Effective refractive index of face-centered-cubic and hexagonal close-packed 250 nm-SiO₂ based colloidal crystals

A quantitative kinematic analysis, of the refraction properties of face-centered-cubic and hexagonal close-packed 250 nm-SiO₂-based colloidal crystals, was performed using the plane wave expansion method. The angle-dependent effective refractive index, for different frequencies, was calculated taking into account the continuity of the tangential component of the wave vector across the interface and the energy conservation principle as well. The results demonstrate that the unusual optical properties, of the close packed SiO₂-based colloidal crystals, depend strongly on the sphere-packing symmetry rather than from the material itself.