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The Plane Problems of the Electrodynamics of Pulsed Waves for Compact Open Resonators with the Waveguide Feeder Line. Gratings as Pattern Forming Structures


V.F. Kravchenko, V.L. Pazynin, K.Y. Sirenko, Y.K. Sirenko

In the theory of unsteady electromagnetic waves, there exists a number of problems that have not been yet obtained universal, justified, and practically feasible solutions. This fact affects a quality of models and restricts potentialities of the time-domain methods in the study of transient processes phenomena and regularities of space-time transformations of pulsed waves. Among these problems is a problem of correct and efficient truncation of a computational domain in the so-called open problems, i.e. in the problems whose analysis domain is unlimited along one or several directions. In addition, mention may be made of the far-field zone problem, the problem of large and distant sources, and others. The solution of these problems has advanced greatly within the last few years with the help of the approach based on the construction of transport operators functioning in the space of evolutionary bases of signals. These operators determine space-time transformations of pulsed waves on the finite sections of their free propagation in regular channels of various natures such as waveguides, Floquet channels, and ‘regular’ segments of free space. In our previous work [1], within the framework of this approach, we solved rigorously model two-dimensional initial boundary-value problems allowing one to study space-time and space-frequency electromagnetic field transformations in compact electrodynamic systems with waveguide feed lines. The algorithms oriented on numerical solution of a wide class of urgent theoretical and applied problems of antenna theory and engineering, high-power electronics, and resonant quasi-optics have been constructed and implemented in software. It is of first importance that these algorithms eliminate the possibility of unpredictable behavior of computing errors for large observation times and, as a consequence, ensure reliable data on resonant processes. The present paper confirms the efficiency of the solutions constructed in [1]. We consider rather complicated applied problems associated with the analysis of antennas with finite periodic structures as their principal unit. The space-time and space-frequency electromagnetic field transformations in the antennas of this kind have been studied. We have also analyzed physical processes occurring during a directional radiation formation. New data on the intensity and directivity of the radiation from open resonant structures with semitransparent grating-mirrors have been obtained. A number of key theoretical problems of the synthesis of phased antenna arrays have been rigorously analyzed for the first time.
June 24, 2020
May 29, 2020

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