Transmission and Refraction of Electromagnetic Waves in Transmission Lines,Photonic Crystals and Left Handed Materials: Localized States in the Photonic Gap

摘要

Using multi scale modeling, the Maxwell's equations are solved for different electromagnetic systems including transmission filters, photonic crystals and left-handed materials (metamaterials). The transmitted electromagnetic power is calculated relative to the input power for Transverse Electric (TE) and Transverse Magnetic (TM) modes. The program inputs include the boundary conditions of the system and the index of refraction of the materials involved. The dielectric constant and the permittivity of the materials involved are given as a function of wavelength or as discreet values. The systems studied include transmission filters and photonic crystals configured as pillars of Gas or Si in air or pillars of air (holes) in GaAs or Si. For several of the systems modeled, the transmitted spectrum of photonic crystals shows clearly photonic gaps for various ranges of wavelengths. When disorder is introduced in the photonic crystal localized states appear in the gap which eventually lead to the emergence of additional gaps or the disappearance of the gaps in case of strong disorder. In case of metamaterials, the refraction of the E&M waves from a wedge of an orthogonal prism is clearly demonstrated in agreement with the Snefl's law for negative index of refraction materials. The focusing of the refracted beam from the metamaterial is demonstrated and is compared to the equivalent behavior of a refracted beam by a normal material for the same geometric setting. The above result demonstrates the possibility of construction of a "perfect lens". For certain combinations of the dielectric constant and permittivity of the left handed material, the electromagnetic wave is totally dissipated rendering the metamaterial impenetrable to the electromagnetic radiation. In particular geometries where a metamaterial is cloaking a region of a normal material a beam of electromagnetic wave is rerouted around the normal material, thus concealing the normal material and rendering it invisible to electromagnetic radiation.