Ab initio theory of quantum fluctuations and relaxation oscillations in multimode lasers

We present an ab initio semi-analytical solution for the noise spectrum of complex-cavity microstructured lasers, including central Lorentzian peaks at the multimode lasing frequencies and additional sidepeaks due to relaxation-oscillation (RO) dynamics. In Phys. Rev. A 91, 063806 (2015), we computed the central-peak linewidths by solving generalized laser rate equations, which we derived from the Maxwell–Bloch equations by invoking the fluctuation–dissipation theorem to relate the noise correlations to the steady-state lasing properties. Here, we generalize this approach and obtain the entire laser spectrum, focusing on the RO sidepeaks. Our formulation treats inhomogeneity, cavity openness, nonlinearity, and multimode effects accurately. We find a number of new effects, including new multimode RO sidepeaks and three generalized α factors. Last, we apply our formulas to compute the noise spectrum of single-mode and multimode photonic-crystal lasers.