Extremely Nonperturbative Nonlinearities in GaAs Driven by Atomically Strong Terahertz Fields in Gold Metamaterials

"Nonperturbative Nonlinearities": Perhaps Less than Meets the Eye

We address challenges in characterizing changes in permittivity and refractive index beyond standard perturbative methods with special attention given to transparent conductive oxides (TCOs). We unveil a realistic limit to permittivity changes under high optical power densities. Our study covers both slow and ultrafast nonlinearities, demonstrating that all nonlinearities induce refractive index changes accurately described by a simple curve with saturation electric field (or irradiance) and maximum change of permittivity at saturation. Our model, grounded in material properties, like oscillator strength and characteristic times, offers a robust framework for understanding and predicting nonlinear optical phenomena in TCOs and other materials. We differentiate between the significance of higher-order nonlinear susceptibilities in ultrafast and slow nonlinear scenarios. We aim to provide valuable insights for researchers exploring strong light-matter interaction.

Terahertz Metasurfaces Exploiting the Phase Transition of Vanadium Dioxide

Artificially designed modulators that enable a wealth of freedom in manipulating the terahertz (THz) waves at will are an essential component in THz sources and their widespread applications. Dynamically controlled metasurfaces, being multifunctional, ultrafast, integrable, broadband, high contrasting, and scalable on the operating wavelength, are critical in developing state-of-the-art THz modulators. Recently, external stimuli-triggered THz metasurfaces integrated with functional media have been extensively explored. The vanadium dioxide (VO2)-based hybrid metasurfaces, as a unique path toward active meta-devices, feature an insulator-metal phase transition under the excitation of heat, electricity, and light, etc. During the phase transition, the optical and electrical properties of the VO2 film undergo a massive modification with either a boosted or dropped conductivity by more than four orders of magnitude. Being benefited from the phase transition effect, the electromagnetic response of the VO2-based metasufaces can be actively controlled by applying external excitation. In this review, we present recent advances in dynamically controlled THz metasurfaces exploiting the VO2 phase transition categorized according to the external stimuli. THz time-domain spectroscopy is introduced as an indispensable platform in the studies of functional VO2 films. In each type of external excitation, four design strategies are employed to realize external stimuli-triggered VO2-based THz metasurfaces, including switching the transreflective operation mode, controlling the dielectric environment of metallic microstructures, tailoring the equivalent resonant microstructures, and modifying the electromagnetic properties of the VO2 unit cells. The microstructures' design and electromagnetic responses of the resulting active metasurfaces have been systematically demonstrated, with a particular focus on the critical role of the VO2 films in the dynamic modulation processes.

Ultrafast strong-field terahertz nonlinear nanometasurfaces

Strong-field terahertz (THz)-matter interaction permits the investigation of nonequilibrium behaviors in the nonperturbative zone. However, the unavailability of a high-field free-space THz source with high repetition rates, excellent beam quality, and high stability hinders its development. In this work, we obtain the nonlinear modulation dynamics of a "THz-nano" metasurface on silicon substrates using a time-resolved strong-field THz-pump THz-probe (TPTP) with a thousand orders local field enhancement through confining THz waves into nano-gaps (15 nm, λ/33,000). By switching the THz field strength, we successfully realize a self-modulation ∼50 GHz frequency shift, which is further verified via the TPTP ultrafast time-resolution technique. The phenomenon is attributed to the impact ionization (IMI) of the silicon substrate under the excitation of extremely confined strong THz fields in nano-gaps. Both strong-field induced intervalley scattering (IVS) and IMI effects of photodoped silicon occurring in nano-gaps and large-area substrates were also observed by 800 nm optical injection of carriers. These aforementioned findings provide a robust research platform for the realization of ultrafast time resolution nanoscale strong-field THz-matter interaction and new ideas for nonextreme laboratories to realize extreme THz science, applications, and THz nonlinear modulation device development.

Custom terahertz waveforms using complementary organic nonlinear optical crystals

Organic nonlinear optical (NLO) crystals are among the most efficient (>1%) terahertz (THz) radiation generators. However, one of the limitations of using organic NLO crystals is that the unique THz absorptions in each crystal make it difficult to obtain a strong, smooth, and broad emission spectrum. In this work, we combine THz pulses from two complementary crystals, DAST and PNPA, to effectively fill in spectral gaps, creating a smooth spectrum with frequencies out to 5 THz. The combination of pulses also increases the peak-to-peak field strength from 1 MV/cm to 1.9 MV/cm.

Active and tunable nanophotonic metamaterials

Metamaterials enable subwavelength tailoring of light-matter interactions, driving fundamental discoveries which fuel novel applications in areas ranging from compressed sensing to quantum engineering. Importantly, the metallic and dielectric resonators from which static metamaterials are comprised present an open architecture amenable to materials integration. Thus, incorporating responsive materials such as semiconductors, liquid crystals, phase-change materials, or quantum materials (e.g., superconductors, 2D materials, etc.) imbue metamaterials with dynamic properties, facilitating the development of active and tunable devices harboring enhanced or even entirely novel electromagnetic functionality. Ultimately, active control derives from the ability to craft the local electromagnetic fields; accomplished using a host of external stimuli to modify the electronic or optical properties of the responsive materials embedded into the active regions of the subwavelength resonators. We provide a broad overview of this frontier area of metamaterials research, introducing fundamental concepts and presenting control strategies that include electronic, optical, mechanical, thermal, and magnetic stimuli. The examples presented range from microwave to visible wavelengths, utilizing a wide range of materials to realize spatial light modulators, effective nonlinear media, on-demand optics, and polarimetric imaging as but a few examples. Often, active and tunable nanophotonic metamaterials yield an emergent electromagnetic response that is more than the sum of the parts, providing reconfigurable or real-time control of the amplitude, phase, wavevector, polarization, and frequency of light. The examples to date are impressive, setting the stage for future advances that are likely to impact holography, beyond 5G communications, imaging, and quantum sensing and transduction.

Optical generation of strong-field terahertz radiation and its application in nonlinear terahertz metasurfaces

Extremely nonlinear terahertz (THz)-matter interactions and applications have positioned themselves as the next frontier in quantum information, nonlinear optics, and particle acceleration. However, the absence of free-space highly intense THz sources and the diffraction limit, which prevents THz waves from being concentrated to the nanoscale scale, are inhibiting the growth of extreme THz. To address this difficulty, suitably extremely concentrated THz sources are being produced, while (non-)resonant artificial metastructures are being widely used to enhance local fields, resulting in deep-subwavelength (<λ/103) confinement of highly enhanced THz fields in micro-/nano-gaps. We discuss solid-state stable sources of intense THz radiation generated by femtosecond lasers in this Review, with a special emphasis on the lithium niobate-based tilted pulse front approach and the nonlinear THz metasurfaces allowed by it. Finally, we forecast the field's future directions in extreme THz research.

Ultrafast and Low-Threshold THz Mode Switching of Two-Dimensional Nonlinear Metamaterials

Judiciously designed two-dimensional THz metamaterials consisting of resonant metallic structures embedded in a dielectric environment locally enhance the electromagnetic field of an incident THz pulse to values sufficiently high to cause nonlinear responses of the environment. In semiconductors, the response is attributed to nonlinear transport phenomena via intervalley scattering, impact ionization, or interband tunneling and can affect the resonant behavior of the metallic structure, which results, for instance, in mode switching. However, details of mode switching, especially time scales, are still debated. By using metallic split-ring resonators with nm-size gaps on intrinsic semiconductors with different bandgaps, we identify the most relevant carrier generation processes. In addition, by combining nonlinear THz time-domain spectroscopy with simulations, we establish the fastest time constant for mode switching to around hundred femtoseconds. Our results not only elucidate dominant carrier generation mechanisms and dynamics but also pave the route toward optically driven modulators with THz bandwidth.

Ultrafast imaging of terahertz electric waveforms using quantum dots

Microscopic electric fields govern the majority of elementary excitations in condensed matter and drive electronics at frequencies approaching the Terahertz (THz) regime. However, only few imaging schemes are able to resolve sub-wavelength fields in the THz range, such as scanning-probe techniques, electro-optic sampling, and ultrafast electron microscopy. Still, intrinsic constraints on sample geometry, acquisition speed and field strength limit their applicability. Here, we harness the quantum-confined Stark-effect to encode ultrafast electric near-fields into colloidal quantum dot luminescence. Our approach, termed Quantum-probe Field Microscopy (QFIM), combines far-field imaging of visible photons with phase-resolved sampling of electric waveforms. By capturing ultrafast movies, we spatio-temporally resolve a Terahertz resonance inside a bowtie antenna and unveil the propagation of a Terahertz waveguide excitation deeply in the sub-wavelength regime. The demonstrated QFIM approach is compatible with strong-field excitation and sub-micrometer resolution-introducing a direct route towards ultrafast field imaging of complex nanodevices in-operando.

Tunable non-integer high-harmonic generation in a topological insulator

When intense lightwaves accelerate electrons through a solid, the emerging high-order harmonic (HH) radiation offers key insights into the material^1-11. Sub-optical-cycle dynamics-such as dynamical Bloch oscillations^2-5, quasiparticle collisions^6,12, valley pseudospin switching¹³ and heating of Dirac gases¹⁰-leave fingerprints in the HH spectra of conventional solids. Topologically non-trivial matter^14,15 with invariants that are robust against imperfections has been predicted to support unconventional HH generation^16-20. Here we experimentally demonstrate HH generation in a three-dimensional topological insulator-bismuth telluride. The frequency of the terahertz driving field sharply discriminates between HH generation from the bulk and from the topological surface, where the unique combination of long scattering times owing to spin-momentum locking¹⁷ and the quasi-relativistic dispersion enables unusually efficient HH generation. Intriguingly, all observed orders can be continuously shifted to arbitrary non-integer multiples of the driving frequency by varying the carrier-envelope phase of the driving field-in line with quantum theory. The anomalous Berry curvature warranted by the non-trivial topology enforces meandering ballistic trajectories of the Dirac fermions, causing a hallmark polarization pattern of the HH emission. Our study provides a platform to explore topology and relativistic quantum physics in strong-field control, and could lead to non-dissipative topological electronics at infrared frequencies.

Tailored Subcycle Nonlinearities of Ultrastrong Light-Matter Coupling

We explore the nonlinear response of tailor-cut light-matter hybrid states in a novel regime, where both the Rabi frequency induced by a coherent driving field and the vacuum Rabi frequency set by a cavity field are comparable to the carrier frequency of light. In this previously unexplored strong-field limit of ultrastrong coupling, subcycle pump-probe and multiwave mixing nonlinearities between different polariton states violate the normal-mode approximation while ultrastrong coupling remains intact, as confirmed by our mean-field model. We expect such custom-cut nonlinearities of hybridized elementary excitations to facilitate nonclassical light sources, quantum phase transitions, or cavity chemistry with virtual photons.

Two-color two-dimensional terahertz spectroscopy: A new approach for exploring even-order nonlinearities in the nonperturbative regime

Nonlinear two-dimensional terahertz (2D-THz) spectroscopy at frequencies of the emitted THz signal different from the driving frequencies allows for exploring the regime of (off-)resonant even-order nonlinearities in condensed matter. To demonstrate the potential of this method, we study two phenomena in the nonlinear THz response of bulk GaAs: (i) The nonlinear THz response to a pair of femtosecond near-infrared pulses unravels novel fourth- and sixth-order contributions involving interband shift currents, Raman-like excitations of transverse-optical phonon and intervalence-band coherences. (ii) Transient interband tunneling of electrons driven by ultrashort mid-infrared pulses can be effectively controlled by a low-frequency THz field with amplitudes below 50 kV/cm. The THz field controls the electron-hole separation modifying decoherence and the irreversibility of carrier generation.

Floquet spin states in OLEDs

Electron and hole spins in organic light-emitting diodes constitute prototypical two-level systems for the exploration of the ultrastrong-drive regime of light-matter interactions. Floquet solutions to the time-dependent Hamiltonian of pairs of electron and hole spins reveal that, under non-perturbative resonant drive, when spin-Rabi frequencies become comparable to the Larmor frequencies, hybrid light-matter states emerge that enable dipole-forbidden multi-quantum transitions at integer and fractional g-factors. To probe these phenomena experimentally, we develop an electrically detected magnetic-resonance experiment supporting oscillating driving fields comparable in amplitude to the static field defining the Zeeman splitting; and an organic semiconductor characterized by minimal local hyperfine fields allowing the non-perturbative light-matter interactions to be resolved. The experimental confirmation of the predicted Floquet states under strong-drive conditions demonstrates the presence of hybrid light-matter spin excitations at room temperature. These dressed states are insensitive to power broadening, display Bloch-Siegert-like shifts, and are suggestive of long spin coherence times, implying potential applicability for quantum sensing.

Transient transmission of THz metamaterial antennas by impact ionization in a silicon substrate

The picosecond dynamics of excited charge carriers in the silicon substrate of THz metamaterial antennas was studied at different wavelengths. Time-resolved THz pump-THz probe spectroscopy was performed with light from a tunable free electron laser in the 9.3-16.7 THz frequency range using fluences of 2-12 J/m². Depending on the excitation wavelength with respect to the resonance center, transient transmission increase, decrease, or a combination of both was observed. The transient transmission changes can be explained by local electric field enhancement, which induces impact ionization in the silicon substrate, increasing the local number of charge carriers by several orders of magnitude, and their subsequent diffusion and recombination. The studied metamaterials can be integrated with common semiconductor devices and can potentially be used in sensing applications and THz energy harvesting.

Nonlinear Charge Transport in InGaAs Nanowires at Terahertz Frequencies

We probe the electron transport properties in the shell of GaAs/In_0.2Ga_0.8As core/shell nanowires at high electric fields using optical pump/THz probe spectroscopy with broadband THz pulses and peak electric fields up to 0.6 MV/cm. The plasmon resonance of the photoexcited charge carriers exhibits a systematic redshift and a suppression of its spectral weight for THz driving fields exceeding 0.4 MV/cm. This behavior is attributed to the intervalley electron scattering that results in the doubling of the average electron effective mass. Correspondingly, the electron mobility at the highest fields drops to about half of the original value. We demonstrate that the increase of the effective mass is nonuniform along the nanowires and takes place mainly in their middle part, leading to a spatially inhomogeneous carrier response. Our results quantify the nonlinear transport regime in GaAs-based nanowires and show their high potential for development of nanodevices operating at THz frequencies.

Impact Ionization Induced by Terahertz Radiation in HgTe Quantum Wells of Critical Thickness

We report on the observation of terahertz (THz) radiation induced band-to-band impact ionization in HgTe quantum well (QW) structures of critical thickness, which are characterized by a nearly linear energy dispersion. The THz electric field drives the carriers initializing electron-hole pair generation. The carrier multiplication is observed for photon energies less than the energy gap under the condition that the product of the radiation angular frequency ω and momentum relaxation time τ l larger than unity. In this case, the charge carriers acquire high energies solely because of collisions in the presence of a high-frequency electric field. The developed microscopic theory shows that the probability of the light-induced impact ionization is proportional to exp ( - E 0 2 / E 2 ) , with the radiation electric field amplitude E and the characteristic field parameter E 0. As observed in experiment, it exhibits a strong frequency dependence for ω τ ≫ 1 characterized by the characteristic field E 0 linearly increasing with the radiation frequency ω.

Propagation of broadband THz pulses: effects of dispersion, diffraction and time-varying nonlinear refraction

We theoretically investigate the propagation of broadband single-cycle terahertz (THz) pulses through a medium with a nonlinear optical response. Our model takes into account non-paraxial effects, self-focusing and diffraction, as well as dispersion, in both the linear and nonlinear optical regimes. We investigate the contribution of non-instantaneous Kerr-type nonlinearity to the overall instantaneous and delayed Kerr effect at the THz frequencies. We show how increasing the nonlinear relaxation time and its dispersion modifies the THz pulse after the propagation through a transparent medium. We also discuss the effect of linear dispersion on self-action during the pulse propagation.

Conductivity Induced by High-Field Terahertz Waves in Dielectric Material

An intense, subpicosecond, relativistic electron beam traversing a dielectric-lined waveguide generates very large amplitude electric fields at terahertz (THz) frequencies through the wakefield mechanism. In recent work employing this technique to accelerate charged particles, the generation of high-power, narrow-band THz radiation was demonstrated. The radiated waves contain fields with measured amplitude exceeding 2  GV/m, orders of magnitude greater than those available by other THz generation techniques at a narrow bandwidth. For fields approaching the GV/m level, a strong damping has been observed in SiO_{2}. This wave attenuation with an onset near 850  MV/m is consistent with changes to the conductivity of the dielectric lining and is characterized by a distinctive latching mechanism that is reversible on longer timescales. We describe the detailed measurements that serve to clarify the underlying physical mechanisms leading to strong field-induced damping of THz radiation (hω=1.59  meV, f=0.38  THz) in SiO_{2}, a bulk, wide band-gap (8.9 eV) dielectric.

Terahertz beam spot size measurements by a CCD camera

We present the experimental data on the direct measurements of spatial distribution of the terahertz (THz) pulse intensity profile using a commercial silicon-based charge-coupled device (CCD) camera in the spectral range from 1-3 THz. A method to measure the dimensions of a high-intensity THz radiation beam in the focal plane using the CCD camera is proposed and experimentally verified.

Terahertz driven amplification of coherent optical phonons in GaAs coupled to metallic dog-bone resonators

Two-dimensional terahertz spectroscopy on an AlAs/GaAs nanostructure covered by field-enhancing dog-bone resonators shows signatures of coherent optical phonon amplification. Amplification is due to stimulated phonon emission by a terahertz-driven electron current.

Terahertz Driven Amplification of Coherent Optical Phonons in GaAs Coupled to a Metasurface

We demonstrate amplification of longitudinal optical (LO) phonons by polar-optical interaction with an electron plasma in a GaAs structure coupled to a metallic metasurface using two-color two-dimensional spectroscopy. In a novel scheme, the metamaterial resonator enhances broadband terahertz fields, which generate coherent LO phonons and drive free electrons in the conduction band of GaAs. The time evolution of the LO phonon amplitude is monitored with midinfrared pulses via the LO-phonon-induced Kerr nonlinearity of the sample, showing an amplification of the LO phonon amplitude by up to a factor of 10, in agreement with a theoretical estimate.

Multimillijoule coherent terahertz bursts from picosecond laser-irradiated metal foils

Terahertz (THz) radiation, with frequencies spanning from 0.1 to 10 THz, has long been the most underdeveloped frequency band in electromagnetic waves, mainly due to the dearth of available high-power THz sources. Although the last decades have seen a surge of electronic and optical techniques for generating intense THz radiation, all THz sources reported until now have failed to produce above-millijoule (mJ) THz pulses. We present a THz source that enables a THz pulse energy up to tens of mJ, by using an intense laser pulse to irradiate a metal foil.

Ultrahigh-power terahertz (THz) radiation sources are essential for many applications, for example, THz-wave-based compact accelerators and THz control over matter. However, to date none of the THz sources reported, whether based upon large-scale accelerators or high-power lasers, have produced THz pulses with energies above the millijoule (mJ) level. Here, we report a substantial increase in THz pulse energy, as high as tens of mJ, generated by a high-intensity, picosecond laser pulse irradiating a metal foil. A further up-scaling of THz energy by a factor of ∼4 is observed when introducing preplasmas at the target-rear side. Experimental measurements and theoretical models identify the dominant THz generation mechanism to be coherent transition radiation, induced by the laser-accelerated energetic electron bunch escaping the target. Observation of THz-field-induced carrier multiplication in high-resistivity silicon is presented as a proof-of-concept application demonstration. Such an extremely high THz energy not only triggers various nonlinear dynamics in matter, but also opens up the research era of relativistic THz optics.

Terahertz Field Confinement in Nonlinear Metamaterials and Near-Field Imaging

This article reviews recent advances in terahertz science and technology that rely on confining the energy of incident terahertz radiation to small, very sub-wavelength sized regions. We focus on two broad areas of application for such field confinement: metamaterial-based nonlinear terahertz devices and terahertz near-field microscopy and spectroscopy techniques. In particular, we focus on field confinement in: terahertz nonlinear absorbers, metamaterial enhanced nonlinear terahertz spectroscopy, and in sub-wavelength terahertz imaging systems.

Distinguishing Nonlinear Terahertz Excitation Pathways with Two-Dimensional Spectroscopy

High-field terahertz (THz) spectroscopy is enabling the ultrafast study and control of matter in new and exciting ways. However, when intense electromagnetic pulses are used in any kind of pump-probe spectroscopy, several nonlinear excitation pathways can result, leading to scenarios that required the development of multidimensional spectroscopies to illuminate the observed dynamics. Here we demonstrate a clear example where two-dimensional (2D) THz vibrational spectroscopy is needed to distinguish between nonlinear-excitation pathways in CdWO_{4}. We nonlinearly excite a set of Raman-active vibrational modes in CdWO_{4} with broadband THz pulses, and 2D spectroscopy allows us to determine the dominant excitation pathway. We provide a general framework for 2D THz and multi-THz nonlinear phonon spectroscopy in solid systems, which has important implications in contributing needed clarity to the nascent field of nonlinear phononics.

Artificial Generation of High Harmonics via Nonrelativistic Thomson Scattering in Metamaterial

High harmonic generation allows one to extend the frequency of laser to a much broader regime and to study the electron dynamics of matters. However, severely limited by the vague high-order process in natural material and the unfriendly state of the commonly applied gas and plasma media, the ambitious goal of custom-design high harmonics remains exceptionally challenging. Here, we demonstrate that high harmonics can be artificially designed and tailored based on a metamaterial route. With the localized reconstruction of magnetic field in a metamaterial, the nonlinear Thomson scattering, a ubiquitous electromagnetic process which people used to believe that it only occurs with the relativistic velocity, can be stimulated in a nonrelativistic limit, which drives anharmonic oscillation of free electrons and generates high harmonics. An explicit physical model and the numerical simulations perfectly demonstrate the artificial generation and tailoring of the high harmonics. This novel mechanism is entirely dominated by the artificial structure instead of the natural nonlinear compositions. It not only provides unprecedented design freedom to the high harmonic generation but breaks the rigorous prerequisite of the relativistic velocity of the nonlinear Thomson scattering process, which offers fascinating possibilities to the development of new light source and ultrafast optics, and opens up exciting opportunities for the advanced understanding of electrodynamics in condensed matters.

Artificial Generation of High Harmonics via Nonrelativistic Thomson Scattering in Metamaterial

High harmonic generation allows one to extend the frequency of laser to a much broader regime and to study the electron dynamics of matters. However, severely limited by the vague high-order process in natural material and the unfriendly state of the commonly applied gas and plasma media, the ambitious goal of custom-design high harmonics remains exceptionally challenging. Here, we demonstrate that high harmonics can be artificially designed and tailored based on a metamaterial route. With the localized reconstruction of magnetic field in a metamaterial, the nonlinear Thomson scattering, a ubiquitous electromagnetic process which people used to believe that it only occurs with the relativistic velocity, can be stimulated in a nonrelativistic limit, which drives anharmonic oscillation of free electrons and generates high harmonics. An explicit physical model and the numerical simulations perfectly demonstrate the artificial generation and tailoring of the high harmonics. This novel mechanism is entirely dominated by the artificial structure instead of the natural nonlinear compositions. It not only provides unprecedented design freedom to the high harmonic generation but breaks the rigorous prerequisite of the relativistic velocity of the nonlinear Thomson scattering process, which offers fascinating possibilities to the development of new light source and ultrafast optics, and opens up exciting opportunities for the advanced understanding of electrodynamics in condensed matters.

Observation of crossover from intraband to interband nonlinear terahertz optics

In this Letter, we investigate the nonlinear effects of extremely intense few-cycle terahertz (THz) pulses (generated from the organic crystal 4-NN, NN-dimethylamino-4^'4^'-N^'N^'-methyl-stilbazolium 2, 4, 6 trimethylbenzenesulfonate, with peak electrical fields of a few MV/cm) on the carrier dynamics in n-doped semiconductor thin film In_0.53Ga_0.47As. By performing open-aperture Z-scan measurements and recording the transmitted THz energy through semiconductor sample, we observed a strong THz absorption bleaching effect at high fields, followed by an absorption enhancement at even higher fields. We attribute our observations to a crossover from pure intraband carrier dynamics to an interplay between intraband carrier heating and interband carrier generations.

Zener Tunneling Breakdown in Phase-Change Materials Revealed by Intense Terahertz Pulses

We have systematically investigated the spatial and temporal dynamics of crystallization that occur in the phase-change material Ge_{2}Sb_{2}Te_{5} upon irradiation with an intense terahertz (THz) pulse. THz-pump-optical-probe spectroscopy revealed that Zener tunneling induces a nonlinear increase in the conductivity of the crystalline phase. This fact causes the large enhancement of electric field associated with the THz pulses only at the edge of the crystallized area. The electric field concentrating in this area causes a temperature increase via Joule heating, which in turn leads to nanometer-scale crystal growth parallel to the field and the formation of filamentary conductive domains across the sample.

Terahertz microscopy assisted by semiconductor nonlinearities

Terahertz (THz) imaging is currently based on linear effects, but there is great interest on how nonlinear effects induced by terahertz radiation could be exploited to provide extra information that is unobtainable by conventional imaging schemes. In particular, at field strengths on the order of 100  kV cm^-1 to 1  MV cm^-1, transmission properties inside semiconductor materials are largely affected at the picosecond time-scale, which raise the prospect of interesting nonlinear imaging applications at THz frequencies. Here, we experimentally investigate a method to map the two-dimensional nonlinear near-field distribution of an intense THz pulse passing through a thin film-doped semiconductor. By inserting a metamaterial structure between the electro-optic sensor and the doped film, the nonlinear near-field dynamics shows a different and enhanced contrast of the sample when compared to its linear counterpart.

Single-silicon CCD-CMOS platform for multi-spectral detection from terahertz to x-rays

Charge-coupled devices (CCDs) are a well-established imaging technology in the visible and x-ray frequency ranges. However, the small quantum photon energies of terahertz radiation have hindered the use of this mature semiconductor technological platform in this frequency range, leaving terahertz imaging totally dependent on low-resolution bolometer technologies. Recently, it has been shown that silicon CCDs can detect terahertz photons at a high field, but the detection sensitivity is limited. Here we show that silicon, complementary metal-oxide-semiconductor (CMOS) technology offers enhanced detection sensitivity of almost two orders of magnitude, compared to CCDs. Our findings allow us to extend the low-frequency terahertz cutoff to less than 2 THz, nearly closing the technological gap with electronic imagers operating up to 1 THz. Furthermore, with the silicon CCD/CMOS technology being sensitive to mid-infrared (mid-IR) and the x-ray ranges, we introduce silicon as a single detector platform from 1 EHz to 2 THz. This overcomes the present challenge in spatially overlapping a terahertz/mid-IR pump and x-ray probe radiation at facilities such as free electron lasers, synchrotron, and laser-based x-ray sources.

Terahertz-Driven Luminescence and Colossal Stark Effect in CdSe-CdS Colloidal Quantum Dots

Optical properties of colloidal semiconductor quantum dots (QDs), arising from quantum mechanical confinement of charge, present a versatile testbed for the study of how high electric fields affect the electronic structure of nanostructured solids. Studies of quasi-DC electric field modulation of QD properties have been limited by electrostatic breakdown processes under high externally applied electric fields, which have restricted the range of modulation of QD properties. In contrast, here we drive CdSe-CdS core-shell QD films with high-field THz-frequency electromagnetic pulses whose duration is only a few picoseconds. Surprisingly, in response to the THz excitation, we observe QD luminescence even in the absence of an external charge source. Our experiments show that QD luminescence is associated with a remarkably high and rapid modulation of the QD bandgap, which changes by more than 0.5 eV (corresponding to 25% of the unperturbed bandgap energy). We show that these colossal energy shifts can be explained by the quantum confined Stark effect even though we are far outside the regime of small field-induced shifts in electronic energy levels. Our results demonstrate a route to extreme modulation of material properties and to a compact, high-bandwidth THz detector that operates at room temperature.

Subcycle Extreme Nonlinearities in GaP Induced by an Ultrastrong Terahertz Field

We report on the experimental observation of extreme laser spectral broadening and a change in optical transmission in gallium phosphite induced by 25  MV/cm terahertz (THz) single-cycle internal field. Such intense THz radiation leads to twofold transient modifications of the optical properties in the electro-optical crystal. First, the electric field provokes extensive cross-phase modulation via the χ^{(2)} and χ^{(3)} nonlinearities on a copropagating 50 fs near infrared laser pulse which turns into 500% spectral broadening. Second, we observe an instantaneous change of the optical transmission occurring at the THz field which is alleged to interband Zener tunneling and charge carrier density modification by impact ionization turning the semiconductor in a metal-like transient state. The presented scheme displays a pathway to coherently control the optical properties of semiconductors on an ultrafast time scale by a strong THz field.

Hybrid metamaterial switching for manipulating chirality based on VO2 phase transition

Polarization manipulations of electromagnetic waves can be obtained by chiral and anisotropic metamaterials routinely, but the dynamic and high-efficiency modulations of chiral properties still remain challenging at the terahertz range. Here, we theoretically demonstrate a new scheme for realizing thermal-controlled chirality using a hybrid terahertz metamaterial with embedded vanadium dioxide (VO₂) films. The phase transition of VO₂ films in 90° twisted E-shaped resonators enables high-efficiency thermal modulation of linear polarization conversion. The asymmetric transmission of linearly polarized wave and circular dichroism simultaneously exhibit a pronounced switching effect dictated by temperature-controlled conductivity of VO₂ inclusions. The proposed hybrid metamaterial design opens exciting possibilities to achieve dynamic modulation of terahertz waves and further develop tunable terahertz polarization devices.

Photoinduced Nonlinear Mixing of Terahertz Dipole Resonances in Graphene Metadevices

The first experimental demonstration of nonlinear terahertz difference-frequency generation in a hybrid graphene metadevice is reported. Decades of research have revealed that terahertz-wave generation is impossible in single-layer graphene. This limitation is overcome and nonlinear terahertz generation by ultra-short optical pulse injection is demonstrated. This device is an essential step toward atomically thin, nonlinear terahertz optoelectronic components.

High-performing nonlinear visualization of terahertz radiation on a silicon charge-coupled device

Photoinduced electron transitions can lead to significant changes of the macroscopic electronic properties in semiconductors. This principle is responsible for the detection of light with charge-coupled devices. Their spectral sensitivity is limited by the semiconductor bandgap which has restricted their visualization capabilities to the optical, ultraviolet, and X-ray regimes. The absence of an imaging device in the low frequency terahertz range has severely hampered the advance of terahertz imaging applications in the past. Here we introduce a high-performing imaging concept to the terahertz range. On the basis of a silicon charge-coupled device we visualize 5–13 THz radiation with photon energy under 2% of the sensor's band-gap energy. The unprecedented small pitch and large number of pixels allow the visualization of complex terahertz radiation patterns in real time and with high spatial detail. This advance will have a great impact on a wide range of terahertz imaging disciplines.

The absence of an imaging device in the low frequency terahertz range has hindered the advance of applications. Here, Shalaby et al. introduce a silicon based charge coupled device allowing the visualization of terahertz radiation in real time and at high spatial detail.

Terahertz Quantum Plasmonics of Nanoslot Antennas in Nonlinear Regime

Quantum tunneling in plasmonic nanostructures has presented an interesting aspect of incorporating quantum mechanics into classical optics. However, the study has been limited to the subnanometer gap regime. Here, we newly extend quantum plasmonics to gap widths well over 1 nm by taking advantage of the low-frequency terahertz regime. Enhanced electric fields of up to 5 V/nm induce tunneling of electrons in different arrays of ring-shaped nanoslot antennas of gap widths from 1.5 to 10 nm, which lead to a significant nonlinear transmission decrease. These observations are consistent with theoretical calculations considering terahertz-funneling-induced electron tunneling across the gap.