The properties of a lossless Veselago lens is examined when the material parameters epsilon and mu are frequency dispersive. A complete solution is presented that is based on the use of Fourier transforms in the frequency domain and is obtained in terms of the residues at the poles and branch cut integrals. It is shown that for an incident field with a finite frequency spectrum the excited evanescent field consists of resonant even and odd surface wave modes that do not grow exponentially within the slab. For a lossless slab and a sinusoidal signal of finite duration, at a single frequency corresponding to that where the relative values of epsilon and mu equal -1, Pendry's solution is obtained along with excited surface wave modes and other interfering waves that makes it impossible to obtain a coherent reconstruction of the spatial spectrum of the object field at the image plane. If the slab material is lossy the excited interfering surface wave modes will decay away in a relatively short time interval, but as shown by other investigators the resolution of the lens will be reduced in a very substantial way if the losses are moderate to large.
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