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Results and Discussion. Dependence of the SHG signal as a function of the time delay between the THz-pump and near- infrared probe pulses for non-centrosymmetric BST and centrosymmetric SrTiO3 shows in Figs. 1(b) and 1(c), respectively. Figure 1. THz-induced dynamics of nonlinear-optical response of the crystals. (a) — time-domain amplitude of THz pulse; SHG responses from BST (b) and SrTiO3 (c). (d) dependence of the SHG intensity on the THz field (logarithmic scale). The shape of the SHG response from BST qualitatively coincided with the shape of the THz pulse. Its mean, that the non-linear response should be linear to the THz electric field. The time-domain signal from STO qualitatively recalls square shape of the THz pulse. Power dependencies of the SHG intensity on the THz electric field (Fig. 1(e)) show linear and quadratic for BST and STO, respectively. In centrosymmetric crystals (STO), in the electric-dipole approximation, the only allowed effect is electric field (in our case THz electric field) induced second harmonic (TEFISH). This explains the fact that the signal from the STO in the negative delay is equal to zero. Induced polarization can be described as P˜TEFISH(2ω)= χ((3))E˜ΩE˜ω E˜ω , where E˜ω — electric field of optical pulse, E˜Ω — electric field of THz pulse, χ((n)) — n-th-order susceptibilities tensor. In noncentrosymmetric crystal with nonzero electric dipole contribution P˜cryst(2ω), formally the same description can be applied for the electric-field dependent part of polarization: (1) When the in-plane electric field is applied along the axis at the angle respect to [100] axis, part of domain line up along the field. In analogy with Ref. [7], it will be seen in the net response as the normalized volume fractions of domains V+ and Vi−(i = x, y) — (i = [100], [010]) with the electric polarization vector oriented parallel or antiparallel with respect to the one of two crystallographic axes in the plane of the sample. The differences of the fractions of the positively and the negatively oriented domains determines the electric field dependent contribution to the nonlinear optical polarization as ΔVi = V+ − V− : P001 + ΔViPi. Thus, the volume contributions to the corresponding domain directions for any angle ψ of applied THz E-field results in the following dependences: ΔVx = γ cos ψ, ΔVy = γ sin ψ, ΔVz = 1 − ΔVx2 − ΔVy2, (2) where γ is the ratio of in-plane switched domain fraction to [001]-oriented unswitched domain fraction. In general case, SHG intensity for the THz E-field oriented along arbitrary direction in the plane of the sample can be written as 2ω 2ω 2ω Ω 2ω Ω I ∝ P 001ΔV + P 100(E )ΔV + P 010(E )ΔV 2 . (3) where P001 is polarization without THz E-field, P100(EΩ) and P010(EΩ) are polarization induced 2ω by THz E-field. 2ω 2ω To confirm this model, we measured SHG intensity of the Pout and Sout analyzer states as a function of the probe (ϕ) and pump polarization (ψ) angles (Fig. 2(a) — no THz radiation, 2(b) and 2(c) — zero time-delay between pump and probe pulses, respectively). (a) (b)