Power spectrum of directly modulated single-mode semiconductor lasers: Chirp-induced fine structure

The time-averaged power spectrum of a single-mode semiconductor laser under direct current modulation is calculated using the small-signal analysis of the stochastic rate equations. The general formalism includes the effect of frequency chirping owing to current modulation as well as the effect of phase diffusion related to spontaneous emission. Chirp-induced dynamic line broadening is shown to result from a superposition of the additional unresolved sidebands generated at multiples of the modulation frequency on both sides of the optical line. The effect of intensity modulation is to introduce an asymmetry such that the low-frequency sideband has a relatively higher amplitude. The theory explains reasonably well the reported experimental observations. At the same time it provides physical insight into the dynamic process of frequency chirping and its relation to the frequency modulation. In particular, the frequency and the decay rate of transient relaxation oscillations govern the interplay between simultaneously occurring intensity and frequency modulations.