Terahertz-field-induced second optical harmonic generation from Si(111) surface

We study, both experimentally and theoretically, the second-harmonic (SH) generation (SHG) of optical radiation assisted by intense terahertz electromagnetic pulses from the surface of high-resistivity Si(111). The study was performed within the framework of the analysis of the superposition of different SH sources, including the surface-dipole, bulk-quadruple, and electric-field-induced (EFI) bulk-dipole (arising from internal built-in and external terahertz fields) contributions. Azimuthal rotation anisotropy of SHG for an arbitrary mutual polarization of the terahertz, fundamental, and SH optical fields was calculated and experimentally verified. The strongest impact of the terahertz field on SHG was observed in the case where the polarizations of the terahertz and SH fields coincide. In these polarization configurations, the terahertz field added mainly an isotropic term to the SH azimuthal dependences. It has been demonstrated that the application of the terahertz field can be helpful for distinguishing the SHG mechanism. For the sample under study, the contribution to the SH energy from the built-in field-induced source was found to be >4 times greater than the contribution from the surface and quadrupole nonlinear sources. The dominance of the EFISHG allowed us to find the ratio between the components of a silicon third-order nonlinear tensor ${\ensuremath{\chi}}_{}⁽³⁾(2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},0)$: ${\ensuremath{\chi}}₁₁₂₂={\ensuremath{\chi}}₁₂₁₂\ensuremath{\approx}0.51{\ensuremath{\chi}}₁₁₁₁$ and ${\ensuremath{\chi}}₁₂₁₂\ensuremath{\approx}{\ensuremath{\chi}}₁₂₂₁$ for the fundamental optical wavelength 790 nm.