We study the behaviour of the Poynting vector for resonance scattering of a plane H-polarized electromagnetic wave by a gyrotropic cylinder. A comparison of this behavior is made with that one caused by the scattering on an isotropic cylinder. The Poynting-vector line structure is shown to be asymmetric in the case of a gyrotropic scatterer, the absolute value of the vector quantity at the boundary of the gyrotropic cylinder being significantly more than that one in the case of the isotropic scatterer.
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