Coherent transmission and reflection spectra of ordered structures from spherical alumina particles

Abstract

We have studied the transmission of light through a multilayer system of plane-parallel monolayers of monodisperse nonabsorbing spherical alumina particles under conditions of normal illumination in the wavelength range of 0.3–1.0 μm. In the quasi-crystalline approximation of the theory of multiple scattering of waves, we have calculated the coefficients of coherent transmission and reflection of partially ordered monolayers of particles and monolayers of particles with a nearly regular packing (planar photonic crystals with a nonideal lattice). Based on these calculations, using the transfer matrix method, we have calculated the coefficients of coherent transmission and reflection of the multilayer system. The influence of the spatial distribution of particles in individual monolayers on the coherent transmission and reflection spectra of the system has been analyzed. Characteristic minima in transmission spectra of layers caused by the interference of waves have been described. One of these minima is determined by the concentration and optical properties of particles. It appears in the spectrum of a monolayer at ratios of wavelengths and particle sizes roughly corresponding to one of the main maxima of the extinction. The second minimum is determined by the regularity of distribution of particles in the plane of the monolayer. It occurs in the spectrum of the monolayer at particle sizes comparable with the wavelength. The third minimum is the photonic band gap. It appears in the spectrum of a multilayer structure at spacings between monolayers comparable with the wavelength and is caused by the periodicity of the structure. The results make it possible to solve problems of monitoring of the degree of ideality of packing of particles by analysis of the spectral dependences of the coefficients of coherent transmission and reflection, problems of creating multilayer selective reflectors and bandpass filters, diffusers, and other elements based on alumina, which is used, e.g., in novel display technologies. The results of calculations agree well with the available experimental data for the position of the photonic band gap.