Speaker
Description
The historical development of the concept of caustics and its applications in science and technology is shown, starting from the works of Leonardo da Vinci (LdV) to contemporary achievements in the field of radio astronomy.
Starting from LdV research in the field of light propagation, caustics present in his drawings on the topic of reflecting light by concave mirrors were analyzed. The discovery of LdV is presented, according to which, at an infinitely distant source of rays, a small fragment of the canopy is enough to generate a focus, while the rest of the mirror forms a caustic for which LdV did not indicate an application.
Based on the principles of geometrical optics, an analytical description of caustics generated in a spherical mirror is presented. A mathematical description of the concentration of energy on caustics is given, taking into account the energy loss during reflection. The occurrence of a singularity, the physical equivalent of which is the focus of the mirror, is shown. Attention is drawn to the difference in the formation of caustics in spherical and parabolic mirrors. In the first case, it is an indelible element of the mirror's operation, while in the second, under appropriate conditions, caustics can completely disappear, transforming into a point focus. Using acoustic and electromagnetic waves as examples, the formation of caustics in a wave field was investigated taking into account the scalar and vector nature of the field. Based on the general principles of wave motion, symmetry was shown in the description of energy dependencies in acoustics and electromagnetism.
In the practical part the presence of caustics in the field of room acoustics and radio astronomy was indicated. It was explained why in the sound field in existing halls, instead of the entire caustics, only its cusp is observed, which is perceived as a point-like focus of sound. In relation to radio astronomy, the influence of caustics on the efficiency of spherical and parabolic antennas was presented. It was shown how the development of receiving techniques allows the use of energy contained in caustics to increase the aperture of a spherical mirror, which significantly improves the observation possibilities. Implementation of these improvements is demonstrated at the 305-meter Arecibo radio telescope in Puerto Rico, and the 500-meter FAST radio telescope in Dawodang, China.
