Correction to the Casimir force due to the anomalous skin effect

The surface impedance approach is discussed in connection with the precise calculation of the Casimir force between metallic plates. It allows to take into account the nonlocal connection between the current density and electric field inside of metals. In general, a material has to be described by two impedances $Z_{s}(\omega,q)$ and $Z_{p}(\omega,q)$ corresponding to two different polarization states. In contrast with the approximate Leontovich impedance they depend not only on frequency $\omega$ but also on the wave vector along the plate $q$. In this paper only the nonlocal effects happening at frequencies $\omega<\omega_{p}$ (plasma frequency) are analyzed. We refer to all of them as the anomalous skin effect. The impedances are calculated for the propagating and evanescent fields in the Boltzmann approximation. It is found that $Z_p$ significantly deviates from the local impedance as a result of the Thomas-Fermi screening. The nonlocal correction to the Casimir force is calculated at zero temperature. This correction is small but observable at small separations between bodies. The same theory can be used to find more significant nonlocal contribution at $\omega\sim\omega_p$ due to the plasmon excitation.Comment: 29 pages. To appear in Phys. Rev.

Theory of imaging a photonic crystal with transmission near-field optical microscopy

While near-field scanning optical microscopy (NSOM) can provide optical images with resolution much better than the diffraction limit, analysis and interpretation of these images is often difficult. We present a theory of imaging with transmission NSOM that includes the effects of tip field, tip/sample coupling, light propagation through the sample and light collection. We apply this theory to analyze experimental NSOM images of a nanochannel glass (NCG) array obtained in transmission mode. The NCG is a triangular array of dielectric rods in a dielectric glass matrix with a two-dimensional photonic band structure. We determine the modes for the NCG photonic crystal and simulate the observed data. The calculations show large contrast at low numerical aperture (NA) of the collection optics and detailed structure at high NA consistent with the observed images. We present calculations as a function of NA to identify how the NCG photonic modes contribute to and determine the spatial structure in these images. Calculations are presented as a function of tip/sample position, sample index contrast and geometry, and aperture size to identify the factors that determine image formation with transmission NSOM in this experiment.Comment: 28 pages of ReVTex, 14 ps figures, submitted to Phys. Rev.

Computational lens for the near field

A method is presented to reconstruct the structure of a scattering object from data acquired with a photon scanning tunneling microscope. The data may be understood to form a Gabor type near-field hologram and are obtained at a distance from the sample where the field is defocused and normally uninterpretable. Object structure is obtained by the solution of the inverse scattering problem within the accuracy of a perturbative, two-dimensional model of the object

Computing the optical near-field distributions around complex subwavelength surface structures: A comparative study of different methods

Some 15 years ago, optical topographic signals with subwavelength resolution were obtained independently by several experimental teams. Since this exploratory period, a growing number of experimental configurations have been proposed and continuously developed. Simultaneously, this research field was supported by different theoretical works, aimed at developing our understanding of the interaction of optical fields with mesoscopic objects. Over the past three years, several theoretical frameworks have been proposed (Green's functions, field susceptibility, boundary conditions methods, multiple multipoles expansions, etc.). In this paper, an attempt at a careful comparison between two classes of numerical models is presented. Using the same test object, we discuss and compare the numerical solutions issued from a reciprocal-space perturbative method (Rayleigh approximation) and the solution originating from a direct-space integral approach (Green's function or field susceptibility). The discussion is given for different values of the relevant experimental parameters. The convergence of both approaches is investigated

Pseudo-surface acoustic waves in hypersonic surface phononic crystals

We present a theoretical framework allowing to properly address the nature of surfacelike eigenmodes in a hypersonic surface phononic crystal, a composite structure made of periodic metal stripes of nanometer size and periodicity of 1 um, deposited over a semi-infinite silicon substrate. In surface-based phononic crystals there is no distinction between the eigenmodes of the periodically nanostructured overlayer and the surface acoustic modes of the semi-infinite substrate, the solution of the elastic equation being a pseudosurface acoustic wave partially localized on the nanostructures and radiating energy into the bulk. This problem is particularly severe in the hypersonic frequency range, where semi-infinite substrate s surface acoustic modes strongly couple to the periodic overlayer, thus preventing any perturbative approach. We solve the problem introducing a surface-likeness coefficient as a tool allowing to find pseudosurface acoustic waves and to calculate their line shapes. Having accessed the pseudosurface modes of the composite structure, the same theoretical frame allows reporting on the gap opening in the now well-defined pseudo-SAW frequency spectrum. We show how the filling fraction, mass loading, and geometric factors affect both the frequency gap, and how the mechanical energy is scattered out of the surface waveguiding modes

Gender differences in the use of cardiovascular interventions in HIV-positive persons; the D:A:D Study

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