Diffraction in crystalline colloidal-array photonic crystals.

We characterized the diffraction and crystal structure of a crystalline colloidal array (CCA) photonic crystal composed of 270 nm diameter polystyrene spheres which have a nearest neighbor spacing of approximately 540 nm. This CCA diffracts light in first order at approximately 1200 nm and shows strong diffraction in the visible spectral region from higher order planes. We quantitatively examined the relative diffraction intensities of the putative fcc (111), (200), (220), and (311) planes. Comparing these intensities to those calculated theoretically we find that the crystal structure is fcc with significant stacking faults. Essentially, no light transmits at the Bragg angle for the fcc (111) planes even through thin approximately 40 microm thick CCA. However, much of this light is diffusely scattered about the Bragg angle due to crystal imperfections. Significant transmission occurs from thin samples oriented at the Bragg condition for the fcc (200), (220), and (311) planes. We also observe moderately intense two-dimensional diffraction from the first few layers at the crystal surfaces. We also examined the sample thickness dependence of diffraction from CCA photonic crystals prepared from approximately 120 nm polystyrene spheres whose fcc (111) planes diffract in the visible spectral region. These experimental observations, aided by calculations based upon a simple but flexible model of light scattering from an arbitrary collection of colloidal spheres, make clear that fabrication of three-dimensional photonic band gap crystals will be challenged by crystal imperfections.