Absolute phase and amplitude of second-order nonlinear optical susceptibility components at Si(001) interfaces

We determine the absolute phase and amplitude of four dominant components of the susceptibility tensor that governs second-harmonic generation (SHG) from Si(001) interfaces, including both bulk and surface contributions. Measurements of crystal-orientation-dependent SHG intensity with linearly polarized excitation alone yield two possible values of the relative phase of bulk and surface SHG, corresponding to dual solutions of quadratic equations. We resolve this ambiguity by measuring the handedness difference of SHG with circularly polarized excitation. Then, using frequency-domain interferometric SHG calibrated to a quartz crystal, we obtain the following absolute phases and amplitudes at the fundamental wavelength 745 nm for a Si(001)/dielectric sample: surface dipole susceptibility components d(15)=1.2 x 10(-18) exp(i0.46 pi) m(2)/V, d(31) + gamma/epsilon=4.3 x 10(-20) exp(-i0.53 pi) m(2)/V, and d(33)-d(31) approximate to d(33) = 5.8 x 10(-18) exp(i0.38 pi) m(2)/V; anisotropic bulk quadrupole susceptibility component zeta = 4.4 x 10(-18) exp(-i0.62 pi) m(2)/V. Here, gamma is an undetermined isotropic bulk quadrupole susceptibility component and epsilon the dielectric function of Si. If gamma/epsilon is negligible, all contributions are determined. The estimated error in each amplitude and phase is a single unit of the last significant digit.