New Possibilities for Constructing Heuristic Solutions to Problems of Electromagnetic Diffraction

The paper formulates the foundations of a recently developed approach, named the method of fundamental components, intended for constructing heuristic solutions in problems of electromagnetic diffraction, for the first time. The difference between the new method and the known heuristic approaches lies in the application of an adjustment procedure that increases the accuracy. The possibility of the mentioned method for obtaining new results is illustrated with the help of the author’s previously published works. The advantages of the new method in constructing high-speed solvers and in the physical interpretation of numerical solutions are shown.

Methods of the diffraction theory for microwave aquametry of paper materials

We present a short review of several fundamental results, which have been obtained within frameworks of one trend of the wide spread of investigations, carried out during 1970 –2010s under the leadership of doctor of science, corresponding member of the National Academy of Sciences of Belarus P. D. Kukharchik, whose scientific interests were connected with the study of physical properties of heterogeneous dielectric and metal-containing industrial materials by the methods of holography, holographotomography, digital radiography, microwave and infrared introscopy. In this review, by the example of several base problems, we describe the semi-analytical methods of rigorous theoretical simulation of electromagnetic fields, arising under electromagnetic diffraction by slots in perfectly conducting screens of arbitrary thickness in absence and in the presence of plane dielectrics in the plane and cylindrical geometries of electromagnetic propagation. It demonstrates application of the these methods to simulation of processes of moisture measuring of paper sheet using microwave cavities with slots, which are employed on enterprises of pulp and paper industry.

An asymptotic model based on matching far and near field expansions for thin gratings problems

In this paper, we devise an asymptotic model for calculating electromagnetic diffraction and absorption in planar multilayered structures with a shallow surface-relief grating. Far from the grating, we assume that the solution can be written as a power series in terms of the grating thickness δ , the coefficients of this expansion being smooth up to the grating. However, the expansion approximates the solution only sufficiently far from the grating (far field approximation). Near the grating, we assume that there exists another expansion in powers of δ (near field approximation). Moreover, there is an overlapping zone where both expansion are valid. The proposed model is based on matching the two expansions on this overlapping domain. Then, by truncating terms of order δ 2 or higher, we obtain explicitly the equations satisfied by the lowest order terms in the power series. Under appropriate assumptions, we prove second order convergence of the error with respect to δ . Finally, an alternative form, more convenient for implementation, is derived and discretized with finite elements to perform some numerical tests.