Light scattering from self-affine fractal silver surfaces with nanoscale cutoff: Far-field and near-field calculations

We study the light scattered from randomly rough, one-dimensional self-affine fractal silver surfaces with nanoscale lower cutoff, illuminated by s- or p-polarized Gaussian beams a few microns wide. By means of rigorous numerical calculations based on the Green theorem integral equation formulation, we obtain both the far- and near-field scattered intensities. The influence of diminishing the fractal lower scale cutoff (from below a hundred, down to a few nanometers) is analyzed in the case of both single realizations and ensemble average magnitudes. For s polarization, variations are small in the far field, being only significant in the higher spatial frequency components of evanescent character in the near field. In the case of p polarization, however, the nanoscale cutoff has remarkable effects stemming from the roughness-induced excitation of surface-plasmon polaritons. In the far field, the effect is noticed both in the speckle pattern variation and in the decrease of the total reflected energy upon ensemble averaging, due to increased absorption. In the near field, more efficient excitation of localized optical modes is achieved with smaller cutoff, which in turn leads to huge surface electric field enhancements.Comment: REVTeX 4, 10 page

Quantum calculations of the carrier mobility in thin films: Methodology, Matthiessen's rule and comparison with semi-classical approaches

We discuss the calculation of the carrier mobility in silicon films within the quantum Non-Equilibrium Green's Functions (NEGF) framework. We introduce a new method for the extraction of the carrier mobility that is free from contact resistance contamination, and provides accurate mobilities at a reasonable cost, with minimal needs for ensemble averages. We then introduce a new paradigm for the definition of the partial mobility $\mu_{M}$ associated with a given elastic scattering mechanism "M", taking phonons (PH) as a reference ($\mu_{M}^{-1}=\mu_{PH+M}^{-1}-\mu_{PH}^{-1}$). We argue that this definition makes better sense in a quantum transport framework as it is free from long range interference effects that can appear in purely ballistic calculations. As a matter of fact, these mobilities satisfy Matthiessen's rule for three mechanisms [surface roughness (SR), remote Coulomb scattering (RCS) and phonons] much better than the usual, single mechanism calculations. We also discuss the problems raised by the long range spatial correlations in the RCS disorder. Finally, we compare semi-classical Kubo-Greenwood (KG) and quantum NEGF calculations. We show that KG and NEGF are in reasonable agreement for phonon and RCS, yet not for SR. We point to possible deficiencies in the treatment of SR scattering in KG, opening the way for further improvements.Comment: Submitted to Journal of Applied Physic

Numerical studies of the scattering of light from a two-dimensional randomly rough interface between two dielectric media

The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the case where p- or s-polarized light is incident on this interface, with no assumptions being made regarding the dielectric functions of the media. Rigorous, purely numerical, nonperturbative solutions of this equation are obtained. They are used to calculate the reflectivity and reflectance of the interface, the mean differential reflection coefficient, and the full angular distribution of the intensity of the scattered light. These results are obtained for both the case where the medium of incidence is the optically less dense medium, and in the case where it is the optically more dense medium. Optical analogues of the Yoneda peaks observed in the scattering of x-rays from metal surfaces are present in the results obtained in the latter case. Brewster scattering angles for diffuse scattering are investigated, reminiscent of the Brewster angle for flat-interface reflection, but strongly dependent on the angle of incidence. When the contribution from the transmitted field is added to that from the scattered field it is found that the results of these calculations satisfy unitarity with an error smaller than $10^{-4}$.Comment: 25 pages, 14 figure

Optomagnetic composite medium with conducting nanoelements

A new type of metal-dielectric composites has been proposed that is characterised by a resonance-like behaviour of the effective permeability in the infrared and visible spectral ranges. This material can be referred to as optomagnetic medium. The analytical formalism developed is based on solving the scattering problem for considered inclusions with impedance boundary condition, which yields the current and charge distributions within the inclusions. The presence of the effective magnetic permeability and its resonant properties lead to novel optical effects and open new possible applications.Comment: 48 pages, 13 figures. accepted to Phys. Rev. B; to appear vol. 66, 200

A full wave method for rough surface scattering using fictitious current distributions

Rough surface scattering is a current topic of interest in many diverse fields. But, despite its importance, the two most widely used solution methods, the Kirchhoff and first order perturbation methods, are valid only for a restricted range of surface types. There is a large range of surface statistics for which neither of these theories is valid. There are purely numerical solutions to the problem, i.e., the integral equation technique and FDTD method, but these methods require a prohibitively large amount of computer time and storage space for use in practical applications. A full wave method has been introduced by E. Bahar which agrees with the Kirchhoff method in its range of validity, but does not bridge the gap between the later two standard theories and does not provide understanding of the physical processes involved in rough surface scattering. Consequently, it has been a center of controversy since modifications made to improve the method seem arbitrary and are without mathematical or physical justification. The method presented here is a new full wave method which uses equivalent currents to provide insight into the physical scattering processes. This full wave method analytically reduces to the two standard theories in their respective regions of validity and bridges the gap between the two, which was shown by comparison to the integral equation method. The results presented here are for statistically rough surfaces with Gaussian distributed heights and slopes. A Monte Carlo procedure is used to generate the radar cross section data for this new full wave method

Trefftz Difference Schemes on Irregular Stencils

The recently developed Flexible Local Approximation MEthod (FLAME) produces accurate difference schemes by replacing the usual Taylor expansion with Trefftz functions -- local solutions of the underlying differential equation. This paper advances and casts in a general form a significant modification of FLAME proposed recently by Pinheiro & Webb: a least-squares fit instead of the exact match of the approximate solution at the stencil nodes. As a consequence of that, FLAME schemes can now be generated on irregular stencils with the number of nodes substantially greater than the number of approximating functions. The accuracy of the method is preserved but its robustness is improved. For demonstration, the paper presents a number of numerical examples in 2D and 3D: electrostatic (magnetostatic) particle interactions, scattering of electromagnetic (acoustic) waves, and wave propagation in a photonic crystal. The examples explore the role of the grid and stencil size, of the number of approximating functions, and of the irregularity of the stencils.Comment: 28 pages, 12 figures; to be published in J Comp Phy