A rigorous analysis of tunable semiconductor lasers with built-in grating-assisted vertical coupler filter

A general theoretical model is established and analyzed for a tunable semiconductor laser with a built-in co-directional grating-assisted vertical coupler filter. Possible internal reflection at the gain-coupler junction is included. A rigorous coupled-mode formulation based on the composite modes in the absence of the grating perturbation and a mode-matching method at the waveguide junctions is combined with multimode rate equation analysis. The dispersion of the semiconductor material is also included in the model. The accuracy and the scope of validity of the model are verified for both weakly and strongly coupled filter structures. Simple expressions for equivalent mirror reflectance, lasing wavelength, threshold gain and side-mode suppression ratio (SMSR) are derived and typical examples examined. The effects of the filter and the internal reflection on the longitudinal mode selectivity are discussed