Diffraction in crystalline colloidal-array photonic crystals

We characterized the diffraction and crystal structure of a crystalline colloidal array (CCA) photonic crystalcomposed of 270 nm diameter polystyrene spheres which have a nearest neighbor spacing of ,540 nm. ThisCCA diffracts light in first order at<1200 nm and shows strong diffraction in the visible spectral region fromhigher 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 thecrystal structure is fcc with significant stacking faults. Essentially, no light transmits at the Bragg angle for thefcc (111) planes even through thin ,40 mm thick CCA. However, much of this light is diffusely scatteredabout the Bragg angle due to crystal imperfections. Significant transmission occurs from thin samples orientedat 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 thicknessdependence of diffraction from CCA photonic crystals prepared from ,120 nm polystyrene spheres whose fcc(111) planes diffract in the visible spectral region. These experimental observations, aided by calculationsbased 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 crystalimperfections.DOI: 10.1103/PhysRevE.69.066619 PACS number(s): 42.25.Dd, 82.70.Dd, 78.67.2n, 61.72.NnI. INTRODUCTION