Abstract
A consistent physical and mathematical model of the propagation of electromagnetic waves in an inhomogeneous medium with strong discontinuities of the electromagnetic field at the interface of two media, which is a rough surface, was developed. Mathematical modeling of rough surfaces and their profiles was carried out using fractal geometry, which allows us to display the topology of the object as close as possible to reality. For real heterogeneous rough structures, we have developed a through-counting method that takes into account the continuity of the total current at the interfaces of adjacent media, the effect of induced surface charge and surface current. This approach lets one avoid the necessity to set surface impedances depending on the structure of the field being determined and on the material properties.
Highlights
Imperfectness of the shielding surface is the main factor determining the loss of the guide electrodynamic structure
Mathematical modeling of rough surfaces and their profiles was carried out using fractal geometry, which allows us to display the topology of the object as close as possible to reality
For real heterogeneous rough structures, we have developed a through-counting method that takes into account the continuity of the total current at the interfaces of adjacent media, the effect of induced surface charge and surface current
Summary
Imperfectness of the shielding surface is the main factor determining the loss of the guide electrodynamic structure. These include the method of laser smoothing consisting in fast high-temperature exposure and cooling; laser microstructuring of the surface, based on local evaporation of the substance; laser roughness control by focusing laser radiation on the treated surface; laser surface microstructuring using surface electromagnetic waves The latter method realized in several stages: a surface electromagnetic wave is excited at the interface between two media; after the interference of this wave with the incident wave on the surface, a new intensity distribution of light is formed; spatial non-uniform surface heating takes place, as a result of which spatial periodic structures arise. During the numerical simulation of the interaction of an electromagnetic wave with a rough fractal surface, the continuity conditions of the total current and the Dirichlet average theorem in the presence of a strong electromagnetic field discontinuity at the interfaces of inhomogeneous, angular structures are used for the first time. The results of the work can be used to study the influence of the roughness of the shielding surfaces of waveguides for antenna devices and in laser polishing of surfaces
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