The effective-mass equations using the Luttinger-Kohn Hamiltonian taking into account the strain effects are solved numerically by Finite Difference Method. The effects of valence band mixing on the nonlinear gains are analysed based on the transition matrix formalism and the reduced density of states. Detailed numerical results and significant features for compressively and tensilely strained $Ga_xIn_{1-x}As$ grown on an $In_{1-x}Ga_xAs_yP_{1-y}$ lattice matched to InP are presented. In particular, for a Ga mole fraction x less than 0.468 (compression), the gain of the TE mode is larger than that of TM mode up to the certain carrier density limit. Since the density of states in valence bands are very close to that of C1 band, the low transparency current density and high differential gain is expected for VCSELs based on compressively strained quantum well active layers. For greater than 0.468(tension), the gain of TM mode is dominant and the maximum gain is twice greater than the other cases. So, high power and stable single mode are expected for tensile-strained quantum well layers.
