9 - Non-resonant dielectric metamaterials

Abstract

The area of non-resonant dielectric metamaterials comprises phenomena which occur at long wavelengths, where Mie resonances and Bragg diffraction in ordered structures do not play a role. In this spectral range effective-medium theories can be applied quite well and are therefore revisited in the first part of the chapter. Isotropic as well as anisotropic effective media are discussed and the dispersion relation for light predicted by the effective-medium theories is compared to exact photonic bandstructures in ordered metamaterials, demonstrating overall very good correspondence in the long wavelength range. After a short look at more advanced modern homogenization methods experimental techniques are discussed to determine the effective parameters. In particular measurements based on interference effects are suggested to determine group velocity, effective indices and birefringence with greater confidence. The power to control the effective refractive index and anisotropy on a local level by arranging and shaping the scattering elements in a designed way is employed to create a large variety of graded effective-index structures. These can be used to realize designs originating from transformation optics. Recent examples of graded index landscapes for metasurfaces, 2D in-plane light guiding, subwavelength structured waveguides and antireflection coatings are presented. Most of the discussed designs are based on silicon as a high index material facilitating a large range of effective refractive indices and exploiting existing nanofabrication methods. While most of the artificially created metamaterials exhibit a strict periodic order, in the last section disordered systems are discussed and possibilities of hyperuniform arrangements of scattering elements outlined.