Slow Surface Plasmon Polaritons 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.

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.

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.

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.

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.

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.

Integrated fiber-coupled launcher for slow plasmon-polariton waves

We propose and numerically demonstrate an integrated fiber-coupled launcher for slow surface plasmon-polaritons. The device is based on a novel plasmonic mode-converter providing efficient power transfer from the fast to the slow modes of a metallic nanostripe. Total coupling efficiency with standard single-mode fiber approaching 30% (including ohmic losses) has been numerically predicted for a 25-µm long gold-based device operating at 1.55 µm telecom wavelength.

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.

Dual-channel broadband slow surface plasmon polaritons in metal gap waveguide superlattices

We propose and demonstrate a kind of low-loss plasmonic superlattice with a few coupled resonant cavities to realize dual-channel broadband slow surface plasmon polaritons (SPPs) around two telecom wavelengths of 1550 nm and 1310 nm. The dual-channel slow SPPs result from the introduction of two kinds of coupled cavities into the superlattices. Theoretical analysis is confirmed by the finite-difference time domain (FDTD) numerical simulations. Our structures offer another avenue for researchers to explore novel slow SPP technologies and thereby may inspire further exploration of advanced photonic devices for next-generation telecommunication, optical data processing, and on-chip integration.

Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial

We apply the concept of slow surface-plasmon polariton standing-wave resonances to model the plasmon resonances which exist on split-ring resonators (U-shaped nanowires) forming the unit cell of a metamaterial at infrared frequencies. We compare the expected resonances predicted by the model with full electrodynamic three-dimensional simulations of the U-shaped nanowires for varying geometrical parameters and find a reasonably good agreement. We also consider how far-field dipolar coupling between unit-cells and near-field coupling between the U-shaped nanowire's arms should be taken into account. In addition, we study how the different resonances give rise to negative constitutive parameters for the metamaterial and adjust the geometrical parameters so that the second and third order slow-SPP standing-wave resonances of the U-shaped nanowires result in a double-negative behavior at far-infrared wavelengths without the need of further wires or particles. Finally, we study the effects of stacking $N$ layers of such metamaterial, where each resonant mode splits into $N$ normal mode resonances, showing different electric or magnetic responses. This simple stacked structure maintains the left-handed behavior, exhibiting backward wave propagation.

Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons

Gap plasmon-polariton (GPP) nanoresonators based on a metal nanostrip separated with a small gap from a metal surface or metal block are considered. Scattering resonances and field enhancements are studied for two-dimensional structures using the Green's-function surface integral equation method (GFSIEM). For small gaps, we show that the scattering resonances occur due to the constructive interference of counterpropagating GPPs, forming standing waves. By varying the gap size we find that the resonance wavelength can be tuned over a wide range of wavelengths, which makes the resonators interesting for spectroscopic and sensing applications, and observe the transition between GPP-based resonators (for narrow gaps) and slow surface plasmon-polariton (SPP) strip resonators (for wide gaps). Considering the resonant field distributions, we find that, for an insulator thickness of 10 nm, the maximum field enhancement (with respect to the incident field) can reach values close to 50 along the line passing through the gap center. For the case of a strip placed close to a metal surface, two scattering channels, viz., the out-of-plane scattering and the scattering into SPPs (propagating along the surface) are evaluated separately using a generalized version of the GFSIEM. We find that, even though the out-of-plane scattering is in general dominating in the considered range of parameters, scattering into SPPs can be very efficient for smaller gaps featuring a cross section that at resonance even exceeds the strip width. The considered properties of GPP nanoresonators, i.e., resonant scattering and local-field enhancements along with efficient scattering into SPPs, hold promises for their useful applications within plasmonic sensing devices.

Two-photon mapping of localized field enhancements in thin nanostrip antennas

Resonant scattering and local field enhancements by 11-nm-thin gold nanostrip antennas due to constructive interference of counter propagating slow surface plasmon polaritons is investigated. We characterize nanostrips of widths between 50-530 nm using both reflection spectroscopy and nonlinear scanning optical microscopy, in which two-photon-excited photoluminescence (TPL) excited with a strongly focused laser beam at the wavelength 745 nm is detected. We use TPL images to map the local field enhancements from individual nanostrips at a resolution of 0.35 microm and compare results with theoretical calculated reflection spectra, enhancement levels and field distributions across the strip.

Slow-plasmon resonant nanostructures: Scattering and field enhancements

Resonances in metal nanostructures supporting propagation of slow surface plasmon-polariton (SPP) modes are considered. Resonant enhancements in scattering and built-up electric fields of nm thin submicron-wide metal strips are investigated using a surface integral equation method and ascribed to the excitation of strip-cavity modes formed by short-range SPPs. A properly positioned narrow gap $(5\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ in the strip is found to lead, by virtue of boundary conditions, to significant field enhancement ($\ensuremath{\sim}30$, inside the gap), as well as to a noticeable $(\ensuremath{\sim}10%)$ blueshift in the resonance wavelength.

General properties of slow-plasmon resonant nanostructures: nano-antennas and resonators

General properties of retardation-based resonances involving slow surface plasmon-polariton (SPP) modes supported by metal nanostructures are considered. Explicit relations for the dispersion of SPP modes propagating along thin metal strips embedded in dielectric and in narrow gaps between metal surfaces are obtained. Strip and gap subwavelength resonant structures are compared with respect to the achievable scattering and local-field enhancements lending thereby their distinction as nano-antennas and nano-resonators, respectively. It is shown that, in the limit of extremely thin strips and narrow gaps, both structures exhibit the same Q factor of the resonance which is primarily determined by the complex dielectric function of metal.

Diffraction gratings for measuring slow mode surface plasmon polaritons

Electron beam lithography and reactive ion etching were used to fabricate diffraction gratings with periods between 70 and 110 nm. The gratings were formed in a thermally grown SiO2 layer and used as substrates for aluminum–aluminum oxide–gold tunnel junctions. The light emission from the tunnel junctions under direct-current bias conditions is due to the scattering of the surface plasmon polaritons (SPPs). In particular, by isolating the scattering of the slow mode SPP off the gratings the dispersion relation of the slow mode was determined.

Calculation of slow mode surface plasmon polariton properties related to experimental observations

Recent experimental results definitively showed, for the first time, optical radiation mediated by the slow mode surface plasmon polariton of metal-oxide-metal tunnel junctions. Here, dispersion curves for this mode are calculated. They are consistent with first-order grating coupling to light at the energies of the experimental emission peaks. The curves are then used to analyze second-order and high-energy (≳2.35 eV) grating coupling of the polaritons to radiation. Finally, variation of slow mode damping as a function of energy is used to explain qualitatively the relative experimental peak emission intensities and the absence of radiation peaks above 2.35 eV.