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Several technologies, including photodetection, imaging and data communication, could greatly benefit from the availability of fast and controllable conversion of terahertz (THz) light to visible light. Here, we demonstrate that the exceptional properties and dynamics of electronic heat in graphene allow for THz-to-visible conversion, which is switchable at a sub-nanosecond timescale. We show a tunable on/off ratio of more than 30 for the emitted visible light, achieved through electrical gating using a gate voltage on the order of one Volt. We also demonstrate that a grating-graphene metamaterial leads to an increase in THz-induced emitted power in the visible range by two orders of magnitude. The experimental results are in agreement with a thermodynamic model that describes black-body radiation from the electron system heated through intraband Drude absorption of THz light. These results provide a promising route towards novel functionalities of optoelectronic technologies in the THz regime.

Achieving efficient, high-power harmonic generation in the terahertz (THz) spectral domain has technological applications, for example in sixth generation (6G) communication networks [1, 2]. Massless Dirac fermions possess extremely large THz nonlinear susceptibilities and harmonic conversion efficiencies [3–7]. However, the observed maximum generated harmonic power is limited, because of saturation effects at increasing incident powers, as shown recently for graphene [8]. Here, we demonstrate room-temperature THz harmonic generation in a Bi2Se3 topological insulator (TI) and TI-grating metamaterial structures with surface-selective THz 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 THz (opto)electronic applications.

Graphene is conceivably the most nonlinear optoelectronic material. Its nonlinear optical coefficients in the terahertz (THz) frequency range surpass those of other materials by many orders of magnitude. This, in particular, allows one to use graphene for extremely efficient up-conversion of sub-THz electronic input signals into the THz frequency range at room temperature and under ambient conditions, thus paving the way for practical graphene-based ultrahigh-frequency electronic technology. Here, we show that the THz nonlinearity of graphene 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 THz third-harmonic generation in graphene by about two orders of magnitude. We demonstrate gating control of THz nonlinearity of graphene for both ultrashort single-cycle and quasi-monochromatic multi-cycle input signals. Our experimental results are in quantitative agreement with a physical model of 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 ultra-high 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 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 frequencyof 0.7 THz. This nonlinearity is 50 times larger than what we obtain for graphene without grating. Such an enhancement corresponds to third-harmonic signal with an intensity that is three 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 9th harmonic. Grating-graphene metamaterials thus constitute an outstanding platform for commercially viable, CMOS compatible, room temperature, chip-integrated,THz nonlinear conversion 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 with TI samples with vary- ing 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 femtosec- onds), 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 effciencies, and high-bandwidth optoelectronic and spintronic information and communication applications.

This research data publication contains: - Experimental datasets which were evaluated and presented in the corresponding article. - Origin software file that contains the raw data as well as the different steps of the data analysis, the results of which are presented in the article.

This research data publications contains the sorted pulse-resolved data and metadata corresponding to the linked publication: Electrical tunability of terahertz nonlinearity in graphene. The final data evaluation and preparation of figures was done externally by Dr. Hassan Hafez, who should be contacted in terms of assigning raw data to data shown in publication.

Research data for used for the publication: "Grating-graphene metamaterial as a platform for terahertz nonlinear photonics". Datasets measured at the TELBE accelerator-based THz source are measured using a pulse-resolved detection scheme. The data points are sorted according to the absolute arrival time measurement. The four columns hold the following data: 1) absolute time in picoseconds 2) Signal of the emitted THz measured by electro-optic sampling. 3) Relative THz intensity measured using a pyroelectric detector. THz intensity is proportional to absolute power of the signal. 4) Data corresponding to the relative timing of each pulse. Not used for further analysis of the data. The filenumbers of the measurements used for the figures are as follows: Fig. 1a: File 003 Fig. 1b-c: File 043 Fig. 1d-e: File 086 Fig. 2a: Files 080..088 (bare graphene) and 031..049 (grating) Fig. 2b: same Fig. 3a: Files 050..057 Fig. 3c: Files 076..079 Fig. 4. Table top measurements; no file numbers Supp. Fig. 2: File 030 Supp. Fig. 4: File 024..025 Supp. Fig. 7a: Files 031..034 and 036..041 Supp. Fig. 7b: Files 080..083 Supp. Fig. 7d: Files 031..049 and 080..086 Supp. Fig. 9a: Files 031..046 Supp. Fig. 9b: Files 080..085 and 087..088 The datasets measured using a table-top laser source contain two columns. The first one is the position of the optical delay stage in mm that has to be multiplied by 6.667 ps/mm to define the time axis. The second column contains the THz signal as measured using electro-optic sampling.

Graphene has long been predicted to show exceptional nonlinear optical properties, especially in the technologically important terahertz (THz) frequency range. Recent experiments demonstrated that this atomically-thin material indeed exhibits possibly the largest nonlinear coefficients of any material known to date. These findings in particular pave ways for practical graphene-based applications in ultrafast electronics and optoelectronics operating at THz rates. Here we report on the advances in the booming field of nonlinear THz optics of graphene, and describe the state-of-the-art understanding of the nature of the nonlinear interaction of electrons in graphene with intense THz fields based on the thermodynamic model of electron transport in graphene. We also provide a comparison between different mechanisms of nonlinear interaction of graphene with light fields in THz, infrared and visible frequency ranges. We conclude the report with the perspectives for the expected technological applications of graphene based on its extraordinary THz nonlinear properties. This report covers the evolution of the field of THz nonlinear optics of graphene from the very pioneering to the state-of-the-art works. It also serves as a concise overview of the current understanding of THz nonlinear optics of graphene, and as a compact reference for researchers entering the field, as well as for the technology developers.

The conversion of light into free electron-hole pairs constitutes the key process in the fields of photodetection and photovoltaics. The efficiency of this process depends on the competition of different relaxation pathways and can be greatly enhanced when photoexcited carriers do not lose energy as heat, but instead transfer their excess energy into the production of additional electron-hole pairs through carrier-carrier scattering processes. Here we use optical pump-terahertz probe measurements to probe different pathways contributing to the ultrafast energy relaxation of photoexcited carriers. Our results indicate that carrier-carrier scattering is highly efficient, prevailing over optical-phonon emission in a wide range of photon wavelengths and leading to the production of secondary hot electrons originating from the conduction band. As hot electrons in graphene can drive currents, multiple hot-carrier generation makes graphene a promising material for highly efficient broadband extraction of light energy into electronic degrees of freedom, enabling high-efficiency optoelectronic applications., United States. Office of Naval Research (Grant N00014-09-1-0724)

Controlling the energy flow processes and the associated energy relaxation rates of a light emitter is of fundamental interest and has many applications in the fields of quantum optics, photovoltaics, photodetection, biosensing and light emission. Advanced dielectric, semiconductor and metallic systems have been developed to tailor the interaction between an emitter and its environment. However, active control of the energy flow from an emitter into optical, electronic or plasmonic excitations has remained challenging. Here, we demonstrate in situ electrical control of the relaxation pathways of excited erbium ions, which emit light at the technologically relevant telecommunication wavelength of 1.5 μm. By placing the erbium at a few nanometres distance from graphene, we modify the relaxation rate by more than a factor of three, and control whether the emitter decays into electron–hole pairs, emitted photons or graphene near-infrared plasmons, confined to <15 nm from the graphene sheet. These capabilities to dictate optical energy transfer processes through electrical control of the local density of optical states constitute a new paradigm for active (quantum) photonics and can be applied using any combination of light emitters and two-dimensional materials., Postprint (author’s final draft)

Photoexcitation of graphene leads to an interesting sequence of phenomena, some of which can be exploited in optoelectronic devices based on graphene. In particular, the efficient and ultrafast generation of an electron distribution with an elevated electron temperature and the concomitant generation of a photo-thermoelectric voltage at symmetry-breaking interfaces is of interest for photosensing and light harvesting. Here, we experimentally study the generated photocurrent at the graphene–metal interface, focusing on the time-resolved photocurrent, the effects of photon energy, Fermi energy and light polarization. We show that a single framework based on photo-thermoelectric photocurrent generation explains all experimental results., Peer Reviewed, Postprint (author’s final draft)

Graphene is a promising material for ultrafast and broadband photodetection. Earlier studies have addressed the general operation of graphene-based photothermoelectric devices and the switching speed, which is limited by the charge carrier cooling time, on the order of picoseconds. However, the generation of the photovoltage could occur at a much faster timescale, as it is associated with the carrier heating time. Here, we measure the photovoltage generation time and find it to be faster than 50 fs. As a proof-of-principle application of this ultrafast photodetector, we use graphene to directly measure, electrically, the pulse duration of a sub-50 fs laser pulse. The observation that carrier heating is ultrafast suggests that energy from absorbed photons can be efficiently transferred to carrier heat. To study this, we examine the spectral response and find a constant spectral responsivity of between 500 and 1,500 nm. This is consistent with efficient electron heating. These results are promising for ultrafast femtosecond and broadband photodetector applications., Peer Reviewed, Postprint (published version)

Photoexcitation of graphene leads to an interesting sequence of phenomena, some of which can be exploited in optoelectronic devices based on graphene. In particular, the efficient and ultrafast generation of an electron distribution with an elevated electron temperature and the concomitant generation of a photo-thermoelectric voltage at symmetry-breaking interfaces is of interest for photosensing and light harvesting. Here, we experimentally study the generated photocurrent at the graphene–metal interface, focusing on the time-resolved photocurrent, the effects of photon energy, Fermi energy and light polarization. We show that a single framework based on photo-thermoelectric photocurrent generation explains all experimental results., United States. Air Force Office of Scientific Research (Grant FA9550-11-1-0225), David & Lucile Packard Foundation (Fellowship)

The photoresponse of graphene at mid-infrared frequencies is of high technological interest and is governed by fundamentally different underlying physics than the photoresponse at visible frequencies, as the energy of the photons and substrate phonons involved have comparable energies. Here, we perform a spectrally resolved study of the graphene photoresponse for mid-infrared light by measuring spatially resolved photocurrent over a broad frequency range (1000-1600 cm-1). We unveil the different mechanisms that give rise to photocurrent generation in graphene on a polar substrate. In particular, we find an enhancement of the photoresponse when the light excites bulk or surface phonons of the SiO2 substrate. This work paves the way for the development of graphene-based mid-infrared thermal sensing technology.

The conversion of light into free electron–hole pairs constitutes the key process in the fields of photodetection and photovoltaics. The efficiency of this process depends on the competition of different relaxation pathways and can be greatly enhanced when photoexcited carriers do not lose energy as heat, but instead transfer their excess energy into the production of additional electron–hole pairs through carrier–carrier scattering processes. Here we use optical pump–terahertz probe measurements to probe different pathways contributing to the ultrafast energy relaxation of photoexcited carriers. Our results indicate that carrier–carrier scattering is highly efficient, prevailing over optical-phonon emission in a wide range of photon wavelengths and leading to the production of secondary hot electrons originating from the conduction band. As hot electrons in graphene can drive currents, multiple hot-carrier generation makes graphene a promising material for highly efficient broadband extraction of light energy into electronic degrees of freedom, enabling high-efficiency optoelectronic applications., United States. Office of Naval Research (Grant N00014-09-1-0724)

Peer Reviewed, Postprint (published version)