Wave diffraction by periodic system of arbitrary shaped dielectric cylinders with partial metal covering

The subject of the presentation is consequent (from more to less simple) constructions of mathematical and numerical methods for simulation of the following three key problems. The first one is diffraction of electromagnetic waves by a dielectric cylinder of arbitrary smooth shape, which is a problem of high importance in modern radioscience. The next, more interesting, but more complicated problem is numerical simulation of electromagnetic waves diffraction by such cylinder, but in the case, when it is partially covered by one or a few curvilinear metal strips. This structure numerical simulation is in great demand nowadays, because it is rather realistic model of artificial and natural open resonators, waveguides, antennae and etc. The importance of the third problem comes from both the modern optics problems and from rapid growing of artificial materials scientific and engineering areas for such application as photonic crystals, frequency selective surfaces or media and so on. Namely, methods of computational simulation of periodic system of dielectric and metal-dielectric cylinders above mentioned will be the principal topic of the presentation. We suggest new mathematically strong and numerically efficient (in particular, numerically stable) approach for all the problems above mentioned. Our approach is based on our previous results in scope of analytical regularization method (Tuchkin, 1998). The approach results in corresponding infinite algebraic system of the second kind: (I+H)x=b in space of square summable infinite sequences with compact operator H. Various difficulties of numerical implementation of the method and our choices for solving them will be considered also.