We study the evanescent wave's behavior on a device made of a plane interface separating vacuum from a perfect negative index material. The system is described by the macroscopic Maxwell's equations with frequency-dependent permittivity and permeability. Assuming that electromagnetic sources with sinusoidal time dependence are switched on at an initial time, we show that, as time increases, evanescent waves result in surface modes at the plane interface. The time dependence of these surface modes is oscillating but not harmonic since their amplitude linearly increases with time. As a consequence, we find that the image of a point source is not a point image. The analysis avoids any ambiguity related with causality and finite energy requirements.