Surface Shape Resonances Research Articles

The Properties of Electromagnetic Light in Metals

The recent years have seen a rapid expansion of research of the excitation of electromagnetic surface shaperesonances in lamellar metallic gratings by light in the visible to near-infrared range based on the model ofsurface plasmon–polaritons. We argue that these electromagnetic waves propagate along metal–dielectricinterfaces and can be guided by metallic nanostructures beyond the new fundamental Bose-particles with spinone and rest mass e m ? 2.5?10?5m (where e m is the mass of the electron). We call these light bosons becausethey induce the electromagnetic field. The existence of light bosons is confirmed by experiment connected withoriginal type of the Bose-Einstein condensation. In this letter, we treat the interaction between light boson modesand electron modes in a metallic medium which leads to existence of the polaritons. These polaritons acquire aproperty of the charged electron gas with the Coulomb interaction and are excited into a fixed interval of wavenumbers.

Surface shape resonances and surface plasmon polariton excitations in bottle-shaped metallic gratings.

We study surface plasmon polariton excitations and surface shape resonances in a lossy metallic grating with bivalued cavities. The modal formalism is used to solve the diffraction problem for the infinite grating and the homogeneous problem for a single cavity in a plane surface. Both polarization modes are considered. We provide curves of reflected efficiency versus wavelength as well as near-field plots. The resonances are identified as dips in the reflected efficiency, which imply significant power absorptions. Results for various depths of the cavities and for several angles of incidence are shown, where the different types of resonant behavior can be appreciated. Particular attention is paid to the changes introduced by the finite conductivity of the metal in relation to the results obtained for a perfect conductor.

Resonant modes of a bottle-shaped cavity and their effects in the response of finite and infinite gratings

The resonant frequencies of a one-dimensional bottle-shaped cavity embedded in a ground plane are calculated using a modal approach for s and p polarizations. The same formalism is used to solve the problem of scattering from a surface with a finite number of cavities and from an infinite periodic grating. We show numerical results where the resonant behavior is evidenced as dips in the curve of intensity specularly reflected from a surface with one or several bottle-shaped grooves. The surface shape resonances of a single cavity are also shown to have a great influence on the efficiency distribution of the diffracted orders from infinite gratings made of bottle-shaped cavities. The excitation of even and odd modes is analyzed for both polarizations.

Large scale correlations for energy injection mechanisms in swirling turbulent flows

The spectrum of surface shape resonances associated with a finite number of ridges on one interface of an otherwise plane film is calculated. The frequencies are obtained numerically by solving the homogeneous integral equations which describe the electrostatic field in the vicinity of a surface defect. The calculations are performed for a surface with ridges with Gaussian, Lorentzian and sinusoidal profiles. The results show a strong dependence of the localized plasmon frequencies on the surface profile, on the distance between the ridges, and on the thickness of the film.

Signatures of electromagnetic surface-shape resonances in scattering of pulsed beams from surface defects

We predict theoretically that electromagnetic resonances supported by surface defects can be detected experimentally by study of the scattering of electromagnetic pulses from these defects, and we formulate the optimal conditions for such experiments. Numerical scattering simulations confirm that the proposed scattering probes unambiguously identify resonance signatures. The approach that we suggest proves to be superior to conventional analysis of features in the dependence of the far-field intensity of scattered monochromatic light on its frequency, since these features do not necessarily point at resonant frequencies.

Surface Shape Resonances in Lamellar Metallic Gratings

The specular reflectivity of lamellar gratings of gold with grooves $0.5\ensuremath{\mu}\mathrm{m}$ wide separated by a distance of $3.5\ensuremath{\mu}\mathrm{m}$ was measured on the 2000-- $7000{\mathrm{cm}}^{\ensuremath{-}1}$ spectral range for p-polarized light. Experimental evidence of the excitation of electromagnetic surface shape resonances for optical frequencies is given. In these resonances the electric field is highly localized inside the grooves and is almost zero in all other regions. For grooves of depth equal to $0.6\ensuremath{\mu}\mathrm{m}$, we have analyzed one of these modes whose wavelength ( $3.3\ensuremath{\mu}\mathrm{m}$) is much greater than the lateral dimension of the grooves.

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.

Scattering of Surface Plasmon Polaritons by a Circularly Symmetric Surface Defect

By the use of the method of reduced Rayleigh equations, we develop a theory of the scattering of a surface plasmon polariton from a cirularly symmetric defect on a metal surface. We derive and solve one-dimensional integral equations for the scattering amplitudes corresponding to different rotational numbers $m$. We calculate the differential cross sections for scattering into the vacuum and into other surface waves, and the field intensity near the surface. The results show agreement with recent experimental data. We also consider resonant scattering due to surface shape resonances.

Resonant scattering of electromagnetic waves from a rectangular groove on a perfectly conducting surface

The frequencies of the electromagnetic surface shape resonances of both p- and s-polarizations associated with a rectangular groove on the otherwise planar surface of a perfect conductor, and the scattering of a Gaussian beam of p- and s-polarized light from the same groove, are calculated by both a modal approach and a numerical method based on Green's second integral identity. On the basis of the results of these calculations we show that the dips in the frequency dependence of the intensity of the scattered light in s-polarization for fixed angles of incidence and scattering found in earlier work by Zuniga-Segundo and Mata-Mendez [Phys. Rev. B 46 (1992) 536], and which we find in the scattering of p-polarized light as well, do not occur at the frequencies of the surface shape resonances as asserted by these authors, and we give the correct explanation for these features. In addition, we show that while the dips in the frequency dependence of the intensity of the scattered light associated with s-polarized surface shape resonances are masked by the dips found by Zuniga-Segundo and Mata-Mendez, this is not the case for dips associated with p-polarized surface shape resonances. The latter should therefore be observable in experimental studies of the scattering of p-polarized light from a rectangular groove on an otherwise planar surface of a highly conducting metal.

Acoustic surface shape resonances of circularly symmetric defects on solid surfaces

We present a formally exact Green’s tensor approach to the calculation of the frequencies of elastic vibrations localized in the vicinity of a circularly symmetric protuberance or indentation on an otherwise planar, stress-free surface of a semi-infinite, isotropic elastic medium–acoustic surface shape resonances. The method is illustrated by applying it to the determination of the frequencies of several of the lowest frequency acoustic surface shape resonances associated with protuberances or indentations of several different forms.

Resonant scattering of surface acoustic waves by hydrogen crystallites.

Surface acoustic (Rayleigh) waves have been used to study the annealing behavior of quench condensed hydrogen films. At temperatures far below the triple point such films undergo drastic structural changes, forming larger crystallites of typically 1 \ensuremath{\mu}m diameter. The rearrangement of the film structure could be traced in situ by changes of sound velocity and attenuation arising from scattering of the Rayleigh waves by inhomogeneities. The dominant scattering mechanism appears to be well described by a resonant interaction between surface acoustic waves and elastic eigenmodes of the hydrogen crystallites (``surface shape resonances''). We propose a very simple model for this scattering process, where the resonant modes are essentially treated as harmonic oscillators, and find wide agreement with our experiments.

Roughness induced surface acoustic resonances

The vibrational and electronic spectra of a semi-infinite crystal with a planar surface is modified in presence of surface inhomogeneities or roughness such as ridges or grooves, quantum wires or tips… Using a Green's function formalism, we present an exact numerical method for obtaining the variation of the density of states associated with the adsorption of a ridge on a flat surface or with a groove cut into an otherwise planar surface. This general method is applied to the determination of the acoustic resonances of shear horizontal polarization associated with such deterministic surface protuberances or indentations. The positions and widths of the peaks in the total or local densities of states give the frequencies and lifetimes of the resonances, which may be more or less pronounced features depending on the relative parameters of the substrate and ridge materials. We also investigate the modifications of these acoustic surface shape resonances due to the interaction between two such defects. This calculation can also be transposed to the study of electronic structure of a wire near a flat surface, in the framework of an effective mass model.

Green's function theory of acoustic surface shape resonances

We present an exact numerical method for obtaining the frequencies of acoustic surface shape resonances of shear horizontal polarization associated with an isolated ridge or groove of rather general shape on the otherwise planar, stress-free surface of an isotropic elastic medium. The method is illustrated by applying it to the determination of the frequencies of the lowest frequency acoustic surface shape resonances associated with ridges and grooves of several different forms.

Acoustic surface shape resonances

Acoustic surface shape resonances are vibrational excitations that are localized in the vicinity of an isolated protuberance or indentation on the otherwise planar, stress-free surface of a semi-infinite elastic medium. The protuberance may be fabricated from the same material as the substrate, or from a different material. In general, there is an infinite number of such resonances associated with a given surface perturbation. Their frequencies are discrete because of the loss of translational symmetry caused by the surface perturbation; they are complex because they overlap the range of frequencies allowed the vibrations of the substrate, into which they can decay; and they depend on the shape of the protuberance or indentation, and on the relation of the material properties of the protuberance (mass density, elastic moduli) to those of the substrate. Methods for calculating the frequencies of the acoustic surface shape resonances associated with protuberances or indentations of simple forms are described. Results are presented that suggest that acoustic surface shape resonances can be studied experimentally by the scattering of acoustic waves from the structure supporting them.

Shear horizontal acoustic surface shape resonances.

We have calculated the discrete frequencies of the elastic vibration modes localized in the vicinity of a rectangular ridge fabricated from one material that is bonded to the planar surface of a substrate of a second material. These acoustic surface shape resonances correspond to a displacement field that is polarized parallel to the ridge (i.e., it has shear horizontal polarization). The frequencies of these modes are complex because the range in which they occur overlaps the continuum of frequencies of the bulk and surface modes of the substrate, so that they can radiate energy into the latter. The modes are damped thereby, and this damping depends sensitively on the aspect ratio of the ridge and on the material parameters of the ridge and substrate.

Electrostatic and electromagnetic surface shape resonances

The homogeneous integral equations that give the electromagnetic field in the vicinity of a protuberance or a depression on the otherwise planar interface with vacuum of a semi-infinite dielectric medium or a thin dielectric film on a semi-infinite substrate have been obtained. The Rayleigh hypothesis, the vectorial equivalent of the Kirchhoff integral, and the extinction theorem have been used for this purpose. The assumption that the perturbation of the vacuum dielectric interface has cylindrical symmetry about the normal to the nominal surface allows a significant simplification of these integral equations to be carried out. We have used Gaussian quadrature schemes to convert the resulting integral equations into matrix equations, and have obtained the frequencies of the shape resonances by equating to zero the determinants of the matrices obtained. Calculations have been carried out for Gaussian (x3=Aexp(−x ‖ 2 /R2)) and exponential (x3=Aexp(−x‖/R)) surface profiles, and convergent results obtained for values ofA/R of the order of unity.

Surface shape resonances

The system consisting of a hemispheroidal bump protruding from a dielectric half-space possesses surface electromagnetic resonances whose resonant frequencies are a sensitive function of the shape of the bump. The widths of the resonances are determined by couplings to delocalized excitations such as surface plasmons, photons, and by resistive losses due to inelastic electron scattering, in the case of electronic excitations, and surface phonons, photons, and acoustic phonons in the case of ionic lattice excitations.