Non compact single-layers of dielectric spheres electromagnetc behaviour

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 epsilon = 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.