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Using Time Independent Density Functional Theory (TIDFT) it is shown that the2nd order optical susceptibilities of narrow (1nm-2nm) Silicon Nanowires (SiNW)are enhanced due to surface termination. The value of $\chi^{(2)}$ is enhancedup to 200 pm/V which is promising a strong Second Harmonic Generation (SHG) inSiNWs. For [100], [110] and [111] SiNWs, yxx component of $\chi^{(2)}$ tensoris 81, 225 and 81 pm/V, respectively. These are in close agreement with$\chi^{(2)}$ values reported for strained silicon waveguides in experiments.The 3rd order susceptibility, $\chi^{(3)}$, is within the range of(0.1-12)x$10^{-18} \frac{m^{2}}{V^{2}}$ which is close to the experimentalvalues of bulk silicon (0.1-0.2)x$10^{-18} \frac{m^{2}}{V^{2}}$ for [110] and[100] SiNWs and it is 100 times better for [111] SiNW. This study suggestspossibilities of enhancing SHG in SiNWs through symmetry breaking via strainand surface termination/reconstruction as well as suitability of this DFT-basedmethod in predicting nonlinear optical susceptibilities of nano structures.

Ab initio Study of Nonlinear Optical Susceptibilities in Silicon Nanowires