THz Electric Field-Induced Second Harmonic Generation in Inorganic Ferroelectric

Abstract

Second Harmonic Generation induced by the electric field of a strong nearly single-cycle terahertz pulse with the peak amplitude of 300 kV/cm is studied in a classical inorganic ferroelectric thin film of (Ba_0.8Sr_0.2)TiO₃. The dependences of the SHG intensity on the polarization of the incoming light is revealed and interpreted in terms of electric polarization induced in the plane of the film. As the THz pulse pumps the medium in the range of phononic excitations, the induced polarization is explained as a dynamical change of the ferrolectric order parameter. It is estimated that under action of the THz pulse the ferroelectric order parameter acquires an in-plane component up to 6% of the net polarization.

Figure 1

Experimental geometry and polarization diagrams of the SHG intensity for various experimental geometries. (a) Experimental geometry. The axes of the chosen laboratory frame X_L, Y_L, Z_L correspond to [100], [010] and [$\mathrm{00}\overline{\mathrm{1}}$] crystallographic directions, respectively. φ - the angle between the electric field of near-infrared probe and the X_L-axis. ψ - the angle between the electric field of the THz pump pulse and the X_L-axis; (b) dependence of the SHG signal on φ without any THz pump; (c) dependence of the SHG signal on φ when the THz field is applied parallel with respect to the X_L-axis. The polarization of the SHG signal was set either in the P_out or S_out-state; (d) dependence of the SHG signal on ψ when the probe polarization was set to the P-state (φ = 0). The polarization of the SHG signal was set either in the P_out or S_out-state. Dots correspond to experimental data and lines are fits (calculations see in Supplementary Information). Values for S-state multiplied by 3, 2 and 50 for (b–d) respectively.

Figure 2

THz-induced dynamics of nonlinear-optical response of the crystals. (a) Time trace of the electric field of the THz pump pulse; intensities of the SHG-signal: (b) for BST, (c) for STO (red line) and Si (black line); (d–f) Fourier transform spectra of the time traces shown in panels (a–c), respectively ((f) plotted in doubled frequency scale); (g) dependence of the SHG intensity on the THz field (logarithmic scale) for BST (top line) and STO (bottom line).

Figure 3

Effect of the electric field on electric polarization and SHG. (a) Hysteresis loops of the electric polarization obtained by the Soyer-Tower technique (bottom solid line); SHG hysteresis loop reconstructed from low-frequency measurements (top line). To compare with the hysteresis loop for the electric polarization, left side of the graph is plotted with an inversed sign (dashed line); SHG loops reconstructed from the experiment with THz pump pulses (points). Error bars on ΔI_SHG show s.d. from the 15 measured samples; (b) diagram showing the domain structure and its sensitivity to the external THz pulse.

Figure 4

Polarization dependences obtained within the suggested model for different γ: (a,d) γ = 0.05; (b,e) γ = 0.5; (c,f) γ = 1. Blue and red lines on (a and d) represent the linear plots of fitting curve from Fig. 1c and d.