Dispersion engineering via nonlocal transformation optics

Transformation optics (TO) is one of the most powerful and versatile frameworks for the systematic design of artificial media. Recently (G. Castaldi et al., Phys. Rev. Lett., 108, 063902, 2012), we have proposed an extension of this approach that enables the manipulation and control of nonlocal light-matter interactions, which are becoming increasingly relevant in a variety of metamaterial applications, including artificial magnetism and ultrafast nonlinear optics. Instead of spatially-changing refractive properties, we introduced a framework of transformation media that can tailor the wave interaction in the reciprocal space of spatial wave-numbers, so as to induce desired nonlocal effects. This approach relies on the increased availability of nonlocal homogenization models, and admits a powerful geometrical interpretation in terms of direct manipulation of the equifrequency contours. Overall, it allows designing artificial materials with much broader degrees of freedom, including the possibility of nonlocal signal processing.