Slow Surface Plasmon Research Articles

Resonant amplification of slow surface plasmon polaritons in a DC current pumped semiconductor/graphene waveguide with a groove defect

We propose the principle of a planar surface plasmon polariton amplifier composed of a complex waveguide structure based on a semiconductor thin film separated from a dielectric substrate by a graphene monolayer. The amplification of surface plasmon polaritons in that waveguide in the terahertz regime is driven by a direct current in the graphene layer under a synchronism condition that allows an efficient energy exchange from the collective flux of charge carriers in graphene and the surface electromagnetic wave in the semiconductor film. Positive feedback required for resonant amplification is achieved through surface plasmon polariton reflections at the edges of the active waveguide, one of which is formed by a local thickness defect (a groove) at the upper surface of the semiconductor film that also provides an exit channel for the energy of the amplified surface wave to be transferred to an adjacent passive thin film semiconductor waveguide. We determine the conditions required for the resonant amplification of surface plasmon polaritons in that complex structure, which are essentially governed by the geometry of the groove as well as by the characteristic parameters of the active and passive waveguides.

Atomic-Scale Confinement and Negative Refraction of Plasmons by Twisted Bilayer Graphene.

Moiré superlattices provide in-plane quantum restriction for light-matter interactions in twisted bilayer graphene (tBLG), leading to the exotic photon-Moiré physics and potential applications for light manipulation. Recently, our experiment identified a highly confined slow surface plasmons polaritons (SPPs) mode in tBLG. Here, we demonstrate that the propagation of the slow SPPs mode in tBLG is spatially tailored and steered at deep subwavelengths. Analysis by the perturbation theory indicates that the coupling between the slow SPPs mode and the Moiré system is greatly strengthened, which regulates the wavefront at the atomic scale and makes tBLG serve as a universal optical metamaterial. Consequently, the negative refraction is achieved at the interface of monolayer graphene and tBLG, by which a metalens with a controllable focal length and an extremely high resolution up to 1/150 of wavelength is devised. Our work paves the way for constructing optical metamaterial at the atomic scale and develops future photon-Moiré interaction systems.

Tunable dual-channel slow light in a graphene grating plasmonic waveguide.

We propose a plasmonic waveguide comprising a single-layer graphene, a silica dielectric layer, and a silicon grating substrate to realize dual-channel slow surface plasmon polaritons. The dual-channel results from the introduction of two kinds of periodic structures with defects in the waveguide. According to the Bragg equation, we match the appropriate structure parameters to ensure the slow light dual-channel working around λ1=9369.1nm (32 THz) and λ2=7138.2nm (42 THz). The influence of the structure parameters on the slow light effect is discussed, and the largest value of the normalized delay bandwidth product (NDBP) is up to 7.38. Then, by shifting the gate voltage, obvious linear blueshift of the dual-channel is achieved. In this process, the slow light performance of the dual-channel exhibits good stability, and the average values of the NDBP are 4.5 and 4.4. Due to the flexible tunability, the waveguide may pave the way for the design of slow light devices.

Arrays of Carbon Nanotubes in a Field of Continuous Laser Radiation

A numerical analysis of the phase-matching conditions during the incidence of one or two counterpropagating laser beams on an ordered array of single-walled carbon nanotubes (CNTs) is performed. The conditions for the generation of slow surface plasmon waves of the terahertz (THz) and far infrared range propagating along the nanotubes of the irradiated array are determined. It is shown that the plasmon frequency can be controlled by changing the angle of incidence of laser radiation on the structure under study. Thus, it is possible to fulfill the condition of longitudinal resonance, in which each array nanotube is a dipole antenna radiating at the plasmon frequency. In this case, the array forms a system of a large number of in-phase emitters, which allows increasing the efficiency of conversion of laser radiation into THz radiation in comparison with a single nanoantenna.

Slow light enabled high-modulation-depth graphene modulator with plasmonic metasurfaces.

Graphene has attracted the interest of researchers seeking to develop compact optical modulators with the flexible tunability of graphene conductivity by tuning the Fermi level. Plasmonic structures have provided a robust way to enhance the modulation depth (MD) of graphene optical modulators, but the available schemes suffer from low MD, fabrication complexities, or both. Here, an ultra-thin plasmonic metasurface structure capable of guiding slow surface plasmons (SPs) is proposed to construct graphene-based optical modulators. The designs take advantage of the strong field enhancement of slow SP modes as well as the orientation match between the electric field and the graphene plane. A typical 0.96-μm-long metasurface-based graphene modulator presents a significantly improved MD of 4.66dB/μm and an acceptable insertion loss of 1.4dB/μm, while still having ease of fabrication.

Generation of Slow Surface Plasmon Polaritons in a Complex Waveguide Structure with Electric Current Pump

AbstractA planar spaser structure composed of semiconducting film and graphene with DC current is proposed and theoretically explored. Graphene possesses velocity of drift current carriers comparable with the phase velocity of surface plasmon polaritons (SPPs) in ultrathin semiconducting film at the terahertz regime. When the synchronism condition between current and slow surface electromagnetic waves is realized, the amplification of plasmons by electric current takes place. In the proposed complex waveguide structure, positive feedback is realized due to reflections from the edges of the active waveguide, and the SPPs are decoupled into light by a microscopic grating manufactured on the semiconducting film surface.

Continuous-wave laser generation of slow THz surface plasmons in an array of single-walled carbon nanotubes

The mechanism of generation of surface plasmon polaritons in the THz and far-IR ranges by laser irradiation of arrays of single-walled carbon nanotubes is considered. It is shown that by varying the angle of incidence of the laser beam, one can change the frequency of generated surface plasmon polaritons. As consequence, the nanotube length can be matched to the laser wavelength for efficient conversion of cw laser radiation to the THz range.

On the Condition for Transformation of a Fast Surface Wave into a Slow Surface Wave

Surface plasmons (polaritons) along the boundary between vacuum and a dissipative half-space with given complex permittivity, including the case of placing an electrically thin dielectric layer (system of layers) on the boundary, are considered. Conditions for transformation of a fast gliding Zenneck surface wave (polariton) into a slow wave (slow surface plasmon) are considered. The behavior of the group velocity and the energy velocity of motion (transfer) in such structures are analyzed. The reflection coefficient of the Zenneck wave along the sea for the ice pack of a given thickness is determined. It has been shown that rigorous solution of the Sommerfeld problem by means of numerical calculation of integrals in the near zone allows obtaining the solution of the inverse problem of the structure of the surface region on the basis of redundant experimental data on components of the electromagnetic field on the surface at different ranges from the antenna.

Ultra-broadband and tunable slow surface plasmon polaritions in a simple graphene-based waveguide

The strongly delayed wave with large bandwidth in a graphene-based grating waveguide has been reported previously. However, a clear slow wave performance in a simple graphene-based uniform waveguide has not been explored. Here, we analyzed for the first time a delayed surface wave in this waveguide. The strongly delayed wave with extremely large bandwidth can be dynamically controlled via the bias-voltage dependent optical properties of graphene. The simple waveguide is an excellent candidate for slow light applications because of easy fabrication, ultra-high slowdown factor, ultra-large bandwidth and conveniently tunable group velocity.

Theoretical study of ultra-wideband slow light in dual-stub-coupled plasmonic waveguide

We propose and demonstrate a metal-insulator-metal (MIM) waveguide side coupled double stubs to realize broadband slow surface plasmon polaritons (SPPs) around the telecom frequency 193.5THz. When the depth of single stub is approximately equal to integral multiple of half plasmon wavelength, owing to the constructive interferences between the electromagnetic wave propagating through the MIM waveguide and that reflected from the stubs, wideband slow light effect appears. The improved transmission line theory calculation indicates that the group velocity of SPPs in the plasmonic waveguide system for stub depth 1111nm is 0.1c (c is light speed in vacuum.) over a broad bandwidth of 69THz. Exploiting the finite-difference time-domain (FDTD) numerical simulation, the group velocity of pulse for width 20fs (Full width at half high) is calculated. The result agrees well with that predicted by the transmission line theory. This plasmonic waveguide for slow light effect has important potential application in optical delay lines.

Wideband slow light based on plasmon-induced transparency at telecom frequency

We propose and demonstrate a metal–insulator–metal (MIM) waveguide side coupled with a series of stubs to realize broadband slow surface plasmon polaritons (SPPs) around the telecom wavelength 193.5THz. The obviously slow light effect results from the strong normal dispersion around the frequency of the plasmon-induced transparency. Theoretical calculations indicate that the plasmonic waveguide system of the length 11μm works on a broad bandwidth of 20THz. The group velocity of SPPs predicted by the improved transmission line theory is about 0.2c (c is light speed in vacuum), which is confirmed by the finite-difference time-domain (FDTD) numerical simulation. The waveguide system for slow light effect has important potential application in optical delay lines.

Graphene-based active slow surface plasmon polaritons.

Finding new ways to control and slow down the group velocity of light in media remains a major challenge in the field of optics. For the design of plasmonic slow light structures, graphene represents an attractive alternative to metals due to its strong field confinement, comparably low ohmic loss and versatile tunability. Here we propose a novel nanostructure consisting of a monolayer graphene on a silicon based graded grating structure. An external gate voltage is applied to graphene and silicon, which are separated by a spacer layer of silica. Theoretical and numerical results demonstrate that the structure exhibits an ultra-high slowdown factor above 450 for the propagation of surface plasmon polaritons (SPPs) excited in graphene, which also enables the spatially resolved trapping of light. Slowdown and trapping occur in the mid-infrared wavelength region within a bandwidth of ~2.1 μm and on a length scale less than 1/6 of the operating wavelength. The slowdown factor can be precisely tuned simply by adjusting the external gate voltage, offering a dynamic pathway for the release of trapped SPPs at room temperature. The presented results will enable the development of highly tunable optoelectronic devices such as plasmonic switches and buffers.

Slow surface plasmon pulse excitation in metal-insulator-metal plasmonic waveguide with chirped grating.

A scheme for the excitation of slow surface plasmon pulses using photonic interband transition in a metal-insulator-metal (MIM) waveguide is proposed. An investigation the mode transition behavior inside the binary grating confirmed that the proposed concept can be understood in terms of the coupling of symmetric and anti-symmetric plasmonic modes. We observed that, although a binary grating that is optimized for a single frequency can excite slow surface plasmon pulses, it is inadequate for broadband mode conversion. To rectify this, a chirped grating was designed for the demonstration of broadband mode conversion by applying a cascade mode transition with different frequencies.

Ultracompact Slow Surface Plasmon Polaritons Superlattice with Broad Bandwidth and Super-High Normalized Delay-Bandwidth Product

In this paper, we propose an ultracompact low-loss plasmonic superlattice for slow surface plasmon polaritons. The superlattice consists of a two-dimensional metal gap waveguide (Ag-SiO2-Ag) inserted with thin metal films working as coupled reflectors. Theoretical calculations indicate that the device is working on a broad bandwidth of 37 THz including the two telecom wavelengths of 1,310 and 1,550 nm and with mean group refractive index of 3.5 and mean transmission of 60 %. As the total geometric thickness is only 1.6 μm, the normalized delay-bandwidth product of the superlattice is as high as 0.44. All the theoretical prediction based upon the transfer matrix method is validated by the finite-difference time-domain numerical simulation on surface plasmon polaritons propagating in the superlattice.

Spatially Dispersive Graphene Single and Parallel Plate Waveguides: Analysis and Circuit Model

The propagation of surface waves along spatially dispersive graphene-based 2-D waveguides is investigated in detail. Graphene is characterized using a full-k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sub> conductivity model under the relaxation-time approximation, which allows to obtain analytical and closed-formed expressions for the wavenumber of plasmons supported by sheets and parallel plate waveguides, respectively. Per unit length equivalent circuits are introduced to accurately characterize the propagation in different waveguides, and analytical relations between the effective TM-mode circuit lumped elements and graphene conductivity are derived. The proposed circuits allow identifying the different mechanisms involved in spatially dispersive plasmon propagation, explaining their connection with the intrinsic properties of graphene. Results demonstrate that spatial dispersion, which significantly decreases the confinement and the losses of slow surface plasmons, must be accurately assessed in the design of graphene-based plasmonic components at millimeter-waves and low terahertz frequencies.

Rainbow trapping based on long-range plasmonic Bragg gratings at telecom frequencies

The group velocity of long-range surface plasmon polaritons (LRSPPs) in a wide frequency bandwidth at infrared frequencies is significantly reduced by dielectric gratings of graded thickness on both sides of a thin metal film. This structure can reduce the propagation loss of slow surface plasmons in “rainbow trapping" systems based on plasmonic Bragg gratings. Compared with dielectric gratings of graded thickness on a single side of a metal film, the proposed structure is able to guide slow light with a much longer propagation distance for the same group index factor. Finite-difference time-domain simulation results show that slow LRSPPs with the group velocity of c/14.5 and the propagation distance of 10.4 μm are achieved in dielectric gratings of uniform thickness on both sides of a thin metal film at 1.62 μm.

Fine tuning slow group velocity and small pulse broadening of surface plasmon polaritons along metal–nonlinear Kerr medium interface

We propose and demonstrate a new method to fine control the group velocity of slow surface plasmon polaritons (SPPs) propagating in a metal–nonlinear Kerr medium (MNKM) waveguide by changing the incident peak electric field intensity. Tunable group velocity results from nonlinear dispersion relationship of waveguide induced by Kerr effect. The validity of this method is confirmed by numerical simulations with the finite-difference time-domain (FDTD). When the pulse with center wavelength 400nm and width 240fs propagates in MNKM waveguide of length 6μm, the largest pulse broadening is only 3.4% of the input pulse width. Our method offers a new avenue for potential applications of the tunable slow SPP pulse with small pulse broadening.

Slow surface plasmon polaritons with a large normalized delay bandwidth product in an ultracompact metal gap superlattice

We propose a metal gap superlattice that can decrease the group velocity of surface plasmon polaritons (SPPs) with a large normalized delay bandwidth product (NDBP) and small high-order dispersion. The length of the superlattice is only 8.60μm and the transmission is 0.4. The multiple reflections of photons in the nanocavity result in slow SPP group velocity. The numerical analysis exploiting the transfer matrix method (TMM) is confirmed by the finite-difference time-domain (FDTD) numerical simulations. In addition, we also analyze the reason for pulse deformation.

Precise Control of Group Velocity by Pulse Width in a Plasmonic Superlattice

We propose and demonstrate a new method to control precisely the group velocity of slow surface plasmon polaritons propagating in a superlattice by changing incident pulsewidth. The validity of this method is confirmed by numerical simulations with the finite-difference time-domain. The group velocities for different frequency components are different. Therefore, for the Gaussian pulse, the group velocity is varied with the pulsewidth. Our method of control group velocity offers a new avenue for potential applications of the tunable slow surface plasmon polaritons.

Slowing surface plasmon polaritons on plasmonic coupled cavities by tuning grating grooves

We investigate slow surface plasmon polaritons (SPPs) in plasmonic waveguiding bands formed by coupled plasmonic cavities on Moiré surfaces. We demonstrate controlling the group velocity and dispersion of the SPPs by varying the depth of the plasmonic Bragg grating groove. Changing the grating depth results in modification of coupling coefficients between the cavities and hence the SPPs group velocity is altered. Variation in the group velocity and dispersion of SPPs can be measured with polarization dependent spectroscopic reflection measurements. Dispersion of SPPs has been calculated by finite-difference time-domain method in agreement with the experimental data.