Analytical formulas for modulation responses of semiconductor DFB lasers

Analytical expressions for the modulation responses of semiconductor DFB lasers are derived from a rigorous standing-wave rate equation formulations. With proper approximations, these expressions are reduced to simple and insightful formulas, similar to those obtained from the conventional rate equations. Salient features of the DFB lasers, such as complex-couplings, phase-shifts, facet conditions, as well as variations of carrier and photon densities along the cavity caused by the longitudinal hole-burning, are considered in these approximate formulas. It is demonstrated that the modulation responses, predicted by the simple formulas are in excellent agreement with the exact solutions