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.

Amplified bursts of laser pulses are sought for various machining, deposition, spectroscopic, and strong-field applications. Standard frequency- and time-domain techniques for pulse division become inadequate when intraburst repetition rates reach the terahertz (THz) range as a consequence of inaccessible spectral resolution, requirement for interferometric stability, and collapse of the chirped-pulse amplification (CPA) concept due to the loss of usable bandwidth needed for safe temporal stretching. Avoiding the burst amplification challenge and resorting to lossy post-division of an isolated laser pulse after CPA leaves the limitations of frequency- and time-domain techniques unsolved. In this Letter, we demonstrate an approach that successfully combines amplitude and phase shaping of THz bursts, formed using the Vernier effect, with active stabilization of spectral modes and efficient energy extraction from a CPA regenerative amplifier. As proof of concept, the amplified bursts of femtosecond near-infrared pulses are down-converted into tunable THz-frequency pulses via optical rectification.

Open-aperture Z-scan measurements have been carried out to investigate the three-photon (3 PA) and four-photon absorption (4 PA) coefficients at 800 nm and 1030 nm wavelengths, respectively in congruent and stoichiometric lithium niobate (cLN, sLN) with different concentrations of Mg doping. The laser pulse duration at the two wavelengths were 40 and 190 fs. The peak intensity inside the crystals varied between approximately 110 and 550 GW/cm². The 3 PA and 4 PA coefficients were evaluated using a theoretical model and the results suggest that their minima are at or around the Mg doping level corresponding to the threshold for suppressing photo-refraction for both cLN and sLN. This result can be attributed to the contribution of crystal defects to the 3 PA and 4 PA processes. Furthermore, the 4 PA at 1030 nm exhibited greater nonlinear absorption than the 3 PA at 800 nm under the same intensity level. Possible reasons for this unexpected behavior are discussed. Overall, comparing the 3 PA and 4 PA values of these crystals will enable for selection of the optimum composition of LN crystal for efficient THz generation and for other nonlinear optical processes requiring high pump intensities.

We present designs of semiconductor contact grating high energy terahertz pulse sources pumped by femtosecond pulses in the 1 to 5 µm wavelength range. Nearly wavelength-independent diffraction efficiencies as high as 69% and 75% in the ± 1 st diffraction orders in the transverse electric field polarization state were predicted in GaAs and GaP, respectively, based on a rectangular grating. Numerical simulations—including, for the first time, to our knowledge, the effects of both a nonlinear refractive index and free carrier absorption—were performed to investigate the possible advantage of using longer pumping wavelengths to suppress the two- to seven-photon absorption. Conversion efficiency larger than 1.0% is predicted for both crystals. We also recognized that the nonlinear refractive index and the wavelength-dependent optical parametric amplifier efficiency can significantly reduce the overall terahertz generation efficiency; thus, optimum pump wavelengths exist for the highest conversion efficiency, which are 2 and 3 µ m for GaP and GaAs, respectively.

A novel, to the best of our knowledge, compact, imaging-free, tilted-pulse-front (TPF) pumped terahertz (THz) source based on a LiNbO₃ slab with a small wedge angle (< 8°) and with an echelon microstructure on its input surface has been demonstrated. Single-cycle pulses of more than 40-µJ energy and 0.28-THz central frequency have been generated by 100-mJ, 400-fs pump pulses with 4.1 × 10^–4 efficiency and excellent focusability. The peak electric field value focused by a single parabolic mirror was 540 kV/cm. Using 200-fs-long pump pulses, the efficiency increased to 1.0 × 10^–3, which is in qualitative agreement with the measured increased diffraction efficiency in the velocity matched diffraction order. A further ∼8x increase in efficiency is expected by pumping a cryogenically cooled wedged echelon with appropriate step sizes, better microstructured surface quality, and antireflection coating on both the input and the output sides. THz generation efficiency maxima were found at ∼2.7-mm crystal thickness for both pump pulse durations. The focused THz beam was diffraction limited within 5% accuracy. Compared to conventional THz sources, this setup is very compact, easy to align, can be pumped by larger beam sizes maintaining the high THz generation efficiency, and produces THz pulses with superior focusability.

Organic crystals offer promising potential for THz generation, but face limitations in wavelength tunability and damage threshold. By applying tilted pulse‐front pumping to organic crystals an additional degree of freedom is introduced into the pumping conditions enabling a wider range of pumping wavelengths without compromising phase matching. Additionally, the lifespan of organic materials can be extended by using longer pumping wavelength and eliminate lower‐order multi‐photon absorption, allowing for higher pumping intensity without significant free‐carrier absorption, thus increasing the damage threshold. Simulations predict significant improvement for four out of six investigated crystals when tilted pulse‐front pumping is applied. By using volume phase holographic grating one can achieve pulse‐front tilt in organic crystals in collinear geometry with high diffraction efficiency. Design parameters are also presented.