The study of high-order nonlinear behavior,prompted by single-cycle or subcycle strong terahertz pulses,has been scarce,primarily due to the limitations of highly stable and high-intensity terahertz radiation sources. The strong terahertz field–matter interaction leads to new avenues for exploring and understanding various novel nonlinear phenomena. The employment of a femtosecond laser to pump a lithium niobate (LiNbO₃) crystal has been considered as a major strategy for generating strong terahertz radiation. The strong terahertz pulse acquired by this technique can coherently detect and manipulate the optical properties of materials on an ultrafast timescale and can play a crucial role in discovering new phenomena and revealing new mechanisms. In this study,to explore the nonlinear effects of materials under strong terahertz pulse irradiation,a strong terahertz pump-optical probe spectroscopy system is developed by utilizing the tilted wavefront technique based on a lithium niobate crystal. Specifically,the highest terahertz output energy of 2.6 μJ and a focused terahertz peak electric field strength of 632 kV/cm are realized. Meanwhile,the nonlinear crystal gallium selenide (GaSe) is examined with this system,and we demonstrate that the strong change in the terahertz pulse-induced refractive index of GaSe is due to Pockels and Kerr effects.

A strong terahertz pump-optical probe spectroscopy system is established (Fig.1). This system operates on a Ti∶sapphire laser amplifier that can deliver laser pulses with a single-pulse energy of 2 mJ,a pulse duration of 120 fs,and a repetition rate of 1 kHz. A small portion of the femtosecond laser is divided by a beam splitter to sample the birefringence signal of the material induced by the terahertz pulse,whereas the residual 90% of the laser energy is used to pump the lithium niobate crystal to generate a strong terahertz pulse. A diffraction grating of 1800 line/mm is used to tilt the wavefront of the pump laser. A half-wave plate behind the grating changes the polarization of the pump laser from horizontal to vertical,making it parallel to the optical axis of the lithium niobate crystal. A 4f-lens geometry is used to image the pump spot with a tilted pulse front onto lithium niobate. The polarization distribution of terahertz pulses delivered from the lithium niobate is vertical. Subsequently,strong terahertz pulses are focused on the surface of the sample using a series of off-axis parabolic mirrors. A weak 780-nm probe beam overlaps with the terahertz pumping beam on the sample,and it is transmitted through the sample. An assembly of a quarter-wave plate,a Wollaston prism,and a balanced detector is used to sample changes in the refractive index of the material. A pair of wire-grid polarizers is used to tune the electric field intensity of terahertz pulses.

The transient optical responses of the GaSe crystal are measured under different terahertz peak electric fields (Fig.3). The transient signal intensity increases as the terahertz peak electric field strength increases. In essence,when strong terahertz pulses are incident on the GaSe crystals,the refractive index is modulated. Subsequently,the delayed probe light experiences birefringence induced by intense terahertz pulses as it passes through the GaSe crystal,and the two polarization components parallel and perpendicular to the terahertz polarization direction produce a phase retardation in the propagation direction. The maximum transient signals under different terahertz electric fields are extracted to analyze the potential nonlinear behavior of the experimental phenomena. A function that considers the coexistence of χ⁽²⁾ and χ⁽³⁾ nonlinear processes is used to fit the extracted maximum. The fitted curve can reproduce the experimental data in a better manner,indicating that the strong terahertz pulses simultaneously cause Pockels and Kerr effects in the GaSe crystal. Finally,we present the relationship between the change in the refractive index,induced by strong terahertz pulses,and electro-optic coefficient,along with the nonlinear refractive index.

A strong terahertz pulse with a single pulse energy of 2.6 μJ and peak electric field strength of 632 kV/cm is generated by employing the tilted wavefront technique based on lithium niobate crystals. The nonlinear optical response of a gallium selenide crystal is examined using a terahertz pump-optical probe system. The optical birefringence induced by sub-cycle terahertz pulses is observed,and the analysis suggests that the changes in polarization are related to Pockels and Kerr effects. This study provides a pathway for the analysis of the nonlinear effect in a medium under strong terahertz pumping and offers a reference for the determination of the electro-optic coefficient and nonlinear refractive index of materials.