Theory of linewidth for multielectrode laser diodes with spatially distributed noise sources

A general theory of linewidth for single-frequency semiconductor lasers is presented. The effects of spatially distributed noise sources together with spatially varying carrier and photon densities and injection current are analyzed in a rigorous manner by solution of the scalar wave equation. A new rate equation for the electric field is derived, in which the longitudinal effects are represented in the form of the weight functions C_N(z) and C_S(z). These functions express the sensitivity of the (output) field to local changes in carrier and photon density at the position z. For Fabry-Perot laser´s the z dependence of the C factors is shown to be negligible, in agreement with the fact that spatial hole burning is not considered to be important for Fabry-Perot lasers. For distributed-feedback (DFB) lasers, however, the z dependence is shown to be very significant