Based on a structure consisting of a single graphene layer situated on a periodic dielectric grating, we show theoretically that intense terahertz (THz) radiations can be generated by an electron bunch moving atop the graphene layer. The underlying physics lies in the fact that a moving electron bunch with rather low electron energy ($\sim$1 keV) can efficiently excite graphene plasmons (GPs) of THz frequencies with a strong confinement of near-fields. GPs can be further scattered into free space by the grating for those satisfying the phase matching condition. The radiation patterns can be controlled by varying the velocity of the moving electrons. Importantly, the radiation frequencies can be tuned by varying the Fermi level of the graphene layer, offering tunable THz radiations that can cover a wide frequency range. Our results could pave the way toward developing tunable and miniature THz radiation sources based on graphene.
We reveal that there exists a class of graphene structures (a sub-class of bilayer graphene nanoribbons) which has unusually strong optical response in the terahertz (THz) and far infrared (FIR) regime. The peak conductance of terahertz/FIR active bilayer ribbons is around two orders of magnitude higher than the universal conductance of $e^2/4\hbar$ observed in graphene sheets. The criterion for the terahertz/FIR active sub-class is a bilayer graphene nanoribbon with one-dimensional massless Dirac Fermion energy dispersion near the $Γ$ point. Our results overcome a significant obstacle that hi…
We investigated ultrafast carrier dynamics in graphene with near-infrared transient absorption measurement after intense half-cycle terahertz pulse excitation. The terahertz electric field efficiently drives the carriers, inducing large transparency in the near-infrared region. Theoretical calculations using the Boltzmann transport equation quantitatively reproduce the experimental findings. This good agreement suggests that the intense terahertz field should promote remarkable impact ioniza- tion process, which leads to suppression of optical phonon emission and results in efficient carrier t…
Graphene is a two-dimensional crystal consisting of a monatomic layer of carbon atoms. Electrons and holes in graphene behave as quasi-relativistic particles with zero effective mass and large (as compared to semiconductors) Fermi velocity. These unique physical properties can be used for designing detectors, emitters and modulators of terahertz radiation. Here we discuss several ideas of using graphene based structures for emission of terahertz radiation.
The terahertz emission from difference-frequency in biased superlattices is calculated with the excitonic effect included. Owing to the doubly resonant condition and the excitonic enhancement, the typical susceptibility can be as large as $10^{-5}$ m/V. The doubly resonant condition can always be realized by adjusting the bias voltage and the laser frequencies, thus the in-situ tunable emission is efficient in a range of several terahertz. Continuous wave operation with 1% quantum efficiency and $μ$W output power is feasible as the signal absorption in undoped superlattices is negligible.
We report on noise and thermal conductance measurements taken in order to determine an upper bound on the performance of graphene as a terahertz photon detector. The main mechanism for sensitive terahertz detection in graphene is bolometric heating of the electron system. To study the properties of a device using this mechanism to detect terahertz photons, we perform Johnson noise thermometry measurements on graphene samples. These measurements probe the electron-phonon behavior of graphene on silicon dioxide at low temperatures. Because the electron-phonon coupling is weak in graphene, superc…
It is well known that impurities play a central role in the linear and nonlinear response of graphene at optical and terahertz frequencies. In this work, we calculate the bands and intraband dipole connection elements for nitrogen-doped monolayer graphene using a density functional tight binding approach. Employing these results, we calculate the linear and nonlinear response of the doped graphene to terahertz pulses using a density-matrix approach in the length gauge. We present the results for the linear and nonlinear mobility as well as third harmonic generation in graphene for adsorbed and…
Observations of terahertz loss to gain switching in transmission through gates on biased graphene sandwiches are explained by response under electron streaming in graphene. Basing on this consideration the terahertz source is proposed consisting of silicon resonator placed on the sandwich with current flow in graphene. It should provide tunable by bias emission in wide terahertz band. The source is direct terahertz analog of tunable microwave laser demonstrated.
We propose and discuss terahertz electro-absorption modulators based on graphene plasmonic structures. The active device consists of a self-gated pair of graphene layers, which are patterned to structures supporting THz plasmonic resonances. These structures allow for efficient control of the effective THz optical conductivity, thus absorption, even at frequencies much higher than the Drude roll-off in graphene where most previously proposed graphene-based devices become inefficient. Our analysis shows that reflectance-based device configurations, engineered so that the electric field is enhan…
Terahertz field induced photocurrents in graphene were studied experimentally and by microscopic modeling. Currents were generated by cw and pulsed laser radiation in large area as well as small-size exfoliated graphene samples. We review general symmetry considerations leading to photocurrents depending on linear and circular polarized radiation and then present a number of situations where photocurrents were detected. Starting with the photon drag effect under oblique incidence, we proceed to the photogalvanic effect enhancement in the reststrahlen band of SiC and edge-generated currents in …
We have fabricated a centimeter-size single-layer graphene device, with a gate electrode, which can modulate the transmission of terahertz and infrared waves. Using time-domain terahertz spectroscopy and Fourier-transform infrared spectroscopy in a wide frequency range (10-10000 cm^{-1}), we measured the dynamic conductivity change induced by electrical gating and thermal annealing. Both methods were able to effectively tune the Fermi energy, E_F, which in turn modified the Drude-like intraband absorption in the terahertz as well as the '2E_F onset' for interband absorption in the mid-infrared…
We demonstrate efficient terahertz (THz) modulation by coupling graphene strongly with a broadband THz metasurface device. This THz metasurface, made of periodic gold slit arrays, shows near unity broadband transmission, which arises from coherent radiation of the enhanced local-field in the slits. Utilizing graphene as an active load with tunable conductivity, we can significantly modify the local-field enhancement and strongly modulate the THz wave transmission. This hybrid device also provides a new platform for future nonlinear THz spectroscopy study of graphene.
The gate-tunable terahertz (THz) absorption of graphene layers with a resonant metal back reflector (RMBF) is theoretically investigated. We demonstrate that the THz absorption of graphene with RMBF can vary from nearly negligible to nearly total by tuning the external gate voltage. This peculiar nearly total THz absorption can be attributed to the Fabry-Perot cavity effect, which enhances the absorption and reduces the reflection of graphene. The absorption spectra of the graphene-RMBF structure can also be tailored in bandwidth and center frequency by changing the thickness and dielectric co…
We consider the nonlinear terahertz response of n-doped monolayer graphene at room temperature using a microscopic theory of carrier dynamics. Our tight-binding model treats the carrier-field interaction in the length gauge, includes phonon as well as short-range neutral-impurity scattering, and fully accounts for the intrinsic nonlinear response of graphene near the Dirac point. Treating each interaction microscopically allows us to separate contributions from current clipping, phonon creation, and elastic impurity scattering. Although neutral impurity scattering and phonon scattering are bot…
We use time dependent perturbation theory to study quantum size effects on the terahertz nonlinear response of metallic graphene armchair nanoribbons of finite length under an applied electric field. Our work shows that quantization due to the finite length of the nanoribbon, the applied field profile, and the broadening of the graphene spectrum all play a significant role in the resulting nonlinear conductances. In certain cases, these effects can significantly enhance the nonlinearity over that for infinitely-long metallic armchair graphene nanoribbon.
We report on reflective electro-optic sampling measurements of TeraHertz emission from nanometer-gate-length InGaAs-based high electron mobility transistors. The room temperature coherent gate-voltage tunable emission is demonstrated. We establish that the physical mechanism of the coherent TeraHertz emission is related to the plasma waves driven by simultaneous current and optical excitation. A significant shift of the plasma frequency and the narrowing of the emission with increasing channel's current are observed and explained as due to the increase of the carriers density and drift velocit…
When light is absorbed by a semiconductor, photoexcited charge carriers enhance the absorption of far-infrared radiation due to intraband transitions. We observe the opposite behavior in monolayer graphene, a zero-gap semiconductor with linear dispersion. By using time domain terahertz (THz) spectroscopy in conjunction with optical pump excitation, we observe a reduced absorption of THz radiation in photoexcited graphene. The measured spectral shape of the differential optical conductivity exhibits non-Drude behavior. We discuss several possible mechanisms that contribute to the observed low-f…
We investigate the pseudospin-dependent density-energy relation (whose differential with respect to energy is density of states) of a monolayer graphene under intense terahertz laser field by exactly solving the time-dependent Schrödinger equation with help of Floquet's theorem. We find that psedospin polarization can be induced by a circular polarized terahertz laser field. The psedospin polarization in K and K$^{\prime}$ valleys can be exactly opposite sign when the electron densities in these two calleys are equivalent. Further more, we find that the psedospin polarization can be manipulate…
Epitaxial graphene mesas and ribbons are investigated using terahertz (THz) nearfield microscopy to probe surface plasmon excitation and THz transmission properties on the sub-wavelength scale. The THz near-field images show variation of graphene properties on a scale smaller than the wavelength, and excitation of THz surface waves occurring at graphene edges, similar to that observed at metallic edges. The Fresnel reflection at the substrate SiC/air interface is also found to be altered by the presence of graphene ribbon arrays, leading to either reduced or enhanced transmission of the THz wa…
We theoretically investigate the ultrafast terahertz(THz) properties of monolayer graphene. The analytical formulations of the photon carrier, electric polarization and optical current are obtained by solving the Bloch-equations in present of the ultrafast THz Gaussian pulse. Graphene shows a large nonlinear and ultrafast optical response at THz frequencies due to the gapless and relativistic Dirac particles with nearly linear energy dispersion. It is found that the photon carrier density, electric polarization and optical current density increase with increasing the frequency of the THz pulse…
We have measured the ultrafast anisotropic optical response of highly doped graphene to an intense single cycle terahertz pulse. The time profile of the terahertz-induced anisotropy signal at 800 nm has minima and maxima repeating those of the pump terahertz electric field modulus. It grows with increasing carrier density and demonstrates a specific nonlinear dependence on the electric field strength. To describe the signal, we have developed a theoretical model that is based on the energy and momentum balance equations and takes into account optical phonons of graphene and substrate. Accordin…
We propose and analyze the detector of modulated terahertz (THz) radiation based on the graphene field-effect transistor with mechanically floating gate made of graphene as well. The THz component of incoming radiation induces resonant excitation of plasma oscillations in graphene layers (GLs). The rectified component of the ponderomotive force between GLs invokes resonant mechanical swinging of top GL, resulting in the drain current oscillations. To estimate the device responsivity, we solve the hydrodynamic equations for the electrons and holes in graphene governing the plasma-wave response,…
We analyze the operation of the graphene n+-i-n-n+ field-effect transistors (GFETs) and lateral diodes (GLDs) with the injection of ballistic electrons into the n-region. The momentum transfer of the injected ballistic electrons could lead to an effective Coulomb drag of the quasi-equilibrium electrons in the n-region and the plasma instability in the GFETs and GLDs. The instability enables the generation of terahertz radiation. The obtained results can be used for the optimization of the structures under consideration for different devices, in particular, terahertz emitters.
We use an exact solution of the relaxation-time Boltzmann equation in a uniform AC electric field to describe the nonlinear optical response of graphene in the terahertz (THz). The cases of monolayer, bilayer and ABA-stacked trilayer graphene are considered, and the monolayer species is shown to be the most appropriate one to exploit the nonlinear free electron response. We find that a single layer of monolayer graphene shows an optical bistability in the THz range, within the electromagnetic power range attainable in practice. The current associated with the third harmonic generation is also …
In the presence of strong magnetic fields the electronic bandstructure of graphene drastically changes. The Dirac cone collapses into discrete non-equidistant Landau levels, which can be externally tuned by changing the magnetic field. In contrast to conventional materials, specific Landau levels are selectively addressable using circularly polarized light. Exploiting these unique properties, we propose the design of a tunable laser operating in the technologically promising terahertz spectral range. To uncover the many-particle physics behind the emission of light, we perform a fully quantum …
We show that charge carrier transport in graphene exhibit sharp resonances in the presence of spatially and temporarily modulated scattering. Resonances occur when the period of an applied a-c field corresponds to the time taken by quasi-ballistic carriers to drift over a spatial scattering period, provided the latter is shorter than the distance taken by carriers to emit an optic phonon. We show that such system can be achieved with interdigitated gates energized with an a-c bias on graphene layers. Gate separation and fields to achieve ballistic transport would result in resonances in the te…
Recent measurements of the conductivity of nanoperforated graphene are interpreted in terms of edges states existing near the edge of each nanohole. The perimetric quantization of edge states should result in the formation of a quasi-equidistant ladder of quasistationary energy levels. Dirac fermions filling this ladder rotate about each nanohole in the direction determined by the valley index. It is shown that the irradiation of this system by circularly polarized terahertz radiation leads to a resonance in absorption in one of the valleys. The magnitude of absorption at the resonance frequen…
We propose and substantiate the concept of terahertz (THz) laser enabled by the resonant electron radiative transitions between graphene layers (GLs) in double-GL structures. We estimate the THz gain for TM-mode exhibiting very low Drude absorption in GLs and show that the gain can exceed the losses in metal-metal waveguides at the low end of the THz range. The spectrum of the emitted photons can be tuned by the applied voltage. A weak temperature dependence of the THz gain promotes an effective operation at room temperature.
We theoretically study the population inversion and negative dynamic conductivity in intrinsic graphene in the terahertz (THz) frequency range upon pulse photoexcitation with near-/mid-infrared wavelength. The threshold pulse energy required for the population inversion and negative dynamic conductivity can be orders-of-magnitude lower when the pulse photon energy is lower, due to the inverse proportionality of the photoexcited carrier concentration to the pulse photon energy and to the weaker carrier heating. We also investigate the dependence of the dynamic conductivity on the momentum relax…
A multiple-graphene-layer (MGL) structure with a stack of GLs and a highly conducting bottom GL on SiC substrate pumped by optical radiation is considered as an active region of terahertz (THz) and far infrared (FIR) lasers with external metal mirrors. The dynamic conductivity of the MGL structure is calculated as a function of the signal frequency, the number of GLs, and the optical pumping intensity. The utilization of optically pumped MGL structures might provide the achievement of lasing with the frequencies of about 1 THz at room temperature due to a high efficiency.
We study the interaction between polarized terahertz (THz) radiation and micro-structured large-area graphene in transmission geometry. In order to efficiently couple the radiation into the two-dimensional material, a lateral periodic patterning of a closed graphene sheet by intercalation doping into stripes is chosen, yielding unequal transmittance of the radiation polarized parallel and perpendicular to the stripes. Indeed, a polarization contrast up to 20% is observed. The effect even increases up to 50% when removing graphene stripes in analogy to a wire grid polarizer. The polarization de…
Graphene is considered as a promising platform for detectors of high-frequency radiation up to the terahertz (THz) range due to graphene$'$s superior electron mobility. Previously it has been shown that graphene field effect transistors (FETs) exhibit room temperature broadband photoresponse to incoming THz radiation thanks to the thermoelectric and/or plasma wave rectification. Both effects exhibit similar functional dependences on the gate voltage and therefore it was found to be difficult to disentangle these contributions in the previous studies. In this letter, we report on combined exper…
Injection or optical generation of electrons and holes in graphene bilayers (GBLs) can result in the interband population inversion enabling the terahertz (THz) radiation lasing. The intraband radiative processes compete with the interband transitions. We demonstrate that remote doping enhances the indirect interband generation of photons in the proposed GBL heterostructures. Therefore such remote doping helps surpassing the intraband (Drude) absorption and results in large absolute values of the negative dynamic THz conductivity in a wide range of frequencies at elevated (including room) temp…
We compute the terahertz third-order nonlinear conductance of metallic armchair graphene nanoribbons using time-dependent perturbation theory. Significant enhancement of the intrinsic third-order conductance over the result for instrinsic 2D single-layer graphene is observed over a wide range of temperatures. We also investigate the nonlinear response of extrinsic metallic acGNR with |E_F|<<200 meV. We find that the third-order conductance exhibits a strong Fermi level dependence at low temperatures. A third-order critical field strength of between 1 and 5 kV/m is computed for the Kerr conduct…
In a semiconductor illuminated by a strong terahertz field, optically excited electron-hole pairs can recombine to emit light in a broad frequency comb evenly spaced by twice the terahertz frequency. Such high-order terahertz sideband generation is of interest both as an example of extreme nonlinear optics and also as a method for ultrafast electro-optical modulation. So far, this phenomenon has only been observed with large field strengths (~10 kVcm-1), an obstacle for technological applications. Here we predict that bi-layer graphene generates high-order sidebands at much weaker terahertz fi…
We review the use of graphene to develop reconfigurable, miniaturized, and efficient terahertz (THz) antennas and associated feeding networks, and attempt to identify current research trends and mid- and long-term challenges and prospects. We first discuss the state of the art in resonant, leaky-wave and reflectarray antennas, providing a critical assessment of their performance, limitations, and main challenges that remain to be addressed. Next, we examine different integrated feeding networks, including components such as switches, filters, and phase shifters, and we clarify the impact that …
Low-dimensional carbon nanostructures, such as single-wall carbon nanotubes (SWCNTs) and graphene, offer new opportunities for terahertz science and technology. Being zero-gap systems with a linear, photon-like energy dispersion, metallic SWCNTs and graphene exhibit a variety of extraordinary properties. Their DC and linear electrical properties have been extensively studied in the last decade, but their unusual finite-frequency, nonlinear, and/or non-equilibrium properties are largely unexplored, although they are predicted to be useful for new terahertz device applications. Terahertz dynamic…
Boundaries and edges of a two dimensional system lower its symmetry and are usually regarded, from the point of view of charge transport, as imperfections. Here we present a first study of the behavior of graphene plasmons in a strong magnetic field that provides a different perspective. We show that the plasmon resonance in micron size graphene disks in a strong magnetic field splits into edge and bulk plasmon modes with opposite dispersion relations, and that the edge plasmons at terahertz frequencies develop increasingly longer lifetimes with increasing magnetic field, in spite of potential…
In graphene, after the electric field is turned-on, the ballistic acceleration of charge carriers up to the monochromatic optic phonon energy generates a back-and-forth motion of the whole distribution function between the zero point energy and the phonon energy. This effect is predicted to manifest in damped terahertz oscillations of the carrier drift velocity and average energy. The most dramatic feature of this transient phenomenon is the onset of momentum-free areas surrounded by high momentum probability in phase space, and smooth steps or terraces in the distribution function. This dynam…
The gapless energy band spectra make the structures based on graphene and graphene bilayers with the population inversion created by optical or injection pumping to be promising media for the interband terahertz (THz) lasing. However, a strong intraband absorption at THz frequencies still poses a challenge for efficient THz lasing. In this paper, we show that in the pumped graphene bilayer structures, the indirect interband radiative transitions accompanied by scattering of carriers caused by disorder can provide a substantial negative contribution to the THz conductivity (together with the di…
We observe photocurrents induced in single layer graphene samples by illumination of the graphene edges with circularly polarized terahertz radiation at normal incidence. The photocurrent flows along the sample edges and forms a vortex. Its winding direction reverses by switching the light helicity from left- to right-handed. We demonstrate that the photocurrent stems from the sample edges, which reduce the spatial symmetry and result in an asymmetric scattering of carriers driven by the radiation electric field. The developed theory is in a good agreement with the experiment. We show that the…
We propose to utilize multiple-graphene-layer structures with lateral p-i-n junctions for terahertz (THz) and infrared (IR) photodetection and substantiate the operation of photodetectors based on these structures. Using the developed device model, we calculate the detector dc responsivity and detectivity as functions of the number of graphene layers and geometrical parameters and show that the dc responsivity and detectivity can be fairly large, particularly, at the lower end of the THz range at room temperatures. Due to relatively high quantum efficiency and low thermogeneration rate, the ph…
The magnetic circular dichroism and the Faraday rotation are the fundamental phenomena of great practical importance arising from the breaking of the time reversal symmetry by a magnetic field. In most materials the strength and the sign of these effects can be only controlled by the field value and its orientation. Furthermore, the terahertz range is lacking materials having the ability to affect the polarisation state of the light in a non-reciprocal manner. Here we demonstrate, using broadband terahertz magneto-electro-optical spectroscopy, that in graphene both the magnetic circular dichro…
When subjected to electromagnetic radiation, the fluctuation of the electronic current across a quantum conductor increases. This additional noise, called photon-assisted shot noise, arises from the generation and subsequent partition of electron-hole pairs in the conductor. The physics of photon-assisted shot noise has been thoroughly investigated at microwave frequencies up to 20 GHz, and its robustness suggests that it could be extended to the Terahertz (THz) range. Here, we present measurements of the quantum shot noise generated in a graphene nanoribbon subjected to a THz radiation. Our r…
We propose the concept of a terahertz (THz) uncooled bolometer based on n-type and p-type graphene layers (GLs), constituting the absorbing regions, connected by an array of undoped graphene nanoribbons (GNRs). The GLs absorb the THz radiation with the GNR array playing the role of the barrier region (resulting in nGL-GNR-pGL bolometer). The absorption of the incident THz radiation in the GL n- and p- regions leads to variations of the effective temperature of electrons and holes and of their Fermi energy resulting in the variation of the current through the GNRs. Using the proposed device mod…
A density-matrix formalism within the length gauge is developed for the purpose of calculating the nonlinear response of intrinsic bilayer graphene at terahertz frequencies. Employing a tight-binding model, we find that interplay between the interband and intraband dynamics leads to strong harmonic generation at moderate field amplitudes. Specifically, we find that at low temperature (10 K), the reflected field of undoped suspended bilayer graphene exhibits a third harmonic amplitude that is 30% of the fundamental in the reflected field for an incident 1 THz single-cycle pulse with a field amp…
When high-frequency radiation is incident upon graphene subjected to a perpendicular magnetic field, graphene absorbs incident photons by allowing transitions between nearest LLs that follow strict selection rules dictated by angular momentum conservation. Here we show a qualitative deviation from this behavior in high-quality graphene devices exposed to terahertz (THz) radiation. We demonstrate the emergence of a pronounced THz-driven photoresponse, which exhibits low-field magnetooscillations governed by the ratio of the frequency of the incoming radiation and the quasiclassical cyclotron fr…
Among its many outstanding properties, graphene supports terahertz surface plasma waves -- sub-wavelength charge density oscillations connected with electromagnetic fields that are tightly localized near the surface[1,2]. When these waves are confined to finite-sized graphene, plasmon resonances emerge that are characterized by alternating charge accumulation at the opposing edges of the graphene. The resonant frequency of such a structure depends on both the size and the surface charge density, and can be electrically tuned throughout the terahertz range by applying a gate voltage[3,4]. The p…
Exploration of optical non-linear response of graphene predominantly relies on ultra-short time domain measurements. Here we propose an alternate technique that uses frequency modulated continuous wavefront optical fields, thereby probing graphene's steady state non-linear response. We predict frequency sideband generation in the reflected field that originates from coherent electron dynamics of the photo-excited carriers. The corresponding threshold in input intensity for optimal sideband generation provides a direct measure of the third order optical non-linearity in graphene. Our formulatio…
We predict the self-excitation of terahertz (THz) oscillations due to the plasma instability in the lateral n+-i-n-n+$ graphene field-effect transistors (G-FET). The instability is associated with the Coulomb drag of the quasi-equilibrium electrons in the gated channel by the injected ballistic electrons resulting in a positive feedback between the amplified dragged electrons current and the injected current. The plasma excitations arise when the drag effect is sufficiently strong. The drag efficiency and the plasma frequency are determined by the quasi-equilibrium electrons Fermi energy (i.e.…
The efficient modulation and control of ultrafast signals on-chip is of central importance in terahertz (THz) communications and a promising route toward sub-diffraction limit THz spectroscopy. Two-dimensional (2D) materials may provide a platform for these endeavors. We explore this potential, integrating high-quality graphene p-n junctions within two types of planar transmission line circuits to modulate and emit picosecond pulses. In a coplanar stripline geometry, we demonstrate electrical modulation of THz signal transmission by 95%. In a Goubau waveguide geometry, we achieve complete gate…
Phase- and angle-sensitive terahertz hot-electron bolometric plasmonic detectors based on FETs with graphene channel and composite h-BN/black-P/h-BN gate layer
Generating and detecting radiation in the technologically relevant range of the so-called terahertz gap ($0.1 - 10$ THz) is challenging because of a lack of efficient sources and detectors. Quantum dots in carbon nanotubes have shown great potential to build sensitive terahertz detectors usually based on photon-assisted tunnelling. A recently reported mechanism combining resonant quantum dot transitions and tunnelling barriers asymmetries results in a narrow linewidth photocurrent response with a large signal-to-noise ratio under weak THz radiation. That device was sensitive to one frequency, …
