Temperature-Dependent Behavior of the Dirac like Point in the Two Dimensional Photonic Crystal-Based ZRIM in the Cryogenic Region

Abstract

A zero refractive index material (ZRIM) structure containing a two dimensional dielectric photonic crystal in the cryogenic temperature region has been analyzed to investigate the Dirac-like point temperature sensitive behavior. The main effect of temperature variation is deviation of the material refractive index; in this work, silicon is utilized which demonstrates appropriate behavior in THz range. Experimentally reported complex optical index of a n-type Silicon slab with moderate doping for the ZRIM unit cell are considered. Photonic band structure of a cylindrical squared lattice of silicon rods is numerically computed for multiple values of silicon refractive index in accordance with temperature variation. For such deviations, the Dirac point of the ZRIM structure undergoes a slight change in operational frequency. This change is accompanied by a slight deviation of Bloch's wave-vector from center of Brillouin zone (κ = Γ). We have calculated photonic band gap for the assumed structure sweeping the Silicon refractive index and shown that a minimum band gap exists in accordance with a certain temperature. We have also obtained and analyzed the effective refractive index of the photonic crystal unit cell as an auxiliary tool to demonstrate that these structures could satisfy the zero-refraction phenomenon. Variations in operational frequency of the Dirac-point and photonic band gap values are also verified in effective refractive index diagrams. In line with some metamaterial-based applications, the final step includes a comparison made between a single dielectric slab and a row array of the same material in a periodic structure of rods. This simulation is conducted for a more realistic situation while considering the energy transmission coefficient. Consequently, at the frequency in which the minimum band gap was achieved, the extracted transmission coefficient is studied versus the Silicon refractive index (temperature).