The transmission of spectra of different dielectric spheres single layer arrangements has been measured. High dielectric permittivity (epsilon=7) spheres of several millimeters of diameter were used to build the samples whose transmission was measured in the microwave range. The behavior of lattices arranged in square and triangular geometries have been compared in a number of different compactness cases. The same patterns measured have also been calculated by finite-difference time-domain (FDTD) method. Spectra from different geometrical arrangements of the same compactness (measured with the same filling fraction value) are very similar in some cases. Based on the level of similarity we propose three compactness regions. The high compactness region, where the structure effect is important, presents spectra clearly different for the two geometries. In a medium compactness region spectra are almost identical, suggesting a dominant effect of single sphere effects. Finally, in the low compactness region, the spectra from the two geometrical configurations diverge again as the Bragg diffraction values are approached.
Single layers of dielectric spheres are an interesting system to study from the fundamental and applied points of view. In this paper we present a systematic study of the influence of structural disorder on the transmission spectra of arrangements of spheres of different compactness. Glass sphere (ε=7) planes were built and their transmission spectra in the microwave range measured. Transmission behavior of this system is highly tolerant to disorder. Even in completely disordered arrangements, there is a highly rejected band with the dips of the spectrum observable. These results suggest that the collective modes of the sphere planes are formed by weakly coupled Mie modes of the individual spheres, and this coupling is governed by the average distance among the spheres. Disorder tolerance allows simpler fabrication procedures where the position of the spheres does not need to be precisely controlled.
Transmission spectra from single-layers of high dielectric permittivity (ɛ = 7) glass spheres have been measured, in microwave region, for different angular incidences. The same systems have been calculated by Finite-Difference Time-Domain (FDTD) method. The dispersion diagrams of photonic bands in triangular geometries have been obtained for a number of different compactness cases. The experimental and the calculated photonic band structures show a good agreement in all the compactness values studied. They were also compared with the Mie resonances of the isolated spheres. The results indicate that the characteristics of the Mie resonances appear dominant in the photonic band structure as the compactness of the lattice decreases. Dispersion diagrams present several low dispersion photonic bands, independent of incidence-angle, with high Q-values, that could be useful for future applications of the considered structures like filters or solar cells.
Artificial opal-like structures based on spheres and colloidal particles have been fabricated in a controlled way, presenting optical band-gap properties in the optical frequency range. Nonclose packed artificial opals have also been fabricated and studied recently. In order to gain a better understanding of these phenomena, we have studied macroscopic models of nonclose packed fcc lattices using glass spheres (ε=7) of 8 mm diameter, and measuring in the microwave region (from 10 to 30 GHz). The results have shown a Bragg resonance tunable with filling factor of the opal, and a strong rejected band similar, also present in close packed samples, much less affected by compactness. The relation of this high order band with spheres single layer behavior is also discussed.
Several structures of dielectric spheres (glass) have been arranged and the electromagnetic absorption properties of the resulting materials have been measured in the microwave domain. In all cases strong rejected bands are present while keeping nearly transparent for other frequencies. The physical origin of the observed bands is studied by recording the spectra of the materials as they are grown layer by layer. These data show the appearance of a peak attributed to Bragg scattering generated by the spheres layers. Besides, higher order bands are developed over the resonances that are found even in the single layer of spheres. These are caused by a complex interaction of isolated sphere Mie modes and Bragg scattering in planes perpendicular (or nearly) to the incident radiation.
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