Dual Negative Refraction in the Left Hand Materials
W. Aroua1,3, J. Derbali1,3, F. AbdelMalek2,3, and H. Bouchriha3
1National Institute of Applied Science and Technology Tunis Tunisa. Carthage University
BP 676 Cedex 1080 Tunis, Tunisia
2Department of Physics, Jazan University, Kingdom of Saudi Arabia
3Department of Physics Faculty of Sciences of Tunis, Tunisa.
Abstract:
Recently, negative refraction in photonic crystals (PCs) has attracted much attention for their applications in many domains, such as: optical sensing, superlens, superprism…Negative index lenses can be constructed by using negative dielectric materials.
In this work, we use photonic crystal formed by a periodic disposition of air holes, with a radius(r = 0.461a) where a present the triangular lattice constant, in a silicon, as background, having a dielectric constant ε = 11.56. This description is depicted in figure 1. Then a plane wave is lunched at the interface dielectric-air, with a normalized frequency (f = 0.32 a/λ) for versus incident angle θi.
In order to calculate the band structure of the Photonic crystal, the plane wave method is used (Figure2). We see that the TM2 and TM3 bands overlap in the frequency range between 0.22 to 0.34, which may lead to dual refraction at the same electromagnetic wave. Then the study of the light comportment inside the PC has been made by using the Finite Difference Time Domain method (FDTD). The implementation gives a Dual Negative Refraction effect TM2 and TM3, with different intensity, for some angle values (θi = 10° and 15°) as shown in figures (3a), (3b) and for θi = 20°, one of the two mode is completely disappeared (figure 3c). In the end of this study, a nanocavity is added inside the PC we show that the intensities of the two modes became similar (figure 3d).
Reference:
[1] Dual-negative refraction in photonic crystals with hexagonal lattices, G. Y. Dong et al , 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 12119.
[2] Nano-optic label-free biosensors based on photonic crystal platform with negative refraction , W. Aroua, S. Haxha, F. AbdelMalek Optics communication, 2011.
[3]Multi-Refraction with Same Polarisation State in Two Dimensional Triangular Photonic Crystals
G. Dong, et al, Progress In Electromagnetics Research, Vol. 128, 91{103, 2012
it is based on overlapping bands in two-dimensional photonics crystals. This description is depicted in figure 1.
In this study we demonstrate that for one incident wave lunched into this PC can be dispersed into two negative refracted waves. The Finite Difference time Domain method (FDTD) is used to simulate the electromagnetic wave propagation into the left hand material for different incident angle.