A dielectric structure with effective permittivity and permeability close to -1 operating for propagative waves at optical wavelengths is proposed. This structure is a two-dimensional photonic crystal with refractive index -1, coated by appropriate antireflection gratings. Numerical simulations involving a flat lens made of this optimized crystal illustrate the improvements that antireflection gratings can bring. In particular, following Veselago's proposition, this lens "can focus at a point the radiation from a point source" with negligible reflection losses. The proposed design takes into account the fabrication requirements and can be used for optical devices integrated in planar waveguides.

Effective properties of one-dimensional photonic crystals in the resonance domain are investigated. The obtained analytic expressions of effective permittivity and permeability lead to several results. Firstly, in the case of lossless materials, effective permittivity and permeability take, in general, complex values. It is shown that these values are governed by the truncation of the boundary layer. Considering the particular case of a symmetric unit cell, the effective permittivity and permeability become purely real and, by the way, coherent with physics. Finally, in this case with a symmetric unit cell, we show that effective permittivity and permeability can stay nearly constant in a wide range of wavevectors including propagating and evanescent waves.