Surface Plasmon Dispersion Relation Research Articles

Exact surface plasmon dispersion relation with ponderomotive nonlinearity in a metal/dielectric structure

The nonlinear effects in a metal due to the ponderomotive potential, which is induced by a steep spatial gradient in the electric field intensity, on the surface plasmon dispersion relation at a planar metal/dielectric interface are studied exactly. Previous studies invoked an approximation that amounts to keeping only the lowest order Kerr-like term in the metal dielectric constant. Comparing the exact result with the Kerr approximation reveals that the Kerr approximation often overestimates a cutoff frequency for the existence of surface waves and gives erroneous results in the range of frequencies below the overestimated cutoff and the real cutoff. Our result thus sheds light on the applicability of the Kerr approximation. Properly expanding the exact results recovers the standard linear results and the results starting with a Kerr-like approximation.

Surface plasmon modes of infinite cylindrical metallic nanostructures

The surface modes as well as their dispersion relations for surface plasmons (SPs) in some infinite cylindrical metallic nanostructures including wires, cavities, and tubes are investigated theoretically by using plasmon hybridization (PH) theory. We discuss that how the dispersion curves of SP modes for nanotubes depend on the geometry parameters, revealing that hybridization strength between inner and outer SPs strongly relies on the wall thickness of tube. In addition, in the long-wavelength limit, these geometry-dependent properties for nanotubes behave in an extremely similar fashion as that of nanorings.

Cu/ZnO nanorods′ hybrid showing enhanced photoluminescence properties due to surface plasmon resonance

Cu/ZnO nanorods (NRs) hybrids have been synthesized for various concentrations of Cu nanoparticles (NPs). X-ray diffraction patterns and X-ray photoelectron spectroscopy show the phase purity of the hybrids. A detailed study on the photoluminescence (PL) properties of Cu/ZnO NRs hybrids show that the near band edge emission (NBE) of ZnO is enhanced eight times after Cu loading over that of pristine ZnO NRs. The mechanism behind luminescence enhancement has been analyzed by the surface plasmon dispersion relations of Cu/air and Cu/ZnO systems. It has been confirmed that the enhanced emission is due to the surface plasmon resonance coupling of the NBE emission between Cu and ZnO.

Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal

Through analytical calculations, the transverse magnetic surface plasmon (SP) dispersion relations for a monolayer graphene and a graphene parallel-plate waveguide (PPWG) in the presence of a one-dimensional photonic crystal (1D PC) as a substrate and a symmetric/asymmetric cladding medium are obtained. For the monolayer graphene case, we show that the presence of the 1D PC leads to significant modification in propagation length (PL) and localization length (LL) of THz SPs, as compared with the SPs of monolayer graphene on SiO2 substrate. And the SPs with largest PL and small LL, named as optimized SPs, could be supported when the 1D PC is used only as a substrate. For the graphene PPWG case with the plate separation “D” (here, 10 nm≤D≤1 μm), in addition to support of typical upper and lower branches of coupled THz SPs, presence of the 1D PC leads to support of an extra branch when 10 nm≪D≤1 μm. Moreover, as far as supporting optimized 0–2 THz SPs are concerned, the case in which the graphene PPWG with D = 1 μm is sandwiched between two symmetric 1D PC could be the best candidate. Whereas the graphene PPWG on the 1D PC, with D = 10 nm, supports optimized SPs in a frequency range from 2 to 4.5 THz. Therefore, using 1D PC improves the capability of monolayer graphene and also graphene PPWG for sensing and waveguide applications in THz frequencies.

Surface plasmon dispersion relation of a metallic wire in a nonlinear dielectric medium

The surface plasmon dispersion relation of a cylindrical metallic rod embedded in a Kerr nonlinear dielectric medium is studied using an integral approach. A formalism for the dispersion relation of the azimuthal symmetric mode is presented, in which an integral has to be treated numerically. We invoke an approximation based on weak nonlinearity. The results are in good agreement with numerical results obtained by requiring the fields to decay properly away from the rod. The formalism recovers the previous results of a metallic rod in a linear dielectric medium and a planar metallic/nonlinear interface as special cases.

Surface plasmon-enhanced terahertz spectroscopic distinguishing between isomers in powder form

The effect of a dielectric overlayer on terahertz transmission through a freestanding metallic array of subwavelength holes is experimentally presented. There is a remarkable resonance redshift from 0.600 to 0.498 THz at the surface plasmon (SP) metal-dielectric resonance mode with increasing film thickness. When the overlayer film is thicker than a critical thickness, the resonance frequency becomes steady at the final resonance frequency ω(f). On the basis of the dispersion relation of SPs, two kinds of glutamic acid enantiomers are distinguished by use of SP-enhanced terahertz spectra of metallic array of subwavelength holes according to the result of ω(f). The terahertz plasmonic hole array with the sensitive nature provides an approach to distinguish trace amount of powder substances, which has a promising application prospect in the fields of public security and biomedical science, such as distinguishing between isomers and identifying expensive medicines and drugs.

Experimental consequences of predicted charge rigidity of superconductors

The theory of hole superconductivity predicts that in superconductors the charged superfluid is about a million times more rigid than the normal electron fluid. We point out that this physics should give rise to large changes in the bulk and surface plasmon dispersion relations of metals entering the superconducting state, that have not yet been experimentally detected and would be in stark contradiction with the expected behavior within conventional BCS-London theory. We also propose that this explains the puzzling experimental observations of Avramenko et al. [1] on electron sound propagation in superconductors and the puzzling experiments of de Heer et al. [2] detecting large electric dipole moments in small metal clusters, as well as the Tao effect [3] on aggregation of superconducting microparticles in an electric field. Associated with the enhanced charge rigidity is a large increase in the electric screening length of superconductors at low temperatures that has not yet been experimentally detected. The physical origin of the enhanced charge rigidity and its relation to other aspects of the theory of hole superconductivity is discussed.

Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies

We investigate through analytic calculations the surface plasmon dispersion relation for monolayer graphene sheets and a separated parallel pair of graphene monolayers. An approximate form for the dispersion relation for the monolayer case was derived, which was shown to be highly accurate and offers intuition to the properties of the supported plasmon mode. For parallel graphene pairs separated by small gaps, the dispersion relation of the surface plasmon splits into two branches, one with a symmetric and the other with an antisymmetric magnetic field across the gap. For the symmetric (magnetic field) branch, the confinement may be improved at reduced absorption loss over a wide spectrum, unlike conventional surface plasmon modes supported on metallic surfaces that are subjected to the tradeoff between loss and confinement. This symmetric mode becomes strongly suppressed for very small separations, however. On the other hand, its antisymmetric counterpart exhibits reduced absorption loss for very small separations or long wavelengths, serving as a complement to the symmetric branch. Our results suggest that graphene plasmon structures could be promising for waveguiding and sensing applications in the midinfrared and terahertz frequencies.

Scattering matrix method for optical excitation of surface plasmons in metal films with periodic arrays of subwavelength holes

We present the formulation of a scattering matrix method for the study of light-scattering properties of metal films. The method is employed for the study of the optical excitation of surface plasmons in a gold film of 15-230 nm thickness, patterned periodically with subwavelength nanoholes. The gold film is placed on a thick SiO2 wafer, and the nanoholes as well as the top side of the gold film are filled with H2O. Light is incident on the gold film from either the SiO2 or the H2O side. The extinction and reflectance spectra of the system, as well as the electromagnetic field distributions at certain characteristic wavelengths, are calculated. The extinction spectra show, depending on system parameters, one or several peaks in the visible wavelength range. The extinction peaks are found to be caused by surface plasmons. A simple model based on the dispersion relation for surface plasmons in an unperforated gold film is shown to predict the peak positions of the extinction for thick perforated films very well. Even for thin films, this simple model, which includes coupling of surface plasmons on both surfaces of the film, predicts peak positions of the extinction well if the hole diameter is small enough. As the hole diameter increases, the extinction peaks of thin films show redshifts. Extinction peaks caused by surface plasmons at the SiO2/Au interface in thick films exhibit strong redshifts when the film thickness is decreased. However, the extinction peaks caused by surface plasmons at the H2O/Au interface in thick films show a completely different behavior. In this case, the extinction peaks do not move noticeably when the film thickness is decreased. Instead, they are weakened and finally disappear. It is also found that each extinction peak is accompanied by an extinction dip and that a reflectance dip is located in the wavelength between the extinction peak and the dip. This arrangement of an extinction peak, a reflectance dip, and an extinction dip is a general property of the surface-plasmon excitation. The calculated electromagnetic field distributions in both thick and thin films show clearly the signature of the excitation of surface plasmons at the extinction peaks, the extinction dips, and the reflectance dips. In thick films with small holes, the electric-field strength in the vicinity of the holes is weak at wavelengths for which surface plasmons are excited. In contrast to this, for thin films at the surface-plasmon excitations, a much stronger electric field is seen in the vicinity of the holes. (Less)

Surface-plasmon-enhanced visible-light emission of ZnO/Ag grating structures

We investigated the optical properties of ZnO/Ag grating structures fabricated by sputtering and nanoimprint lithography. The grating structures exhibited multiple peak features in broad visible-range photoluminescence (PL) spectra. The PL intensity of the grating was larger than that of a planar thin film by up to two orders of magnitude. The surface plasmon (SP) dispersion relation suggested excitation of SPs with various energies of the grating, explaining the broad PL emission. The spectral dependence of the PL intensity was also well supported by the experimental reflectance spectra and the simulated electric field distribution at the ZnO/Ag interface.

Theoretical and experimental studies of surface plasmons excited at metal-uniaxial dielectric interface

In this letter, surface plasmons (SPs) excited at the metal-uniaxial dielectric interface are investigated both theoretically and experimentally. The dispersion relations of SPs are derived for the cases where the optical axis of uniaxial medium is parallel the interface or in the incident plane perpendicular to the interface. The theoretical predictions are verified by a Kretschmann–Raether [W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature (London) 424, 824 (2003)] configuration with azobenzene polymer as photoinduced uniaxial medium. The attenuated total reflection spectra clearly show that the dependence of the SPs propagation properties on the orientations of optical axis, which is consistent with the theoretical analysis. The results of this study provide a useful approach to modulate SPs through adjusting the azobenzene molecular orientation.

Enhancement of extraction efficiency by metallic photonic crystal embedding in light-emitting diode

The bandgap effect of photonic crystals (PCs) and the effect of grating diffraction can be used to improve the extraction efficiency of light from the light-emitting diode (LED). The transmission of light at certain wavelength through periodic sub-wavelength hole arrays in metal films is extraordinary, surface plasmon (SP) effects effectively. In this letter, silver metallic photonic crystals with square lattice of cylinder unit cells are fabricated in GaN layer of GaN-based blue LED. We use the finite-difference time-domain (FDTD) method to investigate the optical transmission, the results show that the light extraction efficiency is enhanced by more than four times. Then we use the surface plasmon dispersion relation to analyze the mechanism of antireflection.

The dispersion relations for surface plasmon in a nonlinear–metal–nonlinear dielectric structure

In the asymmetric and symmetric nonlinear-metal-nonlinear dielectric structures, this paper studies the analytic dispersion relation for surface plasmon in a system consisting of a thin metallic film covered on two sides media of intensity-dependent refractive indexes by applying a generalised first integral approach. Especially in the symmetric waveguide structure, two possible modes can exist: the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the squared magnitude of the electric field at the interface appears and alters the dispersion relations. Numerical results are compared to those from a certain approximate treatment.

Nonlocal and nonlinear effects on the dispersion relation for surface plasmon at ametal–Kerr medium interface

We present a theoretical study on the dispersion relation for surface plasmons at ametal–Kerr medium interface where the metal is described by a nonlocal dielectric functionaccording to the hydrodynamic model. The Kerr effect leads to a shift of the surfaceplasmon frequency depending on the electric field intensity, the magnitude aswell as the sign of the Kerr coefficient, and the wavevector. We further observethat this frequency shift is largely quenched for large wavenumbers for whichthe nonlocal effect is significantly manifested. We account for this quenchingquantitatively by a calculation showing how the nonlocality weakens the sensitivityin the metal’s response to the variation of the dielectric function of the Kerrmedium. A possible experimental observation of this new effect is briefly discussed.

Quasiguided surface plasmon excitations in anisotropic materials

We present a theoretical study of surface plasmon polaritons in a configuration where a metal layer is bounded by a homogeneous anisotropic dielectric. We consider uniaxial and biaxial dielectrics with the optical axis lying in the plane defined by the metal/dielectric interface. Through a systematic study of the in-plane surface plasmon dispersion relation we confirm the existence of several propagation regimes for different values and signs of the birefringence. We report the discovery of the existence of quasiguided surface plasmon polaritons characterized by non-null radiative components. We identify the conditions for the existence of such modes, and explain their peculiar properties in terms of the hybridization of radiative and guided modes.

Long-range surface plasmons in dielectric-metal-dielectric structure with highly anisotropic substrates

We present a theoretical study of long-range surface plasmons propagating in a thin metallic film clad between two identical uniaxial anisotropic dielectric crystals. We show that the proper orientation of the optical axis of the crystal with respect to the metal surface enhances the propagation length of surface plasmons. Since the proper orientation depends on surface plasmon frequency, we give the results for the propagation length in a wide range of frequencies, including the telecommunication region. To increase the role of anisotropy, we consider artificial substrates from photonic crystals, which possess an order of magnitude stronger anisotropy than the natural optical crystals. We propose Kronig-Penney model for plasmonic crystal where the substrate is a periodic sequence of dielectric delta peaks. In this model the dispersion relation for surface plasmon has a band structure where the band width tends to zero when the frequency approaches the resonant frequency.

The dispersion relation for surface plasmon at a metal-Kerr nonlinear medium interface

The dispersion relation of transverse magnetic（TM） wave and transverse electric（TE） wave for surface plasmon at a metal-Kerr nonlinear medium interface are analyzed based on the Maxwell equations and the boundary conditions. The dispersion relation of TM wave is complex, due to the nonlinearity, and it has a dielectric coefficient and intensity-dependent expression. However, the TE wave does not exist at this interface as in the linear case.

Exact surface plasmon dispersion relations in a linear-metal-nonlinear dielectric structure of arbitrary nonlinearity

Exact analytic expression for obtaining the surface plasmon (SP) dispersion relations in a system consisting of a thin metallic film sandwiched between a linear dielectric and a nonlinear dielectric of arbitrary nonlinearity is derived, based on a generalized first integral approach. The changes in SP dispersion relations on film thicknesses and nonlinearity are studied by model calculations. The thick-film limit generalizes previous results on metal/Kerr-type nonlinear interface to arbitrary nonlinearity. An analytic expression is obtained for the limiting SP frequency at large wave vectors with previous result recovered as a special case.

Study of geometrical effects on the characteristics of metallic double-walled carbon nanotube waveguides through quantum hydrodynamics

By assuming the metallic double-walled carbon nanotubes as two coaxial free electron gas layers with linearized hydrodynamic model, it is shown that surface plasmons coupled with electromagnetic fields can be excited on a metallic double-walled carbon nanotube and propagate along its axis. Dispersion relations of surface plasmons for E-type and B-type waves in various inner-outer radii and various interlayer distances for long metallic double-walled carbon nanotubes are obtained.

Plasmon hybridization in metallic nanotubes with a nonconcentric core

We develop a theory of plasmon excitations in a metallic nanotube with a nonconcentric core using the plasmon hybridization method. We apply the two-center cylindrical coordinate system for mathematical convenience and find an explicit form of the dispersion relation for surface plasmons, in terms of interaction between the bare plasmon modes of the individual surfaces of the nanotubes. We present numerical result displaying the effect of the offset distant d of the inner core from the nanotube center, when there is no angular momentum transfer, i.e., m = 0 . For large offsets, the plasmon shifts is strong, but weak for small offset.