Method of partial overlapping regions for the analysis of diffraction problems

The technique of regularisation of the mode-matching method´s equations for two-dimensional diffraction problems in waveguiding structures with complicated geometry of boundary is developed and substantiated. The approach is shown to have the clear geometry representation: a whole complex domain of field determination is subdivided into a number of overlapping regions. The method of partial overlapping regions generates the resulting operator, a principal part of which is an idem-factor and additional part is a ω-complete continuous operator