Rainbow Trapping on Plasmonic Surface Gratings and Beyond

The recent reported trapped “rainbow” storage of light using metamaterials and plasmonic graded surface gratings has generated considerable interest for on-chip slow light. The potential for controlling the velocity of broadband light in guided photonic structures opens up tremendous opportunities to manipulate light for optical modulation, switching, communication and light-matter interactions. However, previously reported designs for rainbow trapping are generally constrained by inherent difficulties resulting in the limited experimental realization of this intriguing effect. Here we propose a hyperbolic metamaterial structure to realize a highly efficient rainbow trapping effect, which, importantly, is not limited by those severe theoretical constraints required in previously reported insulator-negative-index-insulator, insulator-metal-insulator and metal-insulator-metal waveguide tapers, and therefore representing a significant promise to realize the rainbow trapping structure practically.

Accompanied by the rise of plasmonic materials beyond those based on noble metals and the development of advanced materials processing techniques, it is important to understand the plasmonic behavior of materials with large-scale inhomogeneity (such as gradient permittivity materials) because they cannot be modeled simply as scatterers. In this paper, we theoretically analyze the excitation and propagation of surface plasmon polaritons (SPPs) on a planar interface between a homogeneous dielectric and a material with a gradient of negative permittivity. We demonstrate the following: (i) free-space propagating waves and surface waves can be coupled by a gradient negative-permittivity material and (ii) the coupling can be enhanced if the material permittivity variation is suitably designed. This theory is then verified by numerical simulations. A direct application of this theory, ‘rainbow trapping’, is also proposed, considering a realistic design based on doped indium antimonide. This theory may lead to various applications, such as ultracompact spectroscopy and dynamically controllable generation of SPPs.

Plasmonic graded nano-gratings enable rainbow trapping of multiple resonant modes over a wide wavelength spectrum, useful for multi-channel Surface Enhanced Raman Spectroscopy (SERS) of molecular species. However, rectangular nano-gratings have limitations in achieving efficient rainbow trapping and localizing a wide spectrum of plasmonic modes due to their stepwise geometry, which induces high dissipation of surface plasmon polaritons into the substrate. An alternative platform of graded triangular nano-gratings enables increased localization and more efficient adiabatic transformation between neighboring grooves. Varying groove angles, depths, and periods in the tapered geometry allow for smooth adjustment of the surface plasmon polariton propagation constant, reducing losses and maximizing nano-focusing inside the groove tips. To overcome the limitation of low aspect ratio in wet-etching silicon, we employed a multi-step process of reactive ion etching of a SiO2 barrier layer to generate aperture width, followed by anisotropic wet-etching. The resulting graded triangular nano-gratings showed excellent SERS enhancement along three laser wavelength excitations. The enhancement factors of 638 and 785 nm wavelengths are 8.5 × 109 and 9 × 108, respectively, for the detection of 1 µM Rhodamine 6G. In addition, graded triangular nano-gratings show similar enhancement factors for other species, specifically the lipid DPEE-PEG, at the 532 nm laser excitation wavelength with an excellent SERS enhancement factor of 1.5 × 109. Owing to the ability of the graded triangular gratings to elicit pronounced SERS responses across three distinct laser excitations, they unequivocally qualify as “rainbow trapping” structures. Wider apertures, lower ohmic losses, and the ability to tune the groove angle beyond conventional etching methods bode well for graded triangular gratings as a superior platform for miniature sensors.

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.

In this paper, we demonstrate the feasibility of exciting surface plasmon polaritons (SPPs) using intrinsic indium antimonide (InSb) graded grating structure, which exhibits extraordinary properties of trapping and releasing electromagnetic waves in terahertz range. The dispersive properties of the gradient-corrugate InSb grating structure is characterized using the computer simulation technology (CST). Furthermore, the propagation characteristics of the InSb grating grooves are thorough analyzed by the dispersive relation curves, electron field magnitude distribution. It is proved that the graded grating grooves based on intrinsic InSb are capable of exciting SPPs. The electric field magnitude distributions of the grating waveguide in fixed frequency at different temperatures are compared, which demonstrates the InSb grating structure is an excellent candidate for trapping and releasing SPPs at terahertz (THz). The thermo-optic property of InSb gives rise to the meaningful application for future compact communication devices.

Research in terahertz (THz) science and technology has been booming in view of its potential application in a variety of light-matter interaction areas. Intrinsic indium antimonide (InSb) is an excellent tunable candidate material that supports surface plasmon polaritons (SPPs) in the THz range. In this paper, we present calculations to demonstrate the feasibility of exciting SPPs using an InSb graded grating structure. The InSb structure exhibits an extraordinary property of trapping and releasing electromagnetic waves in terahertz regimes (0.084–0.326 THz). With a fixed frequency, the electric field magnitude distributions of the gradient InSb grating waveguide at different temperatures are compared; these show that the InSb grating structure is an excellent candidate for trapping and releasing SPPs in the THz range. The thermo-optic property of InSb permits the meaningful application for compact low-frequency surface-plasmon optical devices in the future.

We report on “trapping rainbow” on silver films covered by a one-dimensional chirped dielectric grating. We attribute the trapping effect to correlative dispersive relation between the excited surface plasmon polaritons (SPPs) and the lattice constant of the dielectric grating on the metal film, which results in localization of SPPs of different frequencies at different spatial positions. We further reveal that, by attaching another uniform dielectric grating on the other side of the metal film and real time tuning the refractive index of the grating, the trapped rainbow can be released in sequence. Analytical results are demonstrated by finite-difference time-domain simulation.

We propose and numerically analyze a scheme to trap a broadband surface plasmon polariton (SPP) wave on a sheet of monolayer graphene with gradient chemical potential distribution. Different frequency components of the incident wave are trapped at different locations according to the chemical potential, resulting in “rainbow trapping” effect. By appropriately tuning the chemical potential distribution over the graphene sheet, graphene conductivity distribution is modified so that the trapped SPP wave is released. In the proposed structure, the group velocity of the trapped SPP waves is as low as the 10−8 times of the light speed in free space, and the lifetime of the trapped SPP wave is 3.14 ps when the relaxation of the graphene is 0.5 ps. This slow light system offers advantages simultaneously including broadband operation, ultracompact footprint, and dynamic control of group velocity without any complicated and expensive device geometry engineering.

We have theoretically analyzed the excitation and propagation of surface plasmon polaritons on a planar interface between a homogeneous dielectric and a gradient negative permittivity material. This theory may lead to various applications, including “rainbow trapping”.

This study shows unique capability of deep-subwavelength metal-insulator-metal (MIM) width-graded nano-gratings in offering high intensity electromagnetic field. The plasmonic field is underpinned by the strong coupling of the surface plasmon polaritons on the sidewalls of the nanogrooves. We present quantitative SERS detection of various biomolecule species at an ultra-low concentration corresponding to detection of single molecule. We report limit of detection of a gold coated bullseye width-graded plasmonic nano-grating as a SERS platform in detecting small molecule (such as propylene glycol) or sepsis biomarkers (such as protein c) at multiple wavelengths of light.

We summarize our study of the ultrawideband slow-light system based on plasmonic-graded metallic gratings for “rainbow” trapping at terahertz (THz) frequencies. The dispersion relations for a perfect conducting plane hosting an array of 1-D grooves having a constant depth were derived. Since the dispersion relations for the fundamental surface mode resemble those for the surface plasmon polaritons (SPPs) at optical frequencies, such a uniform grating can be used to effectively guide THz waves. The dispersion relations for these spoof SPPs can be tailored by choosing the geometric parameters of the surface structures. We show that a graded metallic surface grating can be used to trap THz waves at different locations along the surface grating corresponding to the different wavelengths. Theoretical and experimental studies of rainbow trapping at shorter wavelengths, e.g., in visible and near-infrared domains, are also briefly summarized.

The unique optical and physical properties of surface plasmon polaritons (SPP) has brought about a series of novel phenomena such as SPP-enhanced transmission, local resonance, etc., and SPP has become a research hotspot around the world. In this paper, the dispersion characteristics and modes of rectangular metal grating based on spoof surface plasmons (SSP) are studied theoretically and numerically. The electromagnetic fields of SSP which are below and above the grating surface are presented using eigenmode expansion method and under periodic boundary conditions, besides the fact that the SSP dispersion relations are obtained by matching the boundary conditions of electromagnetic fields both for rectangular metal grating with roofed metal plate and that without roofed metal plate. Results for these two different cases are given according to numerical calculation and it is found that the roofed metal plate can introduce an additional fast wave mode which is beyond the light line in the dispersion diagram. And the results of analytical SSP dispersion are verified by electromagnetic simulations based on the finite difference method and finite integration method. The dependence of the dispersion characteristics and mode distributions on various parameters of metal grating is studied theoretically. It is shown that the dispersion relations obtained by eigenmode expansion method agree well with the results of electromagnetic simulations. The phase velocity of SSP on the grating surface can be decreased by increasing metal grating depth or decreasing grating period. The bandwidth of electron beam-SSP interaction can be extended by increasing grating period ratio. The influence of the distance between the roofed metal plate and the grating surface on the SSP dispersion is studied and is found that the role of roofed metal plate is insensitive to the slow wave SSP mode. The SSP dispersion and modes for the 3-D metal grating which are extended from the above 2-D SSP dispersion are also given. The SSP symmetric modes and anti-symmetric modes manifest themself alternately in the dispersion diagram on the 3-D grating surface. Compared with the 2-D SSP bound mode without roofed metal plate, it is found that in the 3-D grating structure the slow wave SSP modes and fast wave SSP modes coexist. The 3-D SSP mode with various grating lateral width is studied, and the competition and degeneracy of modes are analyzed particularly. The SSP mode intervals can be enlarged by decreasing the lateral width of the grating, which is optimum for avoiding mode competitions. Studies on dispersion and modes of the 2-D and 3-D metal grating structures based on SSP will lay the foundations for further studies of electron beam-SSP interaction, and development of the novel terahertz vacuum electronic source with high-efficiency and wide-bandwidth.

Hybrid Newmark-conformal FDTD modeling of thin spoof plasmonic metamaterials

Grating-coupled propagating surface plasmons associated with silver-nanoparticle 2D crystalline sheets exhibit sensitive plasmonic resonance tuning. Multilayered silver-nanoparticle 2D crystalline sheets are fabricated on gold or silver grating surfaces by the Langmuir– Blodgett method. We show that the deposition of Ag crystalline nanosheets on Au or Ag grating surfaces causes a drastic change in propagating surface plasmon resonance (SPR) both in angle measurements at fixed wavelengths and in fixed incident-angle mode by irradiation of white light. The dielectric constant of the multilayered silver nanosheet is estimated by a rigorous coupled-wave analysis. We find that the dielectric constant drastically increases as the number of silver-nanosheet layers increases. The experimentally obtained SP dispersions of Ag crystalline nanosheets on Au and Ag gratings are compared with the calculated SP dispersion curves. The drastic change in the surface plasmon resonance caused by the deposition of Ag-nanoparticle 2D crystalline sheets on metal grating surfaces suggests the potential for applications in highly sensitive sensors or for plasmonic devices requiring greatly enhanced electric fields.Electronic supplementary materialThe online version of this article (doi:10.1186/2193-1801-3-284) contains supplementary material, which is available to authorized users.

Narrow peaks are observed in the transmission spectra of p-polarized light passing through a thin gold film that is coated on the surface of a transparent diffraction grating. The spectral position and intensity of these peaks can be tuned over a wide range of wavelengths by simple rotation of the grating. The wavelengths where these transmission peaks are observed correspond to conditions where surface plasmon resonance occurs at the gold-air interface. Light diffracted by the grating couples with surface plasmons in the metal film to satisfy the resonant condition, resulting in enhanced light transmission through the film. Notably, this phenomenon is not observed at flat, gold-coated surfaces or uncoated gratings, where coupling to surface plasmons does not occur. The nature of the coupling and, thus, the details of light transmission are governed by the momentum matching conditions between the diffracted light and the surface plasmons. In the presence of bound analytes or surface films, the enhanced transmission peaks are red-shifted, making a simple, yet highly responsive sensing platform. The utility of this platform is demonstrated for ex situ sensing by analyzing thin films of various thicknesses and detecting a model immunoreaction between bovine serum albumin and anti-bovine serum albumin. This grating-based transmission surface plasmonic device represents a simple and sensitive platform, which can be readily tuned to enhance performance and be used in the study of a variety of surface adsorption processes or analysis of biomolecular interactions.