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.

No abstract

Light confinement induced by resonant states in aperiodic photonic structures are interesting for many applications. A particular case of these resonances can be found in 2D quasi-crystalline arrangements of dielectric cylinders. These systems present a rather isotropic band gap as well as isolated in-gap photonic states (as a result of spatially localized resonances). These states are built by high symmetry polygonal clusters that can be regarded as photonic molecules. In this paper we study the transmission properties of a slab of glass cylinders arranged in approximants of decagonal quasi-crystalline structure. In particular, we investigate the influence of the slab width in the transmission contrast between the states and the gap. The study is both experimental and numerical in the microwave regime. We find that the best transmission contrast is found for a width of around 3 times the radiation wavelength. The transmission at the band gap region is mediated by the resonances of the photonic molecules. If the samples are thin enough they become transparent except around a resonance of the photonic molecule which reflects the incoming light. In this case the behavior is reminiscent of an "absorbing" molecule.

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 layer of dielectric spheres is a recognized model for the basic understanding of some aspects of photonic crystals. Here we present a systematic study of the effect of compacting in the electromagnetic transmission of dielectric spheres monolayers. Experiments were performed in the microwave domain (from 10 GHz to 30 GHz) with glass spheres of high dielectric permittivity ε = 7. Time Domain Finite Integration (TDFI) calculations were also accomplished. Experimental data and TDFI calculations agreement provides a double check on the lack of experimental artefacts and the correctness of simulation settings. Following the evolution of the lower frequency spectral peak with layer compacting ratio, we established three different electromagnetic regimes. For the higher and lower compacting ratio regimes, the peak frequency matches isolated sphere pure resonances, while for intermediate values of compacting, some transition between these two modes takes place. Extending the study to the complete frequency range, we find that sphere single layers transmission spectra become closer to isolated sphere scattering calculations as the compacting ratio is decreased. However as the agreement remains imperfect even for our lowest compacting measurable layer, we conclude that some structure contribution cannot be neglected even for low compact layers.