can someone explain me what are media having negative permittivity and permeability.
How they work, what changes in EM waves propagation, which are the advantages and applications?
Media having negative permeability and/or permitivity are a short names for having the real part of the permeability and permitivity phasors to be negative. Let me remind that the real part is for the propagation and the imaginary part is for the attenuation or loss. It has many applications especially in antenna because it can reduce the size of antenna, and correct the phase loss. It is also applied in optics to overcome the diffraction limit of lenses. Some researchers think they can use those material to fabrcate flat convergent or divergent lenses.
You are completely right, teckyiau. There are no such material but we can microfabricate metamaterial that have similar electromagnetic effect. As long as the dimensions of the components that you fabricate is much smaller (maybe 10 times) than the wavelength of interest then the metamaterial will behave just fine as you expected.