Browsing by Author "Kavaklioglu, Oemer"

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Citation - WoS: 3
On Floquet-Twersky Representation for the Diffraction of Obliquely Incident Plane H-Polarized Electromagnetic Waves by an Infinite Grating of Insulating Dielectric Circular Cylinders
(Elsevier Science Inc, 2008) Kavaklioglu, Oemer; Schneider, Baruch
The exact analytical solution for the classical electromagnetic problem of the diffraction of obliquely incident plane H-polarized electromagnetic waves by infinite periodic structures made of infinitely long insulating dielectric circular cylinders is investigated. Exploiting the Sommerfeld integral representation of the Hankel function in the transverse electric multiple scattering representation of the infinite periodic array of insulating dielectric circular cylinders for obliquely incident waves [O. Kavaklioglu, On Schlomilch series representation for the transverse electric multiple scattering by an infinite grating of insulating dielectric circular cylinders at oblique incidence, Journal of Physics A: Mathematical and General 35 (9) (2002) 2229-2248], which is expressed in terms of cylindrical modes, a rigorous exact representation for the generalized transmitted and reflected fields of the infinite grating excited by an obliquely incident horizontally polarized plane electromagnetic wave is acquired in terms of 'Twersky's elementary function representations for Schlomilch series', and as a linear superposition of propagating and evanescent 'Floquet plane wave modes' traveling in the directions of diffraction angles. (C) 2007 Elsevier Inc. All rights reserved.
Citation - WoS: 2
On the Asymptotic Solution for the Fourier-Bessel Multiple Scattering Coefficients of an Infinite Grating of Insulating Dielectric Circular Cylinders at Oblique Incidence
(Elsevier Science Inc, 2008) Kavaklioglu, Oemer; Schneider, Baruch
The 'asymptotic solution' for the classical electromagnetic problem of the diffraction of obliquely incident plane E-polarized waves by an infinite array of infinitely long insulating dielectric circular cylinders is investigated. Exploiting the elementary function representations of 'Schlomilch series', which was originally developed by Twersky [ V. Twersky, Elementary function representations of Schlomilch series. Arch. Ration. Mech. Anal. 8 ( 1961) 323 - 332.], we have obtained a 'new' set of equations describing the behavior of the 'Fourier-Bessel multiple scattering coefficients' of an infinite grating of circular dielectric cylinders for vertically polarized obliquely incident plane electromagnetic waves when the grating spacing 'd' is small compare to a wavelength. In addition, we have achieved to acquire the 'asymptotic solution for the multiple scattering coefficients of the infinite grating at oblique incidence' as a function of the ratio of the cylinder radius 'a' to grating spacing. (c) 2007 Elsevier Inc. All rights reserved.
Citation - WoS: 9
Poincare-Bertrand Formula on a Piecewise Liapunov Curve in Two-Dimensional
(Elsevier Science Inc, 2008) Schneider, Baruch; Kavaklioglu, Oemer
The Poincare-Bertrand formula for interchanging the order of integration in singular integral operators is generalized to the case of quaternionic singular integrals on a piecewise Liapunov curve in two-dimensional. (C) 2008 Elsevier Inc. All rights reserved.