Full-band-structure calculation of first-, second-, and third-harmonic optical response coefficients of ZnSe, ZnTe, and CdTe

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Abstract
We report full-band-structure calculations of the frequency-dependent second- and third-harmonic response functions of ZnSe, ZnTe, and CdTe, as well as our results for the dielectric function of these semiconductors. We use a linear combination of Gaussian orbitals technique, in conjunction with the Xα method, to obtain the energy band structures and optical matrix elements of each material. The expressions for ε→(ω) and χ→ (2)(-2ω;ω,ω) are evaluated utilizing a linearized sampling method for integrating over an irreducible segment of the Brillouin zone; the expression for χ→ (3)(-3ω;ω,ω,ω) is evaluated using a random-sampling method. The results of our calculations of ε→2(ω) are in good agreement with experimental results. Our calculated value of χ14(2)(0)=24.8×10−8 esu for CdTe is in excellent agreement with the measured value [G. H. Sherman and P. D. Coleman, J. Appl. Phys. 44, 238 (1973)] of χ14(2)(λ=28 μm)=(28±11)×10−8 esu. We argue that the experimental results for χ14(2)(λ=10.6 μm) of ZnSe and ZnTe [C. K. N. Patel, Phys. Rev. Lett. 16, 613 (1966)] are likely to be inaccurate and that there is a need for additional measurements. Our calculations show that both χ→ (2)(0) and χ→ (3)(0) are positive for the materials considered in this work. We analyze the prominent features of ε→2(ω), χ→ (2)(-2ω;ω,ω), and χ→ (3)(-3ω;ω,ω,ω) over a wide range of frequencies. Our results indicate that the effects of weak optical transitions are much more pronounced in the second- and third-order optical response functions than in the linear-response functions.