Nonlinear Graphene Research Articles

On the Ability of TE- and TM-waves Propagation in a Dielectric Layer Covered with Nonlinear Graphene

On the Ability of TE- and TM-waves Propagation in a Dielectric Layer Covered with Nonlinear Graphene

The Nonlinear Eigenvalue Problem of Electromagnetic Wave Propagation in a Dielectric Layer Covered with Graphene

The paper focuses on the problem of a monochromatic terahertz TE-polarized wave propagation in a plane dielectric layer filled with a homogeneous isotropic medium; one of the boundaries of the waveguide is covered with a layer of graphene. In fact, the paper aims to find the eigenwaves of the described waveguiding structure. On the one hand, in the study, energy losses both in the dielectric layer and in the graphene layer are neglected; the latter assumption is reasonable in the terahertz range of electromagnetic radiation (on which the paper focuses), where graphene has a strong plasmonic response and much less loss. On the other hand, this study takes into account the significant third-order nonlinearity resulting from the interaction of the electromagnetic wave with the charge carriers in the graphene layer. The paper aims to study the guiding properties of the above structure using primarily an analytical approach. The wave propagation problem is reduced to an eigenvalue problem, where one of the boundary conditions is nonlinear with respect to the sought-for function. The main result of the paper is a dispersion equation allowing for a waveguide of a given thickness to determine a set of its propagation constants and, consequently, a set of its eigenwaves. It is worth noting that the dispersion equation being written in an explicit form can be used to obtain deep qualitative results related to the solvability of the problem and the properties of its solutions. For example, in the paper, the existence of several propagation constants (and, consequently, the eigenwaves) of the studied waveguiding structure is proved under some conditions. Besides studying the problem analytically, the paper presents some numerical results as well. In particular, the presented figures demonstrate how the nonlinearity in graphene affects the propagation constants and eigenwaves, providing the dispersion curves and eigenwaves for nonlinear graphene as well as for the linear one.

Enhanced Supercontinuum Generation in Integrated Waveguides Incorporated with Graphene Oxide Films

AbstractEnhanced supercontinuum generation (SCG) is experimentally demonstrated in integrated silicon nitride (Si3N4) waveguides incorporating highly nonlinear graphene oxide (GO) in the form of 2D films. On‐chip integration of the 2D GO films with precise control of their thickness is realized by using a transfer‐free and layer‐by‐layer coating method. The control of the film length and coating position is achieved via window opening in the upper silica cladding of the photonic integrated chips. Detailed SCG measurements are performed using the fabricated devices with different waveguide geometries and GO film thicknesses, and the results are compared with devices without GO. Significantly improved spectral broadening of ultrashort optical pulses with ultrahigh peak powers exceeding 1000 W is observed for the hybrid devices, achieving up to 2.4 times improvement in the spectral bandwidth relative to devices without GO. Theoretical analyses for the influence of GO film thickness, coating length, coating position, and waveguide geometry are also provided by fitting the experimental results with theory, showing that there is still significant room for further improvement. This work opens up a new avenue toward improving the SCG performance of photonic integrated devices by incorporating functional 2D materials.

Atomic-Scale Defects Might Determine the Second Harmonic Generation from Plasmonic Graphene Nanostructures.

In this work, we theoretically investigate the impact of the atomic scale lattice imperfections of graphene nanoflakes on their nonlinear response enhanced by the resonance between an incident electromagnetic field and localized plasmon. As a case study, we address the second harmonic generation from graphene plasmonic nanoantennas of different symmetries with missing carbon atom vacancy defects in the honeycomb lattice. Using the many-body time-dependent density matrix approach, we find that one defect in the nanoflake comprising over five thousand carbon atoms can strongly impact the nonlinear hyperpolarizability and override the symmetry constraints. The effect reported here cannot be captured using the relaxation time approximation within the quantum or classical framework. Results obtained in this work have thus important implications for the design of nonlinear graphene devices.

Nonlocal and cascaded effects in nonlinear graphene nanoplasmonics.

The ability of plasmons to focus light on nanometer length scales opens a wide range of enticing applications in optics and photonics, among which the enhancement of nonlinear light-matter interactions for all-optical modulation and spectral diversification emerges as a prominent theme. However, the subwavelength plasmonic near-field enhancement in good plasmonic materials such as noble metals is hindered by large ohmic losses, while conventional phase-matching of fields in bulk nonlinear crystals is not suitable for realizing nonlinear optical phenomena on the nanoscale. In contrast, anharmonic electron motion of free charge carriers in highly-doped graphene, which supports long-lived, highly-confined, and actively-tunable plasmons, renders the carbon monolayer an excellent platform for both plasmonics and nonlinear optics. Here we theoretically explore the enhancement in nonlinear response that can be achieved by interfacing multiple graphene nanostructures in close proximity to trigger nonlocal effects associated with large gradients in the electromagnetic near field. Focusing on second- and third-harmonic generation, we introduce a semianalytical formalism to describe interacting graphene nanoribbons with independent width, location, and electrical doping, so as to realize configurations in which plasmonic resonances may simultaneously enhance both the fundamental optical excitation frequency and harmonic intermediary and/or output frequencies. Our findings reveal the importance of both passive and active tuning in the design of atomically-thin nanostructures for nonlinear optical applications, and in particular emphasize the role played by nonlocal effects in generating an even-ordered nonlinear response that may contribute to other nonlinear optical processes through a cascaded interaction. We anticipate that our findings can aid in the design of actively-tunable nonlinear plasmonic resonators and metasurfaces.

Numerical Evaluation of the Errors of the Perturbation Method in Solving the Problem of the Reflection of an Electromagnetic Wave from a Nonlinear Graphene Layer

Numerical Evaluation of the Errors of the Perturbation Method in Solving the Problem of the Reflection of an Electromagnetic Wave from a Nonlinear Graphene Layer

Tunable optical bistability based on Bloch surface waves in one-dimensional photonic crystal with graphene

Graphene possesses large nonlinear conductivity in terahertz region, which makes it a very promising material for nonlinear bistable devices. In this paper, we theoretically study the optical bistability (OB) of reflected beam in a multilayer structure with graphene embedded between the truncated layer and the substrate. The Bloch surface wave excited by the one-dimensional photonic crystal (1D PC) coupling structure significantly enhances the local electric field near the nonlinear graphene, which provides a positive condition for the realization of low-threshold OB. Through parameter optimization, we obtain a threshold electric field with an incident electric field of 105 V/m levels. Furthermore, the influences of graphene’s Fermi energy and relaxation time, as well as those of the incidence angle, on the hysteretic behavior and the threshold of OB are clarified. This approach may provide a feasible scheme for the nonlinear optical bistable devices.

Design of strongly nonlinear graphene nanoelectromechanical systems in quantum regime

We report on the analysis and design of atomically thin graphene resonant nanoelectromechanical systems (NEMS) that can be engineered to exhibit anharmonicity in the quantum regime. Analysis of graphene two-dimensional (2D) NEMS resonators suggests that with device lateral size scaled down to ∼10–30 nm, restoring force due to the third-order (Duffing) stiffness in graphene NEMS can rise to equal or even exceed the force of linear stiffness, enabling strongly nonlinear NEMS resonators with anharmonic potential energy that produces sufficient deviation from a quantum harmonic spectrum, which is necessary toward realizing NEMS qubits. Furthermore, the calculations provide device design guidelines and scaling of anharmonicity in graphene NEMS to facilitate future fabrication of graphene NEMS qubits with the desired nonlinear dynamical characteristics and performance. The results in this work shall help open possibilities for engineering a new type of qubits based on 2D resonant NEMS, which may offer a much more miniaturized, densely packed, and scalable qubit platform, supplementing today's mainstream technologies such as superconducting and trapped ion qubits.

Conformal Graphene Directly Synthesized on a Femtosecond Laser-Scribed In-Fiber Microstructure for High-Energy Ultrafast Optical Pulses.

Despite extensive efforts to explore femtosecond lasers functionalized by nonlinear graphene (Gf) that relies on the traditional transfer process, maximizing the efficiency, customizing the nonlinear interaction, and minimizing the optical loss remain critical challenges, especially in high-energy pulse generation. We demonstrate an ultrafast nonlinear all-fiber device based on conformal Gf directly synthesized in three dimensions on the surface of an in-fiber microstructure. A femtosecond laser-induced selective etching process is used to fabricate a customized microstructure that ensures the minimum but efficient laser-Gf interaction as well as possesses excellent surface conditions to suppress absorption and scattering loss. Conformal Gf is prepared by a spatial diffusion-based atomic carbon spraying process that enables nanocrystals to be synthesized homogeneously even onto the complex surface of the microstructure. The demonstration of high-energy pulses from the Gf saturable absorber highlights its simple, process-efficient, adjustable, and robust performance. The resultant hyperbolic secant pulses display individual pulse energy and peak power of up to 13.2 nJ and 20.17 kW, respectively.

A unified atomic energy release rate criterion for nonlinear brittle fracture in graphene nanoribbons

The existence of a notch in a single-atom-thick graphene nanoribbon brings about significant nonlinearity in deformation within the extremely confined stress concentration field of only a few nanometers near the notch root. However, whether the continuum-based mechanics theory is still valid for fracture due to such strongly-nonlinear and extremely small stress concentration is questionable. Here, we demonstrate that stress-based criterion with linear-media assumption breaks down at a critical size of ΛSC=19.7nm, and moreover the one based on nonlinear-media assumption also fails to describe the nonlinear brittle fracture in a notched graphene nanoribbon below a lower dimensional limit of ΛNLC=2.4nm because of the atomic discreteness. By fully considering the nonlinearity and atomic discreteness, an atomic energy release rate (ERR) theory is proposed, and it is found that the atomic ERR criterion works well for a notch in nonlinear graphene nanoribbon even below the lower limit of continuum-based mechanics. It finally brings about an ultimate unification in describing nonlinear brittle fracture in both notched and cracked systems. These results demonstrate that the proposed atomic ERR criterion is not only size-independent but also shape-independent for all scales.

Генерация третьей гармоники терагерцовых волн нелинейной графеновой многослойной метаповерхностью

The nonlinear diffraction of an electromagnetic wave by multilayer nonlinear metasurfaces consisting of rectangular graphene finite length ribbons array located on dielectric layers is studied at terahertz (THz) frequencies. It is shown that the third harmonic generation efficiency increases by several orders of magnitude at surface plasmon-polariton resonance frequencies, which can be controlled by dynamic tuning the chemical potential without changing the geometry and dimensions of the nonlinear graphene metasurface.

Generation of Third Harmonic of Terahertz Waves by a Nonlinear Graphene Multilayer Metasurface

Generation of Third Harmonic of Terahertz Waves by a Nonlinear Graphene Multilayer Metasurface

Tunable terahertz optical bistability and multistability in photonic metamaterial multilayers containing nonlinear dielectric slab and graphene sheet

In this study, optical bistability and multistability phenomena are numerically investigated in the terahertz frequency domain based on the quasiperiodic photonic metamaterial multilayers, in which both the regular positive index and special negative index materials are artificially arranged, according to the interesting Fibonacci sequence structure. In order to obtain the tunable bistability and multibistability behaviors, the Kerr-type nonlinear dielectric layer and graphene sheet are sandwiched between two Fibonacci quasiperiodic one-dimensional photonic crystals. Results show that the intensity-dependent hysteresis curves including bistability and multistability are thoroughly discussed by judiciously changing the systematical parameters such as the frequency of incident wave, thickness of each layer, incident angle, as well as the chemical potential of graphene which can produce strong influences on the switch-up/down threshold values and widths of hysteresis loops.

Strong Light–Matter Interactions Enabled by Polaritons in Atomically Thin Materials

AbstractPolaritons, resulting from the hybridization of light with polarization charges formed at the boundaries between media with positive and negative dielectric response functions, can focus light into regions much smaller than its associated free‐space wavelength. This property is paramount for a plethora of applications in nanophotonics, ranging from biological sensing to photocatalysis to nonlinear and quantum optics. In the two‐dimensional (2D) limit, represented by atomically thin and van der Waals (vdW) materials of single‐layers bound by weak vdW attraction, polaritons are characterized by extremely small wavelengths associated with extreme optical confinement, and furthermore can exhibit long lifetimes, electrical tunability, and extreme sensitivity to their dielectric environment, among many other desirable qualities in nano‐optical device applications. Here, the fundamentals of polaritons in atomically thin materials are summarized, emphasizing plasmon and exciton polaritons, their strong light–matter interactions, and nonlinear plasmonics. More specifically, this review opens with a pedagogical discussion of plasmons in extended and nanostructured graphene, providing a classical electrodynamical model in a nonretarded theoretical framework, and the ultraconfined acoustic plasmons supported by hybrid graphene–dielectric–metal structures. In addition, the basic principles are introduced and the recent developments on nonlinear graphene plasmonics and on strong coupling physics with atomically thin transition metal dichalcogenides are reviewed. Finally, potentially new, promising research directions in the burgeoning field of 2D nanophotonics are identified.

Correction to "Nonlinear Graphene Nanoplasmonics".

ADVERTISEMENT RETURN TO ISSUEPREVAddition/CorrectionNEXTORIGINAL ARTICLEThis notice is a correctionCorrection to “Nonlinear Graphene Nanoplasmonics”Joel D. Cox*Joel D. CoxMore by Joel D. Coxhttp://orcid.org/0000-0002-5954-6038 and F. Javier Garcı́a de Abajo*F. Javier Garcı́a de AbajoMore by F. Javier Garcı́a de Abajohttp://orcid.org/0000-0002-4970-4565Cite this: Acc. Chem. Res. 2019, 52, 10, 2994Publication Date (Web):September 30, 2019Publication History Received19 September 2019Published online30 September 2019Published inissue 15 October 2019https://doi.org/10.1021/acs.accounts.9b00495Copyright © 2019 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views802Altmetric-Citations1LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (212 KB) Get e-Alerts Get e-Alerts

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.

Design of high-efficiency small-size passive all-optical diodes based on photonic crystal and graphene

Light propagation in an asymmetric multilayered structure composed of a linear defective photonic crystal and nonlinear graphene layer is theoretically investigated. A (BA)4/graphene/(AB)4(AABB)4 structure with a slight perturbation in the (AABB)4 part can provide non-reciprocal transmission to achieve an optical diode. This structure was optimized in order to have a low-operation input intensity, high-contrast, small-size all-optical diode without an additional pump signal. In this work, four different passive all-optical diodes are presented. The best contrast ratio is 6.3, and the minimum operation input intensity for diode action is 2.7×10−3 MWcm2. This structure gives an all-optical diode with a smaller size and higher efficiency in comparison to previous works.

Tunable Bistability in the Goos–Hänchen Effect with Nonlinear Graphene**Supported by the National Natural Science Foundation of China under Grant No 11774252, the Natural Science Foundation of Jiangsu Province under Grant No BK20161210, the Qing Lan project, the ‘333’ project under Grant No BRA2015353, and the PAPD of Jiangsu Higher Education Institutions.

We present a planar model system of a silica covered with a monolayer of nonlinear graphene to achieve a tunable Goos–Hänchen (GH) shift in the terahertz range. It is theoretically found that the transition between a negative shift and a large positive one can be realized by altering the intensity of incident light. Moreover, by controlling the chemical potential of graphene and the incident angle of light, we can further control the tunable GH shift dynamically. Numerical simulations for GH shifts based on Gaussian waves are in good agreement with our theoretical calculations.

Pseudospin‐Mediated Optical Spin–Spin Interaction in Nonlinear Photonic Graphene

AbstractDynamic manipulation of the spin of photons is important for many applications ranging from optical sensing to optical information processing. In the past, the study on controlling the spin of light has focused on chiral materials, three‐dimensional structures lacking any mirror symmetries. However, the complexity of fabrication of such structures has hindered their practical applications. In this work, the dynamic switching of optical chirality in two‐dimensional honeycomb photonic crystal—the so‐called photonic graphene is explored. In particular, optical spin–spin interaction mediated by the pseudospin states of the photonic graphene is proposed. A circularly polarized pumping beam can lift the degeneracy at the Dirac cones, leading to chiral responses for a probe beam incident along the direction of the Dirac points. Interestingly, the chirality is determined by the both the valley index and the spin of the pumping beam. The proposed nonlinear photonic graphene offers a new route to manipulate valley‐ and spin‐dependent phenomena in 2D photonic systems.

Efficient Optical Saturable Absorbers with Graphene on Polymer Waveguides for Femtosecond Laser Pulse Formation

AbstractPhotonic integrated circuits (PICs) are notable for their enhanced functionalities with material flexibilities to find applications in wearable high‐speed data management systems. Due to the miniaturized dimensions of PICs, the employment of a nanomaterial having significant optical nonlinearity is critical. Here, it is demonstrated that a polymer waveguide can be harmonized with nonlinear graphene to form ultrashort laser pulses. The graphene works as nonlinear saturable absorber on the polymer waveguide prepared with a perfluorinated acrylic resin. The evanescent field of a laser propagating through the waveguide interacts with graphene to induce intracavity intensity modulation for femtosecond‐scale pulse formation. The laser output is characterized quantitatively as the central wavelength, spectral width, repetition rate, extinction ratio, and pulse duration, which are 1553.32 nm, 10.21 nm, 4.18 MHz, 76.03 dB, and 874 fs, respectively. Stable operation is verified over 3 h.