Effect of strain on $$\hbox {GaAs}_1-x-y\hbox {N}_x\hbox {Bi}_y/\hbox {GaAs}$$ GaAs 1 - x - y N x Bi y / GaAs to extract the electronic band structure and optical gain by using 16-band $$\varvec{kp}$$ kp Hamiltonian

(hbox {GaAs}_1-x-yhbox {N}_xhbox {Bi}_y) is a suitable candidate for (1.06,{upmu }hbox {m}) solid state lasers and high-efficiency solar cells. Mathematical models such as 16-band kp model is used to study the band structure, strain generated effect, band offset and variation of their parameters with Bi and N concentrations. Lattice constants of alloy (hbox {GaAs}_1-x-yhbox {N}_xhbox {Bi}_y) with (x/y=0.58) can match those of GaAs with the incorporation of Bi and N into GaAsNBi. Arsenic atom substitution due to the incorporation of N and Bi impurity atoms causes a significant band gap reduction of (sim )200 meV for (hbox {GaAs}_0.937hbox {N}_0.023hbox {Bi}_0.04) alloys under lattice-matched conditions and in addition, by tuning the concentrations of N and Bi, the electrical and optical properties of GaAsNBi can be controlled. Optical gain of (hbox {GaAs}_1-x-yhbox {N}_xhbox {Bi}_y) quantum well (QW) and GaAs as a barrier are calculated in generalized mode and observed the effect of the energy level of GaAs barrier on the GaAsNBi QW.