Refraction properties of fcc and hcp SiO₂-based colloidal crystals

Close-packed 3D colloidal crystals, regular arrangement of mono-disperse silica or polymer spheres with diameter within the wavelength range of visible light, show many novel optical phenomena that are strongly dependent of the sphere-packing symmetry. From both analytical and experimental results, is well known that there are two predominant ways of stacking mono-disperse spheres to minimize the interstitial volume in a colloidal crystal. One of them leads to a close packed face-centered-cubic (fcc) structure, called synthetic opal, and, the other one, to an hexagonal close packed (hcp) structure. Although computer simulations show that the fcc structure is more stable, there are a lot of papers in which a hcp phase is observed. In this work, the photonic band structure of the fcc and hcp 200nm SiO₂ based colloidal crystals are calculated using the plane wave expansion method (PWEM). A comparative kinematic study of the refraction properties of the fcc and hcp structures is presented, showing that the effective refractive index depends basically of the dispersion relations and of the plane of polarization and that it is not limited by the refractive index of the composing materials.