Transformation optics: approaching broadband electromagnetic cloaking

An approach to broadband cloaking of light waves is analysed for a simplified case of a scaling transformation for a general cylindrical coordinate system. The proposed approach requires metamaterials with specifically engineered dispersion. The restriction on the signs of gradients in the dispersion dependencies of the dielectric permittivity and the magnetic permeability for different operational wavelengths is revealed and is shown to cause difficulties unless additional gain-assisted compensation for losses or electromagnetically induced transparency is introduced in the cloaking system.