# Electromagnetically Induced Transparency in All-Dielectric U-Shaped Silicon Metamaterials
## 1 Introduction  
Electromagnetically induced transparency (EIT) as a quantum interference phenomenon has been a research topic in quantum optics in recent years. EIT is a coherent process. It was initially demonstrated in a three-level atomic system, where the resonant coupling between the dipole-allowed transition of the ground state (10\(>\)) to an upper energy level (11\(>\)) and the transition of the energy level (11\(>\)) to a metastable level (12\(>\)) by two coherent laser pump leads to a destructive interference between two transition pathways, namely, 10\(>\rightarrow\) 11\(>\) and 10\(>\rightarrow\) 11\(>\rightarrow\) 12\(>\rightarrow\) 11\(>\)[1]. This results in a narrow transmission window (NTW). The NTW allows that the light can propagate freely through a medium that is initially optically opaque but becomes transparent due to the light-matter interactions. This phenomenon contributes to the understanding of the optical properties and processes of media [2; 3]. It has been proved that the properties of EIT, especially high transmission and strong dispersion, are crucial for a number of potential applications such as optical sensing [4; 5], slow-light devices [6; 7; 8; 9; 10], and storage of quantum information [11; 12].  
The implementation of EIT in atomic systems requires stringent experimental conditions including cryogenic temperature and high-intensity laser [13], so the analogue of EIT based on metamaterials has attracted much attention in the last several years, which is not limited by the above experimental conditions. Metamaterials are artificially engineered media with unit cells smaller than the operating wavelength [14; 15] and can be used to achieve EIT-like phenomenon at room temperature. The previouswork about classical analogue of EIT mainly focused on metal plasmonic metamaterials, which rely on a Fano-type interference between a broadband bright mode resonator and a narrowband dark mode resonator [16; 17; 18]. The bright mode can couple to the incident light whereas the dark mode can only couple to the bright mode. The near-field coupling between them can produce a destructive interference and result in a narrow transmission window, which is analogous to the EIT effect. However, it has been indicated that a large non-radiative loss caused by ohmic damping is an important disadvantage for metal plasmonic Fano-resonant systems [19; 20], which restricts the achievement of high transmittance and quality-factor (Q-factor) of the EIT-like effect. An effective solution to the issue of material loss is to appeal the high refractive index silicon-based dielectric structures, which can reach a higher Q-factor and minimal absorption loss [21; 22]. Recently, several geometries of Si dielectric metamaterials, such as rectangular bar-ring resonator [23], rectangular bar-cylinder resonator [24; 25], asymmetric Si nanobar pairs [26], straight and bent Si nanorod dimer [27], cross rectangular bars [28], and E-shaped Si array [29], have been proposed to achieve low-loss EIT with high Q-factor, and have shown potential applications from biosensors to low-loss optical modulation devices.  
In this paper, we design a new U-shaped Si-based structure consisting of two vertical nanoscale bars and one horizontal nanoscale bar, and theoretically investigate the characteristic EIT-like response based on finite-difference time-domain (FDTD) method [30]. The achievement of a high Q-factor of 130 and a transmittance of 92% depends largely on coherent interaction among the bar resonators. In addition, the sensitivity of the Si metamaterial on the change of refractive index as well as slow-light effect is also surveyed. The proposed Si-based metamaterials with a simple shape exhibit higher Q-factor and refractive index sensitivity than many Fano-resonant and EIT-like plasmonic metal nanostructures, and render the possibility of using such metamaterials for the application in bio/chemical sensing, enhancing optical radiation, optical switching, and low-loss slow-light devices.