A Study of Uniform Approximation of Plane Gratings by Oblique Incidence

AbstractWe report the observation of strongly anisotropic scattering of laser light at oblique incidence on (100)-oriented porous silicon layers. We performed angle-resolved light scattering measurements and three concentric rings were observed. Modeling porous silicon by means of nanometric columnar air pores and an effective anisotropic uniaxial dielectric constant explains the observed phenomenon, and besides, the observation of the angle aperture of these rings allows a direct measurement of relative birefringence. We finally study the changes of optical anisotropy after different modifications of the structure.

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Pb Electrodeposition in the Presence of Chlorine Ions on Cu(100): An in Situ Optical Reflectivity Difference Study

MRS Proceedings ◽

10.1557/proc-781-z4.10 ◽

2003 ◽

Vol 781 ◽

Author(s):

J. Gray ◽

W. Schwarzacher ◽

X.D. Zhu

Keyword(s):

Oblique Incidence ◽

Opposite Sign ◽

Bulk Phase ◽

Phase Layer ◽

Optical Reflectivity ◽

Scan Rate ◽

Different Types ◽

Chlorine Ions ◽

High Overpotentials

AbstractWe studied the initial stages of the electrodeposition of Pb in the presence of chlorine ions on Cu(100), using an oblique-incidence optical reflectivity difference (OIRD) technique. The OI-RD results reveal that immediately following the underpotential deposition (UPD) of the first Pb monolayer, two different types of bulk-phase films grow depending upon the magnitude of overpotential and cyclic voltammetry (CV) scan rate. At low overpotentials and/or slow scan rates, we propose that a bulk-phase Pb film grows on top of the UPD monolayer. At high overpotentials and/or fast scan rates, either a PbO, PbCl2, or a rough Pb bulk-phase layer grows on top of the UPD layer such that the reflectivity difference signal from such a film has an opposite sign.

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A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm

Journal of Applied Probability ◽

10.1239/jap/1395771410 ◽

2014 ◽

Vol 51 (1) ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

Dawei Hong ◽

Shushuang Man ◽

Jean-Camille Birget ◽

Desmond S. Lun

Keyword(s):

Brownian Motion ◽

Convergence Rate ◽

Fractional Brownian Motion ◽

Parallel Algorithm ◽

Uniform Approximation ◽

Haar Wavelets ◽

Hurst Index ◽

Sample Paths ◽

Vanishing Moment ◽

Uniform Expansion

We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (Bt(H))_t∈[0,1] of Hurst index H ∈ (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H ∈ (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.

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Calculation of the Ion Optical Properties of Inhomogeneous Magnetic Sector Fields Part 3: Oblique Incidence and Exit at Curved Boundaries

Zeitschrift für Naturforschung A ◽

10.1515/zna-1959-0911 ◽

1959 ◽

Vol 14 (9) ◽

pp. 822-827 ◽

Cited By ~ 22

Author(s):

H. A. Tasman ◽

A. J. H. Boerboom ◽

H. Wachsmuth

Keyword(s):

Oblique Incidence ◽

Normal Incidence ◽

Second Order ◽

Resolving Power ◽

High Mass ◽

Curved Boundaries ◽

Magnetic Sector ◽

Mass Resolving Power ◽

Mass Dispersion ◽

Fringing Fields

In previous papers 1.2we presented the radial second order imaging properties of inhomogeneous magnetic sector fields with normal incidence and exit at plane boundaries. These fields may provide very high mass resolving power and mass dispersion without increase in radius or decrease of slit widths. In the present paper the calculations are extended to include the effect of oblique incidence and exit at curved boundaries. The influence of the fringing fields on axial focusing when the boundaries are oblique, is accounted for. It is shown that the second order angular aberration may Le eliminated by appropriate curvature of the boundaries.

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