High energy single- to few-cycle terahertz pulses enable the exploration of the frontier of science, such as electron acceleration, strong-field physics, and spectroscopy. One important method of generating such terahertz pulses is to use the tilted-pulse-front (TPF) technique. However, due to the non-collinear phase-matching, the large angular dispersion leads to a spatial and temporal break-up of the optical pump, limiting the terahertz generation efficiency and reducing the few-cycle character of the generated terahertz fields. To reduce the effects caused by angular dispersion, multiple schemes with discrete pulse-front-tilt have been suggested. We propose a terahertz generation scheme, where a spatio-temporally chirped (STC) pump pulse is utilized. With our 2D+1 numerical model, we perform a systematic comparative study of the conventional TPF scheme, three discrete TPF schemes, and the STC scheme. This model predicts smaller optimal interaction length and significantly smaller conversion efficiency compared to simple 1D models. We conclude that the STC scheme delivers spatially homogeneous few-cycle terahertz pulses with the highest conversion efficiency. Additionally, given a short interaction length, the discrete TPF schemes cannot outperform the continuous ones. In general, this work gives guidance to choose the most appropriate setup for a given terahertz experiment
A 2-D spatio-temporal analysis of terahertz generation by optical rectification of tilted-pulse-fronts is presented. Closed form expressions of terahertz transients and spectra in two spatial dimensions are furnished in the undepleted limit. Importantly, the analysis incorporates spatio-temporal distortions of the optical pump pulse such as angular dispersion, group-velocity dispersion due to angular dispersion, spatial and temporal chirp as well as beam curvature. The importance of the radius of curvature to the tilt-angle and group-velocity dispersion due to angular dispersion to terahertz f…
The tilted-pulse-front setup utilizing a diffraction grating is one of the most successful methods to generate single- to few-cycle terahertz pulses. However, the generated terahertz pulses have a large spatial inhomogeneity, due to the noncollinear phase matching condition and the asymmetry of the prism-shaped nonlinear crystal geometry, especially when pushing for high optical-to-terahertz conversion efficiency. A 3D+1 (x,y,z,t) numerical model is necessary in order to fully investigate the terahertz generation problem in the tilted-pulse-front scheme. We compare in detail the differences be…
A new type of tilted-pulse-front pumped terahertz (THz) source has been demonstrated, which is based on a lithium niobate plane-parallel slab with an echelon structure on its input surface. Single-cycle pulses of 1 microjoule energy and 0.30 THz central frequency have been generated with 0.05% efficiency from such a source. One order-of-magnitude increase in efficiency is expected by pumping a cryogenically cooled echelon of increased size and thickness with a Ti:sapphire laser. The use of a plane-parallel nonlinear optical crystal slab enables straightforward scaling to high THz pulse energie…
We analytically show how a superposition of beamlets produces terahertz radiation with greater spatial homogeneity and efficiency compared to tilted-pulse-fronts generated by diffraction gratings. The advantages are particularly notable for large pump bandwiths and beam sizes, alluding to better performance in the presence of cascading effects and higher energy pumping. A theory of terahertz generation using a superposition of beamlets is developed. It is shown how such an arrangement produces a distortion free tilted-pulse-front. Closed form expressions for terahertz spectra and transients in…
We propose a high resolution spatial diagnostic method via inserting a millimeter-gap grating into the collimated terahertz beam to monitor the minute variation of the terahertz beam in strong-field terahertz sources, which is difficult to be resolved in conventional terahertz imaging systems. To verify the method, we intentionally fabricate tiny variations of the terahertz beam through tuning the iris for the infrared pumping beam before the tilted pulse-front pumping (TPFP) setups. The phenomena can be well explained by the the theory based on tilted pulse front technique and terahertz diffr…
Electromagnetic pulses with tilted pulse fronts are instrumental in enhancing the efficiency of many light-matter interaction processes, with prominent examples including terahertz generation by optical rectification, dielectric laser acceleration, ultrafast electron imaging and X-ray generation from free electron lasers. Here, we find closed-form expressions for tilted-pulse-front pulses that capture their exact propagation dynamics even in deeply nonparaxial and sub-single-cycle regimes. By studying the zero-bandwidth counterparts of these pulses, we further obtain classes of nondiffracting …
We experimentally investigate the limits to 800 nm-to-terahertz (THz) energy conversion in lithium niobate at room temperature driven by amplified Ti:Sapphire laser pulses with tilted-pulse-front. The influence of the pump central wavelength, pulse duration, and fluence on THz generation is studied. We achieved a high peak efficiency of 0.12% using transform limited 150 fs pulses and observed saturation of the optical to THz conversion efficiency at a fluence of 15 mJ/cm2. We experimentally identify two main limitations for the scaling of optical-to-THz conversion efficiencies: (i) the large s…
Terahertz (THz) generation by optical rectification (OR) using tilted-pulse-fronts is studied. One-dimensional (1-D) and 2-D spatial models, which simultaneously account for (i) the nonlinear coupled interaction of the THz and optical radiation, (ii) angular and material dispersion, (iii) absorption, iv) self-phase modulation and (v) stimulated Raman scattering are presented. We numerically show that the large experimentally observed cascaded frequency down-shift and spectral broadening (cascading effects) of the optical pump pulse is a direct consequence of THz generation. In the presence of …
A tilted-pulse-front pumped terahertz pulse source is proposed for the generation of extremely high field single-cycle terahertz pulses. The very simple and compact source consists of a single crystal slab having a blazed reflection grating grooved in its back surface. Its further important advantages are the energy scalability and the symmetric THz beam profile. Generation of 50 MV/cm focused field with 5.6 mJ terahertz pulse energy is predicted for a 5 cm diameter LiNbO$_3$ crystal, if the pump pulse is of 450 mJ energy, 1030 nm central wavelength and 1 ps pulse duration. Such sources can ba…
The intense terahertz (THz) pulses facilitate the observation of various nonlinear optical effects and manipulation of material properties. In this work, we report a convenient approach that can produce strong broadband terahertz pulses with center frequency tunable between 2-4 THz. The coherent THz light source with pulse energy of 1.2 microjoule can be generated from a low-cost crystalline quartz pumped by an ultrashort tilted wave-front pulse. Thanks to the wide transparent spectral window and high damage threshold, our theoretical analysis and experiment show that the optical rectification…
Using an affordable ytterbium laser with sub-mJ of energy combined with a novel pulse compression technique, we demonstrate an extremely competitive state-of-the-art terahertz (THz) source with 53 mW of average power and 310 kV/cm at focus from the tilted-pulse front pumping scheme in lithium niobate at room temperature. Key points of this demonstration include the use of a pump pulse duration of 280 fs in combination with an echelon mirror. Our results present unmatched combined characteristics and are highly competitive with the existing THz sources pumped at the mJ range. This demonstration…
A model for THz generation by optical rectification using tilted-pulse-fronts is developed. It simultaneously accounts for (i) the spatio-temporal distortions of the optical pump pulse, (ii) the nonlinear coupled interaction of THz and optical radiation in two spatial dimensions (2-D), (iii) self-phase modulation and (iv) stimulated Raman scattering. The model is validated by quantitative agreement with experiments and analytic calculations. We show that the optical pump beam is significantly broadened in the transverse-momentum (kx) domain as a consequence of the spectral broadening caused by…
We obtained an optical-to-terahertz (THz) energy conversion efficiency of 0.5% using the tilted-pulse-front technique in lithium niobate at a cryogenically cooled temperature of 100 K pumped by amplified Ti:sapphire laser pulses with ~150 fs pulse duration at 800 nm wavelength. Compared with the optimized conversion efficiency of 0.18% achieved at room temperature, we achieved more than 2.5 times enhancement in conversion efficiency upon cryogenically cooling the crystal due to reduction of THz absorption. Further improvements to the conversion efficiency can be made by optimizing the out-coup…
Conventional diffractive and dispersive devices introduce angular dispersion (AD) into pulsed optical fields thus producing so-called 'tilted pulse fronts'. Naturally, it is always assumed that the functional form of the wavelength-dependent propagation angle associated with AD is differentiable with respect to wavelength. Recent developments in the study of space-time wave packets -- pulsed beams in which the spatial and temporal degrees of freedom are inextricably intertwined -- have pointed to the existence of non-differentiable AD: field configurations in which the propagation angle does n…
We demonstrate a tilted pulse-front transient grating technique that allows to optimally utilize time-resolution as well as transient grating line density while probing under grazing incidence as typically done in extreme ultraviolet (EUV) or soft x-ray (SXR) experiments. Our optical setup adapts the pulse front tilt of the two pulses that create the transient grating to the relative tilt grazing incident pulse. We demonstrate the technique using all 800 nm femtosecond laser pulses for transient grating generation on a vanadium dioxide film. We probe that grating via diffraction of a third 800…
Using the tilted-pulse-intensity-front scheme, we generate single-cycle terahertz (THz) pulses by optical rectification of femtosecond laser pulses in LiNbO3. In the THz generation setup, the condition that the image of the grating coincides with the tilted-optical-pulse front is fulfilled to obtain optimal THz beam characteristics and pump-to-THz conversion efficiency. The designed focusing geometry enables tight focus of the collimated THz beam with a spot size close to the diffraction limit, and the maximum THz electric field of 1.2 MV/cm is obtained.
Femtosecond light pulses carrying optical angular momentums (OAMs), possessing intriguing properties of helical phase fronts and ultrafast temporal profiles, enable many applications in nonlinear optics, strong-field physics and laser micro-machining. While generation of OAM-carrying ultrafast pulses and their interactions with matters have been intensively studied in experiments, three-dimensional characterization of ultrafast OAM-carrying light beams in spatio-temporal domain has, however, proved difficult to achieve. Conventional measurement schemes rely on the use of a reference pulsed lig…
Terahertz (THz) waves have been significantly developed in the last fifteen years because of their great potential for applications in industrial and scientific communities1,2. The unique properties of THz waves as transparency for numerous materials and strong absorption for water-based materials are expected to broadly impact biosensing3 such as medical imaging4, chemical identifications5, and DNA recognition6. In particular, for accessing information within a scale comparable to the cell size where interactions between cell membrane and other organelle structures occur, micron size spatial …
Ultrafast optical excitation with intense mid-infrared and terahertz pulses has emerged as a new tool to control materials dynamically. As most experiments are performed with femtosecond pulse excitation, typical lifetimes of most light-induced phenomena in solids are of only few picoseconds. Yet, many scientific applications require longer drive pulses and lifetimes. Here, we describe a mid-infrared pump - terahertz-probe setup based on a CO$\mathrm{_2}$ laser seeded with 10.6 $\mathrmμ$m wavelength pulses from an optical parametric amplifier, itself pumped by a Ti:Al$\mathrm{_2}$O$\mathrm{_3…
Free-space super-strong terahertz (THz) electromagnetic fields offer multifaceted capabilities for reaching extreme nonlinear THz optics, accelerating and manipulating charged particles, and realizing other fascinating applications. However, the lack of powerful solid-state THz sources with single pulse energy >1 mJ is impeding the proliferation of extreme THz applications. The fundamental challenge lies in hard to achieve high efficiency due to high intensity pumping caused crystal damage, linear absorption and nonlinear distortion induced short effective interaction length, and so on. Here, …
Deriving single or few cycle terahertz pulse (THz) by intense femtosecond laser through cascaded optical rectification in electro-optic crystals is a crucial technique in cutting-edge time-resolved spectroscopy to characterize micro-scale structures and ultrafast dynamics. In the past decade, lithium niobate (LN) crystal implementation of wave-front tilt scheme has been prevalently used, while painstaking efforts have been invested in order to achieve higher THz conversion efficiency. In this research we developed a brand new type of LN crystal possessing dual-face-cut and Brewster coupling, a…
Optical rectification of ultrashort laser pulses in LiNbO3 by tilted-pulse-front excitation is a powerful way to generate near single-cycle terahertz (THz) pulses. Motivated by various applications, calculations were carried out to optimize the THz peak electric field strength. The results predict THz output with peak electric field strength on the MV/cm level in the 0.3-1.5 THz frequency range by using optimal pump pulse duration of about 500 fs, optimal crystal length, and cryogenic temperatures for reducing THz absorption in LiNbO3. The THz electric field strength can be increased further t…
The sub-luminal phase velocity of electromagnetic waves in free space is generally unobtainable, being closely linked to forbidden faster than light group velocities. The requirement of effective sub-luminal phase-velocity in laser-driven particle acceleration schemes imposes a fundamental limit on the total acceleration achievable in free-space, and necessitates the use of dielectric structures and waveguides for extending the field-particle interaction. Here we demonstrate a new travelling-source and free space propagation approach to overcoming the sub-luminal propagation limits. The approa…
Streaking of photoelectrons with optical lasers has been widely used for temporal characterization of attosecond extreme ultraviolet pulses. Recently, this technique has been adapted to characterize femtosecond x-ray pulses in free-electron lasers with the streaking imprinted by farinfrared and Terahertz (THz) pulses. Here, we report successful implementation of THz streaking for time-stamping of an ultrashort relativistic electron beam of which the energy is several orders of magnitude higher than photoelectrons. Such ability is especially important for MeV ultrafast electron diffraction (UED…
We present a novel method for THz generation in lithium niobate using a reflective stair-step echelon structure. The echelon produces a discretely tilted pulse front with less angular dispersion compared to a high groove-density grating. The THz output was characterized using both a 1-lens and 3-lens imaging system to set the tilt angle at room and cryogenic temperatures. Using broadband 800 nm pulses with a pulse energy of 0.95 mJ and a pulse duration of 70 fs (24 nm FWHM bandwidth, 39 fs transform limited width), we produced THz pulses with field strengths as high as 500 kV/cm and pulse ener…
We demonstrate THz generation using the tilted pulse front method in Lithium Niobate, driven at unprecedented high average power of more than 100 W and at 13.3 MHz repetition rate, provided by a compact amplifier-free modelocked thin-disk oscillator. The conversion efficiency was optimized with respect to pump spot size and pump pulse duration, enabling us to generate a maximum THz average power of 66 mW, which is the highest reported to date from a laser-driven, few-cycle THz source. Furthermore, we identify beam walk-off as the main obstacle that currently limits the conversion efficiency in…
This paper discusses numerical and experimental results on frequency downshifting and upshifting of a 10 $μ$m infrared laser to cover the entire wavelength (frequency) range from $λ$=1-150 $μ$m ($ν$=300-2 THz) using two different plasma techniques. The first plasma technique utilizes frequency downshifting of the drive laser pulse in a nonlinear plasma wake. Based on this technique, we have proposed and demonstrated that in a tailored plasma structure multi-millijoule energy, single-cycle, long-wavelength IR (3-20 $μ$m) pulses can be generated by using an 810 nm Ti:sapphire drive laser. Here w…
