On Scattering of Waves by the Infinite Grating of Circular Dielectric Cylinders at Oblique Incidence.

The scattering of obliquely incident plane electromagnetic waves by an infinite grating of dielectric circular cylinders is analyzed. The lnternal electric field of the infinite dielectric grating is employed to approximate the internal electric field of the finite grating for wavelengths larger than the grating spacing. The dyadic scattering amplitudes which contains the "mutual coupling effects" are obtained in the far field as a function (a/d), (a is the radii of the dielectric cylinders, and d is the distance between the centers of the cylinders). In addition, the returns from a half space of an ensemble of finite gratings of N dielectric cylinders are computed, and the results are compared with the independent scatterers as the density and size of the scatterers remain constant. Several representations of the scattered fields by the infinite grating are derived. The first representation is obtained by employing the separation-of-variables technique in cylindrical coordinates. The exact equations for the scattering coefficients of the infinite grating are derived by the application of the boundary conditions on the surface of the dielectric cylinders. This approach leads to an infinite number of equations for the infinite number of unknown external electric and magnetic field scattering coefficients in coupled form. The second method is the expansion of the scattered fields as a superposition of plane waves. In this approach, the grating equation is solved to determine the propagating and evanescent Floquet modes. The Schlomilch series is introduced to represent alternative solutions for the scattering coefficients when the wavelength is larger than the grating spacing. An ansatz is introduced to obtain an approximate set of equations for the scattering coefficients when the radius of the cylinders is small compared to a wavelength. The scattering coefficients are approximated in terms of an infinite series as a function of (a/d). This solution is compared with the one obtained by Twersky. It is demonstrated that his solution is a special case of the generalized oblique solution presented here. A new model for the finite grating of N dielectric cylinders is developed using the result of the infinite grating. The new model successfully demonstrates the significance of the "mutual coupling effects" among the constituent cylinders of the finite grating of N dielectric cylinders. It is stressed that the internal electric field associated with this new model is highly sensitive to the relative dielectric constant of the grating, and the returns corresponding to vv-polarization are considerably higher due to the "mutual coupling effects" among the constituent dielectric cylinders of the grating.