributed feedback laser structures

A transfer matrix model for the spectral behavior of complicated distributed feedback lasers is presented. The rigorous numerical approach permits the accurate solution of the one-dimensional wave equation without any approximation. Hole burning effects are taken into account by splitting up the whole structure into subsections with uniform parameters and finding the self-consistent solution for the longitudinal mode intensity, the carrier density, and the carrier induced refractive index change by an iteration procedure. The resulting distributions are used to calculate the spectrum by a summation over the multiple reflected spontaneous emission originating from each subsection. The method can be applied to arbitrary complex device structures both below and above threshold and is easy to implement with high accuracy and good computational performance