Nonlinear graphene plasmonics

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.

Asymmetrically Engineered Nanoscale Transistors for On-Demand Sourcing of Terahertz Plasmons

Terahertz (THz) plasma oscillations represent a potential path to implement ultrafast electronic devices and circuits. Here, we present an approach to generate on-chip THz signals that relies on plasma-wave stabilization in nanoscale transistors with specific structural asymmetry. A hydrodynamic treatment shows how the transistor asymmetry supports plasma-wave amplification, giving rise to pronounced negative differential conductance (NDC). A demonstration of these behaviors is provided in InGaAs high-mobility transistors, which exhibit NDC in accordance with their designed asymmetry. The NDC onsets once the drift velocity in the channel reaches a threshold value, triggering the initial plasma instability. We also show how this feature can be made to persist beyond room temperature (to at least 75 °C), when the gating is configured to facilitate a transition between the hydrodynamic and ballistic regimes (of electron-electron transport). Our findings represent a significant step forward for efforts to develop active components for THz electronics.

All-optical graphene-on-silicon slot waveguide modulator based on graphene's Kerr effect

All-optical graphene-based optical modulators have recently attracted much attention because of their ultrafast and broadband response characteristics (bandwidth larger than 100 GHz) in comparison with the previous graphene-based optical modulators, which are electrically tuned via the graphene Fermi level. Silicon photonics has some benefits such as low cost and high compatibility with CMOS design and manufacturing technology. On the other hand, graphene has a unique large nonlinear Kerr coefficient, which we calculate using graphene's tight-binding model based on the semiconductor Bloch equations. Its real and imaginary parts are negative at the wavelength of 1.55 µm and E_F=0.1eV. To simultaneously use the benefits mentioned above, we present an all-optical, CMOS-compatible, and graphene-on-silicon slot (GOSS) waveguide extinction and phase modulator that consists of two different geometries. The first one consists of a one-stage GOSS waveguide with a single layer of graphene. To increase the light-graphene interaction and consequently enhance the modulation efficiency (ME), another stage of the GOSS waveguide is placed over the first one. This two-stage configuration is called a graphene-on-silicon double-slot (GOSDS) waveguide. The ME, insertion loss (IL), and modulation depth (MD) for a 12.5 µm GOSDS waveguide modulator with a double layer of graphene can reach 0.241 dB/µm, 1.31 dB, and 77%, respectively, at optical pump intensities about 9MWcm^-2. Our design has a smaller waveguide length (17.6 times) than the previous all-optical graphene-on-silicon ribbon waveguide extinction modulator and high MD (about 2 times) in comparison with a graphene-clad microfiber all-optical extinction modulator. Compared with an all-optical Mach-Zehnder interferometer phase modulator, our design has short graphene coated waveguide length (≈0.1 times) and low local optical intensities (≈0.043 times) needed for π phase shift. This study may promote the design and realization of high-performance, wideband, compact, and all-optical control on a single chip with a reasonable contrast level.

Extraordinary Optical Transmission by Hybrid Phonon-Plasmon Polaritons Using hBN Embedded in Plasmonic Nanoslits

Hexagonal boron nitride (hBN) exhibits natural hyperbolic dispersion in the infrared (IR) wavelength spectrum. In particular, the hybridization of its hyperbolic phonon polaritons (HPPs) and surface plasmon resonances (SPRs) induced by metallic nanostructures is expected to serve as a new platform for novel light manipulation. In this study, the transmission properties of embedded hBN in metallic one-dimensional (1D) nanoslits were theoretically investigated using a rigorous coupled wave analysis method. Extraordinary optical transmission (EOT) was observed in the type-II Reststrahlen band, which was attributed to the hybridization of HPPs in hBN and SPRs in 1D nanoslits. The calculated electric field distributions indicated that the unique Fabry–Pérot-like resonance was induced by the hybridization of HPPs and SPRs in an embedded hBN cavity. The trajectory of the confined light was a zigzag owing to the hyperbolicity of hBN, and its resonance number depended primarily on the aspect ratio of the 1D nanoslit. Such an EOT is also independent of the slit width and incident angle of light. These findings can not only assist in the development of improved strategies for the extreme confinement of IR light but may also be applied to ultrathin optical filters, advanced photodetectors, and optical devices.

Hyperbolic Cooper-Pair Polaritons in Planar Graphene/Cuprate Plasmonic Cavities

Hyperbolic Cooper-pair polaritons (HCP) in cuprate superconductors are of fundamental interest due to their potential for providing insights into the nature of unconventional superconductivity. Here, we critically assess an experimental approach using near-field imaging to probe HCP in Bi₂Sr₂CaCu₂O_8+x (Bi-2212) in the presence of graphene surface plasmon polaritons (SPP). Our simulations show that inherently weak HCP features in the near-field can be strongly enhanced when coupled to graphene SPP in layered graphene/hexagonal boron nitride (hBN)/Bi-2212 heterostructures. This enhancement arises from our multilayered structures effectively acting as plasmonic cavities capable of altering collective modes of a layered superconductor by modifying its electromagnetic environment. The degree of enhancement can be selectively controlled by tuning the insulating spacer thickness with atomic precision. Finally, we verify the expected renormalization of room-temperature graphene SPP using near-field infrared imaging. Our modeling, augmented with data, attests to the validity of our approach for probing HCP modes in cuprate superconductors.

Observation of strong magneto plasmonic nonlinearity in bilayer graphene discs

Graphene patterned into plasmonic structures like ribbons or discs strongly increases the linear and nonlinear optical interaction at resonance. The nonlinear optical response is governed by hot carriers, leading to a red-shift of the plasmon frequency. In magnetic fields, the plasmon hybridizes with the cyclotron resonance, resulting in a splitting of the plasmonic absorption into two branches. Here we present how this splitting can be exploited to tune the nonlinear optical response of graphene discs. In the absence of a magnetic field, a strong pump-induced increase in on-resonant transmission can be observed, but fields in the range of 3 T can change the characteristics completely, leading to an inverted nonlinearity. A two temperature model is provided that describes the observed behavior well.

Graphene H-Waveguide for Terahertz Lasing Applications: Electromagnetic Quasi-Linear Theory

A novel graphene H-waveguide is proposed for active terahertz components. A graphene film illuminated by strong pumping light shorts the parallel conductor plates. The terahertz modes propagating along this film are amplified at certain conditions. A rigorous electromagnetic (EM) quasi-linear method of analytical calculations of TEy and TMy eigenmodes is used in this paper to select these conditions. Among them is the use of bound TEy modes interacting with graphene plasmons at frequencies of negative graphene resistance, minimizing conductor loss associated with parallel plates, and excluding the current-crowding effect from the waveguide design. The limitations of the used theory are considered, and the applications of this waveguide are proposed.

Device architectures for low voltage and ultrafast graphene integrated phase modulators

The atomic layer thin geometry and semi-metallic band diagram of graphene can be utilized for significantly improving the performance matrix of integrated photonic devices. Its semiconductor-like behavior of Fermi-level tunability allows graphene to serve as an active layer for electro-optic modulation. As a low loss metal layer, graphene can be placed much closer to active layer for low voltage operation. In this work, we investigate hybrid device architectures utilizing semiconductor and metallic properties of the graphene for ultrafast and energy efficient electro-optic phase modulators on semiconductor and dielectric platforms. (1) Directly contacted graphene-silicon heterojunctions. Without oxide layer, the carrier density of graphene can be modulated by the directly contact to silicon layer, while silicon intrinsic region stays mostly depleted. With doped silicon as electrodes, carrier can be quickly injected and depleted from the active region in graphene. The ultrafast carrier transit time and small RC constant promise ultrafast modulation speed (3dB bandwidth of 67 GHz) with an estimated V_π·L of 1.19 V·mm. (2) Graphene integrated lithium niobite modulator. As a transparent electrode, graphene can be placed close to integrated lithium niobate waveguide for improving coupling coefficient between optical mode profile and electric field with minimal additional loss (4.6 dB/cm). Numerical simulation indicates 2.5× improvement of electro-optic field overlap coefficient, with estimated V _π of 0.2 V.

Tunable Optical Bistability, Tristability and Multistability in Arrays of Graphene

The optical bistability, tristability and multistability are explored in arrays of graphene. The arrays are periodically arranged spatially by single sheets of graphene. Optical bistability could be achieved with a strong enough incident intensity of light wave. The thresholds of optical bistability and the intervals between the upper and lower thresholds change with the surface conductivity of graphene and the incident wavelength. By increasing the intensity of incident light, tristability and multistability can be induced as well. Furthermore, the thresholds of bistability, tristability and multistability can be regulated via the chemical potential of graphene. This study may have potential applications in optical logic gates, all-optical switches and photomemory.

Graphene Oxide-Based Silico-Phosphate Composite Films for Optical Limiting of Ultrashort Near-Infrared Laser Pulses

The development of graphene-based materials for optical limiting functionality is an active field of research. Optical limiting for femtosecond laser pulses in the infrared-B (IR-B) (1.4-3 μm) spectral domain has been investigated to a lesser extent than that for nanosecond, picosecond and femtosecond laser pulses at wavelengths up to 1.1 μm. Novel nonlinear optical materials, glassy graphene oxide (GO)-based silico-phosphate composites, were prepared, for the first time to our knowledge, by a convenient and low cost sol-gel method, as described in the paper, using tetraethyl orthosilicate (TEOS), H3PO4 and GO/reduced GO (rGO) as precursors. The characterisation of the GO/rGO silico-phosphate composite films was performed by spectroscopy (Fourier-transform infrared (FTIR), Ultraviolet-Visible-Near Infrared (UV-VIS-NIR) and Raman) and microscopy (atomic force microscopy (AFM) and scanning electron microscope (SEM)) techniques. H3PO4 was found to reduce the rGO dispersed in the precursor's solution with the formation of vertically agglomerated rGO sheets, uniformly distributed on the substrate surface. The capability of these novel graphene oxide-based materials for the optical limiting of femtosecond laser pulses at 1550 nm wavelength was demonstrated by intensity-scan experiments. The GO or rGO presence in the film, their concentrations, the composite films glassy matrix, and the film substrate influence the optical limiting performance of these novel materials and are discussed accordingly.

Graphene Plasmonics in Sensor Applications: A Review

Surface plasmon polaritons (SPPs) can be generated in graphene at frequencies in the mid-infrared to terahertz range, which is not possible using conventional plasmonic materials such as noble metals. Moreover, the lifetime and confinement volume of such SPPs are much longer and smaller, respectively, than those in metals. For these reasons, graphene plasmonics has potential applications in novel plasmonic sensors and various concepts have been proposed. This review paper examines the potential of such graphene plasmonics with regard to the development of novel high-performance sensors. The theoretical background is summarized and the intrinsic nature of graphene plasmons, interactions between graphene and SPPs induced by metallic nanostructures and the electrical control of SPPs by adjusting the Fermi level of graphene are discussed. Subsequently, the development of optical sensors, biological sensors and important components such as absorbers/emitters and reconfigurable optical mirrors for use in new sensor systems are reviewed. Finally, future challenges related to the fabrication of graphene-based devices as well as various advanced optical devices incorporating other two-dimensional materials are examined. This review is intended to assist researchers in both industry and academia in the design and development of novel sensors based on graphene plasmonics.

Graphene-based all-optical modulators

All-optical devices, which are utilized to process optical signals without electro-optical conversion, play an essential role in the next generation ultrafast, ultralow power-consumption optical information processing systems. To satisfy the performance requirement, nonlinear optical materials that are associated with fast response, high nonlinearity, broad wavelength operation, low optical loss, low fabrication cost, and integration compatibility with optical components are required. Graphene is a promising candidate, particularly considering its electrically or optically tunable optical properties, ultrafast large nonlinearity, and high integration compatibility with various nanostructures. Thus far, three all-optical modulation systems utilize graphene, namely free-space modulators, fiber-based modulators, and on-chip modulators. This paper aims to provide a broad view of state-of-the-art researches on the graphene-based all-optical modulation systems. The performances of different devices are reviewed and compared to present a comprehensive analysis and perspective of graphene-based all-optical modulation devices.

Effects of the Van der Waals Force on the Vibration of Typical Multi-layered Two-dimensional Nanostructures

Recently, two-dimensional nanostructures have caught much attention because of their magnificent physical characteristics. The vibrational behavior of typical multi-layered two-dimensional nanostructures (TMLTNs) is extraordinary significant to TMLTN-based nanoresonantors. In this investigation, the vibrational behavior of TMLTNs, taking black phosphorus (BP), graphene and BN as examples, is studied adopting molecular dynamics (MD) simulations and the sandwich plate model (SPM). The MD results show that the fundamental resonant frequency of multi-layered BP (MLBP) and multi-layered BN (MLBN) increase obviously with the number of layers. However, the fundamental resonant frequency of a multi-layered graphene sheet (MLGS) rise slightly when the number of layers increases. This phenomenon is caused by the shear modulus in the xz-plane and yz-plane resulted by the vdW force. Hence, an SPM considering the shear modulus in the xz-plane and yz-plane caused by the vdW force is used to investigate the vibration of the TMLTN. Compared with the MD results, it is shown that the SPM can better predict the vibration of the TMLTN.

Optical Kerr effect and third harmonic generation in topological Dirac/Weyl semimetal

We study the nonlinear optical response generated by the massless Dirac quasiparticles residing around the topologically-protected Dirac/Weyl nodal points in three-dimensional (3D) topological semimetals. Analytical expressions of third-order interband nonlinear optical conductivities are obtained based on a quantum mechanical formalism which couples 3D Dirac fermions with multiple photons. Our results reveal that the massless Dirac fermions in three dimensions retains strong optical nonlinearity in terahertz frequency regime similar to the case of the two-dimensional Dirac fermions in graphene. At room temperature, the Kerr nonlinear refractive index and the harmonic generation susceptibility are found to be n₂ = 10^-11 ∼ 10^-8 m²W^-1 and χ⁽³⁾ = 10^-14 ∼ 10^-8 m²V^-2, respectively, in the few terahertz frequency regimes, which is comparable to graphene and orders of magnitudes stronger than many nonlinear crystals. Importantly, because 3D topological Dirac/Weyl semimetals possess bulk structural advantage not found in the strictly two-dimensional graphene, greater design flexibility and improved ease-of-fabrication in terms of photonic and optoelectronic device applications can be achieved. Our finding reveals the potential of 3D topological semimetals as a viable alternative to graphene for nonlinear optics applications.

High Sensitivity Surface Plasmon Resonance Sensor Based on Two-Dimensional MXene and Transition Metal Dichalcogenide: A Theoretical Study

MXene, a new class of two-dimensional nanomaterials, have drawn increasing attention as emerging materials for sensing applications. However, MXene-based surface plasmon resonance sensors remain largely unexplored. In this work, we theoretically show that the sensitivity of the surface plasmon resonance sensor can be significantly enhanced by combining two-dimensional Ti 3 C 2 T x MXene and transition metal dichalcogenides. A high sensitivity of 198 ∘ /RIU (refractive index unit) with a sensitivity enhancement of 41.43% was achieved in aqueous solutions (refractive index ∼1.33) with the employment of monolayer Ti 3 C 2 T x MXene and five layers of WS 2 at a 633 nm excitation wavelength. The integration of Ti 3 C 2 T x MXene with a conventional surface plasmon resonance sensor provides a promising approach for bio- and chemical sensing, thus opening up new opportunities for highly sensitive surface plasmon resonance sensors using two-dimensional nanomaterials.

Polarization dependent plasmonic modes in elliptical graphene disk arrays

Plasmonic modes at mid-infrared wavelengths in elliptical graphene disk arrays were studied. Theoretically, analytical expressions for the modes and their dependence on the size, Fermi energy and the permittivity of substrate materials of the ellipses were derived. Experimentally, the elliptical graphene disks were fabricated and their plasmonic modes were characterized with the polarization-resolved extinction spectra. Both experimental and analytical results show that two electrical dipole modes, whose dipole moments are orthogonal to each other and along the major and minor axis of the ellipse respectively, exist in the elliptical disks. By adjusting the polarization directions of the incident light, the two orthogonal plasmonic modes could be excited either together or separately, showing that the optical properties of elliptical graphene disks are highly polarization dependent. By using ultraviolet illumination to change the Fermi energy of the elliptical graphene disks, the two modes can be tuned dynamically. Moreover, the highly polarization dependent modes are able to couple with the surface phonons of the substrate, leading to polarized plasmon-phonon polaritons. Thus the elliptical graphene disks can provide more degrees of freedom to design the mid-infrared polarization-resolved photonic devices.

Ultrafast all-optical plasmonic graphene modulator

By utilizing the ultrafast dynamics of the photo-excited electrons in graphene, we theoretically present an ultrafast all-optical plasmonic modulator. With the help of an external pump, the femtosecond thermodynamics of the hot carriers can tune the Fermi level of the graphene sheet in less than 1 ps, which is the dependence of the support for the surface plasmonic wave. This device shows the ability to operate from the near-infrared regime to the far-infrared spectrum with the extinction ratio over 10 dB and the pump fluence of 0.41  mJ/cm². Such an ultrafast modulator may pave the way for designing the ultrahigh speed integrated photonics circuits.