Efficient terahertz generation by optical rectification at 1035 nm

Three-photon and four-photon absorption in lithium niobate measured by the Z-scan technique

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.

Highly Efficient Spintronic Terahertz Emitter Utilizing a Large Spin Hall Conductivity of Type-II Dirac Semimetal PtTe2

The remarkable spin-charge interconversion ability of transition metal dichalcogenides (TMDs) makes them promising candidates for spintronic applications. Nevertheless, their potential as spintronic terahertz (THz) emitters (STEs) remains constrained mainly due to their sizable resistivity and low spin Hall conductivity (SHC), which consequently result in modest THz emission. In this work, the TMD PtTe2, a type-II Dirac semimetal is effectively utilized to develop efficient STEs. This high efficiency primarily results from the large SHC of PtTe2, stemming from its low resistivity and significant spin-to-charge conversion efficiency, attributed to surface states and the local Rashba effect in addition to the inverse spin Hall effect. Remarkably, the peak THz emission from PtTe2/Co-STE exceeds that of Pt/Co-STE by ∼15% and is nearly double that of a similarly thick Pt/Co-STE. The efficient THz emission in the PtTe2/Co heterostructure opens new possibilities for utilizing the semimetal TMDs for developing THz emitters.

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.

High-field THz source centered at 2.6 THz

We demonstrate a table-top high-field terahertz (THz) source based on optical rectification of a collimated near-infrared pulse in gallium phosphide (GaP) to produce peak fields above 300 kV/cm with a spectrum centered at 2.6 THz. The experimental configuration, based on tilted-pulse-front phase matching, is implemented with a phase grating etched directly onto the front surface of the GaP crystal. Although the THz generation efficiency starts showing a saturation onset as the near-infrared pulse energy reaches 0.57 mJ, we can expect our configuration to yield THz peak fields up to 866 kV/cm when a 5 mJ generation NIR pulse is used. This work paves the way towards broadband, high-field THz sources able to access a new class of THz coherent control and nonlinear phenomena driven at frequencies above 2 THz.

Increasing bandwidth of Cherenkov-type terahertz emitters by free carrier generation

We found experimentally that Cherenkov-type terahertz radiation produced by optical rectification of ultrashort laser pulses in LiNbO3 can experience strong spectral broadening in the regime of multiphoton laser absorption. The broadening is attributed to the terahertz emission from a surge current of the optically generated carriers. The effect can be used to improve the bandwidth of optical-to-terahertz converters based on optical rectification.

Optimized terahertz pulse generation with chirped pump pulses from an echelon-based tilted-pulse-front (TPF) scheme

We successfully demonstrated the generation of single-cycle terahertz (THz) pulses through tilted-pulse-front (TPF) pumping using a reflective echelon in a lithium niobate crystal. By optimizing the pump pulse duration using a chirp, we achieved a maximum pump-to-THz conversion efficiency of 0.39%. However, we observed that the saturation behavior began at a relatively low pump energy (0.37 mJ), corresponding to a pump intensity of 22 GW/cm2. To elucidate this behavior, we measured the near- and far-field THz beam profiles and found variations in their beam characteristics, such as the beam size, location, and divergence angle in the plane of the tilted pulse direction, with the pump energy (intensity). This nonlinear behavior is attributed to the reduced effective interaction length, which ultimately leads to the saturation of THz generation. The results obtained from our study suggest that it is feasible to develop an effective THz source using echelon-based TPF pumping while also considering the impact of nonlinear saturation effects.

Enhancement of THz generation in LiNbO3 waveguides via multi-bounce velocity matching

To realize the full promise of terahertz polaritonics (waveguide-based terahertz field generation, interaction, and readout) as a viable spectroscopy platform, much stronger terahertz fields are needed to enable nonlinear and even robust linear terahertz measurements. We use a novel geometric approach in which the optical pump is totally internally reflected to increase the distance over which optical rectification occurs. Velocity matching is achieved by tuning the angle of internal reflection. By doing this, we are able to enhance terahertz spectral amplitude by over 10x compared to conventional single-pass terahertz generation. An analysis of the depletion mechanisms reveals that 3-photon absorption and divergence of the pump beam are the primary limiters of further enhancement. This level of enhancement is promising for enabling routine spectroscopic measurements in an integrated fashion and is made more encouraging by the prospect of further enhancement by using longer pump wavelengths.

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.

Time-frequency analysis of two-photon absorption effect during optical rectification in a ZnTe crystal pumped at 1.024 µm

Optical rectification in nonlinear crystals is a well-established method for generating terahertz (THz) waves from ultra-short optical pulses. To achieve high conversion efficiency, the phase-matching conditions between the pump pulse and the generated THz wave within the nonlinear medium must be satisfied. For a ytterbium laser operating at 1.024 µm, a severe phase mismatch occurs in the zinc telluride (ZnTe) crystal, preventing the efficient generation of broadband THz pulses. Using time-frequency analysis, we show that the ultrafast charge carrier dynamic, mainly induced by two-photon absorption, generated in the nonlinear medium during optical rectification processes in ZnTe, plays a crucial role in the filtering of the out-of-phase components of the THz signal, thus enabling the recovery of broadband THz pulse generations.

Milliwatt average power, MHz-repetition rate, broadband THz generation in organic crystal BNA with diamond substrate

We demonstrate a 13.3 MHz repetition rate, broadband THz source with milliwatt- average power, obtained by collinear optical rectification of a high-power Yb-doped thin-disk laser in the organic crystal BNA (N-benzyl-2-methyl-4-nitroaniline). Our source reaches a maximum THz average power of 0.95 mW with an optical-to-THz efficiency of 4×10^-4 and a spectral bandwidth spanning up to 6 THz at -50 dB, driven by 2.4 W average power (after an optical chopper with duty cycle of 10%), 85 fs-pulses. This high average power excitation was possible without damaging the crystal by using a diamond-heatsinked crystal with significantly improved thermal properties. To the best of our knowledge, this result represents the highest THz average power reported so far using the commercially available organic crystal BNA, showing the potential of these crystals for high average power, high repetition rate femtosecond excitation. The combination of high power, high dynamic range, high repetition rate and broadband spectrum makes the demonstrated THz source highly attractive to improve various time-domain spectroscopy applications. Furthermore, we present a first exploration of the thermal behavior of BNA in this excitation regime, showing that thermal effects are the main limitation in average power scaling in these crystals.

A Narrowband Spintronic Terahertz Emitter Based on Magnetoelastic Heterostructures

Narrowband terahertz (THz) radiation is crucial for high-resolution spectral identification, but a narrowband THz source driven by a femtosecond (fs) laser has remained scarce. Here, it is computationally predicted that a metal/dielectric/magnetoelastic heterostructure enables converting a fs laser pulse into a multicycle THz pulse with a narrow linewidth down to ∼1.5 GHz, which is in contrast to the single-cycle, broadband THz pulse from the existing fs-laser-excited emitters. It is shown that such narrowband THz pulse originates from the excitation and long-distance transport of THz spin waves in the magnetoelastic film, which can be enabled by a short strain pulse obtained from fs laser irradiation of the metal film when the thicknesses of the metal and magnetoelastic films both fall into a specific range. These results therefore reveal an approach to achieving optical generation of narrowband THz pulse based on heterostructure design, which also has implications in the design of THz magnonic devices.

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.

Analysis of THz generation using the tilted-pulse-front geometry in the limit of small pulse energies and beam sizes

Optical rectification in lithium niobate using the tilted-pulse-front geometry is one of the most commonly used techniques for efficient generation of energetic single-cycle THz pulses and the details of this generation scheme are well understood for high pulse energy driving lasers, such as mJ-class, kHz-repetition rate Ti:Sa amplifier systems. However, as modern Yb-based laser systems with ever increasing repetition rate become available, other excitation regimes become relevant. In particular, the use of more moderate pulse energies (in the few µJ to multi-10 µJ regime), available nowadays by laser systems with MHz repetition rates, have never been thoroughly explored. As increasing the repetition rate of THz sources for spectroscopy becomes more relevant in the community, we present a thorough numerical analysis of this regime using a 2+1-D numerical model. Our work allows us to confirm experimental trends observed in this unusual excitation regime and shows that the conversion efficiency is naturally limited by the small pump beam sizes as a consequence of spatial walk-off between the pump and THz beams. Based on our findings, we discuss strategies to overcome the current limitations, which will pave the way for powerful THz sources approaching the watt level with multi-MHz repetition rates.

Variable Repetition Rate THz Source for Ultrafast Scanning Tunneling Microscopy

Broadband THz pulses enable ultrafast electronic transport experiments on the nanoscale by coupling THz electric fields into the devices with antennas, asperities, or scanning probe tips. Here, we design a versatile THz source optimized for driving the highly resistive tunnel junction of a scanning tunneling microscope. The source uses optical rectification in lithium niobate to generate arbitrary THz pulse trains with freely adjustable repetition rates between 0.5 and 41 MHz. These induce subpicosecond voltage transients in the tunnel junction with peak amplitudes between 0.1 and 12 V, achieving a conversion efficiency of 0.4 V/(kV/cm) from far-field THz peak electric field strength to peak junction voltage in the STM. Tunnel currents in the quantum limit of less than one electron per THz pulse are readily detected at multi-MHz repetition rates. The ability to tune between high pulse energy and high signal fidelity makes this THz source design effective for exploration of ultrafast and atomic-scale electron dynamics.

Broadband terahertz wave generation from an epsilon-near-zero material

Broadband light sources emitting in the terahertz spectral range are highly desired for applications such as noninvasive imaging and spectroscopy. Conventionally, THz pulses are generated by optical rectification in bulk nonlinear crystals with millimetre thickness, with the bandwidth limited by the phase-matching condition. Here we demonstrate broadband THz emission via surface optical rectification from a simple, commercially available 19 nm-thick indium tin oxide (ITO) thin film. We show an enhancement of the generated THz signal when the pump laser is tuned around the epsilon-near-zero (ENZ) region of ITO due to the pump laser field enhancement associated with the ENZ effect. The bandwidth of the THz signal generated from the ITO film can be over 3 THz, unrestricted by the phase-matching condition. This work offers a new possibility for broadband THz generation in a subwavelength thin film made of an ENZ material, with emerging physics not found in existing nonlinear crystals.

Thermal lensing effects and nonlinear refractive indices of fluoride crystals induced by high-power ultrafast lasers

Thermo-optical and nonlinear property characterization of refractive optical components is essential for endoscopic instrumentation that utilizes high-power, high-repetition-rate ultrafast lasers. For example, ytterbium-doped fiber lasers are well suited for ultrafast laser microsurgery applications; however, the thermo-optical responses of many common lens substrates are not well understood at 1035 nm wavelength. Using a z-scan technique, we first measured the nonlinear refractive indices of CaF₂, MgF₂, and BaF₂ at 1035 nm and found values that match well with those from the literature at 1064 nm. To elucidate effects of thermal lensing, we performed z-scans at multiple laser repetition rates and multiple average powers. The results showed negligible thermal effects up to an average power of 1 W and at 10 W material-specific thermal lensing significantly altered z-scan measurements. Using a 2D temperature model, we could determine the source of the observed thermal lensing effects. Linear absorption was determined as the main source of heating in these crystals. On the other hand, inclusion of nonlinear absorption as an additional heat source in the simulations showed that thermal lensing in borosilicate glass was strongly influenced by nonlinear absorption. This method can potentially provide a sensitive method to measure small nonlinear absorption coefficients of transparent optical materials. These results can guide design of miniaturized optical systems for ultrafast laser surgery and deep-tissue imaging probes.

Measurement of four-photon absorption in GaP and ZnTe semiconductors

Intensity-dependent effective four-photon absorption (4PA) coefficients in GaP and ZnTe semiconductors were measured by the z-scan method using pump pulses of 1.75 µm wavelength, 135 fs duration, and up to 500 GWcm^-2 intensity. A nonlinear pulse propagation model, including linear dispersion and 4PA was used to obtain the 4PA coefficients from measurements. The intensity-dependent effective 4PA coefficients vary from 2.6 × 10^-4 to 65 × 10^-4 cm⁵GW^-3 in GaP, and from 3.5 × 10^-4 to 9.1 × 10^-4 cm⁵GW^-3 in ZnTe. The anisotropy in 4PA was shown in GaP. The knowledge of 4PA coefficients is important for the design of semiconductor photonics devices.

Iris-assisted terahertz field-induced second-harmonic generation in air

Terahertz field-induced second-harmonic generation (TFISH) is a technique for optical detection of broadband THz fields. We show that by placing an iris at the interaction volume of the THz and optical fields, the TFISH signal increases by several tenfold in atmospheric air. The iris-assisted TFISH amplification is characterized at varying air pressures and probe intensities and provides an elegant platform for studying nonlinear phase matching in the gas phase.

Milliwatt-class broadband THz source driven by a 112 W, sub-100 fs thin-disk laser

We demonstrate a high repetition-rate, single-cycle THz source with a maximum average power of 1.35 mW, operating at a center frequency of 2 THz. This result was obtained by optical rectification (OR) in GaP using an amplifier-free, nonlinearly compressed modelocked thin-disk oscillator based on Yb:YAG, delivering 8.4 µJ pulses with 88 fs duration at a repetition rate of 13.4 MHz, resulting in driving pulses for OR with 112 W average power and 80 MW peak power. To the best of our knowledge, our result represents the highest average power so far achieved with OR in GaP. The demonstrated performance is very attractive for improving current linear THz time-domain spectroscopy experiments, which are currently restricted by low signal-to-noise ratio and long measurement times.

Terahertz-induced cascaded interactions between spectra offset by large frequencies

We explore the dynamics of a system where input spectra in the optical domain with very disparate center frequencies are strongly coupled via highly phase-matched, cascaded second-order nonlinear processes driven by terahertz radiation. The only requirement is that one of the input spectra contain sufficient bandwidth to generate the phase-matched terahertz-frequency driver. The frequency separation between the input spectra (or pump and seed spectra) can be more than ten times larger than the phase-matched terahertz frequency. This is in contrast to our previous work on cascaded parametric amplification, where the frequency separation between the pump and seed is required to be equal to the phase-matched terahertz frequency. A practical application of such a system where the cascading of a narrowband pump line centered at 1064 nm induced by a group of weaker seed lines centered about 1030 nm and separated by the phase-matched terahertz frequency is introduced. This approach is predicted to generate terahertz radiation with percent-level conversion efficiencies and millijoule-level pulse energies in cryogenically-cooled periodically poled lithium niobate. A model that solves for the nonlinear coupled interaction of terahertz and optical waves is employed. The calculations account for second and third-order nonlinearities, dispersion in the optical and terahertz domains as well as terahertz absorption. Ramifications of pulse formats on laser-induced damage are estimated by tracking the generated free-electron density. Strategies to mitigate laser-induced damage are outlined.

Terahertz generation by optical rectification in chalcopyrite crystals ZnGeP2, CdGeP2 and CdSiP2

Optical rectification of near-infrared laser pulses generates broadband terahertz radiation in chalcopyrite crystals CdGeP₂, ZnGeP₂ and CdSiP₂. The emission is characterized using linear-polarized excitation from 0.8 eV to 1.55 eV (1550 nm - 800 nm). All three crystals are (110)-cut and polished to 0.5 mm, thinner than the coherence length across most of the excitation photon energy range, such that they all produce a bandwidth ~2.5 THz when excited with ~100 fs pulses. It is found that CdGeP₂ produced the strongest emission at telecoms wavelengths, while CdSiP₂ is generally the strongest source. Pump-intensity dependence provides the nonlinear coefficients for each crystal.

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.

Optical rectification of a 100 W average power mode-locked thin-disk oscillator

We demonstrate terahertz (THz) generation at megahertz repetition rate by optical rectification in GaP crystals, using excitation average power levels exceeding 100 W. The laser source is a state-of-the-art diode-pumped Yb:YAG SESAM-mode-locked thin-disk laser, capable of generating 580 fs pulses at an average power up to 120 W and a repetition rate of 13.4 MHz directly from a one-box oscillator, without the need for any extra amplification stages. In this first demonstration, we measure a maximum THz average power of 78 μW at a central frequency of 0.8 THz. Our results show that optical rectification of state-of-the-art high average power ultrafast sources in nonlinear crystals is within reach and paves the way toward high average power, ultrafast laser pumped THz sources.

Efficient terahertz generation in highly nonlinear organic crystal HMB-TMS

We report on generation of strong and broadband terahertz (THz) pulses via collinearly phase-matched optical rectification of near-infrared femtosecond pulses in the organic nonlinear optical HMB-TMS (2-(4-hydroxy-3-methoxystyryl)-3-methylbenzo[d]thiazol-3-ium 2,4,6-trimethylbenzenesulfonate) single crystals which exhibit optimal molecular orientation and large macroscopic optical nonlinearity for efficient THz wave generation. Single-cycle THz pulses with a peak electric field strength of 0.66 MV/cm and a bandwidth from 0.1 to 5.4 THz are achieved from an HMB-TMS crystal with only a 2-mm clear aperture pumped by 1350 nm pulses at moderate fluences. The generated THz energy is about 1 µJ and the corresponding pump-to-THz energy conversion efficiency reaches 0.23%.

High efficiency terahertz generation in a multi-stage system

We describe a robust system for laser-driven narrowband terahertz generation with high conversion efficiency in periodically poled Lithium Niobate (PPLN). In the multi-stage terahertz generation system, the pump pulse is recycled after each PPLN stage for further terahertz generation. By out-coupling the terahertz radiation generated in each stage, extra absorption is circumvented and effective interaction length is increased. The separation of the terahertz and optical pulses at each stage is accomplished by an appropriately designed out-coupler. To evaluate the proposed architecture, the governing 2-D coupled wave equations in a cylindrically symmetric geometry are numerically solved using the finite difference method. Compared to the 1-D calculation which cannot capture the self-focusing and diffraction effects, our 2-D numerical method captures the effects of difference frequency generation, self-phase modulation, self-focusing, beam diffraction, dispersion and terahertz absorption. We found that the terahertz generation efficiency can be greatly enhanced by compensating the dispersion of the pump pulse after each stage. With a two-stage system, we predict the generation of a 17.6 mJ terahertz pulse with total conversion efficiency η_total = 1.6% at 0.3 THz using a 1.1 J pump laser with a two-lines spectrum centered at 1 μm. The generation efficiency of each stage is above 0.8% with the out-coupling efficiencies above 93.0%.

Highly efficient generation of 0.2 mJ terahertz pulses in lithium niobate at room temperature with sub-50 fs chirped Ti:sapphire laser pulses

We demonstrate generation of 0.2 mJ terahertz (THz) pulses in lithium niobate driven by Ti:sapphire laser pulses at room temperature. Employing tilted pulse front technique, the 800 nm-to-THz energy conversion efficiency has been optimized to 0.3% through chirping the sub-50 fs pump laser pulses to overcome multi-photon absorption and to extend effective interaction length for phase matching. Our approach paves the way for mJ-level THz generation via optical rectification using existing Ti:sapphire laser systems which can deliver Joule-level pulse energy with sub-50 fs pulse duration.

Generation of high-field terahertz pulses in an HMQ-TMS organic crystal pumped by an ytterbium laser at 1030 nm

We present the generation of high-peak-electric-field terahertz pulses via collinear optical rectification in a 2-(4-hydroxy-3-methoxystyryl)-1-methilquinolinium-2,4,6-trimethylbenzenesulfonate (HMQ-TMS) organic crystal. The crystal is pumped by an amplified ytterbium laser system, emitting 170-fs-long pulses centered at 1030 nm. A terahertz peak electric field greater than 200 kV/cm is obtained for 420 µJ of optical pump energy, with an energy conversion efficiency of 0.26% - about two orders of magnitude higher than in common inorganic crystals collinearly pumped by amplified femtosecond lasers. An open-aperture Z-scan measurement performed on an n-doped InGaAs thin film using such terahertz source shows a nonlinear increase in the terahertz transmission of about 2.2 times. Our findings demonstrate the potential of this terahertz generation scheme, based on ytterbium laser technology, as a simple and efficient alternative to the existing intense table-top terahertz sources. In particular, we show that it can be readily used to explore nonlinear effects at terahertz frequencies.

Generation of broadband terahertz pulses via optical rectification in a chalcopyrite CdSiP2 crystal

We report on the generation of broadband (0.07-6 THz) terahertz (THz) radiation via optical rectification in a ⟨110⟩  CdSiP₂ (CSP) crystal pumped by a 50 fs, 780 nm central wavelength optical pulse. By measuring the THz phase refractive index and the optical pump group refractive index, good phase matching can be achieved for a crystal thickness ≲200  μm. Due to this crystal's high second order nonlinearity and low absorption losses, it is envisioned that THz generation from CSP could be further enhanced by confining the optical pump pulse to sub-wavelength waveguides.

Benzothiazolium Single Crystals: A New Class of Nonlinear Optical Crystals with Efficient THz Wave Generation

Highly efficient nonlinear optical organic crystals are very attractive for various photonic applications including terahertz (THz) wave generation. Up to now, only two classes of ionic crystals based on either pyridinium or quinolinium with extremely large macroscopic optical nonlinearity have been developed. This study reports on a new class of organic nonlinear optical crystals introducing electron-accepting benzothiazolium, which exhibit higher electron-withdrawing strength than pyridinium and quinolinium in benchmark crystals. The benzothiazolium crystals consisting of new acentric core HMB (2-(4-hydroxy-3-methoxystyryl)-3-methylbenzo[d]thiazol-3-ium) exhibit extremely large macroscopic optical nonlinearity with optimal molecular ordering for maximizing the diagonal second-order nonlinearity. HMB-based single crystals prepared by simple cleaving method satisfy all required crystal characteristics for intense THz wave generation such as large crystal size with parallel surfaces, moderate thickness and high optical quality with large optical transparency range (580-1620 nm). Optical rectification of 35 fs pulses at the technologically very important wavelength of 800 nm in 0.26 mm thick HMB crystal leads to one order of magnitude higher THz wave generation efficiency with remarkably broader bandwidth compared to standard inorganic 0.5 mm thick ZnTe crystal. Therefore, newly developed HMB crystals introducing benzothiazolium with extremely large macroscopic optical nonlinearity are very promising materials for intense broadband THz wave generation and other nonlinear optical applications.

Pulse sequences for efficient multi-cycle terahertz generation in periodically poled lithium niobate

The use of laser pulse sequences to drive the cascaded difference frequency generation of high energy, high peak-power and multi-cycle terahertz pulses in cryogenically cooled (100 K) periodically poled Lithium Niobate is proposed and studied. Detailed simulations considering the coupled nonlinear interaction of terahertz and optical waves (or pump depletion), show that unprecedented optical-to-terahertz energy conversion efficiencies > 5%, peak electric fields of hundred(s) of mega volts/meter at terahertz pulse durations of hundred(s) of picoseconds can be achieved. The proposed methods are shown to circumvent laser induced damage limitations at Joule-level pumping by 1µm lasers to enable multi-cycle terahertz sources with pulse energies >> 10 milli-joules. Various pulse sequence formats are proposed and analyzed. Numerical calculations for periodically poled structures accounting for cascaded difference frequency generation, self-phase-modulation, cascaded second harmonic generation and laser induced damage are introduced. The physics governing terahertz generation using pulse sequences in this high conversion efficiency regime, limitations and practical considerations are discussed. It is shown that varying the poling period along the crystal length and further reduction of absorption can lead to even higher energy conversion efficiencies >>10%. In addition to numerical calculations, an analytic formulation valid for arbitrary pulse formats and closed-form expressions for important cases are presented. Parameters optimizing conversion efficiency in the 0.1-1 THz range, the corresponding peak electric fields, crystal lengths and terahertz pulse properties are furnished.

High-energy terahertz pulses from semiconductors pumped beyond the three-photon absorption edge

A new route to efficient generation of THz pulses with high-energy was demonstrated using semiconductor materials pumped at an infrared wavelength sufficiently long to suppress both two- and three-photon absorption and associated free-carrier absorption at THz frequencies. For pumping beyond the three-photon absorption edge, the THz generation efficiency for optical rectification of femtosecond laser pulses with tilted intensity front in ZnTe was shown to increase 3.5 times, as compared to pumping below the absorption edge. The four-photon absorption coefficient of ZnTe was estimated to be β₄=(4±1)×10^-5 cm⁵/GW³. THz pulses with 14 μJ energy were generated with as high as 0.7% efficiency in ZnTe pumped at 1.7 µm. It is shown that scaling the THz pulse energy to the mJ level by increasing the pump spot size and pump pulse energy is feasible.

THz generation using a reflective stair-step echelon

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 energies as high as 3.1 μJ. The highest conversion efficiency we obtained was 0.33%. In addition, we find that the echelon is easily implemented into an experimental setup for quick alignment and optimization.

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.

Tunable multi-cycle THz generation in organic crystal HMQ-TMS

We report on the generation of continuously tunable multi-cycle THz pulses with center frequencies from 0.3 to 0.8 THz in the organic nonlinear crystal, HMQ-TMS [2-(4-hydroxy-3-methoxystyryl)-1-methylquinolinium 2,-4,-6-trimethylbenzenesulfonate], by collinearly phase matched optical rectification of temporally shaped 800 nm pulses. The generation of harmonic frequency components inherent in the pulse shaper is selectively suppressed by varying the generation crystal thickness. THz pulses generated from HMQ-TMS show up to 20 times higher pulse energies compared to the benchmark inorganic THz generator ZnTe under identical conditions. The THz energy conversion efficiencies are measured to be on the order of 10(-5).

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.

800-fs, 330-μJ pulses from a 100-W regenerative Yb:YAG thin-disk amplifier at 300 kHz and THz generation in LiNbO₃

Yb:YAG thin-disk lasers offer extraordinary output power, but systems delivering femtosecond pulses at a repetition rate of hundreds of kilohertz are scarce, even though this regime is ideal for ultrafast electron diffraction, coincidence imaging, attosecond science, and terahertz (THz) spectroscopy. Here we describe a regenerative Yb:YAG amplifier based on thin-disk technology, producing 800-fs pulses at a repetition rate adjustable between 50 and 400 kHz. The key design elements are a short regenerative cavity and fast-switching Pockels cell. The average output power is 130 W before the compressor and 100 W after compression, which at 300 kHz corresponds to pulse energies of 430 and 330 μJ, respectively. This is sufficient for a wide range of nonlinear conversions and broadening/compression schemes. As a first application, we use optical rectification in LiNbO₃ to produce 30-nJ single-cycle THz pulses with 6 W pump power. The electric field exceeds 10  kV/cm at a central frequency of 0.3 THz, suitable for driving structural dynamics or controlling electron beams.

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.

Direct MD Simulations of Terahertz Absorption and 2D Spectroscopy Applied to Explosive Crystals

A direct molecular dynamics simulation of the THz spectrum of a molecular crystal is presented. A time-dependent electric field is added to a molecular dynamics simulation of a crystal slab. The absorption spectrum is composed from the energy dissipated calculated from a series of applied pulses characterized by a carrier frequency. The spectrum of crystalline cyclotrimethylenetrinitramine (RDX) and triacetone triperoxide (TATP) were simulated with the ReaxFF force field. The proposed direct method avoids the linear response and harmonic approximations. A multidimensional extension of the spectroscopy is suggested and simulated based on the nonlinear response to a single polarized pulse of radiation in the perpendicular polarization direction.

Saturation of the free carrier absorption in ZnTe crystals

This study systematically investigates the influence of free carriers on the generation of THz in ZnTe crystals, over a wide range of pumping fluences. As the pumping fluence is increased (< 6.36 mJ/cm(2)), the concentration of free carriers gradually increases and the THz output power is saturated, as clearly demonstrated by the time delay in the THz temporal waveforms, the changes in the THz spectral weight and the red-shift in the PL spectra. For high pumping fluences (> 6.36 mJ/cm(2)), spectacularly, there is a significant quadratic increase in the THz output power when the pumping fluence is increased, as well as at low pumping fluences of < 0.58 mJ/cm(2), because of the saturation of free carriers.

Terahertz vector beam generation using segmented nonlinear optical crystals with threefold rotational symmetry

We propose and demonstrate a simple method for cylindrical vector beam generation in the terahertz frequency region using optical rectification in segmented nonlinear crystals with threefold rotational symmetry. We used segmented GaP(111) plates to generate the terahertz cylindrical vector beam, and obtained clear evidence of the beam generation with a terahertz camera. By this method, a broadband terahertz cylindrical vector beam can be generated, and the radial and azimuth modes can be easily switched. We also report on the direct observation of the longitudinal electric field components at the focal point using a terahertz time-domain spectroscopy technique.

Distributed source model for the full-wave electromagnetic simulation of nonlinear terahertz generation

The process of terahertz generation through optical rectification in a nonlinear crystal is modeled using discretized equivalent current sources. The equivalent terahertz sources are distributed in the active volume and computed based on a separately modeled near-infrared pump beam. This approach can be used to define an appropriate excitation for full-wave electromagnetic numerical simulations of the generated terahertz radiation. This enables predictive modeling of the near-field interactions of the terahertz beam with micro-structured samples, e.g. in a near-field time-resolved microscopy system. The distributed source model is described in detail, and an implementation in a particular full-wave simulation tool is presented. The numerical results are then validated through a series of measurements on square apertures. The general principle can be applied to other nonlinear processes with possible implementation in any full-wave numerical electromagnetic solver.

High-efficiency terahertz pulse generation via optical rectification by suppressing stimulated Raman scattering process

We experimentally demonstrate high-efficiency terahertz pulse generation via optical rectification in LiNbO3. The spectral broadening of an excitation pulse via the stimulated Raman scattering process coincides with high-efficiency terahertz pulse generation, which enhances undesired stretching of the excitation pulse owing to the very high group velocity dispersion in LiNbO3. We avoid this by the bandwidth control of the excitation pulse and achieve the highest reported efficiency of 0.21% for energy conversion into a THz pulse.

Widely linear and non-phase-matched optical-to-terahertz conversion on GaSe:Te crystals

We demonstrate the widely linear and broadband terahertz (THz) generation on GaSe:Te crystals by femtosecond laser pulses. It was found that the dopant, Te atoms, in GaSe crystals significantly enhances the efficiency of THz generation, and its central frequency can be tuned by varying the crystal thickness through non-phase-matched optical rectification. Moreover, the wide-ranging linearity for the optical-to-THz conversion and central-frequency-tunable THz generation promise for GaSe:Te crystals to be potential materials for high-power (>1.36 μW) THz applications.

Generation of sub-mJ terahertz pulses by optical rectification

Recent theoretical calculations predicted an order-of-magnitude increase in the efficiency of terahertz pulse generation by optical rectification in lithium niobate when 500 fs long pump pulses are used, rather than the commonly used ~100 fs pulses. Even by using longer than optimal pump pulses of 1.3 ps duration, 2.5× higher THz pulse energy (125 μJ) was measured with 2.5× higher pump-to-THz energy conversion efficiency (0.25%) than reported previously with shorter pulses. These results verify the advantage of longer pump pulses and support the expectation that mJ-level THz pulses will be available by cooling the crystal and using large pumped area.

Towards generation of mJ-level ultrashort THz pulses by optical rectification

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. Calculations were carried out to optimize the output THz peak electric field strength. The results predict peak electric field strengths 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 to tens of MV/cm by focusing. Using optimal conditions together with the contact grating technique THz pulses with 100 MV/cm focused electric field strength and energies on the tens-of-mJ scale are feasible.

Room temperature continuous wave milliwatt terahertz source

We present a continuous wave terahertz source based on intracavity difference frequency generation within a dual color vertical external cavity surface emitting laser. Using a nonlinear crystal with a surface emitting phase matching scheme allows for high conversion efficiencies. Due to the tunability of the dual mode spacing, the entire spectral range of the terahertz gap can be covered. The terahertz output scales quadratically with the intracavity intensity, potentially allowing for terahertz intensities in the range of 10s of milliwatts and beyond.

Design of high-energy terahertz sources based on optical rectification

Detailed analysis of the tilted-pulse-front pumping scheme used for ultrashort THz pulse generation by optical rectification of femtosecond laser pulses is presented. It is shown that imaging errors in a pulse-front-tilting setup consisting of a grating and a lens can lead to a THz beam with strongly asymmetric intensity profile and strong divergence, thereby limiting applications. Optimized setup parameters are given to reduce such distortions. We also show that semiconductors can offer a promising alternative to LiNbO(3) in high-energy THz pulse generation when pumped at longer wavelengths. This requires tilted-pulse-front pumping, however the small tilt angles allow semiconductors to be easily used in such schemes. Semiconductors can be advantageous for generating THz pulses with high spectral intensity at higher THz frequencies, while LiNbO(3) is better suited to generate THz pulses with very large relative spectral width. By using optimized schemes the upscaling of the energy of ultrashort THz pulses is foreseen.

Broadband and high power terahertz pulse generation beyond excitation bandwidth limitation via chi2 cascaded processes in LiNbO3

We proposed a novel THz generation technique beyond the limitation of the input optical pulse width, based on phase modulation via cascaded chi((2)) process. When intense THz electric field generated by optical rectification lies in electro-optic (EO) crystal, emitted THz field gives phase modulation to the optical excitation pulse. The phase modulation causes excitation pulse narrowing and consequently gives rise to the enhancement of conversion efficiency and THz wave bandwidth broadening. We experimentally realize this generation technique with high chi((2)) EO crystal LiNbO(3) and with subpicosecond pulse from Yb-doped fiber laser. It opens new concept of THz technologies.