Analytical characterization of grating-tuned external-cavity semiconductor lasers

Applying the ray-trace method to an external-cavity semiconductor laser (ECLD), an analytical expression for the output spectrum from the end facet has been derived. As a result, we deduced explicit analytical expressions for the nominal threshold carrier density and required length of the extended cavity when the ECLD is tuned to oscillate at grating-selected wavelengths. Combining the spectral pattern with the carrier rate equation, a self-consistent solution to the carrier density deficit has been obtained and used to predict the tunable output power of the ECLD without resorting to a photon rate equation.