We propose a generally applicable velocity matching method for THz-pulse generation by optical rectification in the range below the phonon frequency of the nonlinear material. Velocity matching is based on pulse front tilting of the ultrashort excitation pulse and is able to produce a large-area THz beam. Tuning of the THz radiation by changing the tilt angle is experimentally demonstrated for a narrow line in the range between 0.8-0.97 times the phonon frequency. According to model calculations broadband THz radiation can be generated at lower frequencies. Advantages of the new velocity matching technique in comparison to the electro-optic Cherenkov effect and non-collinear beam mixing are discussed.

The absorption coefficient and the index of refraction of undoped and Mg-doped stoichiometric and congruent ${\mathrm{LiNbO}}_3$ crystals were determined for polarization parallel to the $z$ axis in the far-infrared (FIR) $30-180\text{-}{\mathrm{cm}}^{-1}$ frequency range for different Mg-doping levels and temperatures down to 10 K. For stoichiometric ${\mathrm{LiNbO}}_3$ , smaller absorption and index of refraction were found, than for congruent samples. At a Mg content near the photorefractive threshold, the FIR absorption coefficient has the lowest value in the stoichiometric crystals, which are most suitable for efficient pulse generation in the terahertz range.

Optical rectification of femtosecond laser pulses has emerged as the dominant technique for generating single- and few-cycle terahertz (THz) pulses. The advent of the tilted pulse front pumping (TPFP) velocity matching technique, proposed and implemented two decades ago, has ushered in significant advancements of these THz sources, which are pivotal in the realm of THz pump-probe and material control experiments, which need THz pulses with microjoule energies and several hundred kV/cm electric field strengths. Furthermore, these THz sources are poised to play a crucial role in the realization of THz-driven particle accelerators, necessitating millijoule-level pulses with tens of MV/cm electric field strengths. TPFP has enabled the efficient velocity matching in lithium niobate crystals renowned for their extraordinary high nonlinear coefficient. Moreover, its adaptation to semiconductor THz sources has resulted in a two-hundred-times enhancement in conversion efficiency. In this comprehensive review, we present the seminal achievements of the past two decades. We expound on the conventional TPFP setup, delineate its scaling limits, and elucidate the novel generation TPFP configurations proposed to surmount these constraints, accompanied by their preliminary outcomes. Additionally, we provide an in-depth analysis of the THz absorption, refractive index, and nonlinear coefficient spectra of lithium niobate and widely used semiconductors employed as THz generators, which dictate their suitability as THz sources. We underscore the far-reaching advantages of tilted pulse front pumping, not only for LN and semiconductor-based THz sources but also for selected organic crystal-based sources and Yb-laser-pumped GaP sources, previously regarded as velocity-matched in the literature.