Theory of Linewidth for Multielectrode Laser Diodes with Spatially Distributed Noise Sources

A general theory of linewidth for single-frequency semi- conductor 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 weight functions CN(z) and Cs(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 lasers 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 DFB lasers however the z dependence is shown to be very significant. Examples of variation of the C factors with bias current are presented for a multielectrode DFB laser. A new formula for the spectral linewidth is derived and illustrated by numerical examples. The present theory can also account for time-varying distributions of carrier and photon densities due to noise or modulation. The change of distributions with bias current might have a strong influence on the linewidth and noise behavior.