Non compact single-layers of dielectric spheres electromagnetc behaviour

Abstract

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.

Transmission spectra changes produced by decreasing compactness of opal-like structures

“…In all spectra, two main features are present, a Bragg resonance, tunable with the topology of the opal, and a higher energy rejected band [17][18][19][20][21] which remains much less affected by the compactness. We present the spectra as the layers were built up in our opals in order to clarify the origin of the high energy rejected band and how can it be related to the physical behavior of two dimensional arrays of spheres.…”

Photonic band effects in three dimensional lattices of macroscopic-sized dielectric spheres derived from microwave transmission spectroscopy

“…This photonic structure has been widely studied both experimentally and theoretically. The monolayer is an ordered arrangement of well defined resonators (Andueza and Sevilla 2007;Kondo et al 2004;Ohtaka and Inoue 1982;Ohtaka 1979;Miyazaki et al 2000;Kurokawa et al 2004;Kondo et al 2002) that present collective resonant states. These resonant states are due to a complex combination of isolated sphere scattering (Mie modes) and effects depending on the structure (Miyazaki et al 2000).…”

“…This system consisting in a two dimensional array of spheres, has been extensively studied showing that the rejected bands correspond to collective resonant modes originated from non evident inter-relations between isolated sphere Mie modes and structure factors due to the interaction among the spheres. Therefore it is possible to establish a relation between the higher order bands and the resonances of two-dimensional arrangements of spheres (Andueza and Sevilla 2007;Kondo et al 2004). …”

Electric-Field Distributions of Dielectric Single Layers of Spheres With Different Compactness

“…The lattice geometry used was triangular, with a parameter notation: Φ for the sphere diameter and Λ to refer to the lattice constant, the separation between two consecutive centers in the unit cell. The dielectric constant of the spheres was selected to be ε = 7, similar to Soda Lime glass used in [22][23][24][25][26]. To indicate the compactness of a particular arrangement, filling factor parameter was used and denoted by f f .…”