A 2D problem of diffraction of the TM-polarized plane wave by a quartz nanofiber coated with a silver layer is investigated. The total scattering cross-section is numerically calculated in the range of visible light waves (400–700 nm). It is found that, at certain geometric parameters of the structure, not only dipole but also multipole plasmon resonances arise in the investigated range of wavelengths. Scattering patterns at resonance frequencies are calculated. It is demonstrated that deposition of the silver layer onto a quartz nanofiber can decrease the scattering cross section several times.

The 2D problem of excitation of a hollow circular metamaterial cylinder by a filament source is analytically and numerically investigated. It is found that, when the relative permittivity and permeability are close to minus unity, high-Q resonances exist in hollow cylinders of an electrically small radius. Near- and far-field patterns are calculated. It is found that, under resonance conditions, a multilobe scattering pattern typical of superdirective antennas is formed. The influence of loss on the resonance characteristics is investigated.

The 2D problem of excitation of a circular metamaterial cylinder by a filament source is numerically investigated. It is found that, when the relative permittivity and permeability are close to minus unity, high-Q resonances occur in cylinders of an electrically small diameter. Near- and far-field patterns are calculated. It is discovered that, under resonance conditions, a multilobe scattering pattern typical of superdirective antennas is formed. The influence of loss on the resonance characteristics is investigated.

The 2D problem of excitation of a circular metamaterial cylinder by a filamentary source is numerically investigated. It is found that, for the minus one values of the relative permittivity and permeability, the field on the surface of the cylinder concentrates in a region that is located on the illuminated surface of the cylinder and that is small compared to the wavelength.

The properties of the two-dimensional electromagnetic fields excited by a filamentary source located near planar and cylindrical boundaries of bodies made of metamaterials with their permittivity and permeability close to minus one are considered. The subwavelength field localization effects, the phenomena associated with the resonances of surface waves, and the nonresonant field enhancement effects are investigated.

Two-dimensional problem of excitation of a circular cylinder made of a material with negative permittivity by a plane or a cylindrical wave is considered for the case of TM polarization. Conditions under which resonances of surface plasmons arise in cylinders thin compared to the wavelength are found with the use of strict numerical calculations.