Optical determination of the lattice constants of colloidal crystals without use of the refractive index

Angle-dependent reflectance spectra were measured for charge-stabilized colloidal crystals of polystyrene particles dispersed in water. We found that diffraction peaks due to the two-dimensional surface lattice of the colloidal crystal were observable in the spectra, in addition to normal three-dimensional Bragg peaks. On the basis of the nature of the two-dimensional diffraction, we show that the lattice constant can be determined without the knowledge of the refractive index of the crystal, unlike the case of using three-dimensional Bragg diffraction. The lattice constant depends only on the diffraction angle and the wavelength of light and therefore can be determined with high precision. The accurate determination of the lattice constant would provide a basis for quantitative evaluation and design of colloidal crystals for applications in the optical regime, such as photonic crystals.