S.P. Skobelev, O.N. Smolnikova

Analysis of electromagnetic wave scattering from periodic dielectric structures is of great interest for a number of applications. One of them is creation of artificial dielectric layers for blooming of lens surfaces. The purpose of the present work is development of a hybrid projective method for numerical analysis of electromagnetic wave scattering by doubly periodic dielectric structures with pyramidal and conical elements. The indicated elements are of interest because they provide a few degrees of freedom for optimization of their shape to obtain the best desirable parameters of scattering. The problem to be solved is formulated as determination of the field scattered from a doubly periodic dielectric structure illuminated by plane TE and TM waves. The algorithm we propose for solution is a new modification of a hybrid projective method developed earlier for calculation of waveguide-dielectric array antennas (S. P. Skobelev, Phased Array Antennas with Optimized Element Patterns, Norwood, MA: Artech House, 2011). The hybridity implies here use of expansion of the transverse electric and magnetic fields over transverse functions of the Floquet modes with unknown variable coefficients, projection of the Maxwell\'s equations on the indicated transverse functions, application of the one-dimensional finite element method, and projective matching of the fields on the boundaries of the partial regions. As a result, the problem is reduced to appropriate systems of linear algebraic equations solved numerically. The main feature of our approach is elimination of the redundancy of the unknowns that takes place in the well known relative method of coupled modes (e.g. M. S. Mirotznik, B. L. Good, P. Ransom, D. Wikner, and J. N. Mait, \"Broadband Antireflective Properties of Inverse Motheye Surfaces,\" IEEE Trans. on Antennas and Propagat. 2010, vol. 58, no 9., pp. 2969-2980). The paper also includes the results of validation characterizing the efficiency of our approach, as well as the number of results obtained after optimization of the parameters of artificial matching dielectric layers characterizing their capabilities in blooming of lens antennas.