Efficient nonlinear generation of THz plasmons in graphene and topological insulators

Ultrafast Infrared Plasmonics

Ultrafast plasmonics represents a cutting-edge frontier in light-matter interactions, providing a unique platform to study electronic interactions and collective motions across femtosecond to picosecond timescales. In the infrared regime, where energy aligns with the rearrangements of low-energy electrons, molecular vibrations, and thermal fluctuations, ultrafast plasmonics can be a powerful tool for revealing ultrafast electronic phase transitions, controlling molecular reactions, and driving subwavelength thermal processes. Here, the evolution of ultrafast infrared plasmonics, discussing the recent progress in their manipulation, detection, and applications is reviewed. The future opportunities, including their potential to probe electronic correlations, investigate intrinsic ultrafast plasmonic interactions, and enable advanced applications in quantum information are highlighted, which may be promoted by multi-physical field integrated ultrafast techniques.

Harmonic quantum cascade laser terahertz frequency combs enabled by multilayer graphene top-cavity scatters

Optical frequency comb synthesizers, operating in the harmonic regime, are metrological sources in which the emitted optical power is concentrated in a few modes, spaced by several multiples of the cavity free spectral range (FSR). This behavior reflects in a large correlation degree and, in principle, in an increased optical power per mode. In miniaturized quantum cascade lasers (QCLs), harmonic frequency combs (HFCs) are hence particularly attracting to explore quantum correlation effects between adjacent harmonic modes, enabled by the inherently large gain media third-order χ (3) Kerr nonlinearity, even if controlled generation of stable HFCs of predefined order, is typically demanding in such electrically pumped sources. Here, we demonstrate stable 2nd order and 3rd order HFC emission in terahertz frequency QCLs by respectively patterning an individual or a couple of equally spaced distributed multilayer graphene absorbers on the top metallic waveguides.

2D Material Infrared Photonics and Plasmonics

Two-dimensional (2D) materials including graphene, transition metal dichalcogenides, black phosphorus, MXenes, and semimetals have attracted extensive and widespread interest over the past years for their many intriguing properties and phenomena, underlying physics, and great potential for applications. The vast library of 2D materials and their heterostructures provides a diverse range of electrical, photonic, mechanical, and chemical properties with boundless opportunities for photonics and plasmonic devices. The infrared (IR) regime, with wavelengths across 0.78 μm to 1000 μm, has particular technological significance in industrial, military, commercial, and medical settings while facing challenges especially in the limit of materials. Here, we present a comprehensive review of the varied approaches taken to leverage the properties of the 2D materials for IR applications in photodetection and sensing, light emission and modulation, surface plasmon and phonon polaritons, non-linear optics, and Smith-Purcell radiation, among others. The strategies examined include the growth and processing of 2D materials, the use of various 2D materials like semiconductors, semimetals, Weyl-semimetals and 2D heterostructures or mixed-dimensional hybrid structures, and the engineering of light-matter interactions through nanophotonics, metasurfaces, and 2D polaritons. Finally, we give an outlook on the challenges in realizing high-performance and ambient-stable devices and the prospects for future research and large-scale commercial applications.

Two-dimensional Dirac plasmon-polaritons in graphene, 3D topological insulator and hybrid systems

Collective oscillations of massless particles in two-dimensional (2D) Dirac materials offer an innovative route toward implementing atomically thin devices based on low-energy quasiparticle interactions. Strong confinement of near-field distribution on the 2D surface is essential to demonstrate extraordinary optoelectronic functions, providing means to shape the spectral response at the mid-infrared (IR) wavelength. Although the dynamic polarization from the linear response theory has successfully accounted for a range of experimental observations, a unified perspective was still elusive, connecting the state-of-the-art developments based on the 2D Dirac plasmon-polaritons. Here, we review recent works on graphene and three-dimensional (3D) topological insulator (TI) plasmon-polariton, where the mid-IR and terahertz (THz) radiation experiences prominent confinement into a deep-subwavelength scale in a novel optoelectronic structure. After presenting general light-matter interactions between 2D Dirac plasmon and subwavelength quasiparticle excitations, we introduce various experimental techniques to couple the plasmon-polaritons with electromagnetic radiations. Electrical and optical controls over the plasmonic excitations reveal the hybridized plasmon modes in graphene and 3D TI, demonstrating an intense near-field interaction of 2D Dirac plasmon within the highly-compressed volume. These findings can further be applied to invent optoelectronic bio-molecular sensors, atomically thin photodetectors, and laser-driven light sources.

Dynamic and Active THz Graphene Metamaterial Devices

In recent years, terahertz waves have attracted significant attention for their promising applications. Due to a broadband optical response, an ultra-fast relaxation time, a high nonlinear coefficient of graphene, and the flexible and controllable physical characteristics of its meta-structure, graphene metamaterial has been widely explored in interdisciplinary frontier research, especially in the technologically important terahertz (THz) frequency range. Here, graphene’s linear and nonlinear properties and typical applications of graphene metamaterial are reviewed. Specifically, the discussion focuses on applications in optically and electrically actuated terahertz amplitude, phase, and harmonic generation. The review concludes with a brief examination of potential prospects and trends in graphene metamaterial.

Nonlinear co-generation of graphene plasmons for optoelectronic logic operations

Surface plasmons in graphene provide a compelling strategy for advanced photonic technologies thanks to their tight confinement, fast response and tunability. Recent advances in the field of all-optical generation of graphene’s plasmons in planar waveguides offer a promising method for high-speed signal processing in nanoscale integrated optoelectronic devices. Here, we use two counter propagating frequency combs with temporally synchronized pulses to demonstrate deterministic all-optical generation and electrical control of multiple plasmon polaritons, excited via difference frequency generation (DFG). Electrical tuning of a hybrid graphene-fibre device offers a precise control over the DFG phase-matching, leading to tunable responses of the graphene’s plasmons at different frequencies across a broadband (0 ~ 50 THz) and provides a powerful tool for high-speed logic operations. Our results offer insights for plasmonics on hybrid photonic devices based on layered materials and pave the way to high-speed integrated optoelectronic computing circuits.

Nano-photonic devices based on 2D materials offer a potential solution for the miniaturization of optical computing technologies. Here, the authors demonstrate the implementation of high-speed logic operations via the all-optical generation and electrical control of multiple plasmon polaritons in a hybrid graphene device.

Integrated Terahertz Generator-Manipulators Using Epsilon-near-Zero-Hybrid Nonlinear Metasurfaces

In terahertz (THz) technologies, generation and manipulation of THz waves are two key processes usually implemented by different device modules. Integrating THz generation and manipulation into a single compact device will advance the applications of THz technologies in various fields. Here, we demonstrate a hybrid nonlinear plasmonic metasurface incorporating an epsilon-near-zero (ENZ) indium tin oxide (ITO) layer to seamlessly combine efficient generation and manipulation of THz waves across a wide frequency band. The coupling between the plasmonic resonance of the metasurface and the ENZ mode of the ITO thin film enhances the THz conversion efficiency by more than 4 orders of magnitude. Meanwhile, such a hybrid device is capable of shaping the polarization and wavefront of the emitted THz beam via the engineered nonlinear Pancharatnam-Berry (PB) phases of the plasmonic meta-atoms. The presented hybrid nonlinear metasurface opens a new avenue toward miniaturized integrated THz devices and systems with advanced functionalities.

Multiple interference theoretical model for graphene metamaterial-based tunable broadband terahertz linear polarization converter design and optimization

Terahertz (THz) polarization converters often working as modulators and switches have many applications in THz sensing, imaging and communication, but many of them still suffer from low polarization conversion efficiency, fixed and narrow polarization conversion band, and low output polarization purity, which are mainly due to the lack of theoretical model for THz polarization converter design and optimization. In order to solve the problem, we adopt multiple interference theory to successfully design and optimize a graphene metamaterial-based tunable broadband THz linear polarization converter: it achieves polarization conversion ratio (PCR) over 0.97, polarization azimuth angle of almost ±90° and rather low ellipticity within a broad polarization conversion band of 1.25 THz; and additionally, its polarization conversion band can be actively tuned by adjusting the graphene chemical potential and almost insensitive to the incident THz radiation angle below 50°. Considering the high performance of the optimal graphene metamaterial-based tunable broadband THz linear polarization converter, this work provides an optimal design offering a way in high-quality manipulation of THz radiation polarization; but more importantly, delivers a theoretical model for tunable THz polarization converter design and optimization.

Reversible engineering of topological insulator surface state conductivity through optical excitation

Despite the broadband response, limited optical absorption at a particular wavelength hinders the development of optoelectronics based on Dirac fermions. Heterostructures of graphene and various semiconductors have been explored for this purpose, while non-ideal interfaces often limit the performance. The topological insulator (TI) is a natural hybrid system, with the surface states hosting high-mobility Dirac fermions and the small-bandgap semiconducting bulk state strongly absorbing light. In this work, we show a large photocurrent response from a field effect transistor device based on intrinsic TI Sn-Bi_1.1Sb_0.9Te₂S (Sn-BSTS). The photocurrent response is non-volatile and sensitively depends on the initial Fermi energy of the surface state, and it can be erased by controlling the gate voltage. Our observations can be explained with a remote photo-doping mechanism, in which the light excites the defects in the bulk and frees the localized carriers to the surface state. This photodoping modulates the surface state conductivity without compromising the mobility, and it also significantly modify the quantum Hall effect of the surface state. Our work thus illustrates a route to reversibly manipulate the surface states through optical excitation, shedding light into utilizing topological surface states for quantum optoelectronics.

Stimulated plasmon polariton scattering

Plasmon and phonon polaritons of two-dimensional (2D) and van-der-Waals materials have recently gained substantial interest. Unfortunately, they are notoriously hard to observe in linear response because of their strong confinement, low frequency and longitudinal mode symmetry. Here, we propose an approach of harnessing nonlinear resonant scattering that we call stimulated plasmon polariton scattering (SPPS) in analogy to the opto-acoustic stimulated Brillouin scattering (SBS). We show that SPPS allows to excite, amplify and detect 2D plasmon and phonon polaritons all across the THz-range while requiring only optical components in the near-IR or visible range. We present a coupled-mode theory framework for SPPS and based on this find that SPPS power gains exceed the very top gains observed in on-chip SBS by at least an order of magnitude. This opens exciting possibilities to fundamental studies of 2D materials and will help closing the THz gap in spectroscopy and information technology.

Ellipticity dependence of the third-order nonlinear optical response of graphene irradiated by two-color lights

We theoretically investigate the third-order optical response of graphene irradiated by two-color lights, paying special attention to the quantum interference. Our studies reveal that the interplay between harmonic generation and four-wave mixing leads to unusual nonlinear optical properties with nontrivial ellipticity dependence. It is shown that, unlike the case of monochromatic light with frequencyω0(where the intensity of the third order response (I(3ω0)) decreases monotonically with the ellipticity and becomes zero for circularly polarized light),I(3ω0) may increase monotonically with the ellipticity, or be nearly independent on the ellipticity. In particular, under suitable condition, there exists an optimal nonzero ellipticity for the highestI(3ω0). Moreover, circularly polarized third-order optical response can be generated. We have found effective methods of modulating the nonlinear optical processes, which may have various applications in optical devices based on two dimensional materials.

THz white light cavity with nonlinear dispersion in graphene

A white light cavity (WLC) scheme is proposed to achieve broadband response in the terahertz (THz) region by enhanced nonlinear dispersion in a magnetized graphene system. In the weak probe field limit, the cavity linewidth is narrowed due to electromagnetically induced transparency, and then it becomes nearly as broad as the empty-cavity linewidth under the condition of Autler-Towns splitting. It is interesting to find that the cavity linewidth can be further broadened by enhanced nonlinear dispersion. The simulation result shows that the response range of the cavity is from 6.273 THz to 6.308 THz under the given condition, which is nearly 11 times larger than the empty-cavity linewidth. Furthermore, the improvement in cavity transmission and the response of WLC at different frequencies are investigated.

Nonlinear Graphene Nanoplasmonics

Nonlinear optics is limited by the weak nonlinear response of available materials, a problem that is generally circumvented by relying on macroscopic structures in which light propagates over many optical cycles, thus giving rise to accumulated unity-order nonlinear effects. While this strategy cannot be extended to subwavelength optics, such as in nanophotonic structures, one can alternatively use localized optical resonances with high quality factors to increase light-matter interaction times, although this approach is limited by inelastic losses partly associated with the nonlinear response. Plasmons-the collective oscillations of electrons in conducting media-offer the means to concentrate light into nanometric volumes, well below the light-wavelength-scale limit imposed by diffraction, amplifying the electromagnetic fields upon which nonlinear optical phenomena depend. Due to their abundant supply of free electrons, noble metals are the traditional material platform for plasmonics and have thus dominated research in nanophotonics over the past several decades, despite exhibiting large ohmic losses and inherent difficulties to actively modulate plasmon resonances, which are primarily determined by size, composition, and morphology. Highly doped graphene has recently emerged as an appealing platform for plasmonics due to its unique optoelectronic properties, which give rise to relatively long-lived, highly confined, and actively tunable plasmon resonances that mainly appear in the infrared and terahertz frequency regimes. Efforts to extend graphene plasmonics to the near-infrared and visible ranges involve patterning of graphene into nanostructured elements, thus facilitating the optical excitation of localized resonances that can be blue-shifted through geometrical confinement while maintaining electrical tunability. Besides these appealing plasmonic attributes, the conical electronic dispersion relation of graphene renders its charge carrier motion in response to light intrinsically anharmonic, resulting in a comparatively intense nonlinear optical response. The combined synergy of extreme plasmonic field enhancement and large intrinsic optical nonlinearity are now motivating intensive research efforts in nonlinear graphene plasmonics, the recent progress of which we discuss in this Account. We start with a description of the appealing properties of plasmons in graphene nanostructures down to molecular sizes, followed by a discussion of the unprecedented level of intrinsic optical nonlinearity in graphene, its enhancement by resonant coupling to its highly confined plasmons to yield intense high harmonic generation and Kerr nonlinearities, the extraordinary thermo-optical capabilities of this material enabling large nonlinear optical switching down to the single-photon level, and its strong interaction with quantum emitters.

Unusual terahertz waveforms from a resonant medium controlled by diffractive optical elements

Up to now, full tunability of waveforms was possible only in electronics, up to radio-frequencies. Here we propose a new concept of producing few-cycle terahertz (THz) pulses with widely tunable waveforms. It is based on control of the phase delay between different parts of the THz wavefront using linear diffractive optical elements. Suitable subcycle THz wavefronts can be generated via coherent excitation of nonlinear low-frequency oscillators by few-cycle optical pulses. Using this approach it is possible to shape the electric field rather than the slow pulse envelope, obtaining, for instance, rectangular or triangular waveforms in the THz range. The method is upscalable to the optical range if the attosecond pump pulses are used.

Origins of All-Optical Generation of Plasmons in Graphene

Graphene, despite its centrosymmetric structure, is predicted to have a substantial second order nonlinearity, arising from non-local effects. However, there is disagreement between several published theories and experimental data. Here we derive an expression for the second order conductivity of graphene in the non-local regime using perturbation theory, concentrating on the difference frequency mixing process, and compare our results with those already published. We find a second-order conductivity (σ⁽²⁾ ≈ 10⁻¹⁷ AmV⁻²) that is approximately three orders of magnitude less than that estimated from recent experimental results. This indicates that nonlinear optical coupling to plasmons in graphene cannot be described perturbatively through the electronic nonlinearity, as previously thought. We also show that this discrepancy cannot be attributed to the bulk optical nonlinearity of the substrate. As a possible alternative, we present a simple theoretical model of how a non-linearity can arise from photothermal effects, which generates a field at least two orders of magnitude larger than that found from perturbation theory.

Universal linear and nonlinear electrodynamics of a Dirac fluid

A general relation is derived between the linear and second-order nonlinear ac conductivities of an electron system in the hydrodynamic regime of frequencies below the interparticle scattering rate. The magnitude and tensorial structure of the hydrodynamic nonlinear conductivity are shown to differ from their counterparts in the more familiar kinetic regime of higher frequencies. Due to universality of the hydrodynamic equations, the obtained formulas are valid for systems with an arbitrary Dirac-like dispersion, ranging from solid-state electron gases to free-space plasmas, either massive or massless, at any temperature, chemical potential, or space dimension. Predictions for photon drag and second-harmonic generation in graphene are presented as one application of this theory.

Nonlinear Light Mixing by Graphene Plasmons

Graphene is known to possess strong optical nonlinearity which turned out to be suitable for creation of efficient saturable absorbers in mode locked fiber lasers. Nonlinear response of graphene can be further enhanced by the presence of graphene plasmons. Here, we report a novel nonlinear effect observed in nanostructured graphene which comes about due to excitation of graphene plasmons. We experimentally detect and theoretically explain enhanced mixing of near-infrared and mid-infrared light in arrays of graphene nanoribbons. Strong compression of light by graphene plasmons implies that the described effect of light mixing is nonlocal in nature and orders of magnitude larger than the conventional local graphene nonlinearity. Both second and third order nonlinear effects were observed in our experiments with the recalculated third-order nonlinearity coefficient reaching values of 4.5 × 10^-6 esu. The suggested effect could be used in variety of applications including nonlinear light modulators, light multiplexers, light logic, and sensing devices.

All-optical control on a graphene-on-silicon waveguide modulator

The hallmark of silicon photonics is in its low loss at the telecommunications wavelength, economic advantages and compatibility with CMOS design and fabrication processes. These advantages are however impeded by its relatively low Kerr coefficient that constrains the power and size scaling of nonlinear all-optical silicon photonic devices. Graphene, with its unprecedented high Kerr coefficient and uniquely thin-film structure, makes a good nonlinear material to be easily integrated onto all-optical silicon photonic waveguide devices. We study the design of all-optical graphene-on-silicon (GOS) waveguide modulators, and find the optimized performance of MW cm-2 in optical pump intensities and sub-mm device lengths. The improvements brought by the integration of graphene onto silicon photonic waveguides could bring us a step closer to realising compact all-optical control on a single chip.

Nonlinear graphene plasmonics

The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.

Enhanced Second-Order Nonlinearity for THz Generation by Resonant Interaction of Exciton-Polariton Rabi Oscillations with Optical Phonons

Semiconductor microcavities in the strong-coupling regime exhibit an energy scale in the terahertz (THz) frequency range, which is fixed by the Rabi splitting between the upper and lower exciton-polariton states. While this range can be tuned by several orders of magnitude using different excitonic media, the transition between both polaritonic states is dipole forbidden. In this work, we show that, in cadmium telluride microcavities, the Rabi-oscillation-driven THz radiation is actually active without the need for any change in the microcavity design. This feature results from the unique resonance condition which is achieved between the Rabi splitting and the phonon-polariton states and leads to a giant enhancement of the second-order nonlinearity.

Exploiting nonlinear properties of pure and Sn-doped Bi2Te2Se for passive Q-switching of all-polarization maintaining ytterbium- and erbium-doped fiber lasers

Due to their broadband nonlinear optical properties, low-dimensional materials are widely used for pulse generation in fiber and solid-state lasers. Here we demonstrate novel materials, Bi₂Te₂Se (BTS) and Sn-doped Bi₂Te₂Se (BSTS), which can be used as a universal saturable absorbers for distinct spectral regimes. The material was mechanically exfoliated from a bulk single-crystal and deposited onto a side-polished fiber. We have performed characterization of the fabricated devices and employed them in polarization-maintaining ytterbium- and erbium-doped fiber lasers. This enabled us to obtain self-starting passively Q-switched regime at 1 µm and 1.56 µm. The oscillators emitted stable, linearly polarized radiation with the highest single pulse energy approaching 692 nJ. Both lasers are characterized by the best performance observed in all-polarization maintaining Q-switched fiber lasers with recently investigated new saturable absorbers, which was enabled by a very high damage threshold of the devices. This demonstrates the great potential of the investigated materials for the ultrafast photonics community.

Terahertz plasmonic excitations in Bi2Se3 topological insulator

After the discovery of Dirac electrons in condensed matter physics, more specifically in graphene and its derivatives, their potentialities in the fields of plasmonics and photonics have been readily recognized, leading to a plethora of applications in active and tunable optical devices. Massless Dirac carriers have been further found in three-dimensional topological insulators. These exotic quantum systems have an insulating gap in the bulk and intrinsic Dirac metallic states at any surface, sustaining not only single-particle excitations but also plasmonic collective modes. In this paper we will review the plasmon excitations in different microstructures patterned on Bi₂Se₃ topological insulator thin films as measured by terahertz spectroscopy. We discuss the dependence of the plasmon absorption versus the microstructure shape, wavevector, and magnetic field. Finally we will discuss the topological protection of both the Dirac single-particle and plasmon excitations.

Intensity dependences of the nonlinear optical excitation of plasmons in graphene

Recently, we demonstrated an all-optical coupling scheme for plasmons, which takes advantage of the intrinsic nonlinear optical response of graphene. Frequency mixing using free-space, visible light pulses generates surface plasmons in a planar graphene sample, where the phase matching condition can define both the wavevector and energy of surface waves and intraband transitions. Here, we also show that the plasmon generation process is strongly intensity-dependent, with resonance features washed out for absorbed pulse fluences greater than 0.1 J m^-2 This implies a subtle interplay between the nonlinear generation process and sample heating. We discuss these effects in terms of a non-equilibrium charge distribution using a two-temperature model.This article is part of the themed issue 'New horizons for nanophotonics'.

Second order optical nonlinearity of graphene due to electric quadrupole and magnetic dipole effects

We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order optical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference frequency generation. We discuss in detail the controllability of these effects by tuning the chemical potential, taking advantage of the dominant role played by interband optical transitions in the response.

Third harmonic generation from graphene lying on different substrates: optical-phonon resonances and interference effects

Graphene is a nonlinear material which can be used as a saturable absorber, frequency mixer and frequency multiplier. We theoretically study the third harmonic generation from graphene lying on different dielectric (dispersionless or polar) substrates, metalized or non-metalized on the back side. We show that the third harmonic intensity emitted from graphene lying on a substrate, can be increased by orders of magnitude as compared to the isolated graphene, due the LO-phonon resonances in a polar dielectric or due to the interference effects in the substrates metalized on the back side. In some frequency intervals, the presence of the polar dielectric substrate compensates the strongly decreasing with ω frequency dependence of the third-order conductivity of graphene making the response almost frequency independent. Our results can be used for the development of graphene based frequency multipliers operating in microwave through infrared frequencies.

Analytical investigation of surface plasmon excitation on a graphene sheet using four-wave mixing

In the present paper, the general conditions for exciting graphene surface plasmon polaritons (GSPPs) on a suspended graphene using nonlinear optics are investigated. The approach uses the Green's function analysis to derive GSPP fields generated under the basis of momentum conservation using four-wave mixing (FWM). Since the incident beam polarization is challenging in the nonlinear excitation of GSPPs, the significant target of this paper has been set to achieve the conditions for the third-order susceptibility tensor and the wave vectors so that the incident beams with varied polarizations are able to excite GSPPs. Nonlinear optics, in particular FWM, is utilized to compensate the mismatch between the free-space and GSPPs wave vectors. In addition, it avoids the need for applying any patterning or lithography on graphene or its substrate.

Nonlinear optical observation of coherent acoustic Dirac plasmons in thin-film topological insulators

Low-energy collective electronic excitations exhibiting sound-like linear dispersion have been intensively studied both experimentally and theoretically for a long time. However, coherent acoustic plasmon modes appearing in time-domain measurements are rarely observed due to Landau damping by the single-particle continua. Here we report on the observation of coherent acoustic Dirac plasmon (CADP) modes excited in indirectly (electrostatically) opposite-surface coupled films of the topological insulator Bi₂Se₃. Using transient second-harmonic generation, a technique capable of independently monitoring the in-plane and out-of-plane electron dynamics in the films, the GHz-range oscillations were observed without corresponding oscillations in the transient reflectivity. These oscillations were assigned to the transverse magnetic and transverse electric guided CADP modes induced by the evanescent guided Lamb acoustic waves and remained Landau undamped due to fermion tunnelling between the opposite-surface Dirac states.

Nonlinear Terahertz Absorption of Graphene Plasmons

Subwavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, which could enable nonlinear optics at low intensity in atomically thin, subwavelength devices. To date, the nonlinear response of graphene plasmons and their energy loss dynamics have not been experimentally studied. We measure and theoretically model the terahertz nonlinear response and energy relaxation dynamics of plasmons in graphene nanoribbons. We employ a terahertz pump-terahertz probe technique at the plasmon frequency and observe a strong saturation of plasmon absorption followed by a 10 ps relaxation time. The observed nonlinearity is enhanced by 2 orders of magnitude compared to unpatterned graphene with no plasmon resonance. We further present a thermal model for the nonlinear plasmonic absorption that supports the experimental results. The model shows that the observed strong linearity is caused by an unexpected red shift of plasmon resonance together with a broadening and weakening of the resonance caused by the transient increase in electron temperature. The model further predicts that even greater resonant enhancement of the nonlinear response can be expected in high-mobility graphene, suggesting that nonlinear graphene plasmonic devices could be promising candidates for nonlinear optical processing.

Quantum Effects in the Nonlinear Response of Graphene Plasmons

The ability of graphene to support long-lived, electrically tunable plasmons that interact strongly with light, combined with its highly nonlinear optical response, has generated great expectations for application of the atomically thin material to nanophotonic devices. These expectations are mainly reinforced by classical analyses performed using the response derived from extended graphene, neglecting finite-size and nonlocal effects that become important when the carbon layer is structured on the nanometer scale in actual device designs. Here we show that finite-size effects produce large contributions that increase the nonlinear response of nanostructured graphene to significantly higher levels than those predicted by classical theories. We base our analysis on a quantum-mechanical description of graphene using tight-binding electronic states combined with the random-phase approximation. While classical and quantum descriptions agree well for the linear response when either the plasmon energy is below the Fermi energy or the size of the structure exceeds a few tens of nanometers, this is not always the case for the nonlinear response, and in particular, third-order Kerr-type nonlinearities are generally underestimated by the classical theory. Our results reveal the complex quantum nature of the optical response in nanostructured graphene, while further supporting the exceptional potential of this material for nonlinear nanophotonic devices.

Plasmons of topological crystalline insulator SnTe with nanostructured patterns

Using the finite-difference time-domain method and density functional theory, we theoretically investigate the plasmons of topological crystalline insulator (TCI) SnTe with nanostructured patterns.

Interplay of Surface and Dirac Plasmons in Topological Insulators: The Case of Bi_{2}Se_{3}

We have investigated plasmonic excitations at the surface of Bi_{2}Se_{3}(0001) via high-resolution electron energy loss spectroscopy. For low parallel momentum transfer q_{∥}, the loss spectrum shows a distinctive feature peaked at 104 meV. This mode varies weakly with q_{∥}. The behavior of its intensity as a function of primary energy and scattering angle indicates that it is a surface plasmon. At larger momenta (q_{∥}~0.04 Å^{-1}), an additional peak, attributed to the Dirac plasmon, becomes clearly defined in the loss spectrum. Momentum-resolved loss spectra provide evidence of the mutual interaction between the surface plasmon and the Dirac plasmon of Bi_{2}Se_{3}. The proposed theoretical model accounting for the coexistence of three-dimensional doping electrons and two-dimensional Dirac fermions accurately represents the experimental observations. The results reveal novel routes for engineering plasmonic devices based on topological insulators.

Plasmon excitation on flat graphene by s-polarized beams using four-wave mixing

Graphene plasmons have received significant attention recently due to its attractive properties such as high spatial confinement and tunability. However, exciting plasmons on graphene effectively still remains a challenge owing to the large wave-vector mismatch between the optical beam in air and graphene plasmon. In this paper, we present a novel scheme capable of exciting graphene surface plasmons (GSPs) on a flat suspended graphene by using only s-polarized optical beams through four-wave mixing (FWM) process, where the GSPs fields were derived analytically based on the Green's function analysis, under the basis of momentum conservation. By incorporating the merits of nonlinear optics, the presented scheme avoids any patterning of either graphene or substrate. We believe that the proposed scheme potentially paves the way towards an efficient pure optical excitation, switching and modulation of GSPs for realizing graphene-based nano-photonic and optoelectronic integrated circuits.

Thickness tunable quantum interference between surface phonon and Dirac plasmon states in thin films of the topological insulator Bi₂Se₃

We report on a >100-fold enhancement of Raman responses from Bi2Se3 thin films if laser photon energy switches from 2.33 eV (532 nm) to 1.58 eV (785 nm), which is due to direct optical coupling to Dirac surface states (SS) at the resonance energy of ∼1.5 eV (a thickness-independent enhancement) and due to nonlinearly excited Dirac plasmon (a thickness-dependent enhancement). Owing to the direct optical coupling, we observed an in-plane phonon mode of hexagonally arranged Se-atoms associated with a continuous network of Dirac SS. This mode revealed a Fano lineshape for films <15 nm thick, resulting from quantum interference between surface phonon and Dirac plasmon states.

Terahertz science and technology of carbon nanomaterials

The diverse applications of terahertz (THz) radiation and its importance to fundamental science makes finding ways to generate, manipulate and detect THz radiation one of the key areas of modern applied physics. One approach is to utilize carbon nanomaterials, in particular, single-wall carbon nanotubes and graphene. Their novel optical and electronic properties offer much promise to the field of THz science and technology. This article describes the past, current, and future of THz science and technology of carbon nanotubes and graphene. We will review fundamental studies such as THz dynamic conductivity, THz nonlinearities and ultrafast carrier dynamics as well as THz applications such as THz sources, detectors, modulators, antennas and polarizers.