Simple analytical approximations for the gain and refractive index spectra in quantum-well lasers

An analytical expression for the low-temperature optical susceptibility of quantum-well semiconductor lasers is presented based on a simple parabolic band model. The optical susceptibility obtained keeps the nonlinear dependence on the carrier density, providing both a broad gain spectrum and a dispersion curve, so it can be used to analyze the dynamics of multimode devices or devices with large carrier density variations. The resulting peak gain, differential peak gain, and linewidth enhancement factor are discussed. cw operation of a single-mode laser is studied as a function of the frequency of the cavity resonance. An analytical approximation to the finite-temperature gain spectrum is also presented, although the refractive index spectrum must be determined numerically. [S1050-2947(98)07501-5].