On Floquet–Twersky representation for the diffraction of obliquely incident plane H-polarized electromagnetic waves by an infinite grating of insulating dielectric circular cylinders

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 [Ö. Kavaklıoğlu, On Schlömilch 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 Schlömilch series’, and as a linear superposition of propagating and evanescent ‘Floquet plane wave modes’ traveling in the directions of diffraction angles.