scholarly journals Exact Matrix Representation of the Transverse Magnetic Multiple Scattering of Obliquely Incident Plane Waves by the Diffraction Grating of Penetrable Cylinders

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Ömer Kavaklıoğlu ◽  
Roger Henry Lang
Keyword(s):  
Multiple Scattering ◽  
Diffraction Grating ◽  
Plane Waves ◽  
Transverse Magnetic ◽  
Circular Cylinders ◽  
Scattering Coefficients ◽  
Obliquely Incident ◽  
Incident Plane ◽  
Inversion Procedure ◽  
Exact Matrix

“An exact matrix conformation model” associated with the equations describing the exact behavior of the Fourier-Bessel multiple scattering coefficients of the diffraction grating consisting of an infinite number of infinitely long parallel penetrable circular cylinders, corresponding to the obliquely incident transverse-magnetic plane waves in “Twersky-Wait-Kavaklıoğlu representation,” originally excogitated in (Kavaklıoğlu, 2000), is acquired, and the exact solution for “the Fourier-Bessel multiple scattering coefficients of the diffraction grating at oblique incidence” is obtained by a matrix inversion procedure.

scholarly journals Asymptotic Analysis of Transverse Magnetic Multiple Scattering by the Diffraction Grating of Penetrable Cylinders at Oblique Incidence

2011 ◽  
Vol 2011 ◽  
pp. 1-30 ◽  
Author(s):  
Ömer Kavaklıoğlu ◽  
Roger Henry Lang
Keyword(s):  
Multiple Scattering ◽  
Oblique Incidence ◽  
Asymptotic Series ◽  
Normal Incidence ◽  
Transverse Magnetic ◽  
Circular Cylinders ◽  
Scattering Coefficients ◽  
Asymptotic Equations ◽  
Grating Spacing ◽  
Asymptotic Forms

We have presented a derivation of the asymptotic equations for transverse magnetic multiple scattering coefficients of an infinite grating of penetrable circular cylinders for obliquely incident plane electromagnetic waves. We have first deducted an “Ansatz” delineating the asymptotic behavior of the transverse magnetic multiple scattering coefficients associated with the most generalized condition of oblique incidence (Kavaklıoğlu, 2000) by exploiting Schlömilch series corresponding to the special circumstance that the grating spacing is much smaller than the wavelength of the incident electromagnetic radiation. The validity of the asymptotic equations for the aforementioned scattering coefficients has been verified by collating them with the Twersky's asymptotic equations at normal incidence. Besides, we have deduced the consequences that the asymptotic forms of the equations at oblique incidence acquired in this paper reduce to Twersky's asymptotic forms at normal incidence by expanding the generalized scattering coefficients at oblique incidence into an asymptotic series as a function of the ratio of the cylinder radius to the grating spacing.

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