Reflection Of Surface Plasmon Polaritons Research Articles

Subwavelength control of light transport at the exceptional point by non-Hermitian metagratings.

The concept of non-Hermitian physics, originally developed in the context of quantum field theory, has been investigated on distinct photonic platforms and created a plethora of counterintuitive phenomena. Interfacing non-Hermitian photonics and nanoplasmonics, here, we demonstrate unidirectional excitation and reflection of surface plasmon polaritons by elaborately designing the permittivity profile of non-Hermitian metagratings, in which the eigenstates of the system can coalesce at an exceptional point. Continuous tuning of the excitation or reflection ratios is also possible through altering the geometry of the metagrating. The controllable directionality and robust performance are attributed to the phase transition near the exceptional point, which is fully confirmed by the theoretic calculation, numerical simulation, and experimental characterization. Our work pushes non-Hermitian photonics to the nanoscale regime and paves the way toward high-performance plasmonic devices with superior controllability, performance, and robustness by using the topological effect associated with non-Hermitian systems.

SPP standing waves within plasmonic nanocavities.

Surface plasmons usually take two forms: surface plasmon polaritons (SPP) and localized surface plasmons (LSP). Recent experiments demonstrate an interesting plasmon mode within plasmonic gaps, showing distinct characters from the two usual forms. In this investigation, by introducing a fundamental concept of SPP standing wave and an analytical model, we reveal the nature of the recently reported plasmon modes. The analytical model includes SPP propagating and SPP reflection within a metal-insulator-metal (MIM) cavity, which is rechecked and supplemented by numerical simulations. We systematically analyze SPP standing waves within various nanocavities. During the discussion, some unusual phenomena have been explained. For example, the hot spot of a nanodimer could be off-tip, depending on the order of standing wave mode; and that a nanocube on metal film can be viewed as a nanocube dimer with the same separation. And many other interesting phenomena have been discussed, such as dark mode of SPP standing wave and extraordinary optical transmission. The study gives a comprehensive understanding of SPP standing waves, and may promote the applications of cavity plasmons in ultrasensitive bio-sensings.

Дослідження ефективності збудження поверхневих плазмон-поляритонів на алюмінієвих гратках з урахуванням дифрагованого випромінювання

Detailed studies of the efficiency of excitation of surface plasmon-polaritons (SPP) on aluminum gratings with a period a = 694 nm, which exceeds the incident wavelength of λ = 632,8 nm, have been carried out. The gratings relief depth (h) range was 6–135 nm. Research samples were formed on As40S30Se30 chalcogenide photoresist films using interference lithography and vacuum thermal deposition of an opaque aluminum layer about 80 nm thick. An atomic force microscope was used to determine the groove profile shape and the grating relief depth. The study of the SPP excitation features was carried out on a stand mounted on the basis of a G5M goniometer and an FS-5 Fedorov stage by measuring the angular dependences of the intensity of specularly reflected and diffracted p-polarized radiation of He-Ne laser. When determining the SPP excitation efficiency, the resonance values of both specular reflection and reflection in the -1st DO were taken into account. It was found that the dependence of the integral plasmon absorption on the grating modulation depth (h/a) is described by a somewhat asymmetric curve with a wide maximum, the position of which corresponds to an h/a value of about 0.07 and a half-width of about 0.123. This allows to excite SPP with an efficiency ≥ 80% of the maximum value on the gratings with the 0,05-0,105 h/a range. The half-width of the plasmon minimum of the reflection in the -1st DO is less than in the specular reflection, which can increase sensitivity of sensor devices when registering the shift of the minimum from angular measurements. The dependence of the half-width of the SPP reflection minima on the grating modulation depth is close to quadratic. In the investigated h/a range (from 0.009 to 0.194), the maximum dynamic range of the reflection coefficient is two orders of magnitude and is achieved in specular reflection for gratings with h/a ≈ 0.075.

Improved Smith–Purcell radiation owing to field localization and reflection of surface plasmon polaritons in grating substrate

Study of Smith–Purcell radiation (SPR) shows that optimal grating depth (groove depth) increases as excitation electrons energy decreases. Difficulty in achieving oversized groove depth grating leads to weak radiation in low energy excitation condition. Due to field localization and reflection of surface plasmon polaritons (SPPs), which significantly decreases optimal groove depth, radiation performance is comprehensively improved in SPPs materials substrate grating. This research shows that the greater the confinement factor of SPPs materials substrate, the more the optimized groove depth decreases. Simulation results show that 10.5 keV (0.2c, c is light speed) electrons exciting the grating of 90 nm period 0.1 duty cycle and 27 nm groove depth, the radiation intensity in Au substrate grating is more than 400 times of PEC grating. Comparing with Au grating, radiation is point frequency enhancement by plasmon while in Au substrate grating it is broadband improvement. The results presented here are of great significance of developing miniature, integratable, broadband, high-power-density light radiation sources at room temperature.

Ridge reflection of surface plasmon-polaritons in a one-dimensional plasmonic cavity

Reflection characteristics of surface plasmon polariton (SPP) by a rectangular ridge on the silver surface were examined theoretically and experimentally. The amplitude and phase shift of the SPP reflection by the rectangular ridge were calculated by SPP scattering theory using Green's tensor method and expressed in terms of ridge width and SPP energy. It was found that this calculation result can be reproduced well by a simple model expressed by superposition of reflections by the two steps constituting the ridge. A one-dimensional cavity composed of a pair of rectangular ridges was fabricated, and the characteristics of the SPP standing wave mode (cavity mode) was clarified for the first time using the scanning transmission electron microscope (STEM) - cathodoluminescence (CL) method and was used to evaluate the theoretical calculations of the reflection coefficient. The cavity mode energies are derived from the angle-resolved spectral (ARS) pattern, and the phase shift of the SPP reflection can be deduced through the cavity condition. We successfully explained the resonance energy of the cavity mode and the spatial distribution of the SPP standing wave by using the SPP reflection coefficient of the rectangular ridge derived by the theory.

Surface plasmon polariton mode in the metal-insulator-metal waveguide

Metal-insulator-metal (MIM) waveguides with subwavelength apertures exhibit unique properties that are considered breakthroughs in surface plasma technology. In this paper, we established a surface plasmon polariton (SPP) mode of MIM structure as well as a theoretical model of reflectivity and excitation coefficients to clarify the SPP mode structure. During simulation calculations, attenuation of the TM ground state mode with large-thickness dielectrics is over the oscillation mode, which is obviously different from the traditional dielectric waveguide. The TE mode exhibits characteristics of anamorphic dielectric optical waveguides, and its propagation distance is longer than that of the TM0 mode. With increasing length, the cavity quality factor Q increases, which indicates that the SPP reflection is limited. The quality factor of the cavity and the end-face have a close relationship. MIM waveguides with larger Q values can produce optical waves coupled with the SPP mode. In this paper, we analyzed SPP propagation constants and attenuation coefficients to promote the development of an integrated surface plasmon.

Wave-vector Spectrum of Monochromatic Terahertz Surface Plasmon Polaritons on Real Surfaces

Experiments at the Novosibirsk free electron laser demonstrating that monochromatic terahertz surface plasmon-polaritons (SPPs) on a real metal surface have a rather wide-band spectrum of their wave-vector are described. The fact was evidenced by detection of bulk waves radiated from the SPP track and by means of SPPs reflection from a mirror installed normally to the sample surface or tilted to it. The cause of the wave-vector splitting is supposed to be SPPs scattering on imperfections of the surface. This splitting leads to substantial radiative losses of the SPPs, which may be the cause of violation of the 1/ω2 SPP propagation length dependence predicted by the Drude model.

Phase-resolved surface plasmon interferometry of graphene.

The surface plasmon polaritons (SPPs) of graphene reflect the microscopic spatial variations of underlying electronic structure and dynamics. Here, we excite and image the graphene SPP response in phase and amplitude by near-field interferometry. We develop an analytic cavity model that can self-consistently describe the SPP response function for edge, grain boundary, and defect SPP reflection and scattering. The derived SPP wave vector, damping, and carrier mobility agree with the results from more complex models. Spatial variations in the Fermi level and associated variations in dopant concentration reveal a nanoscale spatial inhomogeneity in the reduced conductivity at internal boundaries. The additional SPP phase information thus opens a new degree of freedom for spatial and spectral graphene SPP tuning and modulation for optoelectronics applications.

SPP filters and selectors using nanoscale metal waveguide arrays with bends

We investigate numerically filters and selectors formed in metal-insulator-metal (MIM) nanoscale metal waveguide arrays (NMWAs) with bends by using the finite difference time domain (FDTD) method, and good frequency selectivity has been observed. For the central waveguide within the array, the output surface plasmon polaritons (SPPs) frequencies mainly depend on the width and the length of the central waveguide, and the coupling effect and the reflection of SPPs from the end of each waveguide have strong influences on the frequency selections of other waveguides. Thus, by changing widths and lengths of waveguides, and the gaps between adjacent waveguides, specific frequencies can be selected with special designed structures.

Polarization dependant scattering as a tool to retrieve the buried phase information of surface plasmon polaritons

We report on an experimental and theoretical study demonstrating that the phase information of a surface plasmon polariton (SPP) can be retrieved by investigating the cross polarized scattered components in the SPP reflection channel. The method does not require traditional interferometric techniques, optical heterodyning, or polarimetry, instead the method is self referencing. Studies are performed for different excitation wavelengths (561 nm and 795 nm), providing an alternative access route to phase information for sensing applications while also offering a deeper understanding of the scattering behavior of SPPs.

Terahertz surface plasmon polaritons on a conductive right circular cone: Analytical description and experimental verification

We report on an analytical solution of Maxwell's equations for the propagation of surface plasmon polaritons on a right circular cone. The problem was solved for THz frequencies in real metals and was therefore derived using the Leontovich approximation, which is valid for media with small surface impedances. The solution also accounts for both surface plasmon polaritons that are axisymmetric and those that have an angular structure in a plane normal to the cone's axis. This was an important consideration since it is crucial for describing surface phenomena such as surface-enhanced absorption, fluorescence, and Raman scattering. Our findings predict a total reflection of surface plasmon polaritons at the cone's apex, which was experimentally verified by an absence of light emitted from a heated cone's tip into the far-field region.

Analytical Modeling of Resonant Cavities for Plasmonic-Slot-Waveguide Junctions

Transmittance of a straight junction between two plasmonic slot waveguides can be enhanced by either coupling a perpendicular stub to the input waveguide or inserting an intermediate slot section between the waveguides. We derive analytic expressions for the transmission spectra in these two configuration schemes and analyze them to obtain simple formulas, relating the parameters of the stub and intermediate slot section that maximize the transmittance at a given frequency. A considerable advantage of our results over the recently reported approximations is in their broader applicability domain, which is the consequence of the correct accounting for the phase shift resulting from the reflection of the surface plasmon-polariton (SPP) at the end of the stub, and inclusion of ohmic losses. By the example of a 100-fs Gaussian pulse at the telecommunication wavelength of 1.55 m, we demonstrate that both transmission enhancement techniques can almost completely eliminate SPP reflection from the junction of 125- and 25-nm-gap silver-air-silver plasmonic waveguides, whereupon the preference can be given to either of the techniques, depending on the desired design features. Although, for concreteness, we studied a pair of aligned slot waveguides, the concepts of optics and transmission-line theory that we marry in our work are not specific for straight junctions and are well suited for analyzing more complex waveguide geometries. Our solutions to the problem of SPP transmission through the two types of junctions provide a simple tool for design optimization of power-efficient plasmonic interconnects for all-optical supercomputers.

Symmetry in the elementary scattering of surface plasmon polaritons and a generalized symmetry principle

In the elementary scattering of surface plasmon polaritons (SPPs) at individual subwavelength (sub-lambda) objects on metallic surfaces, the in-plane transmission and reflection of SPPs are shown to be two related scattering processes and to satisfy some novel symmetry relations, provided that the objects are mirror symmetric and are narrow enough (<0.1lambda approximately). To interpret these symmetry relations, a new generalized symmetry principle for the scattered field is put forward, which is much less limited than the classical one and is shown to have wide applications for other sub-lambda scattering problems.

Groove-gratings to optimize the electric field enhancement in a plasmonic nanoslit-cavity

We study the spectral properties of a triangular plasmonic nanoslit-cavity with periodic triangular grooves to optimize the field enhancement inside the nanoslit. This work is mainly based on numerical calculations and also partly supported by experimental evidence. In the nanoslit-cavity, we can distinguish following three main contributions to the field enhancement: electrostatic interaction in the nanoslit, surface plasmon polariton standing waves in the cavity and excitation, and reflection of surface plasmon polaritons by the grating. The importance of phase matching between surface plasmons generated at the nanoslit and the gratings is also investigated in order to optimize the local field intensity in the nanoslit.

How grooves reflect and confine surface plasmon polaritons

The reflection of surface plasmon polaritons by deep linear grooves structured into gold surfaces is investigated with numerical finite-difference-in-time-domain as well as boundary-element-method calculations. Groove widths of 25 and 100 nm are studied, with depths as large as 500 nm. The reflection depends strongly on wavelength, groove depth, and width. By systematically varying these parameters and studying the field profiles in the grooves as well as mode dispersion, we relate the resonances of the reflectivity to resonant coupling of propagating planar plasmon modes to cavity modes inside the grooves. By careful design of the groove width and depth the reflectivity can be tuned to values up to at least 30% for either a narrow or wide band of wavelengths.

Slow Propagation, Anomalous Absorption, and Total External Reflection of Surface Plasmon Polaritons in Nanolayer Systems

I predict that a nanoscopic, high-permittivity layer on the surface of a plasmonic metal can cause total external reflection of surface plasmon polaritons (SPPs). Such a layer can be used as a mirror in nanoplasmonics, in particular for resonators of nanolasers and spasers and can also be used in adiabatic nanooptics. I also show that the earlier predicted slow propagating SPP modes, especially those with negative refraction, are highly damped.

Surface Plasmon Polariton Mach–Zehnder Interferometer and Oscillation Fringes

We present a quantitative experimental analysis of a surface plasmon polariton (SPP) interferometer relying on elliptical Bragg mirrors. By using a leakage radiation microscope, we observe oscillation fringes with unit visibility at the two interferometer exits. We study the properties of the SPP beam splitter and determine experimentally both the norm and phase of the SPP reflection and transmission coefficients.

Surface-plasmon polariton scattering from a finite array of nanogrooves∕ridges: Efficient mirrors

The scattering of surface-plasmon polaritons (SPP) by finite arrays of one-dimensional nanodefects on metal surfaces is theoretically investigated on the basis of the reduced Rayleigh equation. Numerical calculations are carried out that rigorously account for all the scattering channels: SPP reflection and transmission, and radiative leakage. We analyze the range of parameters (defect size and number) for which high SPP reflection efficiency (low radiative losses) is achieved within a SPP band gap (negligible SPP transmission), neglecting ohmic losses (justified for array lengths significantly shorter than the SPP inelastic length): Smaller defects play better as SPP mirrors (e.g., efficiency &amp;gt;90% at λ∼650nm for Gaussian ridges∕grooves with sub-30nm height and half-width) than larger defects, since the latter yield significant radiative losses.

Experimental studies of surface plasmon polariton band gap effect.

Surface plasmon polaritons (SPPs) propagation at a gold film surface covered by periodic arrays of approximately 40-nm-high scatterers arranged in a triangular lattice of different periods containing straight line defects is studied using collection scanning near-field optical microscopy. The results reveal the dependence of the SPP band gap (SPPBG) effect manifested via the SPP reflection and guiding (along line defects) on the parameters of the surface structures (period, filling factor and lattice orientation). We find that the SPPBG effect is stronger along GammaK direction for all investigated periodic structures. Our results demonstrate that the SPPBG effect becomes less pronounced with a decrease of the filling factor and disappears for a filling factor close to 0.2. We also observe that the centre of the SPPBG shifts towards longer wavelengths with an increase of the lattice period.