THEORY OF GAIN IN QUANTUM-WIRE LASERS GROWN IN V-GROOVES

Theoretical calculations of gain, refractive index change, differential gain, and threshold current for GaAs-AlGaAs quantum-wire lasers grown in V-shaped grooves are presented. The theoretical model is based on the density-matrix formalism with intraband relaxation and the subband structure is calculated within the effective bond-orbital model. It incorporates band mixing, material anisotropy, the spatial variation in material parameters, and the realistic geometry. For the quantum-wire geometry treated, we find agreement with the observed subband spacings. Although the splitting of the valence subbands is much less than k(B)T at room temperature, the low effective-mass conduction subbands have a splitting comparable to k(B)T, leading to a modest sharpening of the density of states associated with the conduction band. Because of the small overlap of the optical field with the active region for a single quantum wire, lasing threshold is reached only when several subbands are filled. Consequently, the reported operation of the single-quantum-wire laser corresponds closely to that of a very narrow quantum-well laser somewhat enhanced by the lateral confinement. In addition, we consider the case of a stack of quantum wires in which the optical-confinement factor can be significantly higher than for a single quantum wire. We predict minimum threshold currents per wire as low as 100 muA in close agreement with experiment. Also included are results on the change in the refractive index associated with the quantum-wire structure.