Electromagnetic field of a vertical dipole on a non-perfect conductor coated with a negative-index medium

The explicit formulas of the electromagnetic field produced by a vertical electric dipole in a negative-index medium coating a non-perfect conductor slab is derived. The contribution of three kinds of wave number to the total field is discussed and investigated. The wave-number of the surface wave is between the wave-number in the air and that in the negative-index media. Because the contribution of each types of wave varies with the medium parameters, the amplitude of total field as function of distance is complicated.