Metamaterials: from microwaves to the visible region

In a recent paper, J.B. Pendry [J.B. Pendry, Negative refraction makes a perfect lens, Phys. Rev. Lett. 86 (2000) 3966–3969] has mentioned the possibility of making perfect lenses using a slab of left-handed material with relative permeability and permittivity equal to −1. He gave a demonstration of the vital influence of the evanescent waves in this process, arguing that these waves are amplified inside the slab. In the present paper, we first try to give a rigorous electromagnetic demonstration of Pendryʹs statement, and we show that in fact the integral expression of the field in a region of space diverges. Since this divergence does not prove that the perfect lens does not exist, we then give 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. However, thanks to the heterogeneous nature of a metamaterial, it is shown that a material able to focus light more efficiently than current devices (but not perfectly) could exist. Finally, it is shown that a plane slab of dielectric photonic crystal can also focus light, a property which could be crucial for construction of superlenses in the visible and infrared regions. To cite this article: D. Maystre et al., C. R. Physique 6 (2005).