Traveling wave analysis of semiconductor lasers: modulation responses, mode stability and quantum mechanical treatment of noise spectra

We present a traveling wave analysis of a general class of semiconductor lasers, which includes multisection DFB/DBR lasers and gain-coupled DFB lasers. The analysis leads to new semianalytic expressions for the small-signal IM and FM modulation responses, the intensity and FM noise spectra, and the linewidth. The expressions are given in terms of solutions to four coupled linear homogeneous differential equations and can easily be evaluated numerically. We also derive a stability parameter σ, for which σ<0 indicates that the mode is unstable with respect to small-scale fluctuations. The noise spectra are derived from semiclassical calculations as well as from calculations based on quantized fields, and we discuss the limitations of the semiclassical approach. The formalism of the quantum mechanical treatment has a built-in relationship between the relative intensity noise and the noise of the injection current. This relationship is discussed and illustrated by numerical examples