With this invention, it is possible to divert or focus beams, convert divergent beams to quasi-parallel beams and vice versa, and to filter and monochromatize beams. Energy losses in radiation transport are reduced, the useful energy spectrum is broadened, and the concentration of the radiation increased. Large-scale sources can be used without any reduction in the proportion of particles captured and the radiation spectrum can be controlled. To achieve this, the method involves, in addition to the repeated reflection of particles as they interact with alternating media of differing densities, the diffused and potential scattering or interference of the particles diffracted by multiple-layer structures created on reflecting surfaces. The proposed device is provided with a coating of such surfaces in layers with differing electromagnetic properties. The optical system is designed preferably as a set of miniature lenses or half-lenses (28) consisting of a plurality of capillaries or polycapillaries; a suitable coating (22) is applied to the walls of the channels (24) of these capillaries. This arrangement eliminates the need for supporting structures for shaping the profiles of the optical system.