The authors present an analysis of conditions on the boundary between layers having varied electromagnetic properties. The research is performed using consistent theoretical derivation of analytical formulas, and the underlying problem is considered also in view of multiple boundaries including the effect of the propagation of electromagnetic waves with different instantaneous speeds. The paper comprises a theoretical analysis and references to the generated algorithms. The algorithms were assembled to enable simple evaluation of all components of the electromagnetic field in relation to the wave propagation speed in a heterogeneous environment. The proposed algorithms are compared by means of different numerical methods for the modelling of electromagnetic waves on the boundary between materials; moreover, the electromagnetic field components in common points of the model were also subject to comparison. When in conjunction with tools facilitating the analysis of material response to the source of a continuous signal, the algorithms constitute a supplementary instrument for the design of a layered material. Such design allows us to realize, for example, a recoilless plane, recoilless transition between different types of environment, and filters for both optical and radio frequencies.
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