On the asymptotic solution for the Fourier-Bessel multiple scattering coefficients of an infinite grating of insulating dielectric circular cylinders at oblique incidence

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 'Schlömilch series', which was originally developed by Twersky [V. Twersky, Elementary function representations of Schlömilch 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.