Evolution of the electromagnetic modes of a single layer of dielectric spheres with compactness

Abstract

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.

Design of optical filters based on the compactness of 2D-arrays of dielectric spheres

“…In the same way, studies regarding the effect of compacting in the electromagnetic transmission of dielectric spheres monolayers [7]; or the frequency variations in the resonant modes of a single layer of spheres with its compactness [5], or even the absorption properties of dielectric spheres (glass) monolayers in the microwave domain [8]. The behaviour of single layered dielectric spheres arranged in square and triangular geometries was described in [9]; as well as the transmission spectra changes produced by decreasing compactness [10].…”

“…Transmission properties of single layer dielectric spheres are highly dependent on the size and the refractive index of the spheres and on the compactness of the array [5]. The compactness of arrays stands out due to the fact that it allows us to design tunable frequency filters varying the size of the spheres or the distance between them.…”

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

“…For example, TE 11 is the first order from the first TE Mie mode at Φ/λ = 0.353 and TE 12 is the second order from the first TE Mie mode Φ/λ = 0.739. In order to follow the strong dips observed in the transmission spectra for single layers of spheres of different compactness we introduce the "modes map" (Figure 2), a compact representation of the dips frequency position (in the vertical axis in dimensionless units) against compactness (presented as filling factor) [22,24]. Horizontal dashed lines in Figure 2 represent the Mie modes, and the two dashed inclined curves are the first two orders of the Bragg frequency of the structure.…”

“…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 .…”

“…The transmission spectra of single layers of dielectric spheres present significant dips whose position and depth change with layer compactness [22,24]. It is possible to discuss the origin of the photonic bands for an array of dielectric spheres by studying the electric-field intensity distribution.…”