Theoretical Analysis of the Crystalline Colloidal Array Filter

Abstract

The major parameters of a crystalline colloidal array optical filter have been investigated theoretically, and the results compared to published experimental data. This filter consists of an aqueous suspension of polystyrene spheres in a lattice which produces Bragg diffraction of incident light. The development of expressions for the filter bandwidth and attenuation utilized both dynamical x-ray diffraction theory and light scattering theory. The theoretical attenuation function indicates that extremely high absorbance values are achievable with relatively thin filters.

Laser diffraction microscopy

“…They found that due to the large refractive index mismatch between the particles and water, a crystal thickness of 50 layers is enough to diffract essentially all incident light that satisfies the Bragg condition. Dynamical x-ray diffraction theory (Zachariasen 1945) together with optical scattering theory (van de Hulst 1981) is able to account for the observed diffraction of light (Spry andKosan 1986, Rundquist et al 1989). The theory describes the relative intensities of the diffraction maxima and their shift from the Bragg positions observed in light scattering experiments.…”

Restricted meniscus convective self-assembly

“…Coatings of colloidal particles, consisting of single or multiple layers of densely packed nanoparticles, are of interest for applications such as antireflection coatings [1], photonic crystals [2][3][4][5], optical filters [6,7], sensors [8,9], porous membranes [10,11], surface enhanced Raman spectroscopy (SERS) [12], fabrication of ''patchy" nanoparticles [13], and nanosphere lithography [14]. They can be fabricated through a number of different methods [15][16][17], including sedimentation [18][19][20][21], slow evaporation [2,22], spin or drop casting [23][24][25][26], microfluidic packing [6,27], electrostatic assembly [28], covalent attachment [29], or Langmuir-Blodgett methods [30].…”

From nuclei to micro-structure in colloidal crystallization: Investigating intermediate length scales by small angle laser light scattering

“…Interestingly, a randomly oriented crystal will in general not fulfill the Bragg condition and therefore will scatter much less than the surrounding fluid. Only if it meets the Bragg condition, it may -depending on its thickness -scatter much more efficiently [92]. For a suspension of randomly oriented optically thin crystals one therefore expects the transmission to increase during solidification.…”