Approximate boundary conditions for electromagnetic fields in electrodmagnetics

The results of an analytical review of literature sources on the use of approximate boundary conditions for electromagnetic fields of impedance type in solving boundary value problems of electromagnetism for more than 80 recent years are presented. During this period, the impedance approach was generalized to various electrodynamic problems, in which its use made it possible to significantly expand the limits of mathematical modeling, which adequately considers the physical properties of real boundary surfaces. More than eighty years have passed since the publication of approximate boundary conditions for electromagnetic fields. The meaning and value of these conditions lies in the fact that they allow solving diffraction problems about fields outside well-conducting bodies without considering the fields inside them, which greatly simplifies the solution. Since then, numerous publications have been devoted to the application of impedance boundary conditions, the main of which (according to the authors) are presented in this paper. Particular attention is paid to the characteristics of electrically thin impedance vibrators and film-type surface structures as a personal contribution of the authors to the theory of impedance boundary conditions in electromagnetism. The subject of research in this article is the analysis of the limits and conditions for the correct application of impedance boundary conditions. The goal is to systematize the results of using the concept of approximate impedance boundary conditions for electromagnetic fields in problems of electrodynamics based on an analytical review of literature sources. The following results were obtained. The types of metal-dielectric structures are presented, for which methods of theoretical determination of the values of surface impedances for film-type structures are currently known, which are the most promising for creating technological control elements on their basis in centimeter and millimeter wavelength devices. Conclusions. The materials of this paper do not pretend to be a complete reference book covering all the results and aspects of the development of the concept of approximate impedance type boundary conditions in problems of electromagnetism over the past decades. Simultaneously, the authors hope that the information presented in this paper will be useful to specialists in the field of theoretical and applied electrodynamics, as well as graduate students, young scientists and students who are just mastering radiophysics and radio engineering specialties.