Dispersion of the linear and nonlinear optical susceptibilities of the CuAl(S_1-xSe_x)₂ mixed chaclcopyrite compounds

Based on the electronic band structure, we have calculated the dispersion of the linear and nonlinear optical susceptibilities for the mixed CuAl(S_1-xSe_x)₂ chaclcopyrite compounds with x = 0.0, 0.25, 0.5, 0.75, and 1.0. Calculations are performed within the Perdew-Becke-Ernzerhof general gradient approximation. The investigated compounds possess a direct band gap of about 2.2 eV (CuAlS₂), 1.9 eV (CuAl(S_0.75Se_0.25)₂), 1.7 eV (CuAl(S_0.5Se_0.5)₂), 1.5 eV (CuAl(S_0.25Se_0.75)₂), and 1.4 eV (CuAlSe₂) which tuned to make them optically active for the optoelectronics and photovoltaic applications. These results confirm that substituting S by Se causes significant band gaps' reduction. The optical function's dispersion ε2xx(ω) and ε2zz(ω)/ ε2xx(ω), ε2yy(ω), and ε2zz(ω) was calculated and discussed in detail. To demonstrate the effect of substituting S by Se on the complex second-order nonlinear optical susceptibility tensors, we performed detailed calculations for the complex second-order nonlinear optical susceptibility tensors, which show that the neat parents compounds CuAlS₂ and CuAlSe₂ exhibit | χ123(2)(-2ω;ω;ω) | as the dominant component, while the mixed alloys exhibit | χ111(2)(-2ω;ω;ω) | as the dominant component. The features of | χ123(2)(-2ω;ω;ω) | and | χ111(2)(-2ω;ω;ω) | spectra were analyzed on the basis of the absorptive part of the corresponding dielectric function ε2(ω) as a function of both ω/2 and ω.