Light rays and imaging in wave optics

An interpretation of focusing and image formation on scattering of electromagnetic waves by a dielectric cylinder (a cylindrical lens) is proposed on the basis of the full Maxwell theory. It is centered on analysis of the behavior of integral curves of the Poynting vector here called wave rays. These wave rays cannot intersect so that the focusing and imaging spots are identified with regions of high flow concentration. Two-dimensional examples of wave rays and wave fronts in the scattering of plane and cylindrical electromagnetic waves as well as of Gaussian beams by a dielectric cylinder derived from rigorous solution of the Maxwell equations for incident waves perpendicular to and uniform along the scatterer are given. Their qualitative comparison with geometrical and diffraction approximations are provided. Fixed points and vortex structure of the Poynting flow are investigated. An example of (Gaussian-beam) scattering with transparent multiple internal reflections and multiple wave splitting is given.