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Explicit formulas are presented for the linewidth enhancement factor in homogeneously broadened quantum-well lasers. Inspection of these formulas demonstrates clearly for the first time the dependence of the linewidth enhancement on well width, doping and photon energy. As a specific example, we calculate the linewidth enhancement factor for InGaAs/InP quantum wells. It is shown that the optimum strategy for minimal linewidth enhancement is to employ narrow wells, low injected carrier densities and photon energies much greater than the effective band-gap.