Time domain analysis of impulse electromagnetic field at the interface of two media

Abstract

Background. Ultrashort pulses of electromagnetic field are widely used in construction, archeology and demining, etc., by constructing effective georadars of the underlying surface, but theoretical study of physical processes of irradiation of medium is had a limit range of simplified model problems, usually in frequency domain. Therefore, the solutions of the problems of penetration of a pulsed wave with arbitrary time dependence into material medium are of special importance for understanding the possibilities and limitations of georadar’s study. Objectives. To obtain the analytical solution in time domain of the problems of reflection and propagation of a impulse electromagnetic wave through the interface of two media, which is the first model approximation to the description of physical processes that occur during operation of pulsed ultrawideband radar. Materials and methods. The problem of irradiation by nonstationary electric field of a lossless medium with a given permittivity is solved analytically by application of evolutionary approach. It consists in solving of Cauchy’s problem for the second-order partial differential equation Klein–Gordon type with respect to evolutionary coefficients. The components of the electromagnetic field in free space are found by integration by spectral parameters and summation by angular modes with appropriate combinations of basis functions. Results. Cauchy’s problems for differential equations that describe the behavior of reflected and refracted waves are solved. The electrical transverse components of the reflected and refracted waves as a function of time on the longitudinal axis were found for the case of irradiation with the step-like time dependence. Graphs of dependence of electric components on time and coordinates are plotted and analyzed. Conclusion. The phenomenon of an electromagnetic missiles in the medium that was irradiated by a pulsed electromagnetic wave of ultrashort duration was demonstrated for the first time. The obtained results can be generalized for the case of an arbitrary impulse by the Duhamel’s integral method. In addition, the electric field for observation point that do not lie on the longitudinal axis can be considered. An even more interesting continuation of the researches in terms of energy analysis is the study of the behavior of longitudinal electric and transverse magnetic components.