The understanding of how spins move and can be manipulated at pico-and femtosecond time scales is the goal of much of modern research in condensed matter physics, with implications for ultrafast and more energy-efficient data processing and storage applications. However, the limited comprehension of the physics behind this phenomenon has hampered the possibility of realising a commercial technology based on it. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast time scales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report the first direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetisation at a frequency of approximately 0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps.

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.

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.

We demonstrate experimentally the efficiency of a recently proposed scheme of terahertz generation based on Cherenkov emission from ultrashort laser pulses in a sandwich structure. The structure has a thin nonlinear core covered with a prism of low terahertz absorption. Using an 8 mm long Si-LiNbO(3)-BK7 structure with a 50 microm thick LiNbO(3) core, we converted 40 microJ, 50 fs Ti:sapphire laser pulses into terahertz pulses of approximately 3 THz bandwidth with a record efficiency of over 0.1%.

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.

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.

Changes in the amplitude of femtosecond laser pulses and in the energy of terahertz wave radiation induced during their co-propagation in ZnTe and GaP crystals are studied theoretically and experimentally. The results show that variation of the optical field amplitude leads to changes in the laser pulse energy and spectrum shift. We investigate the quantitative correlations between variations of the optical pulse energy, spectrum, phase and terahertz radiation energy. The values of laser pulse energy change and spectrum shift are proportional to the first time derivative of the magnitude of terahertz electric field, which enables coherent electro-optic detection. A simple and convenient calibration technique for terahertz energy detectors based on the correlation between laser and terahertz energy changes is proposed and tested.

Results of experimental and theoretical investigations on generation of terahertz radiation at the interaction of femtosecond laser pulses with a metal surface are presented. Investigations are performed with the laser pulse intensities higher compared with that used in papers [Opt. Lett.29, 2674 (2004); Opt. Lett.30, 1402 (2005)]. The most effective generation is observed for p-polarized optical pulses with incidence angles in the range 5°-10° (from the surface), depending on the kind of metal. For the copper, the exponential growth of terahertz pulse energy with the increase of optical pulse energy was registered. Theoretical interpretation for some of the experimental results is proposed based on the model of free electrons in metal.