Numerical modelling of photonic crystal based switching devices

Abstract

In the last few years research has identified Photonic Crystals (PhCs) as promising material that exhibits strong capability of controlling light propagation in a manner not previously possible with conventional optical devices. PhCs, otherwise known as Photonic Bandgap (PBG) material, have one or more frequency bands in which no electromagnetic wave is allowed to propagate inside the PhC. Creating defects into such a periodic structure makes it possible to manipulate the flow of selected light waves within the PhC devices outperforming conventional optical devices. As the fabrication of PhC devices needs a high degree of precision, we have to rely on accurate numerical modelling to characterise these devices. There are several numerical modelling techniques proposed in literature for the purpose of simulating optical devices. Such techniques include the Finite Difference Time Domain (FDTD), the Finite Volume Time Domain (FVTD), and the Multi-Resolution Time Domain (MRTD), and the Finite Element (FE) method among many others. Such numerical techniques vary in their advantages, disadvantages, and trade-offs. Generally, with lower complexity comes lower accuracy, while higher accuracy demands more complexity and resources. The Complex Envelope Alternating Direction Implicit Finite Difference Time Domain (CE-ADI-FDTD) method was further developed and used throughout this thesis as the main numerical modelling technique. The truncating layers used to surround the computational domain were Uniaxial Perfectly Matched Layers (UPML). This thesis also presents a new and robust kind of the UPML by presenting an accurate physical model of discretisation error. iv This thesis has focused on enhancing and developing the performance of PhC devices in order to improve their output. An improved and new design of PhC based Multiplexer/Demultiplexer (MUX/DEMUX) devices is presented. This is achieved using careful geometrical design of microcavities with respect to the coupling length of the propagating wave. The nature of the design means that a microcavity embedded between two waveguides selects a particular wavelength to couple from one waveguide into the adjacent waveguide showing high selectivity. Also, the Terahertz (THz) frequency gap, which suffers from a lack of switching devices, has been thoroughly investigated for the purpose of designing and simulating potential PhC based switching devices that operate in the THz region. The THz PhC based switching devices presented in this thesis are newly designed to function according to the variation of the resonant frequency of a ring resonator embedded between two parallel waveguides. The holes of the structures are filled with polyaniline electrorheological fluids that cause the refractive index of the holes to vary with applied external electric field. Significant improvements on the power efficiency and wavelength directionality have been achieved by introducing defects into the system.