Dispersion relation for surface plasmon polaritons in metal/nonlinear-dielectric/metal slot waveguides

We present the first (to our knowledge) exact dispersion relation for the transverse-magnetic surface plasmon polariton (SPP) modes of a plasmonic slot waveguide, which is formed by a nonlinear Kerr medium sandwiched between two metallic slabs. The obtained relation is then simplified to the case of small field intensities, while retaining nonlinear terms, to derive approximate dispersion equations for the symmetric and antisymmetric SPP modes.     

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.     

Surface plasmons on corrugated metal films

The dispersion relation for a surface plasmon, propagating across a corrugated metal film on a dielectric substrate, is obtained by the method of reduced Rayleigh equations. It is found that the surface plasmon dispersion curve has an infinite number of branches. Numerical solutions of the dispersion relation are obtained for a film, characterized by a free-electron metal dielectric function and a sinusoidal profile function.     

Tunable Omnidirectional Surface Plasmon Resonance in Cylindrical Plasmonic Structure

The tunable omnidirectional surface plasmon resonance in the optical range is theoretically demonstrated in a cylindrical plasmonic crystal by using rigorous coupled-wave analysis. The cylindrical plasmonic crystal consists of an infinite chain of two-dimensional cylindrical metal--dielectric-dielectric-metal structures. The dispersion relation of the cylindrical plasmonic crystal is obtained by calculating the absorptance as a function of a TM-polarized incident plane wave and its in-plane wave vector. The omnidirectional surface plasmon resonance can be tuned from UV region to visible region by adjusting the thickness of the cylindrical dielectric layers. The absorption spectrum of the infinite chain of nanocylinders is also investigated for comparison.     

Surface plasmon polariton at the interface of dielectric and graphene medium using Kerr effect

We theoretically investigate the control of surface plasmon polariton(SPP) generated at the interface of dielectric and graphene medium under Kerr nonlinearity. The controlled Kerr nonlinear signal of probe light beam in a dielectric medium is used to generate SPPs at the interface of dielectric and graphene medium. The positive, negative absorption, and dispersion properties of SPPs are modified and controlled by the control and Kerr fields. A large amplification(negative absorption) is noted for SPPs under the Kerr nonlinearity. The normal/anomalous slope of dispersion and propagation length of SPPs is modified and controlled with Kerr nonlinearity. This leads to significant variation in slow and fast SPP propagation. The controlled slow and fast SPP propagation may predict significant applications in nano-photonics, optical tweezers, photovoltaic devices, plasmonster, and sensing technology.     

Surface plasmon modes in multi-layer thin-films

The surface plasmon modes in multi-layer thin-film structures of the metal-insulator-metal (MIM) type are modeled using a matrix method for the propagation of electromagnetic waves in stratified media. It is shown that the dispersion relation for the allowed surface plasmon modes is obtained from one of the matrix elements. The fundamental electromagnetic modes are the eigenfunctions of the differential equation for the magnetic field distribution and the eigenvalues are obtained from the dispersion relation. The expansion of an arbitrary wave profile in terms of the eigenfunctions is discussed and applied to the problem of surface plasmons propagating in a structure consisting of seven layers of alternating metal films and dielectrics.     

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.     

Plasmon hybridization in metallic nanotubes

We study theoretical formalism of the plasmon hybridization in a metallic nanotube 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. In the special case when the longitudinal wave vector is zero (q=0), the plasmon hybridization of a nanotube has a behavior similar to the spherical nanoshell.     

Temperature effect on plasmon dispersions in double-layer graphene systems

We investigate the plasmon dispersion relation and damping rate of a double-layer graphene system consisting of two separated monolayer graphenes with no interlayer tunneling at finite temperature. We use the temperature dependent RPA dielectric function which is valid for graphene systems to obtain the plasmon frequencies and damping rates at different temperatures, interlayer correlation parameters and electron densities and then compare them with those obtained from the zero temperature calculations. Our results show that by increasing the temperature, the plasmon frequencies decrease and the decay rate increases. Furthermore, we find that the behavior of a double-layer graphene system at small and large correlation parameters is different from the conventional double-layer two-dimensional electron gas system. Finally, we obtain that in a density imbalanced double-layer graphene system, the acoustic plasmons are more affected by temperature than the equal electron densities one.     

Optical beams in lossy non-local Kerr media

It is discussed that optical beams propagate in non-local Kerr medium waveguides with losses. A variational principle is carried out for the 1 + 1-D non-local non-linear Schrödinger equation in the presence of the losses. In the strongly non-local case, the approximate analytical solutions are obtained. The lossy soliton solution shows that, Unlike its local counterpart, such lossy strongly non-local soliton does not possess the adiabatic property anymore. In addition, the general approximate results for non-soliton cases are gained. The comparisons between our approximate analytic solutions and numerical simulations confirm our variational approximate solutions.     

Surface plasmons propagating parallel to the grooves of a large amplitude grating

The dispersion relation is obtained for a surface plasmon propagating parallel to the grooves of a large amplitude grating. Two variants of the Rayleigh method arc used: the first requires the evaluation of the zeros of a determinant; the second yields the dispersion relation in terms of the solution of a matrix eigenvalue problem. The dispersion relations are solved numerically for a sinusoidal and for a symmetric sawtooth grating profile, yielding in each case an infinity of discrete branches.     

Dispersion of cylindrical surface plasmon polaritons in layered structures

The problem of the existence of cylindrical surface plasmon polaritons on thin metal conductors is considered. A dispersion relation is obtained and analyzed, the domain of existence of dispersion curve with a maximum is found, and parametric relations are derived.     

Low-energy double plasmon satellites in the X-ray spectra of metals

Bohm and Pines' Hamiltonian and their dispersion relation have been extended up to second order to account for double plasmon oscillations in the X-ray emission spectra of solids. The effect of interaction between electrons and plasmons has also been taken into account in the dispersion relation. An expression for the relative intensity of low-energy double plasmon satellites has been derived. Fairly good agreement is obtained between values of the relative intensity calculated using this expression and values observed experimentally by Jenkins and Chung.     

Effect of longitudinal excitations on surface plasmons

The influence of a longitudinal component in surface plasma waves propagating along the boundary between a plasma and vacuum has been investigated theoretically. It is found that the inclusion of the longitudinal component significantly modifies the dispersion relation for surface plasmons. In particular, it is shown that a surface plasmon can have any frequency in the interval from zero to the bulk plasma frequency.     

Light conduction of metallic two-walled carbon nanotubes

The properties of surface plasmon–polariton modes in metallic two-walled carbon nanotubes are studied, taking into account the retardation effects. The dispersion relation of surface waves is obtained, by solving Maxwell and hydrodynamic equations with appropriate boundary conditions. Numerical results show that the difference between plasmon and plasmon–polariton modes is strongly dependent on the inner-outer radii of the system but only in the long-wavelength cases.     

Electrostatic surface shape resonances of a finite number of ridges

The resonance properties of localized electrostatic surface modes associated with a finite number of ridges on an otherwise planar surface are investigated. Numerical solutions of the homogeneous integral equations that describe the electromagnetic fields in the vicinity of the ridges are used to obtain the dispersion relation of surface plasmons. The frequencies of the electrostatic surface shape resonances are calculated for ridges with Gaussian, Lorentzian, sinusoidal, exponential, and triangular profiles. We show the existence of splittings of the plasmon frequencies, which depends on the surface profile function and on the distance between the ridges. Considering the ridge with a sinusoidal profile, we obtain the limit on the number of ridges which generates a frequency splitting of the electrostatic surface shape resonances, whose frequency values converge to those of the dispersion relation of surface plasmons on one-dimensional sinusoidal grating. Received: 24 June 1997 / Received in final form: 5 September 1997 / Accepted: 15 September 1997     

The modes of an ultra-cold strongly magnetized charged Bose gas

The modes of a strongly magnetized charged Bose gas are presented for ultra-low temperatures. For longitudinal oscillations propagating parallel to the magnetic field the dispersion relation is found to be dominated by the one-dimensional field-free plasmon dispersion relation as found by Alexandrov, Beere and Kabanov recently in reference [1], while for propagation perpendicular to the magnetic field they are found to be influenced by the cyclotron motion of the particles. Dispersion relations for these modes known as Bernstein modes are given near the cyclotron frequency and its first two harmonics. The dispersion relations for transverse modes in the system are then presented for the cases of photon propagation perpendicular and parallel to the direction of the magnetic field. Received: 3 July 1997 / Revised: 12 August 1997 / Accepted: 4 November 1997     

Time-Dependent Variational Approach to the Phonon Dispersion Relation of the Commensurate Quantum Frenkel-Kontorova Model

The phonon dispersion relation of the commensurate quantum Frenkel-Kontorova model is studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction for the particles. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty, equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation. It is shown that the strength of the substrate potential and the phonon excitation gap are reduced due to the quantum fluctuations in comparison with those of the classical model. We also compare our results with those previously obtained by using the path-integral molecular dynamics.     

Specific features of linear and nonlinear optical responses of chalcogenide glasses in the As-S-Se and As-Se-Te systems

Transmission and reflection spectra of samples of chalcogenide glasses in the As-S-Se and As-Se-Te systems have been measured in the wavelength range of 0.4–2.5 μm. Spectral dependences of the single-photon absorption coefficient and refractive index are obtained, the parameters characterizing the fundamental absorption edge are determined, and the Kerr constant in the low-frequency limit is calculated. Based on the obtained results and the data in the literature, dispersion curves are plotted for the Kerr constants of As₂S₃ and As₂Se₃ glasses near the absorption edge.     

Transverse plasmon in two-dimensional electrons

We calculated the retarded transverse current-current response function of an ideal two-dimensional electron gas and obtained a dispersion relation for the transverse plasmon in the system.