We investigate ultrafast harmonic generation (HG) in Si:B, driven by intense 300-GHz pump pulses with fields up to 115 kV/cm, at $4 \sim \mathrm{K}$ and $300 \sim \mathrm{K}$. We report several novel findings: (i) Harmonics of order up to n=9 are observed at room temperature, while at low temperature we can resolve harmonics reaching even n=13. (ii) For T=300 K, simulations by multi-valence-band Monte-Carlo calculations combined with finite-difference time-domain propagation show that the HG process, upon increase of the radiation field, becomes more and more dominated by energy-dependent scattering rates over the contribution from band non-parabolicity. (iii) At T=4 K, we observe a drastic rise of the HG yield with the THz field strength, as one reaches the threshold for tunnel ionization at (internal) pump fields of 30 kV/cm. We disentangle the HG contributions in this case into contributions from the initial ‘generational’ and subsequent band-nonlinearities, and show that scattering severely degrades any coherent recollision during the subsequent oscillatory motion of the holes.

Non-linear materials are cornerstones of modern optics and electronics. Strong dependence on the intrinsic properties of particular materials, however, inhibits the at-will extension of demanding non-linear effects, especially those second-order ones, to widely adopted centrosymmetric materials (for example, silicon) and technologically important burgeoning spectral domains (for example, terahertz frequencies). Here we introduce a universal route to efficient non-linear responses enabled by exciting non-linear Thomson scattering, a fundamental process in electrodynamics that was known to occur only in relativistic electrons in metamaterial composed of linear materials. Such a mechanism modulates the trajectory of charges, either intrinsically or extrinsically provided in solids, at twice the driving frequency, allowing second-harmonic generation at terahertz frequencies on crystalline silicon with extremely large non-linear susceptibility in our proof-of-concept experiments. By offering a substantially material- and frequency-independent platform, our approach opens new possibilities in the fields of on-demand non-linear optics, terahertz sources, strong field light-solid interactions and integrated photonic circuits.

Terahertz (THz) absorbers are vital for confining electromagnetic waves in a wide range of light-matter applications. The actively tunable elements for improving the operation bandwidth limitations and the polarization features of absorbers are essential indexes for evaluating their performance. Therefore, THz absorbers with active functionality, polarization sensitivity, and straightforward fabrication are in high demand. Here, we present carbon nanotube (CNT)-based electrically tunable THz absorbers in an asymmetric Fabry-Perot cavity. The selfassembled CNTs provide active electrical tunability as well as polarization selectivity. The experimental results show that absorbers composed of continuous and unstructured films exhibit almost perfect absorbance up to 99% from 0.2 THz to 1.6 THz. The absorbance of broadband absorbers is tuned from 48% to 99% at 1.6 THz, and the modulation depth (MD) is as high as 52%. The proposed electrically tunable absorbers with a straightforward fabrication method outperform most absorbers; these proposed absorbers promote THz applications such as filtering, biosensing, optical switching, polarized imaging, and telecommunication.

2H-NbSe2 is an archetypal system in which superconductivity and charge density wave (CDW) coexist and compete macroscopically with each other. In particular, this interplay also manifests in their dynamical fluctuations. As a result, the superconducting amplitude fluctuation (i.e., Higgs mode) is pushed below the quasiparticle continuum, allowing it to become a coherent excitation observable by Raman scattering. In the present study, we coherently drive the collective oscillations of the two orders and visualize their interplay in the time domain. We find that both collective modes contribute to terahertz third-harmonic generation (THG) and their THG signals interfere below Tc, leading to an antiresonance of the integrated THG signal. The dynamical Ginzburg-Landau model suggests that around the antiresonance a periodic energy transfer between the driven Higgs oscillations and the driven CDW oscillations is possible. Our results illustrate the roles of collective modes in the terahertz THG process, revealing a close connection of this technique to Raman scattering. In systems where the different collective modes are coupled, our experimental scheme also illustrates a paradigm for realizing coherent control via such couplings.

Cuprate high- T c superconductors are known for their intertwined interactions and the coexistence of competing orders. Uncovering experimental signatures of these interactions is often the first step in understanding their complex relations. A typical spectroscopic signature of the interaction between a discrete mode and a continuum of excitations is the Fano resonance/interference, characterized by the asymmetric light-scattering amplitude of the discrete mode as a function of the electromagnetic driving frequency. In this study, we report a new type of Fano resonance manifested by the nonlinear terahertz response of cuprate high- T c superconductors, where we resolve both the amplitude and phase signatures of the Fano resonance. Our extensive hole-doping and magnetic field dependent investigation suggests that the Fano resonance may arise from an interplay between the superconducting fluctuations and the charge density wave fluctuations, prompting future studies to look more closely into their dynamical interactions.

We report on high-order harmonic generation in the two-band superconductor MgB_2 driven by intense terahertz electromagnetic pulses. Third- and fifth-order harmonics are resolved in time domain and investigated as a function of temperature and in applied magnetic fields crossing the superconducting phase boundary. The high-order harmonics in the superconducting phase reflects nonequilibrium dynamics of the superconducting order parameter in MgB_2, which is probed via nonlinear coupling to the terahertz field. The observed temperature and field dependence of the nonlinear response allows to establish the superconducting phase diagram.

Complex frustrated magnetic structures in multiferroic hexaferrites are well tunable by temperature, magnetic field and doping. We investigated the influence of strong THz pulses generated by superradiant THz sources on magnetic structure and related electromagnons’ absorption in Y- and Z-type multiferroic hexaferrites. While in Z-type hexaferrite (Ba0.2Sr0.8)3Co2Fe24O41 polycrystal, the observed changes in transmission spectra were fully described by sample heating, a blue-shift of the electromagnon frequency observed in Y-type hexaferrite Ba0.2Sr1.8Co2(Fe0.96Al0.04)12O22 single-crystal could be possibly ascribed to the transition from the alternating longitudinal conical to the transverse conical magnetic structure. We elaborated a nonlinear model which explained absence of nonlinearity in Z-type hexaferrite (Ba0.2Sr0.8)3Co2Fe24O41. For Y-type hexaferrite Ba0.2Sr1.8Co2(Fe0.96Al0.04)12O22, we discuss possible transient or even permanent effects of both THz electric and magnetic fields on its magnetic structure.

A conceptually new approach to synchronizing accelerator-based light sources and external laser systems is presented. The concept is based on utilizing a sufficiently intense accelerator-based single-cycle terahertz pulse to slice a thereby intrinsically synchronized femtosecond-level part of a longer picosecond laser pulse in an electro-optic crystal. A precise synchronization of the order of 10 fs is demonstrated, allowing for real-time lock-in amplifier signal demodulation. We demonstrate successful operation of the concept with three benchmark experiments using a 4th generation accelerator-based terahertz light source, i.e. (i) far-field terahertz time-domain spectroscopy, (ii) terahertz high harmonic generation spectroscopy, and (iii) terahertz scattering-type scanning near-field optical microscopy.

Achieving efficient, high-power harmonic generation in the terahertz spectral domain has technological applications, for example, in sixth generation (6G) communication networks. Massless Dirac fermions possess extremely large terahertz nonlinear susceptibilities and harmonic conversion efficiencies. However, the observed maximum generated harmonic power is limited, because of saturation effects at increasing incident powers, as shown recently for graphene. Here, we demonstrate room-temperature terahertz harmonic generation in a Bi2Se3 topological insulator and topological-insulator-grating metamaterial structures with surface-selective terahertz field enhancement. We obtain a third-harmonic power approaching the milliwatt range for an incident power of 75 mW-an improvement by two orders of magnitude compared to a benchmarked graphene sample. We establish a framework in which this exceptional performance is the result of thermodynamic harmonic generation by the massless topological surface states, benefiting from ultrafast dissipation of electronic heat via surface-bulk Coulomb interactions. These results are an important step towards on-chip terahertz (opto)electronic applications.

2H-NbSe2 is an archetypal system in which superconductivity and charge-density-wave (CDW) coexist and compete macroscopically with each other. In particular, this interplay also manifests in their dynamical fluctuations. As a result, the superconducting amplitude fluctuations (i.e. Higgs mode) is pushed below the quasiparticle continuum, allowing it to become a coherent excitation observable by Raman scattering. In the present study, we coherently drive the collective oscillations of the two orders and visualize their interplay in the driven states in the time domain. We find that both collective modes contribute to terahertz third harmonic generation (THG) and the THG signals interfere below Tc, leading to an anti-resonance of the integrated THG signal. The dynamical Ginzburg-Landau model suggests that around the anti-resonance a periodic energy transfer between the driven Higgs oscillations and the driven CDW oscillations is possible. In addition to 2H-NbSe2, we also studied an underdoped La2-xSrxCuO4 (x ~ 0.12) driven beyond the perturbative regime of THG. A similar interference between two sources of THG is observed below Tc. While there might be additional sources of THG in these experiments, our results illustrate the roles of coupled modes in the terahertz THG process and the tantalizing possibility of coherent control via such couplings.

Graphene is conceivably the most nonlinear optoelectronic material we know. Its nonlinear optical coefficients in the terahertz frequency range surpass those of other materials by many orders of magnitude. Here, we show that the terahertz nonlinearity of graphene, both for ultrashort single-cycle and quasi-monochromatic multicycle input terahertz signals, can be efficiently controlled using electrical gating, with gating voltages as low as a few volts. For example, optimal electrical gating enhances the power conversion efficiency in terahertz third-harmonic generation in graphene by about two orders of magnitude. Our experimental results are in quantitative agreement with a physical model of the graphene nonlinearity, describing the time-dependent thermodynamic balance maintained within the electronic population of graphene during interaction with ultrafast electric fields. Our results can serve as a basis for straightforward and accurate design of devices and applications for efficient electronic signal processing in graphene at ultrahigh frequencies.

Topologically protected surface states present rich physics and promising spintronic, optoelectronic, and photonic applications that require a proper understanding of their ultrafast carrier dynamics. Here, we investigate these dynamics in topological insulators (TIs) of the bismuth and antimony chalcogenide family, where we isolate the response of Dirac fermions at the surface from the response of bulk carriers by combining photoexcitation with below-bandgap terahertz (THz) photons and TI samples with varying Fermi level, including one sample with the Fermi level located within the bandgap. We identify distinctly faster relaxation of charge carriers in the topologically protected Dirac surface states (few hundred femtoseconds), compared to bulk carriers (few picoseconds). In agreement with such fast cooling dynamics, we observe THz harmonic generation without any saturation effects for increasing incident fields, unlike graphene which exhibits strong saturation. This opens up promising avenues for increased THz nonlinear conversion efficiencies, and high-bandwidth optoelectronic and spintronic information and communication applications.

We report high-harmonic generation up to the ninth order from boron-doped Si at room temperature, pumped by intense THz pulses. For comparison with the experiment, we also performed FDTD simulations coupled to a full-band Monte Carlo device model. The simulations predict a significantly stronger flattening of the conversion efficiency with pump power than that observed in the experiments, which points to less pronounced scattering at high fields than expected.

In this Letter, optical-to-terahertz (THz) conversion of 800 nm femtosecond laser pulses in large-area bias-free InGaAs emitters based on photo-Dember (PD) and lateral photo-Dember (LPD) effects is experimentally investigated. We use metamorphic buffers to grow sub-micrometer thick InxGa1-xAs layers with indium mole fractions x=0.37, 0.53, and 0.70 on a GaAs substrate. A strong enhancement of THz output energy with an increase of indium content is observed. On the surface of the sample providing the strongest emission (x=0.7), we have fabricated a 1.5cm2 area of asymmetrically shaped metallic grating for LPD emission. This LPD emitter allows achieving high conversion efficiency of 0.24⋅10-3 and a broad generation bandwidth of up to 6 THz. We also demonstrate that there is no significant difference in the conversion efficiency when operating at 1 and 200 kHz repetition rates. Our results show that large-area LPD emitters give a convenient, competitive way to generate intense high-repetition-rate THz pulses.

Nonlinear optics is an increasingly important field for scientific and technological applications, owing to its relevance and potential for optical and optoelectronic technologies. Currently, there is an active search for suitable nonlinear material systems with efficient conversion and a small material footprint. Ideally, the material system should allow for chip integration and room-temperature operation. Two-dimensional materials are highly interesting in this regard. Particularly promising is graphene, which has demonstrated an exceptionally large nonlinearity in the terahertz regime. Yet, the light-matter interaction length in two-dimensional materials is inherently minimal, thus limiting the overall nonlinear optical conversion efficiency. Here, we overcome this challenge using a metamaterial platform that combines graphene with a photonic grating structure providing field enhancement. We measure terahertz third-harmonic generation in this metamaterial and obtain an effective third-order nonlinear susceptibility with a magnitude as large as 3 × 10-8 m2/V2, or 21 esu, for a fundamental frequency of 0.7 THz. This nonlinearity is 50 times larger than what we obtain for graphene without grating. Such an enhancement corresponds to a third-harmonic signal with an intensity that is 3 orders of magnitude larger due to the grating. Moreover, we demonstrate a field conversion efficiency for the third harmonic of up to ∼1% using a moderate field strength of ∼30 kV/cm. Finally, we show that harmonics beyond the third are enhanced even more strongly, allowing us to observe signatures of up to the ninth harmonic. Grating-graphene metamaterials thus constitute an outstanding platform for commercially viable, CMOS-compatible, room-temperature, chip-integrated, THz nonlinear conversion applications.

The understanding of how spins move and can be manipulated at pico- and femtosecond timescales has implications for ultrafast and energy-efficient data-processing and storage applications. However, the possibility of realizing commercial technologies based on ultrafast spin dynamics has been hampered by our limited knowledge of the physics behind processes on this timescale. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast timescales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetization at a frequency of ~0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps.

Harmonic generation is a general characteristic of driven nonlinear systems, and serves as an efficient tool for investigating the fundamental principles that govern the ultrafast nonlinear dynamics. Here, we report on terahertz-field driven high-harmonic generation in the three-dimensional Dirac semimetal Cd 3 As 2 at room temperature. Excited by linearly-polarized multi-cycle terahertz pulses, the third-, fifth-, and seventh-order harmonic generation is very efficient and detected via time-resolved spectroscopic techniques. The observed harmonic radiation is further studied as a function of pump-pulse fluence. Their fluence dependence is found to deviate evidently from the expected power-law dependence in the perturbative regime. The observed highly non-perturbative behavior is reproduced based on our analysis of the intraband kinetics of the terahertz-field driven nonequilibrium state using the Boltzmann transport theory. Our results indicate that the driven nonlinear kinetics of the Dirac electrons plays the central role for the observed highly nonlinear response.

In high-energy physics, the Higgs field couples to gauge bosons and fermions and gives mass to their elementary excitations. Experimentally, such couplings can be inferred from the decay product of the Higgs boson, i.e., the scalar (amplitude) excitation of the Higgs field. In superconductors, Cooper pairs bear a close analogy to the Higgs field. Interaction between the Cooper pairs and other degrees of freedom provides dissipation channels for the amplitude mode, which may reveal important information about the microscopic pairing mechanism. To this end, we investigate the Higgs (amplitude) mode of several cuprate thin films using phase-resolved terahertz third harmonic generation (THG). In addition to the heavily damped Higgs mode itself, we observe a universal jump in the phase of the driven Higgs oscillation as well as a non-vanishing THG above T c . These findings indicate coupling of the Higgs mode to other collective modes and potentially a nonzero pairing amplitude above T c .