Light diffraction from colloidal crystals with low dielectric constant modulation: Simulations using single-scattering theory

We theoretically characterized the diffraction properties of both closed-packed and non-closed-packed crystalline colloidal array (CCA) photonic crystals. A general theory based on single-scattering kinematic approach was developed and used to calculate the diffraction efficiency of CCA of different sphere diameters at different incident light angles. Our theory explicitly relates the scattering properties of individual spheres (calculated by using Mie theory) comprising a CCA to the CCA diffraction efficiency. For a CCA with a lattice constant of 380 nm, we calculated the relative diffraction intensities of the fcc (111), (200), and (220) planes and determined which sphere diameter gives rise to the most efficiently diffracting CCA for each set of crystal planes. The effective penetration depth of the light was calculated for several crystal planes of several CCAs of different sphere diameters at different angles of incidence. The typical penetration depth for a CCA comprised of polystyrene spheres was calculated to be in the range of 10-40 CCA layers. A one-dimensional (1D) model of diffraction from the stack of (111) fcc crystal layers was developed and used to assess the role of multiple scattering and to test our single-scattering approach. The role of disorder was studied by using this 1D scattering model. Our methodology will be useful for the optimization of photonic crystal coating materials.