Waveguiding of electromagnetic waves and investigation of negative phase velocity in photonic crystals and metamaterials

Abstract

Electromagnetic wave propagation is characterized in periodic dielectric and metallic structures: Photonic Crystals (PCs) and Metamaterials, respectively. The applications of these structures are demonstrated in the Microwave regime. In the first application, Graded Index (GRIN) PC is used to focus the incoming waves into a small spot. Speaking in terms of PC period a, for an incident beam with Full Width Half Maximum of 9.20a the power of the focusing behavior is quantified by looking at the spot size conversion ratio, which is around 3.9. PCs can act as an efficient input coupler for the PC Waveguide (PCW). The GRIN PC has been experimentally shown to yield a coupling efficiency of 5 dB over the single PCW at 18 GHz. This method can be applied to provide a solution for the input coupling losses between PC structures and other lightwave circuits. PCs can also be used to achieve dual-bandpass and bandstop spatial filtering by proper adjustments of the lattice parameters and the frequency range. For the plane-wave excitation, a wideband spatial filtering is shown to exist due to the specific Fabry-Perot type resonances, which are nearly independent on the angle of incidence. The effect of the finite angular distribution of the Gaussian-beam excitation is also demonstrated. The spatial filtering in the incidence and observation angle domains has been discussed both numerically and experimentally for the non-plane-wave excitations under the light of calculated iso-frequency contours. In addition to bandstop characteristics, the dispersion relation of the PCs can be modified with the proper arrangement, namely by employment of the dimer layer. This surface layer supports the surface waves and serves like a waveguide for the electromagnetic waves. At higher frequencies above the lightline, surface waves radiate into air in the form of backward leaky waves and frequency dependent steering is reported from 0 º to 70º for the outgoing beam. The leaky wave behavior and backward radiation is similar to that is seen in Left-Handed (LH) Metamaterials. Metallic fishnet layers are used to demonstrate negative refractive index (NRI) in conjunction with the left-handed behavior in this class of metamaterial. A wedge structure formed by fishnet layers is used to measure the NRI which was also verified by the retrieval analysis. The limits of homogenization are discussed. The dependence of the LH properties on the fishnet parameters is investigated parametrically. For example, the NRI changes from -1.8 to -1.3 as the interseperation distance of the layers varies from as=λ/10.5 (2mm) to as=λ/4.2 (4mm) at magnetic resonance frequency around 14.3 GHz (ωm). It is also shown that the fishnet layers behave as an LC resonator as well as a TEM waveguide and a 1D transmission line at ωm.