Ab-initio Calculation of Nonlinear Optical Susceptibilities in Germanium Quantum Dots

Using Time Independent Density Functional Theory (TIDFT) implemented in SIESTA® we calculated the 2nd order and 3rd order nonlinear optical susceptibilities of small Germanium Quantum Dots (GeQD). We observe that the symmetry breaking due to surface termination enhances $\chi^{(2)}$ up to 299.1 pm/V which promises a strong Second Harmonic Generation (SHG) in GeQDs. Diagonal components for $\chi^{(2)}$ tensor are 52.5, 11.2, 299.1 pm/V, for xxx, yyy and zzz, respectively. The 3rd order susceptibility, $\chi^{(3)}$, is within the range of $(0.2-0.4)\times 10^{-18}\mathrm{m}^{2}/\mathrm{V}^{2}$ which is close to the reported experimental values of bulk Germanium. This study suggests possibilities of enhancing SHG in GeQDs through symmetry breaking via strain and surface termination/reconstruction as well as suitability of this fast and less-computationally intensive Density Functional Theory (DFT)-based method in predicting nonlinear optical susceptibilities of nano structures.