Frequency multiplication of terahertz signals on a solid state platform is highly sought-after for the next generation of high-speed electronics and the creation of frequency combs. Solutions to efficiently generate extreme harmonics (up to the $31^{\rm{st}}$ harmonic and beyond) of a terahertz signal with modest input intensities, however, remain elusive. Using fully nonperturbative simulations and complementary analytical theory, we show that 3D Dirac semimetals (DSMs) have enormous potential as compact sources of extreme terahertz harmonics, achieving energy conversion efficiencies beyond $10^{-5}$ at the $31^{\rm{st}}$ harmonic with input intensities on the order of $10$ MW/cm$^2$, over $10^5$ times lower than in conventional THz high harmonic generation systems. Our theory also reveals a fundamental feature in the nonlinear optics of 3D DSMs: a distinctive regime where higher-order optical nonlinearity vanishes, arising as a direct result of the extra dimensionality in 3D DSMs compared to 2D DSMs. Our findings should pave the way to the development of efficient platforms for high-frequency terahertz light sources and optoelectronics based on 3D DSMs.
We show that 3D Dirac semimetals are promising candidates for highly efficient optical-to-terahertz conversion due to their extreme optical nonlinearities. In particular, we predict that the conversion efficiency of Cd3As2 exceeds typical materials like LiNbo3 by >5000 times over nanoscale propagation distances. Our studies show that even when no restrictions are placed on propagation distance, Cd3As2 still outperforms LiNbo3 in efficiency by >10 times. Our results indicate that by tuning the Fermi energy, Pauli blocking can be leveraged to realize a step-like efficiency increase in the optica…
As a fascinating topological phase of matter, Weyl semimetals host chiral fermions with distinct chiralities and spin textures. Optical excitations involving those chiral fermions can induce exotic carrier responses, and in turn lead to novel optical phenomena. Here, we discover strong coherent chiral terahertz emission from the Weyl semimetal TaAs and demonstrate unprecedented manipulation over its polarization on a femtosecond timescale. Such polarization control is achieved via the colossal ultrafast photocurrents in TaAs arising from the circular or linear photogalvanic effect. We unravel …
We report on terahertz high-harmonic generation in a Dirac semimetal as a function of the driving-pulse ellipticity and on a theoretical study of the field-driven intraband kinetics of massless Dirac fermions.Very efficient control of third-harmonic yield and polarization state is achieved in electron-doped Cd$_3$As$_2$ thin films at room temperature. The observed tunability is understood as resulting from terahertz-field driven intraband kinetics of the Dirac fermions. Our study paves the way for exploiting nonlinear optical properties of Dirac matter for applications in signal processing and…
Semi-metals might offer a stronger interaction and a better confinement for terahertz wave than semiconductors, while preserve tunability. Particularly, graphene-based materials are envisioned as terahertz modulators, filters and ultra-broadband sources. However, the understanding of terahertz generation from those materials is still not clear, thus limits us recognizing the potential and improving device performances. Graphite, the mother material of graphene and a typical bulk semi-metal, is a good system to study semi-metals and graphene-based materials. Here we experimentally modulate and …
The enhanced photonic spin hall effect (PSHE) plays a positive role in the flexible manipulation of photons. Here, by combining Dirac semimetals with Bragg reflector constructed by one-dimensional photonic crystal, we theoretically design a simple multilayer structure to enhance and manipulate the PSHE. Through the detailed and optimal design of the conductivity characteristics of Dirac semimetals and the structural parameters of the whole model, we realize the excitation of Optical Tamm states (OTSs) in the multilayer structure, so that the PSHE can be enhanced and controllable. The theoretic…
The relaxation dynamics of photoexcited quasiparticles of three-dimensional (3D) Dirac semimetals are vital towards their application in high performance electronic and optoelectronic devices. In this work, the relaxation dynamics of photoexcited carriers of 3D Dirac semimetal Cd3As2 are investigated by transient terahertz spectroscopy. The visible pump-THz probe spectroscopy measurement shows clear biexponential decays with two characteristic time constants. According to the pump-power and temperature dependence, these two characteristic time constants are attributed to the electron phonon co…
The thermoelectric effects of topological semimetals have attracted tremendous research interest because many topological semimetals are excellent thermoelectric materials and thermoelectricity serves as one of their most important potential applications. In this work, we reveal the transient photothermoelectric response of Dirac semimetallic Cd3As2, namely the photo-Seebeck effect and photo-Nernst effect, by studying the terahertz (THz) emission from the transient photocurrent induced by these effects. Our excitation polarization and power dependence confirm that the observed THz emission is …
Giant enhancement of terahertz high-harmonic generation by cavity engineering of a three-dimensional Dirac semimetal
TU Dortmund University（多特蒙德工业大学）；CNR-Istituto Nanoscienze（国家研究委员会纳米科学研究所）；Scuola Normale Superiore（比萨高等师范学院）；University of Basel（巴塞尔大学）；Fudan University（复旦大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）
The topological three-dimensional Dirac semimetal Cd3As2 has drawn great attention for the novel physics and promising applications in optoelectronic devices operating in the infrared and THz regimes. Among the extensive studies in the past decades, one intriguing debate is the underlined mechanism that governing the nonequilibrium carrier dynamics following photoexcitation. In this study, the temperature dependent photocarrier dynamics in Cd3As2 film has been investigated with time-resolved terahertz spectroscopy. The experimental results demonstrate that photoexcitation results in abrupt inc…
Three-dimensional (3D) semimetals have been predicted and demonstrated to have a wide variety of interesting properties associated with its linear energy dispersion. In analogy to two-dimensional (2D) Dirac semimetals, such as graphene, Cd3As2, a 3D semimetal, has shown ultra-high mobility, large Fermi velocity, and has been hypothesized to support plasmons at terahertz frequencies. In this work, we demonstrate synthesis of high-quality large-area Cd3As2 thin-films through thermal evaporation as well as the experimental realization of plasmonic structures consisting of periodic arrays of Cd3As…
Topological Dirac semimetals (TDSM), such as Cd$_3$As$_2$ and Na$_3$Bi, exhibits strong optical dichroism with contrasting dielectric permittivity along different crystal axes. However, such optical dichroism is often overlooked in the study of TDSM-based optoelectronic devices, and whether such optical dichroism can lead to unique functionalities not found under the isotropic approximation remain an open question thus far. Here we show that the optical dischroism in TDSM lead to starkly different terahertz (THz) responses and device performance as compared to the isotropic case. Using finite-…
3D Dirac semimetals (DSMs) are promising materials for terahertz high harmonic generation (HHG). We show that 3D DSMs' high nonlinearity opens up a regime of nonlinear optics where extreme subwavelength current density features develop within nanoscale propagation distances of the driving field. Our results reveal orders-of-magnitude enhancement in HHG intensity with thicker 3D DSM films, and show that these subwavelength features fundamentally limit HHG enhancement beyond an optimal film thickness. This decrease in HHG intensity beyond the optimal thickness constitutes an effective propagatio…
The brightness of a light source defines its applicability to nonlinear phenomena in science. Bright low frequency terahertz (< 5THz) radiation confined to a diffraction-limited spot size is a present hurdle due to the broad bandwidth and long wavelengths associated with single-cycle terahertz pulses as well as due to the lack of terahertz wavefront correctors. Here, using a present-technology system, we employ a new concept of terahertz wavefront manipulation and focusing optimization. We demonstrate a spatio-temporal confinement of terahertz energy at its physical limits to the least possibl…
Terahertz near fields of gold metamaterials resonant at a frequency of $0.88\,\rm THz$ allow us to enter an extreme limit of non-perturbative ultrafast THz electronics: Fields reaching a ponderomotive energy in the keV range are exploited to drive nondestructive, quasi-static interband tunneling and impact ionization in undoped bulk GaAs, injecting electron-hole plasmas with densities in excess of $10^{19}\,\rm cm^{-3}$. This process causes bright luminescence at energies up to $0.5\,\rm eV$ above the band gap and induces a complete switch-off of the metamaterial resonance accompanied by self-…
Weyl semimetals possess unique electrodynamic properties due to a combination of strongly anisotropic and gyrotropic bulk conductivity, surface conductivity, and surface dipole layer. We explore the potential of popular tip-enhanced optical spectroscopy techniques for studies of bulk and surface topological electron states in these materials. Anomalous dispersion, extreme anisotropy, and the optical Hall effect for surface polaritons launched by a nanotip provides information about Weyl node position and separation in the Brillouin zone, the value of the Fermi momentum, and the matrix elements…
The majority of sources of coherent optical radiation rely on laser oscillators driven by population inversion. Despite their technological importance in communications, medicine, industry, and other fields, it remains a challenge to access the spectral range of 0.1-10 THz (the "terahertz gap"), a frequency band for applications ranging from spectroscopy to security and high-speed wireless communications. Here, we propose a way to produce coherent radiation spanning the THz gap by efficient second-harmonic generation (SHG) in low-loss dielectric structures, starting from technologically mature…
A tilted-pulse-front pumped terahertz pulse source is proposed for the generation of extremely high field single-cycle terahertz pulses. The very simple and compact source consists of a single crystal slab having a blazed reflection grating grooved in its back surface. Its further important advantages are the energy scalability and the symmetric THz beam profile. Generation of 50 MV/cm focused field with 5.6 mJ terahertz pulse energy is predicted for a 5 cm diameter LiNbO$_3$ crystal, if the pump pulse is of 450 mJ energy, 1030 nm central wavelength and 1 ps pulse duration. Such sources can ba…
Plasmonic metamaterials and metasurfaces offer new opportunities in developing high performance terahertz emitters and detectors beyond the limitations of conventional nonlinear materials. However, simple meta-atoms for second-order nonlinear applications encounter fundamental trade-offs in the necessary symmetry breaking and local-field enhancement due to radiation damping that is inherent to the operating resonant mode and cannot be controlled separately. Here we present a novel concept that eliminates this restriction obstructing the improvement of terahertz generation efficiency in nonline…
Laser-induced ionization is a fundamental tool for the frequency conversion of lasers into spectral regions so far inaccessible, including both extreme ultraviolet and terahertz. The low-frequency currents induced by laser-driven ionization generate extremely broadband, single-cycle terahertz pulses, with applications ranging from remote sensing to optical pulse diagnostic, yet strong limitations arise from the low conversion efficiencies of this mechanism. We show a remarkable increase of the radiated terahertz energy with the laser wavelength and we relate this observation to the stronger ac…
A one-dimensional photonic-crystal (PC) cavity with nanoholes is proposed for extremely enhancing the THz electric fields by utilizing the electromagnetic (EM) boundary conditions, where both slot effect (for the perpendicular component of the electric displacement field) and anti-slot effect (for the parallel component of the electric field) contribute to the considerable field enhancement. The EM energy density can be enhanced in the high refractive index material by a factor of (εh/εl)^2, where εh and εl are the permittivities of the high and low refractive index materials, respectively. Co…
Ultrafast Terahertz and Optical Spectroscopy under Synergetic Extreme Conditions
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Tsung-Dao Lee Institute, Department of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院紫江研究院）；International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料科学中心）
Graphene is a single layer of covalently bonded carbon atoms, which was discovered only 8 years ago and yet has already attracted intense research and commercial interest. Initial research focused on its remarkable electronic properties, such as the observation of massless Dirac fermions and the half-integer quantum Hall effect. Now graphene is finding application in touch-screen displays, as channels in high-frequency transistors and in graphene-based integrated circuits. The potential for using the unique properties of graphene in terahertz-frequency electronics is particularly exciting; how…
We theoretically study the generation of terahertz (THz) radiation by two-color filamentation of ultrashort laser pulses with different wavelengths. We consider wavelengths in the range from 0.6 to 10.6 $μ$m, thus covering the whole range of existing and future powerful laser sources in the near, mid and far-infrared. We show how different parameters of two-color filaments and generated THz pulses depend on the laser wavelength. We demonstrate that there is an optimal laser wavelength for two-color filamentation that provides the highest THz conversion efficiency and results in generation of e…
Coherent continuous wave (CW) terahertz spectroscopy is an extremely valuable technique that allows for the interrogation of systems that exhibit narrow resonances in the terahertz (THz) frequency range, such as high-quality (high-Q) THz whispering-gallery mode resonators. Unfortunately, common implementations are dramatically impaired by deficiencies in the used data analysis schemes. Here, we show that the physics of the problem presents an elegant solution whose full potential has remained overlooked until now. We argue that, thanks to the causality of physical systems, Hilbert transformati…
Free-space super-strong terahertz (THz) electromagnetic fields offer multifaceted capabilities for reaching extreme nonlinear THz optics, accelerating and manipulating charged particles, and realizing other fascinating applications. However, the lack of powerful solid-state THz sources with single pulse energy >1 mJ is impeding the proliferation of extreme THz applications. The fundamental challenge lies in hard to achieve high efficiency due to high intensity pumping caused crystal damage, linear absorption and nonlinear distortion induced short effective interaction length, and so on. Here, …
Extreme Terahertz Nonlinear Phononics by Coherence-Imprinted Control of Hybrid Order
Ames National Laboratory（艾姆斯国家实验室）；Department of Physics and Astronomy, Iowa State University（爱荷华州立大学物理与天文系）；Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology（北京理工大学物理学院先进光电量子架构与测量教育部重点实验室量子物理中心）；Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems, Beijing Institute of Technology（北京理工大学北京纳米光子学与超精细光电系统重点实验室）；Key Laboratory for Laser Plasmas (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院激光等离子体教育部重点实验室）；Zhangjiang Institute for Advanced Study and Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学张江高等研究院及李政道研究所）
We theoretically study unattenuated electromagnetic guided wave modes in centrosymmetric Weyl semimetal layered systems. By solving Maxwell's equations for the electromagnetic fields and using the appropriate boundary conditions, we derive dispersion relations for propagating modes in a finite-sized Weyl semimetal. Our findings reveal that for ultrathin structures, and proper Weyl cones tilts, extremely localized guided waves can propagate along the semimetal interface over a certain range of frequencies. This follows from the anisotropic nature of the semimetal where the diagonal components o…
We report on the generation of bulk photocurrents in materials driven by non-resonant bi-chromatic fields that are circularly polarized and co-rotating. The nonlinear photocurrents have a fully controllable directionality and amplitude without requiring carrier-envelope-phase stabilization or few-cycle pulses, and are generated with photon energies much smaller than the band gap (reducing heating in the photo-conversion process). We demonstrate with ab-initio calculations that the photocurrent generation mechanism is universal and arises in gaped materials (Si, diamond, MgO, hBN), in semi-meta…
We report extensive enhancement in the refractive index of artificially designed metamaterials by exploiting the deep subwavelength coupling in a free-standing, thin-film metal-dielectric-metal checkboard structure. A record high refractive index of 77.02+43.22i is obtained at terahertz frequencies. The detailed investigations reveal that the enhancement of the effective refractive index of the structure via deep subwavelength coupling in a bilayer design is governed by a power law, which is an effective and simpler approach to design high index metamaterial. The approach relies on deep subwav…
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 Bi$_2$Se$_3$ topological insulator and topological-insulator-grati…
Prototypical three-dimensional (3D) topological Dirac semimetals (DSMs), such as Cd$_3$As$_2$ and Na$_3$Bi, contain electrons that obey a linear momentum-energy dispersion with different Fermi velocities along the three orthogonal momentum dimensions. Despite being extensively studied in recent years, the inherent \emph{Fermi velocity anisotropy} has often been neglected in the theoretical and numerical studies of 3D DSMs. Although this omission does not qualitatively alter the physics of light-driven massless quasiparticles in 3D DSMs, it does \emph{quantitatively} change the optical coeffici…
As a newly emergent type-II Dirac semimetal, Platinum Telluride (PtTe2) stands out from other 2D noble-transition-metal dichalcogenides for the unique structure and novel physical properties, such as high carrier mobility, strong electron-phonon coupling and tunable bandgap, which make the PtTe2 a good candidate for applications in optoelectronics, valleytronics and far infrared detectors. Although the transport properties of PtTe2 have been studied extensively, the dynamics of the nonequilibrium carriers remain nearly uninvestigated. Herein we employ optical pump-terahertz (THz) probe spectro…
We report optical parametric amplification (OPA) of low-frequency infrared pulses in the intermediate region between terahertz (THz) frequency and mid-infrared (MIR), i.e., from 16.9 to 44.8 THz. The 255-fs laser output of the Yb:KGW regenerative amplifier is compressed to 11-fs pulses using a multi-plate broadening scheme, which generates THz-to-MIR pulses with a spectrum extending to approximately 50 THz by intra-p1ulse differential frequency generation (DFG) in GaSe. The THz-to-MIR pulses are further amplified using a two-stage OPA in GaSe. The temporal dynamics and photocarrier effects dur…
Ultrashort electron bunches are useful for applications like ultrafast imaging and coherent radiation production. Currently, however, the shortest achievable bunches, at attosecond time scales, have only been realized in the single or very few electron regime, limited by Coulomb repulsion and electron energy spread. Using ab initio simulations and theoretical analysis, we show that highly-charged bunches are achievable by subjecting relativistic (few MeV-scale) electrons to a superposition of terahertz and optical pulses. Using realistic electron bunches and laser pulse parameters which are wi…
We theoretically study the THz-induced high-order harmonic generation (HHG) and nonlinear electric transport in graphene based on the quantum master equation with the relaxation time approximation. To obtain microscopic insight into the phenomena, we compare the results of the fully dynamical calculations with those under a quasi-static approximation, where the electronic system is approximated as a nonequilibrium steady state. As a result, we find that the THz-induced electron dynamics in graphene can be accurately modeled with the nonequilibrium steady-state at each instance. The population …
