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# PACS number~s!: 42.55.Px, 78.66.2w The analysis of the static and dynamical properties of semiconductor lasers requires a knowledge of the coupling between the active semiconductor material and the optical field within the active region. In a semiclassical approach @1#, which constitutes the foundation for simpler descriptions as the rate equation ~RE! approximation @2#, the optical field is described by means of Maxwell’s equations, and its coupling to the material is described by the electrical susceptibility of the active medium. The imaginary part of the electrical susceptibility describes the energy exchange ~absortion or stimulated emission! between the field and the medium, while its real part describes the dispersive effect ~refractive