## 1 Introduction  
With the rapid development of information technology, the requirement of components tends to be miniaturized and integrated. But, due to the limitation of the diffraction limit, the traditional optoelectronic components in nano-size can not get effective photoelectric information dissemination and utilization. Then, the nanophotonics become a hot research field. For example, the resonant nanostructures [1] have a large scattering cross-section [2], and they can concentrate, redirect, and manipulate light [3; 4] at the surface of many optical devices [5], such as solar cells [6; 7], sensors, etc. They can also optimize the coupling and capture of light. In recent decades, some considerable researches have focused on the design, construction, and synthesis of different plasma nanostructures [8; 9], such as nanorods, nanoshells, nanocyclic rings, nanoscale [10], nanowires, and nano crescents. As a kind of nano-scale optical control method, plasma resonance [11] of metal nanostructures has attracted much attention in optical, biomedical, and nonlinear materials.  
However, the metal nanostructure has a small dielectric constant and a large non-radiation loss (such as ohmic loss) [12; 13; 14]. So, its related application performance is limited to further develop, especially in visible region. In general, the intrinsic dielectric constant of the dielectric material is large, and the non-radiation loss is very low. So, dielectric material with a high refractive index can effectively suppress the radiation loss and non-radiation loss to construct the nanostructure with low absorption loss [15]. Dielectric nanostructured materials with a high refractive index have recently risen to prominence for the control of light [16]. They give a novel way to directly engineer electromagnetic field response at optical frequencies. Specially, these high refractive index nanoparticles can be designed to a new building block for scalable, tunable, and low-loss metamaterials [17]. A single dielectric spherical nanoparticle exhibited both magnetic dipole and magnetic dipole resonances. Unlike plasmonic nanoparticles, the magnetic resonance, demonstrated in silicon [18] and gallium arsenide nanoparticles [19], results from circular displacement currents that are driven by an incident electric field. However, most researches have concentrated upon single nanoparticle or periodic structure [3; 8; 9; 13]. Recently, nanodimer nanoparticles can offer further tunability and engineering capabilities for electric dipole or magnetic dipole resonances [20; 21]. Also, it can reveal the physics of hotspots and near-field distributions, which is important for nanoparticles with Fano-type resonances and strong interparticle interactions [17; 20; 21]. Dimer nanoparticles with high refractive index materials have recently been studied in numerical calculations [22; 23] and in experiments at microwave frequencies [24; 25]. Dielectric nanoparticles can reduce quenching and provide higher quantum efficiency of localized emitters, which is important for engineering emission at the subwavelength scale [22]. Thus, dielectric nanoparticles can be frequently applied in efficient magnetic scatterers [26], with possible application in metamaterials [27], metasurfaces [28], nanoantennas [29], and optical on-chip integration devices exhibiting unusual scattering properties [30].  
In this paper, we systematically studied the resonant scattering and coupling properties of multiple dielectric nanocylinders in visible spectrum. The resonant performances of nanostructures composed of one, two, or three silicon nanocylinders are demonstrated numerically by finite difference time domain method [31]. We also studied the transmission characteristics and resonance of the periodic arrays of the nanocylinder structure. By adjusting the geometric parameters of silicon nanocylinder arrays, the electric dipole and magnetic dipole resonances can be selectively enhanced or suppressed for different applications.