Although lattices of microspheres are considered very interesting forms of photonic crystals both from the fundamental and applied points of view, some fundamental aspects of their behavior are not well understood. Here, we present an experimental study of the frequency variations in the resonant modes of a single layer of spheres with its compactness. Transmission spectra of single layers of dielectric spheres (with a dielectric permittivity of 7.0) were measured for different compactness values, and also simulated by finite-integration time-domain method. The results were gathered in a map of resonant modes of the layer ranging from the compact case to very diluted ones and compared with the resonance values of well known phenomena as the Bragg scattering value and the isolated sphere Mie modes. This comparison allowed establishing different regions dominated by individual effects, being the clearer the tendency to the Bragg scattering limit for low compact layers.
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.
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.
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