Perfect lenses made with left-handed materials: Alice's mirror?

In a recent paper, Pendry [Phys. Rev. Lett. 86, 3966 (2000)] mentioned the possibility of making perfect lenses by using a slab of left-handed material with relative permeability and permittivity equal to -1, a property first stated by Veselago [Sov. Phys. Usp. 10, 509 (1968)]. Pendry gave a demonstration of the vital effect of the evanescent waves in this process, arguing that these waves are amplified inside the slab. We present first a very simple theoretical demonstration that a homogeneous material with both relative permittivity and permeability equal to -1 cannot exist, even for a unique frequency. This demonstration shows that the perfect lens proposed by Pendry can be interpreted as a means to move in real space the virtual perfect image of a point source given by a plane mirror. We show that, owing to evanescent waves, the concept of effective medium for heterogeneous materials is questionable, even when the wavelength of the incident light is much larger than the size of the heterogeneities. The effect of heterogeneities is compared with that of absorption. We conclude that a material able to focus the light more efficiently than the current devices (but not perfectly) could exist.