A.A. Babkin, A.S. Raevskii, S.B. Raevskii

Some features of complex waves of open dielectric waveguides are considered from the point of view of their decomposition onto partial sets of plane waves. Rays, which are corresponding to plane waves that form field symmetric waves, lie on the conical surfaces, while asymmetrical waves - much more on the geometrically complex surfaces. However, in both cases these surfaces can be considered as limiting the areas which can be formulated as homogeneous boundary problem independently for each improper complex wave (CW), which indicates the non-orthogonality of improper waves (both symmetric and asymmetric) between each one. Plane waves, forming field of symmetrical CW, does not interact with each other, and their mutual power flow is zero. Mutual power flow of plane waves which form asymmetrical CW are non-zero. This fact allows the formation of counter power flows within the cross-sectional structure of the guide. If flows are equal, then own CWs exist. Diffraction problems (different guiding structures harmonizing) can be reduced to cross-linking of fields of conical apertures of different waves from the general field of the aperture connects to the dielectric waveguiding structure. The fields at the ends of the conical structures can be re-decomposed by eigenfunctions of formal boundary value problem corresponding to the boundary of the cross-section of the join of two structures to be matched. Further procedure of solving of the diffraction problem is the use of conditions of eigenfunctions orthogonality of formal auxiliary problem, and use of eigenfunctions of the boundary value problem of aligning object.