SIDE-MODE GAIN IN SEMICONDUCTOR-LASERS

Side-mode gain and coupling coefficients in semiconductor laser media are calculated with the use of a multimode Fourier technique valid both for mode spacings that are small compared with the carrier-carrier relaxation rates and for spacings comparable with these rates as predicted by the Boltzmann theory of Binder et al. [Phys. Rev. B 45, 1107 (1992)]. The medium is described by a free-carrier model that provides for carrier-probability pulsations around quasi-equilibrium Fermi-Dirac values. We find that population pulsations play just as important a role as spectral hole burning for mode spacings comparable with the intraband relaxation rates. For the carrier-carrier relaxation rates of Binder et al., side-mode gain is predicted to be smaller than the main-mode gain, leading to single-mode operation. However, for somewhat smaller intraband relaxation rates, side-mode pin is readily found that exceeds the single-mode pin, which would encourage multimode operation. In addition, we find that the gain and coupling coefficient spectra are sensitive to the k dependence of the carrier-carrier relaxation rates and might provide a useful way to measure these rates. We are also able to explain the asymmetric side-mode gain spectra for small beat frequencies in terms of the rapid decrease of the quasi-equilibrium Fermi-Dirac electron distribution just above the gain region.