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We present the results of a study of the Poynting vector field genericsingularities at the resonant light scattering of a plane monochromaticlinearly polarized electromagnetic wave by a subwavelength particle. We revealthe impact of the problem symmetry, the spatial dimension, and the energyconservation law on the properties of the singularities. We show that, in thecases when the problem symmetry results in the existence of an invariant planefor the Poynting vector field lines, a formation of a standing wave in theimmediate vicinity of a singularity gives rise to a saddle-type singular point.All other types of singularities are associated with vanishing at the singularpoints, either (i) magnetic field, for the polarization plane parallel to theinvariant plane, or (ii) electric field, at the perpendicular orientation ofthe polarization plane. We also show that in the case of two-dimensionalproblems (scattering by a cylinder), the energy conservation law restricts thetypes of possible singularities only to saddles and centers in thenon-dissipative media and to saddles, foci, and nodes in dissipative. Finally,we show that dissipation affects the (i)-type singularities much stronger thanthe (ii)-type. The same conclusions are valid for the imaginary part of thePoynting vector in problems where the latter is regarded as a complex quantity.The singular points associated with the formation of standing waves aredifferent for real and imaginary parts of this complex vector field, while allother singularities are common. We illustrate the general discussion byanalyzing singularities at light scattering by a subwavelength Germaniumcylinder with the actual dispersion of its refractive index.

The Poynting vector field generic singularities in resonant scattering of plane linearly polarized electromagnetic waves by subwavelength particles