Generation of sub-mJ terahertz pulses by optical rectification

Millijoule Terahertz Radiation from Laser Wakefields in Nonuniform Plasmas

We report the experimental measurement of millijoule terahertz (THz) radiation emitted in the backward direction from laser wakefields driven by a femtosecond laser pulse of few joules interacting with a gas target. By utilizing frequency-resolved energy measurement, it is found that the THz spectrum exhibits two peaks located at about 4.5 and 9.0 THz, respectively. In particular, the high frequency component emerges when the drive laser energy exceeds 1.26 J, at which electron acceleration in the forward direction is detected simultaneously. Theoretical analysis and particle-in-cell simulations indicate that the THz radiation is generated via mode conversion from the laser wakefields excited in plasma with an up-ramp profile, where radiations both at the local electron plasma frequency and its harmonics are produced. Such intense THz sources may find many applications in ultrafast science, e.g., manipulating the transient states of matter.

Sub-terahertz nearfields for electron-pulse compression

The advent of ultrafast science with pulsed electron beams raised the need to control the temporal features of the electron pulses. One promising suggestion is the nano-selective quantum optics with multi-electrons, which scales quadratically with the number of electrons within the coherence time of the quantum system. Terahertz (THz) radiation from optical nonlinear crystals is an attractive methodology to generate the rapidly varying electric fields necessary for electron compression, with the advantage of an inherent temporal locking to laser-triggered electrons, such as in ultrafast electron microscopes. Longer (picosecond-) pulses require a sub-THz field for their compression. However, the generation of such low frequencies requires pumping with energetic optical pulses and their focusability is fundamentally limited by their mm-wavelength. This work proposes electron-pulse compression with sub-THz fields directly in the vicinity of their dipolar origin, thereby avoiding mediation through radiation. We analyze the merits of nearfields for compression of slow electrons, particularly in challenging regimes for THz radiation, such as small numerical apertures, micro-joule-level optical pump pulses, and low frequencies. This scheme can be implemented within the tight constraints of electron microscopes and reach fields of a few kV/cm below 0.1 THz at high repetition rates. Our paradigm offers a realistic approach for controlling electron pulses spatially and temporally in many experiments, opening the path of flexible multi-electron manipulation for analytic and quantum sciences.

Tilted pulse front pumping techniques for efficient terahertz pulse generation

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.

Generation of 13.9-mJ Terahertz Radiation from Lithium Niobate Materials

Extremely strong-field terahertz (THz) radiation in free space has compelling applications in nonequilibrium condensed matter state regulation, all-optical THz electron acceleration and manipulation, THz biological effects, etc. However, these practical applications are constrained by the absence of high-intensity, high-efficiency, high-beam-quality, and stable solid-state THz light sources. Here, the generation of single-cycle 13.9-mJ extreme THz pulses from cryogenically cooled lithium niobate crystals and a 1.2% energy conversion efficiency from 800 nm to THz are demonstrated experimentally using the tilted pulse-front technique driven by a home-built 30-fs, 1.2-Joule Ti:sapphire laser amplifier. The focused peak electric field strength is estimated to be 7.5 MV cm^-1 . A record of 1.1-mJ THz single-pulse energy at a 450 mJ pump at room temperature is produced and observed that the self-phase modulation of the optical pump can induce THz saturation behavior from the crystals in the substantially nonlinear pump regime. This study lays the foundation for the generation of sub-Joule THz radiation from lithium niobate crystals and will inspire more innovations in extreme THz science and applications.

Cascade bunch focusing on chip using terahertz pulses to drive prism arrays

The dielectric laser accelerator (DLA) is a promising candidate for next-generation table-top and even on-chip particle accelerators. Long-range focusing of a tiny-size electron bunch on chip is crucial for the practical applications of DLA, which has been a challenge. Here we propose a bunch focusing scheme, which uses a pair of readily available few-cycle terahertz (THz) pulses to drive an array of millimeter-scale prisms via the inverse Cherenkov effect. The THz pulses are reflected and refracted multiple times through the prism arrays, synchronizing with and periodically focusing the electron bunch along the bunch channel. Cascade bunch-focusing is realized by making the electromagnetic field phase experienced by electrons in each stage of the array, that is, the synchronous phase, in the focusing phase region. The focusing strength can be adjusted via changing the synchronous phase and THz field intensity, optimization of which will sustain the stable bunch transportation in a tiny-size bunch channel on chip. This bunch-focusing scheme sets a base for developing a long-acceleration-range and high-gain DLA.

Controlling water giant low-inertia nonlinear refractive index in the THz frequency range via temperature variation

To create self-controlled radiation photonics systems, it is necessary to have complete information about the nonlinear properties of the materials used. In this Letter, the vibrational mechanism of the giant low-inertia cubic nonlinearity of the refractive index of water in the terahertz (THz) frequency range is experimentally proven. Its dominance, which manifests itself when the temperature of the liquid changes, is demonstrated. The measured nonlinear refractive index in the THz frequency range for a water jet at temperatures from 14°C to 21°C demonstrates a correlation with the theoretical approach, varies in the range 4-10 × 10^-10 cm²/W, and is characterized by an inertial time constant of less than 1 ps.

400 kHz repetition rate THz-TDS with 24 mW of average power driven by a compact industrial Yb-laser

We demonstrate a high average power terahertz time-domain spectroscopy (THZ-TDS) set-up based on optical rectification in the tilted-pulse front geometry in lithium niobate at room temperature, driven by a commercial, industrial femtosecond-laser operating with flexible repetition rate between 40 kHz - 400 kHz. The driving laser provides a pulse energy of 41 µJ for all repetition rates, at a pulse duration of 310 fs, allowing us to explore repetition rate dependent effects in our TDS. At the maximum repetition rate of 400 kHz, up to 16.5 W of average power are available to drive our THz source, resulting in a maximum of 24 mW of THz average power with a conversion efficiency of ∼ 0.15% and electric field strength of several tens of kV/cm. At the other available lower repetition rates, we show that the pulse strength and bandwidth of our TDS is unchanged, showing that the THz generation is not affected by thermal effects in this average power region of several tens of watts. The resulting combination of high electric field strength with flexible and high repetition rate is very attractive for spectroscopy, in particular since the system is driven by an industrial and compact laser without the need for external compressors or other specialized pulse manipulation.

Terahertz waveform synthesis in integrated thin-film lithium niobate platform

Bridging the "terahertz gap" relies upon synthesizing arbitrary waveforms in the terahertz domain enabling applications that require both narrow band sources for sensing and few-cycle drives for classical and quantum objects. However, realization of custom-tailored waveforms needed for these applications is currently hindered due to limited flexibility for optical rectification of femtosecond pulses in bulk crystals. Here, we experimentally demonstrate that thin-film lithium niobate circuits provide a versatile solution for such waveform synthesis by combining the merits of complex integrated architectures, low-loss distribution of pump pulses on-chip, and an efficient optical rectification. Our distributed pulse phase-matching scheme grants shaping the temporal, spectral, phase, amplitude, and farfield characteristics of the emitted terahertz field through designer on-chip components. This strictly circumvents prior limitations caused by the phase-delay mismatch in conventional systems and relaxes the requirement for cumbersome spectral pre-engineering of the pumping light. We propose a toolbox of basic blocks that produce broadband emission up to 680 GHz and far-field amplitudes of a few V m^-1 with adaptable phase and coherence properties by using near-infrared pump pulse energies below 100 pJ.

Scalable optical-to-terahertz converter with a prism-coupled plane-parallel lithium niobate plate

A nonlinear optical converter of femtosecond laser pulses to terahertz radiation, which combines the tilted-pulse-front pumping and prism coupling techniques, is proposed and experimentally tested. In contrast to the conventional tilted-pulse-front scheme with a prism-shaped LiNbO₃ crystal, the converter consists of a plane-parallel LiNbO₃ plate sandwiched between two dielectric prisms. One prism is used to couple the pump beam into the LiNbO₃ plate, another prism couples the generated terahertz radiation out of the plate. The proposed scheme enables scaling to large-diameter LiNbO₃ wafers and large-aperture high-energy pump laser beams resulting in generation of strong terahertz fields. In a proof-of-principle experiment with a 1-mm thick, small size (1 × 2 cm²) LiNbO₃ plate pumped by a mJ-class laser, the conversion efficiency comparable to that of the conventional scheme (∼0.1%) was demonstrated.

Spatiotemporal modeling of direct acceleration with high-field terahertz pulses

We present an improved model for electron acceleration in vacuum with high-energy THz pulses that includes spatiotemporal effects. In our calculations, we examined the acceleration with 300 GHz and 3.0 THz central frequency THz pulses with properties corresponding to common sources, and compared the Gaussian and Poisson spectral amplitudes and the associated time profiles of the electric fields. Our calculation takes into account both the longitudinal field and the spatio-spectral evolution around the focus. These aspects of the model are necessary due to the tight focusing and the duration towards a single-cycle of the THz pulses, respectively. The carrier-to-envelope phase (CEP) and the tilting angle of the coincident few- or single-cycle THz pulses must be tuned in all cases in order to optimize the acceleration scheme. We reveal additionally that electron beams with different final energies and different divergences can be generated based on simulated THz pulses having different Porras factors, describing the frequency dependence of the spatiotemporal amplitude profile, which may depend strongly on the method used to generate the single-cycle THz pulses.

Parameter sensitivities in tilted-pulse-front based terahertz setups and their implications for high-energy terahertz source design and optimization

Despite the popularity and ubiquity of the tilted-pulse-front technique for single-cycle terahertz (THz) pulse generation, there is a deficit of experimental studies comprehensively mapping out the dependence of the performance on key setup parameters. The most critical parameters include the pulse-front tilt, the effective length of the pump pulse propagation within the crystal as well as effective length over which the THz beam interacts with the pump before it spatially walks off. Therefore, we investigate the impact of these parameters on the conversion efficiency and the shape of the THz beam via systematically scanning the 5D parameter space spanned by pump fluence, pulse-front-tilt, crystal-position (2D), and the pump size experimentally. We verify predictions so far only made by theory regarding the optimum interaction lengths and map out the impact of cascading on the THz radiation generation process. Furthermore, distortions imposed on the spatial THz beam profile for larger than optimum interaction lengths are observed. Finally, we identify the most sensitive parameters and, based on our findings, propose a robust optimization strategy for tilted-pulse-front THz setups. These findings are relevant for all THz strong-field applications in high demand of robust high-energy table-top single-cycle THz sources such as THz plasmonics, high-harmonic generation in solids as well as novel particle accelerators and beam manipulators.

Inverse-Designed Narrowband THz Radiator for Ultrarelativistic Electrons

THz radiation finds various applications in science and technology. Pump-probe experiments at free-electron lasers typically rely on THz radiation generated by optical rectification of ultrafast laser pulses in electro-optic crystals. A compact and cost-efficient alternative is offered by the Smith-Purcell effect: a charged particle beam passes a periodic structure and generates synchronous radiation. Here, we employ the technique of photonic inverse design to optimize a structure for Smith-Purcell radiation at a single wavelength from ultrarelativistic electrons. The resulting design is highly resonant and emits narrowbandly. Experiments with a 3D-printed model for a wavelength of 900 μm show coherent enhancement. The versatility of inverse design offers a simple adaption of the structure to other electron energies or radiation wavelengths. This approach could advance beam-based THz generation for a wide range of applications.

Excitation of high-intensity terahertz surface modes of plasma slab under action of p-polarized two-frequency laser radiation

The excitation of the terahertz (THz) high-intensity surface modes when the two-frequency p-polarized laser radiation interacts with a plasma slab is studied. It was found that the significant amplification of the laser field in the plasma slab occurs when p-polarized laser radiation is incident at the angle of total reflection. It is shown that, under the action of laser radiation ponderomotive forces, the resonant excitation of the THz mode of the plasma slab occurs if the frequency difference of the laser fields coincides with the eigenfrequency of the surface mode. It is established that the giant increase in the energy flux density of the THz mode occurs when p-polarized laser radiation is incident at the angle of total reflection on the near-critical plasma slab with rare electron collisions if the conditions of resonant excitation are satisfied. It is shown that in this case the energy flux density of THz mode can significantly exceed the laser intensity.

Broadband terahertz generation by optical rectification of ultrashort multiterawatt laser pulses near the beam breakup threshold

We identify the physical factors that limit the terahertz (THz) yield of an optical rectification (OR) of ultrashort multiterawatt laser pulses in large-area quadratically nonlinear crystals. We show that the THz yield tends to slow its growth as a function of the laser driver energy, saturate, and eventually decrease as the laser beam picks up a spatiotemporal phase due to the intensity-dependent refraction of the OR crystal. We demonstrate that, with a careful management of the driver intensity aimed at keeping the nonlinear length larger than the coherence length, OR-based broadband THz generation in large-area lithium niobate (LN) crystals is energy-scalable, enabling an OR of multiterawatt laser pulses, yielding ∼10µJ/cm² of THz output energy per unit crystal area. With a 27-fs, 10-TW, 800-nm Ti:sapphire laser output used as a driver for OR in large-area LN crystals, this approach is shown to provide a THz output with a pulse energy above 10 µJ and a bandwidth extending well beyond 6 THz, supporting single-cycle THz waveforms.

THz-driven dielectric particle accelerator on chip

Recently, terahertz (THz)-driven particle accelerators have drawn increasing attention. The development of high-energy-gain THz accelerators on chip has been a challenge. Here we propose a concept of an on-chip THz-driven particle accelerator that uses few-cycle THz pulses to drive dielectric prisms. It avoids the serious waveguide dispersion of previous THz linacs based on dielectric lined waveguides and enhances the electron-energy gain. In addition, we propose to use prism stacks to overcome the asynchronization effect when accelerating low-energy particles, by which a longer acceleration length with even higher energy gain can be realized. Compared with the available on-chip dielectric laser accelerators, the proposed scheme avoids serious dielectric dispersion and enhances accelerated bunch charge. Hence, it promises an attractive particle accelerator on chip.

Wavelength conversion through plasmon-coupled surface states

Surface states generally degrade semiconductor device performance by raising the charge injection barrier height, introducing localized trap states, inducing surface leakage current, and altering the electric potential. We show that the giant built-in electric field created by the surface states can be harnessed to enable passive wavelength conversion without utilizing any nonlinear optical phenomena. Photo-excited surface plasmons are coupled to the surface states to generate an electron gas, which is routed to a nanoantenna array through the giant electric field created by the surface states. The induced current on the nanoantennas, which contains mixing product of different optical frequency components, generates radiation at the beat frequencies of the incident photons. We utilize the functionalities of plasmon-coupled surface states to demonstrate passive wavelength conversion of nanojoule optical pulses at a 1550 nm center wavelength to terahertz regime with efficiencies that exceed nonlinear optical methods by 4-orders of magnitude.

Semiconductor surface states often stand in the way of device performance, but here, the authors take advantage of them for wavelength conversion. They present a compact, passive conversion device insensitive to optical alignment by using plasmon-coupled surface states that enable the efficient conversion without nonlinear phenomena.

Ultrafast multi-cycle terahertz measurements of the electrical conductivity in strongly excited solids

Key insights in materials at extreme temperatures and pressures can be gained by accurate measurements that determine the electrical conductivity. Free-electron laser pulses can ionize and excite matter out of equilibrium on femtosecond time scales, modifying the electronic and ionic structures and enhancing electronic scattering properties. The transient evolution of the conductivity manifests the energy coupling from high temperature electrons to low temperature ions. Here we combine accelerator-based, high-brightness multi-cycle terahertz radiation with a single-shot electro-optic sampling technique to probe the evolution of DC electrical conductivity using terahertz transmission measurements on sub-picosecond time scales with a multi-undulator free electron laser. Our results allow the direct determination of the electron-electron and electron-ion scattering frequencies that are the major contributors of the electrical resistivity.

The electrical conductivity is critical to understand warm dense matter, but the accurate measurement is extremely challenging. Here the authors use multi-cycle THz pulses to measure the conductivity of gold foils strongly heated by free-electron laser, determining the individual contributions of electron-electron and electron-ion scattering.

Intense terahertz radiation: generation and application

Strong terahertz (THz) radiation provides a powerful tool to manipulate and control complex condensed matter systems. This review provides an overview of progress in the generation, detection, and applications of intense THz radiation. The tabletop intense THz sources based on Ti:sapphire laser are reviewed, including photoconductive antennas (PCAs), optical rectification sources, plasma-based THz sources, and some novel techniques for THz generations, such as topological insulators, spintronic materials, and metasurfaces. The coherent THz detection methods are summarized, and their limitations for intense THz detection are analyzed. Applications of intense THz radiation are introduced, including applications in spectroscopy detection, nonlinear effects, and switching of coherent magnons. The review is concluded with a short perspective on the generation and applications of intense THz radiation.

Terahertz aqueous photonics

Developing efficient and robust terahertz (THz) sources is of incessant interest in the THz community for their wide applications. With successive effort in past decades, numerous groups have achieved THz wave generation from solids, gases, and plasmas. However, liquid, especially liquid water has never been demonstrated as a THz source. One main reason leading the impediment is that water has strong absorption characteristics in the THz frequency regime.A thin water film under intense laser excitation was introduced as the THz source to mitigate the considerable loss of THz waves from the absorption. Laser-induced plasma formation associated with a ponderomotive force-induced dipole model was proposed to explain the generation process. For the one-color excitation scheme, the water film generates a higher THz electric field than the air does under the identical experimental condition. Unlike the case of air, THz wave generation from liquid water prefers a sub-picosecond (200-800 fs) laser pulse rather than a femtosecond pulse (~50 fs). This observation results from the plasma generation process in water.For the two-color excitation scheme, the THz electric field is enhanced by one-order of magnitude in comparison with the one-color case. Meanwhile, coherent control of the THz field is achieved by adjusting the relative phase between the fundamental pulse and the second-harmonic pulse.To eliminate the total internal reflection of THz waves at the water-air interface of a water film, a water line produced by a syringe needle was used to emit THz waves. As expected, more THz radiation can be coupled out and detected. THz wave generation from other liquids were also tested.

THz generation by optical rectification of intense near-infrared pulses in organic crystal BNA

Generation of terahertz radiation by optical rectification of intense near-infrared laser pulses in N-benzyl-2-methyl-4-nitroaniline (BNA) is investigated in detail by carrying out a complete characterization of the terahertz radiation. We studied the scaling of THz yield with pump pulse repetition rate and fluence which enabled us to predict the optimal operating conditions for BNA crystals at room temperature for 800 nm pump wavelength. Furthermore, recording the transmitted laser spectrum allowed us to calculate the nonlinear refractive index of BNA at 800 nm.

Terahertz photoconductive waveguide emitter with excitation by a tilted optical pulse front

We explore the tilted-pulse-front excitation technique to control the superradiant emission of terahertz (THz) pulses from large-area photonconductive semiconductor switches. Two cases are studied. First, a photoconductive antenna emitting into free space, where the propagation direction of the optically generated THz beam is controlled by the choice of the tilt angle of the pump pulse front. Second, a THz waveguide structure with an integrated photoconductive window for the generation of THz radiation, where the injection of the THz radiation into a waveguide mode is optimized by the pulse front tilt. By providing long interaction lengths, such a waveguide-based optical-pump/THz-probe set-up may provide a new platform for the study of diverse short-lived optically induced excitations.

Generation of 0.7 mJ multicycle 15 THz radiation by phase-matched optical rectification in lithium niobate

We demonstrate efficient multicycle terahertz pulse generation at 14.6 THz from large-area lithium niobate crystals by using high-energy (up to 2 J) femtosecond Ti:sapphire laser pulses. Such terahertz radiation is produced by phase-matched optical rectification in lithium niobate. Experimentally, we achieve maximal terahertz energy of 0.71 mJ with conversion efficiency of ∼0.04%. Our experimental setup is simple and easily upscalable to produce multi-millijoule, multicycle terahertz radiation with proper lithium niobate crystals.

Towards Intense THz Spectroscopy on Water: Characterization of Optical Rectification by GaP, OH1, and DSTMS at OPA Wavelengths

Water is the most prominent solvent. The unique properties of water are rooted in the dynamical hydrogen-bonded network. While TeraHertz (THz) radiation can probe directly the collective molecular network, several open issues remain about the interpretation of these highly anharmonic, coupled bands. In order to address this problem, we need intense THz radiation able to drive the liquid into the nonlinear response regime. Firstly, in this study, we summarize the available brilliant THz sources and compare their emission properties. Secondly, we characterize the THz emission by Gallium Phosphide (GaP), 2-{3-(4-hydroxystyryl)-5,5-dimethylcyclohex-2-enylidene}malononitrile (OH1), and 4-N,N-dimethylamino-4'-N'-methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate (DSTMS) crystals pumped by an amplified near-infrared (NIR) laser with tunable wavelength. We found that both OH1 as well as DSTMS could convert NIR laser radiation between 1200 and 2500 nm into THz radiation with high efficiency (> 2 × 10-4), resulting in THz peak fields exceeding 0.1 MV/cm for modest pump excitation (~ mJ/cm2). DSTMS emits the broadest spectrum, covering the entire bandwidth of our detector from ca. 0.5 to ~7 THz, also at a laser wavelength of 2100 nm. Future improvements will require handling the photothermal damage of these delicate organic crystals, and increasing the THz frequency.

Classification and characterization of nonequilibrium Higgs modes in unconventional superconductors

Recent findings of new Higgs modes in unconventional superconductors require a classification and characterization of the modes allowed by nontrivial gap symmetry. Here we develop a theory for a tailored nonequilibrium quantum quench to excite all possible oscillation symmetries of a superconducting condensate. We show that both a finite momentum transfer and quench symmetry allow for an identification of the resulting Higgs oscillations. These serve as a fingerprint for the ground state gap symmetry. We provide a classification scheme of these oscillations and the quench symmetry based on group theory for the underlying lattice point group. For characterization, analytic calculations as well as full scale numeric simulations of the transient optical response resulting from an excitation by a realistic laser pulse are performed. Our classification of Higgs oscillations allows us to distinguish between different symmetries of the superconducting condensate.

The lately reported Higgs modes in unconventional superconductors require a classification and characterization allowed by nontrivial symmetry of the gap and the quench pulses. Here, the authors provide a classification scheme of Higgs oscillations with their excitation processes allowing them to distinguish between different symmetries of the superconducting condensate.

Highly enhanced terahertz conversion by two-color laser filamentation at low gas pressures

We present an experimental study on pressure-dependent terahertz generation from two-color femtosecond laser filamentation in various gases. Contrary to short-focusing geometry, we find that long filamentation yields higher terahertz energy at lower gas pressures in most gases. This counter-intuitive phenomenon occurs due to multiple peculiar properties associated with filamentation. In practice, filamentation in low-pressure argon provides a maximum laser-to-terahertz conversion efficiency of 0.1%, about 10 times higher than in atmospheric air. In addition, our pressure-dependent study reveals an anticorrelation between terahertz output energy and local plasma fluorescence brightness. This determines the absolute phase difference between two-color laser fields for maximal terahertz generation, as well as verifies the microscopic mechanism of terahertz generation in two-color laser mixing.

Simultaneous generation and compression of broadband terahertz pulses in aperiodically poled crystals

We introduce a technique to generate compressed broadband terahertz pulses based on cascaded difference-frequency generation. The approach employs a non-uniform sequence of pump pulses in aperiodically poled crystals. The pump-pulse format and poling of crystals conceived are such that the emergent terahertz pulse is already compressed. The method circumvents pump-pulse distortions that result from non-collinear approaches and the need for external compression. While capable of generating even single-cycle pulses, it is particularly efficient for the generation of pulses with few to tens-of-cycles duration. For instance, calculations accounting for cascading effects predict conversion efficiencies in the few percent range for cryogenically-cooled lithium niobate. The focused electric fields are ≫ 100 MV/m in free space.

Tilted-pulse-front excitation of strong quasistatic precursors

It was recently predicted [M. I. Bakunov, A. V. Maslov, and M. V. Tsarev, Phys. Rev. A95, 063817 (2017)10.1103/PhysRevA.95.063817] that concurrent processes of optical rectification and multiphoton absorption of an ultrashort laser pulse in an electro-optic crystal can generate a quasistatic electromagnetic precursor propagating ahead of the laser pulse. The electric and magnetic fields in the precursor can exceed the fields in the ordinary terahertz wave generated behind the laser pulse. We propose a way to enhance the precursor's magnitude tremendously, by at least two orders of magnitude, by using tilted-pulse-front excitation technique and higher orders of multiphoton absorption. In particular, we show that a pulse of 500 fs duration and 70 GW/cm² peak intensity from a Yb-doped laser amplifier can generate in a 5-mm-thick LiNbO₃ crystal a 0.5-mm-long precursor with the strengths of the electric and magnetic fields as high as 0.4 MV/cm and 0.13 T, respectively. Strong quasistatic (subterahertz) fields can be a useful tool for particle acceleration, molecular orientation, ultrafast control of magnetic order in matter, and in terahertz streaking techniques.

Coherent THz Emission Enhanced by Coherent Synchrotron Radiation Wakefield

We demonstrate that emission of coherent transition radiation by a ∼1 GeV energy-electron beam passing through an Al foil is enhanced in intensity and extended in frequency spectral range, by the energy correlation established along the beam by coherent synchrotron radiation wakefield, in the presence of a proper electron optics in the beam delivery system. Analytical and numerical models, based on experimental electron beam parameters collected at the FERMI free electron laser (FEL), predict transition radiation with two intensity peaks at ∼0.3 THz and ∼1.5 THz, and extending up to 8.5 THz with intensity above 20 dB w.r.t. the main peak. Up to 80-µJ pulse energy integrated over the full bandwidth is expected at the source, and in agreement with experimental pulse energy measurements. By virtue of its implementation in an FEL beam dump line, this work promises dissemination of user-oriented multi-THz beamlines parasitic and self-synchronized to EUV and x-ray FELs.

Resonant plasma excitation by single-cycle THz pulses

In this paper, an alternative perspective for the generation of millimetric high-gradient resonant plasma waves is discussed. This method is based on the plasma-wave excitation by energetic single-cycle THz pulses whose temporal length is comparable to the plasma wavelength. The excitation regime discussed in this paper is the quasi-nonlinear regime that can be achieved when the normalized vector potential of the driving THz pulse is on the order of unity. To investigate this regime and determine the strength of the excited electric fields, a Particle-In-Cell (PIC) code has been used. It has been found that by exploiting THz pulses with characteristics currently available in laboratory, longitudinal electron plasma waves with electric gradients up to hundreds MV/m can be obtained. The mm-size nature of the resonant plasma wave can be of great utility for an acceleration scheme in which high-brightness electron bunches are injected into the wave to undergo a strong acceleration. The long-size nature of the acceleration bucket with respect to the short length of the electron bunches can be handled in a more robust manner in comparison with the case when micrometric waves are employed.

Perspective: THz-driven nuclear dynamics from solids to molecules

Recent years have seen dramatic developments in the technology of intense pulsed light sources in the THz frequency range. Since many dipole-active excitations in solids and molecules also lie in this range, there is now a tremendous potential to use these light sources to study linear and nonlinear dynamics in such systems. While several experimental investigations of THz-driven dynamics in solid-state systems have demonstrated a variety of interesting linear and nonlinear phenomena, comparatively few efforts have been made to drive analogous dynamics in molecular systems. In the present Perspective article, we discuss the similarities and differences between THz-driven dynamics in solid-state and molecular systems on both conceptual and practical levels. We also discuss the experimental parameters needed for these types of experiments and thereby provide design criteria for a further development of this new research branch. Finally, we present a few recent examples to illustrate the rich physics that may be learned from nonlinear THz excitations of phonons in solids as well as inter-molecular vibrations in liquid and gas-phase systems.

Highly efficient broadband terahertz generation from ultrashort laser filamentation in liquids

Generation and application of energetic, broadband terahertz pulses (bandwidth ~0.1–50 THz) is an active and contemporary area of research. The main thrust is toward the development of efficient sources with minimum complexities—a true table-top setup. In this work, we demonstrate the generation of terahertz radiation via ultrashort pulse induced filamentation in liquids—a counterintuitive observation due to their large absorption coefficient in the terahertz regime. The generated terahertz energy is more than an order of magnitude higher than that obtained from the two-color filamentation of air (the most standard table-top technique). Such high terahertz energies would generate electric fields of the order of MV cm^-1, which opens the doors for various nonlinear terahertz spectroscopic applications. The counterintuitive phenomenon has been explained via the solution of nonlinear pulse propagation equation in the liquid medium.

Developing simple and efficient table-top sources of intense terahertz radiation is an ongoing pursuit. Here, Dey et al. demonstrate broadband terahertz generation from laser filamentation in liquids with an order of magnitude higher energy than from conventional two-color filamentation in air.

Terahertz induced optical birefringence in polar and nonpolar liquids

The terahertz induced optical birefringence in liquids with polar (acetone, chloroform) and nonpolar (benzene, carbon tetrachloride) molecules has been investigated. Fast and slow responses were extracted from the experimental data and compared with previous studies of the femtosecond optical Kerr effect. Terahertz Kerr constants were found and compared with known DC and optical constants. Analysis of the results obtained showed that, in contrast to the optical excitation, the interaction of a permanent dipole moment of molecules with a THz field makes a significant contribution to the transient birefringence and Kerr constants. This conclusion fully agrees with the direct comparison of the femtosecond optical and THz Kerr effects reported by Sajadi et al. [Nat. Commun. 8, 14963 (2017)].

AXSIS: Exploring the frontiers in attosecond X-ray science, imaging and spectroscopy

X-ray crystallography is one of the main methods to determine atomic-resolution 3D images of the whole spectrum of molecules ranging from small inorganic clusters to large protein complexes consisting of hundred-thousands of atoms that constitute the macromolecular machinery of life. Life is not static, and unravelling the structure and dynamics of the most important reactions in chemistry and biology is essential to uncover their mechanism. Many of these reactions, including photosynthesis which drives our biosphere, are light induced and occur on ultrafast timescales. These have been studied with high time resolution primarily by optical spectroscopy, enabled by ultrafast laser technology, but they reduce the vast complexity of the process to a few reaction coordinates. In the AXSIS project at CFEL in Hamburg, funded by the European Research Council, we develop the new method of attosecond serial X-ray crystallography and spectroscopy, to give a full description of ultrafast processes atomically resolved in real space and on the electronic energy landscape, from co-measurement of X-ray and optical spectra, and X-ray diffraction. This technique will revolutionize our understanding of structure and function at the atomic and molecular level and thereby unravel fundamental processes in chemistry and biology like energy conversion processes. For that purpose, we develop a compact, fully coherent, THz-driven atto-second X-ray source based on coherent inverse Compton scattering off a free-electron crystal, to outrun radiation damage effects due to the necessary high X-ray irradiance required to acquire diffraction signals. This highly synergistic project starts from a completely clean slate rather than conforming to the specifications of a large free-electron laser (FEL) user facility, to optimize the entire instrumentation towards fundamental measurements of the mechanism of light absorption and excitation energy transfer. A multidisciplinary team formed by laser-, accelerator,- X-ray scientists as well as spectroscopists and biochemists optimizes X-ray pulse parameters, in tandem with sample delivery, crystal size, and advanced X-ray detectors. Ultimately, the new capability, attosecond serial X-ray crystallography and spectroscopy, will be applied to one of the most important problems in structural biology, which is to elucidate the dynamics of light reactions, electron transfer and protein structure in photosynthesis.

Generation of 0.19-mJ THz pulses in LiNbO3 driven by 800-nm femtosecond laser

A cylindrical lens telescope tilted-pulse-front pumping scheme was proposed for high energy terahertz (THz) pulse generation. This scheme allows higher pump energy to be used with lower saturation effects under high pump fluence, and higher THz generation efficiency was achieved within large range of pump energy. The optimum pump pulse duration and crystal cooling temperature for THz generation in LiNbO₃ (LN) crystal were also researched systematically. Excited by 800-nm laser, up to 0.19 mJ THz pulse energy and 0.27% conversion efficiency was demonstrated under 800-nm 400-fs laser excitation with ~100-mJ pulse energy and 150-K LN cooling temperature.

Ultra-high dynamic range electro-optic sampling for detecting millimeter and sub-millimeter radiation

Time-domain spectroscopy using coherent millimeter and sub-millimeter radiation (also known as terahertz radiation) is rapidly expanding its application, owing greatly to the remarkable advances in generating and detecting such radiation. However, many current techniques for coherent terahertz detection have limited dynamic range, thus making it difficult to perform some basic experiments that need to directly compare strong and weak terahertz signals. Here, we propose and demonstrate a novel technique based on cross-polarized spectral-domain interferometry to achieve ultra-high dynamic range electro-optic sampling measurement of coherent millimeter and sub-millimeter radiation. In our scheme, we exploit the birefringence in a single-mode polarization maintaining fiber in order to measure the phase change induced by the electric field of terahertz radiation in the detection crystal. With our new technique, we have achieved a dynamic range of 7 × 10⁶, which is 4 orders of magnitude higher than conventional electro-optic sampling techniques, while maintaining comparable signal-to-noise ratio. The present technique is foreseen to have great impact on experiments such as linear terahertz spectroscopy of optically thick materials (such as aqueous samples) and nonlinear terahertz spectroscopy, where the higher dynamic range is crucial for proper interpretation of experimentally obtained results.

Optimization of terahertz generation from LiNbO3 under intense laser excitation with the effect of three-photon absorption

We proposed a three-dimensional model to simulate terahertz generation from LiNbO₃ crystal under intense laser excition (up to ~50 mJ/cm²). The impact of three-photon absorption, which leads to free carrier generation and free carrier saturation (when pump fluence above ~10 mJ/cm²) on terahertz generation was investigated. And further with this model, we stated the optimized experimental conditions (incident postion, beam diameter, and pulse duration, etc) for maximum generation efficiency in commonly-used tilted-pulse-front scheme. Red shift of spectrum, spatial distribution "splitting" effects of emitted THz beam, and primilary experimental verification under intense laser excitation are given.

Terahertz-field-induced optical birefringence in common window and substrate materials

We apply intense terahertz (THz) electromagnetic pulses with field strengths exceeding 2 MV cm(-1) at ~1 THz to window and substrate materials commonly used in THz spectroscopy and determine the induced optical birefringence. Materials studied are diamond, sapphire, magnesium oxide (MgO), polymethylpentene (TPX), low-density polyethylene (LDPE), silicon nitride membrane (SiN) and crystalline quartz. We observe a Kerr-effect-type transient birefringence in all samples, except in quartz and Si, where, respectively, a linear electrooptic signal and a response beyond the perturbative regime are found. We extract the nonlinear refractive indices and the electrooptic coefficient (in the case of quartz) of these materials and discuss implications for their use as windows or substrates in THz pump-optical probe spectroscopy.

Intense, carrier frequency and bandwidth tunable quasi single-cycle pulses from an organic emitter covering the Terahertz frequency gap

In Terahertz (THz) science, one of the long-standing challenges has been the formation of spectrally dense, single-cycle pulses with tunable duration and spectrum across the frequency range of 0.1–15 THz (THz gap). This frequency band, lying between the electronically and optically accessible spectra hosts important molecular fingerprints and collective modes which cannot be fully controlled by present strong-field THz sources. We present a method that provides powerful single-cycle THz pulses in the THz gap with a stable absolute phase whose duration can be continuously selected between 68 fs and 1100 fs. The loss-free and chirp-free technique is based on optical rectification of a wavelength-tunable pump pulse in the organic emitter HMQ-TMS that allows for tuning of the spectral bandwidth from 1 to more than 7 octaves over the entire THz gap. The presented source tunability of the temporal carrier frequency and spectrum expands the scope of spectrally dense THz sources to time-resolved nonlinear THz spectroscopy in the entire THz gap. This opens new opportunities towards ultrafast coherent control over matter and light.

Yb:YAG thin-disk chirped pulse amplification laser system for intense terahertz pulse generation

We have developed a 1 kHz repetition picosecond laser system dedicated for intense terahertz (THz) pulse generation. The system comprises a chirped pulse amplification laser equipped with a Yb:YAG thin-disk amplifier. At room temperature, the Yb:YAG thin-disk regenerative amplifier provides pulses having energy of over 10 mJ and spectral bandwidth of 1.2 nm. The pulse duration achieved after passage through a diffraction grating pair compressor was 1.3 ps. By employing this picosecond laser as a pump source, THz pulses having a peak frequency of 0.3 THz and 4 µJ of energy were generated by means of optical rectification in an Mg-doped LiNbO₃ crystal.

High efficiency THz generation in DSTMS, DAST and OH1 pumped by Cr:forsterite laser

We investigated Terahertz generation in organic crystals DSTMS, DAST and OH1 directly pumped by a Cr:forsterite laser at central wavelength of 1.25 μm. This pump laser technology provides a laser-to-THz energy conversion efficiency higher than 3 percent. Phase-matching is demonstrated over a broad 0.1-8 THz frequency range. In our simple setup we achieved hundred μJ pulses in tight focus resulting in electric and magnetic field larger than 10 MV/cm and 3 Tesla.

Theory of terahertz generation by optical rectification using tilted-pulse-fronts

A model for terahertz (THz) generation by optical rectification using tilted-pulse-fronts is developed. It simultaneously accounts for in two spatial dimensions (2-D) (i) the spatio-temporal variations of the optical pump pulse imparted by the tilted-pulse-front setup, (ii) the nonlinear coupled interaction of THz and optical radiation, (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 its spectral broadening due to THz generation. In the presence of this large frequency and transverse-momentum (or angular) spread, group velocity dispersion causes a spatio-temporal break-up of the optical pump pulse which inhibits further THz generation. The implications of these effects on energy scaling and optimization of optical-to-THz conversion efficiency are discussed. This suggests the use of optical pump pulses with elliptical beam profiles for large optical pump energies. Furthermore, it is seen that optimization of the setup is highly dependent on optical pump conditions. Trade-offs in optimizing the optical-to-THz conversion efficiency on the spatial and spectral properties of THz radiation are discussed to guide the development of such sources.

Demonstration of a low-frequency three-dimensional terahertz bullet with extreme brightness

The brightness of a light source defines its applicability to nonlinear phenomena in science. Bright low-frequency terahertz (<5 THz) radiation confined to a diffraction-limited spot size is a present hurdle because of the broad bandwidth and long wavelengths associated with terahertz (THz) pulses and because of the lack of THz wavefront correctors. Here using a present-technology system, we employ a wavefront manipulation concept with focusing optimization leading to spatio-temporal confinement of THz energy at its physical limits to the least possible three-dimensional light bullet volume of wavelength-cubic. Our scheme relies on finding the optimum settings of pump wavefront curvature and post generation beam divergence. This leads to a regime of extremely bright PW m(-2) level THz radiation with peak fields up to 8.3 GV m(-1) and 27.7 T surpassing by far any other system. The presented results are foreseen to have a great impact on nonlinear THz applications in different science disciplines.

Generation of 0.9-mJ THz pulses in DSTMS pumped by a Cr:Mg₂SiO₄ laser

We report on high-field terahertz transients with 0.9-mJ pulse energy produced in a 400  mm² partitioned organic crystal by optical rectification of a 30-mJ laser pulse centered at 1.25 μm wavelength. The phase-locked single-cycle terahertz pulses cover the hard-to-access low-frequency range between 0.1 and 5 THz and carry peak fields of more than 42 MV/cm and 14 Tesla with the potential to reach over 80 MV/cm by choosing appropriate focusing optics. The scheme based on a Cr:Mg₂SiO₄ laser offers a high conversion efficiency of 3% using uncooled organic crystal. The collimated pump laser configuration provides excellent terahertz focusing conditions.

Terahertz generation in lithium niobate driven by Ti:sapphire laser pulses and its limitations

We experimentally investigate the limits of 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/cm(2) for this pulse duration. We experimentally identify two main limitations for the scaling of optical-to-THz conversion efficiencies: (i) the large spectral broadening of the optical pump spectrum in combination with large angular dispersion of the tilted pulse front and (ii) free-carrier absorption of THz radiation due to multi-photon absorption of the 800 nm radiation.

Efficient generation of THz pulses with 0.4 mJ energy

Efficient generation of THz pulses with high energy was demonstrated by optical rectification of 785-fs laser pulses in lithium niobate using tilted-pulse-front pumping. The enhancement of conversion efficiency by a factor of 2.4 to 2.7 was demonstrated up to 186 μJ THz energy by cryogenic cooling of the generating crystal and using up to 18.5 mJ/cm2 pump fluence. Generation of THz pulses with more than 0.4 mJ energy and 0.77% efficiency was demonstrated even at room temperature by increasing the pump fluence to 186 mJ/cm2. The spectral peak is at about 0.2 THz, suitable for charged-particle manipulation.

Limitations to THz generation by optical rectification using tilted pulse fronts

Terahertz (THz) generation by optical rectification (OR) using tilted-pulse-fronts is studied. A one-dimensional (1-D) model which simultaneously accounts 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 is 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 this large spectral broadening, the large angular dispersion associated with tilted-pulse-fronts which is ~15-times larger than material dispersion, accentuates phase mismatch and degrades THz generation. Consequently, this cascading effect in conjunction with angular dispersion is shown to be the strongest limitation to THz generation in lithium niobate for pumping at 1 µm. It is seen that the exclusion of these cascading effects in modeling OR, leads to a significant overestimation of the optical-to-THz conversion efficiency. The results are verified with calculations based on a 2-D spatial model. The simulation results are supported by experiments.

Effect of extreme pump pulse reshaping on intense terahertz emission in lithium niobate at multimilliJoule pump energies

We report on terahertz (THz) generation via optical rectification in a room-temperature lithium niobate crystal under variable pump pulse durations, ranging from 100 to 300 fs, at 800 nm center wavelength. The efficiency for the process is predicted to have an order of magnitude increase when longer duration Fourier-limited pump pulses are used. Our results confirm this increase in efficiency, and we report a record 800 nm pump energy conversion efficiency of 0.35% with a saturation at >240  fs pulse duration. While promising, our findings show a series of key problems that must be overcome before the theoretical limit can be achieved, including the influence of the pump bandwidth broadening due to the cascaded nonlinearity taking place within the crystal.

Pump pulse width and temperature effects in lithium niobate for efficient THz generation

We present a study on THz generation in lithium niobate pumped by a powerful and versatile Yb:CaF(2) laser. The unique laser system delivers transform-limited pulses of variable duration (0.38-0.65 ps) with pulse energies up to 15 mJ and center wavelength of 1030 nm. From previous theoretical investigations, it is expected that such laser parameters are ideally suited for efficient THz generation. Here, we present experimental results on both the conversion efficiency and the THz spectral shape for variable pump pulse durations and for different crystal temperatures, down to 25 K. We experimentally verify the optimum pump parameters for the most efficient and broadband THz generation.

High-energy terahertz pulses from organic crystals: DAST and DSTMS pumped at Ti:sapphire wavelength

High-energy terahertz pulses are produced by optical rectification (OR) in organic crystals 4-dimethylamino-N-methyl-4-stilbazolium tosylate (DAST) and 4-N, N-dimethylamino-4'-N'-methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate (DSTMS) by a Ti:sapphire amplifier system with 0.8 μm central wavelength. The simple scheme provides broadband spectra between 1 and 5 THz, when pumped by a collimated 60 fs near-IR pump pulse, and it is scalable in energy. Fluence-dependent conversion efficiency and damage threshold are reported, as well as optimized OR at visible wavelengths.