  Wave scattering from a cylinder with a tensor impedance surface is
investigated based on the Lorentz-Mie theory. A practical example of such a
cylinder is a subwavelength metallic rod with helical dielectric-filled
corrugations. The investigation is performed with the aim to maximize
scattering cross-section by tailoring the surface impedance of cylindrical
scatterers. For the normally incident TEz and TMz waves the required surface
impedance of a subwavelength cylinder can be produced by longitudinal (axial)
and transverse (circumferential) corrugations, respectively. It is shown that
such corrugations induce superscattering at multiple frequencies, which can be
widely tuned with either or both the size and permittivity of dielectric-filled
corrugations. In the microwave band, this effect is demonstrated to be robust
to material losses and is validated against the full-wave simulations and
experiment. For the TEz waves the enhanced scattering from the cylinder is
found to have a broad frequency bandwidth, provided that the relative
permittivity of corrugations is low or equal unity. In the latter case, the
corrugated cylinder acts as an all-metal superscatterer. For such cylinders the
near-field measurements are implemented and provide the first experimental
evidence of the superscattering phenomenon for all-metal objects. In addition
to multifrequency superscattering, the dielectric-filled corrugations are shown
to provide multifrequency cloaking of the cylinder under the incidence of the
TMz waves. Simultaneous superscattering and cloaking at multiple frequencies
distinguishes corrugated cylinders from other known practicable scatterers for
potential applications in antenna designing, sensing, and energy harvesting.
