On the effect of third-order dispersion on phase-matched terahertz generation via interfering chirped pulses.

High-energy narrowband terahertz (THz) pulses, relevant for a plethora of applications, can be created from the interference of two chirped-pulse drive lasers. The presence of third order dispersion, an intrinsic feature of many high-energy drive lasers, however, can significantly reduce the optical-to-THz conversion efficiency and have other undesired effects. Here, we present a detailed description of the effect of third-order dispersion (TOD) in the pump pulse on the generation of THz radiation via phase-matching of broadband highly chirped pulse trains. Although the analysis is general, we focus specifically on parameters typical to a Ti:Sapphire chirped-pulse amplification laser system for quasi-phase-matching in periodically-poled lithium niobate (PPLN) in the range of THz frequencies around 0.5 THz. Our analysis provides the tools to optimize the THz generation process for applications requiring high energy and to control it to produce desired THz waveforms in a variety of scenarios.

Analysis of terahertz generation by beamlet superposition.

A theory of terahertz generation using a superposition of beamlets is developed. It is shown how such an arrangement produces a distortion-free tilted pulse front. We analytically show how a superposition of beamlets produces terahertz radiation with greater efficiency and spatial homogeneity compared to tilted pulse fronts generated by diffraction gratings. The advantages are particularly notable for large pump bandwidths and beam sizes, suggesting better performance in the presence of cascading effects and for high energy pumping. Closed-form expressions for terahertz spectra and transients in three spatial dimensions are derived. Conditions for obtaining performance better than conventional tilted pulse fronts and bounds for optimal pump parameters are furnished.

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.

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.

Analysis of terahertz generation using tilted pulse fronts.

A spatio-temporal analysis of terahertz generation by optical rectification of tilted pulse fronts is presented. Closed-form expressions of terahertz transients and spectra in two spatial dimensions are furnished in the undepleted limit. Importantly, the analysis incorporates spatio-temporal distortions of the optical pump pulse such as angular dispersion, group velocity dispersion due to angular dispersion, spatial and temporal chirp, as well as beam curvature. The influence of the radius of curvature on the tilt angle is shown. Furthermore, the impact of group velocity dispersion due to angular dispersion on terahertz frequency, conversion efficiency and peak field is revealed. In particular, the deterioration of terahertz frequency, efficiency and field at large pump bandwidths and beam sizes by group velocity dispersion due to angular dispersion is expressed analytically.

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 ηtotal = 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%.

Narrowband terahertz generation with chirped-and-delayed laser pulses in periodically poled lithium niobate.

We generate narrowband terahertz (THz) radiation in periodically poled lithium niobate (PPLN) crystals using two chirped-and-delayed driver pulses from a high-energy Ti:sapphire laser. The generated frequency is determined by the phase-matching condition in the PPLN and influences the temporal delay of the two pulses for efficient terahertz generation. We achieve internal conversion efficiencies up to 0.13% as well as a record multicycle THz energy of 40 µJ at 0.544 THz in a cryogenically cooled PPLN.

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.

Optical generation of single-cycle 10 MW peak power 100 GHz waves.

We demonstrate the generation of 100 GHz single-cycle pulses with up to 10 MW of peak power using optical rectification and broadband phase matching via the tilted pulse front (TPF) technique in lithium niobate. The optical driver is a cryogenically cooled Yb:YAG amplifier providing tens of mJ energy, ~5 ps long laser pulses. We obtain a high THz pulse energy up to 65 µJ with 31.6 MV/m peak electric field when focused close to its diffraction limit of 2.5 mm diameter. A high optical-to-THz energy conversion efficiency of 0.3% at 85 K is measured in agreement with numerical simulations. This source is of great interest for a broad range of applications, such as nonlinear THz field-matter interaction and charged particle acceleration for ultrafast electron diffraction and table-top X-ray sources.

Cascaded parametric amplification for highly efficient terahertz generation.

A highly efficient, practical approach to high-energy multi-cycle terahertz (THz) generation based on spectrally cascaded optical parametric amplification (THz-COPA) is introduced. Feasible designs are presented that enable the THz wave, initially generated by difference frequency generation between a narrowband optical pump and optical seed (0.1-10% of pump energy), to self-start a cascaded (or repeated) energy downconversion of pump photons in a single pass through a single crystal. In cryogenically cooled, periodically poled lithium niobate, unprecedented energy conversion efficiencies >8% achievable with existing pump laser technology are predicted using realistic simulations. The calculations account for cascading effects, absorption, dispersion, and laser-induced damage. Due to the simultaneous, coupled nonlinear evolution of multiple phase-matched three-wave mixing processes, THz-COPA exhibits physics distinctly different from conventional three-wave mixing parametric amplifiers. This, in turn, governs optimal phase-matching conditions, evolution of optical spectra, and limitations of the nonlinear process. Circumventing these limitations is shown to yield conversion efficiencies ≫10%.

Efficient narrowband terahertz generation in cryogenically cooled periodically poled lithium niobate.

We present an efficiency scaling study of optical rectification in cryogenically cooled periodically poled lithium niobate for the generation of narrowband terahertz radiation using ultrashort pulses. The results show an efficiency and brilliance increase compared to previous schemes of up to 2 orders of magnitude by exploring the optimal pump pulse format at around 800 nm, and reveal saturation mechanisms limiting the conversion efficiency. We achieve >10⁻³ energy conversion efficiencies, µJ-level energies, and bandwidths <20 GHz at ∼0.5 THz, thereby showing unprecedented spectral brightness in the 0.1-1 THz range relevant to terahertz science and technology.

Terahertz-driven linear electron acceleration.

The cost, size and availability of electron accelerators are dominated by the achievable accelerating gradient. Conventional high-brightness radio-frequency accelerating structures operate with 30-50 MeV m(-1) gradients. Electron accelerators driven with optical or infrared sources have demonstrated accelerating gradients orders of magnitude above that achievable with conventional radio-frequency structures. However, laser-driven wakefield accelerators require intense femtosecond sources and direct laser-driven accelerators suffer from low bunch charge, sub-micron tolerances and sub-femtosecond timing requirements due to the short wavelength of operation. Here we demonstrate linear acceleration of electrons with keV energy gain using optically generated terahertz pulses. Terahertz-driven accelerating structures enable high-gradient electron/proton accelerators with simple accelerating structures, high repetition rates and significant charge per bunch. These ultra-compact terahertz accelerators with extremely short electron bunches hold great potential to have a transformative impact for free electron lasers, linear colliders, ultrafast electron diffraction, X-ray science and medical therapy with X-rays and electron beams.

Toward a terahertz-driven electron gun.

Femtosecond electron bunches with keV energies and eV energy spread are needed by condensed matter physicists to resolve state transitions in carbon nanotubes, molecular structures, organic salts, and charge density wave materials. These semirelativistic electron sources are not only of interest for ultrafast electron diffraction, but also for electron energy-loss spectroscopy and as a seed for x-ray FELs. Thus far, the output energy spread (hence pulse duration) of ultrafast electron guns has been limited by the achievable electric field at the surface of the emitter, which is 10 MV/m for DC guns and 200 MV/m for RF guns. A single-cycle THz electron gun provides a unique opportunity to not only achieve GV/m surface electric fields but also with relatively low THz pulse energies, since a single-cycle transform-limited waveform is the most efficient way to achieve intense electric fields. Here, electron bunches of 50 fC from a flat copper photocathode are accelerated from rest to tens of eV by a microjoule THz pulse with peak electric field of 72 MV/m at 1 kHz repetition rate. We show that scaling to the readily-available GV/m THz field regime would translate to monoenergetic electron beams of ~100 keV.

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.

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.

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.

Complex-envelope alternating-direction-implicit FDTD method for simulating active photonic devices with semiconductor/solid-state media.

A complex-envelope (CE) alternating-direction-implicit (ADI) finite-difference time-domain (FDTD) approach to treat light-matter interaction self-consistently with electromagnetic field evolution for efficient simulations of active photonic devices is presented for the first time (to our best knowledge). The active medium (AM) is modeled using an efficient multilevel system of carrier rate equations to yield the correct carrier distributions, suitable for modeling semiconductor/solid-state media accurately. To include the AM in the CE-ADI-FDTD method, a first-order differential system involving CE fields in the AM is first set up. The system matrix that includes AM parameters is then split into two time-dependent submatrices that are then used in an efficient ADI splitting formula. The proposed CE-ADI-FDTD approach with AM takes 22% of the time as the approach of the corresponding explicit FDTD, as validated by semiconductor microdisk laser simulations.