Numerical modelling of photonic crystal based switching devices

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

An Improved 3D Complex-Envelope Four-Stage ADI-FDTD Using The Fundamental Scheme

Three corresponding reference methods are developed. The CE explicit FDTD method is used to solve the problem with a point source and perfect electric conductor (PEC) boundaries. The problem with a point source and absorbing boundary conditions (ABC) is solved by the 3D free-space Green\u27s function in the frequency domain, and then transformed to the time domain using the inverse fast Fourier transform (IFFT). For the problem with a plane wave and ABC, the frequency-domain solution is obtained using the volume integral equations and method of moments (VIE-MOM), and is then transformed into the time-domain solution using the IFFT. Comparison of the numerical results demonstrates the accuracy and computational effectiveness of the 3D CE-4S-FADI-FDTD algorithm

The ADI-FDTD Method for High Accuracy Electrophysics Applications

The Finite-Difference Time-Domain (FDTD) is a dependable method to simulate a wide range of problems from acoustics, to electromagnetics, and to photonics, amongst others. The execution time of an FDTD simulation is inversely proportional to the time-step size. Since the FDTD method is explicit, its time-step size is limited by the well-known Courant-Friedrich-Levy (CFL) stability limit. The CFL stability limit can render the simulation inefficient for very fine structures. The Alternating Direction Implicit FDTD (ADI-FDTD) method has been introduced as an unconditionally stable implicit method. Numerous works have shown that the ADI-FDTD method is stable even when the CFL stability limit is exceeded. Therefore, the ADI-FDTD method can be considered an efficient method for special classes of problems with very fine structures or high gradient fields. Whenever the ADI-FDTD method is used to simulate open-region radiation or scattering problems, the implementation of a mesh-truncation scheme or absorbing boundary condition becomes an integral part of the simulation. These truncation techniques represent, in essence, differential operators that are discretized using a distinct differencing scheme which can potentially affect the stability of the scheme used for the interior region. In this work, we show that the ADI-FDTD method can be rendered unstable when higher-order mesh truncation techniques such as Higdon's Absorbing Boundary Condition (ABC) or Complementary Derivatives Method (COM) are used. When having large field gradients within a limited volume, a non-uniform grid can reduce the computational domain and, therefore, it decreases the computational cost of the FDTD method. However, for high-accuracy problems, different grid sizes increase the truncation error at the boundary of domains having different grid sizes. To address this problem, we introduce the Complementary Derivatives Method (CDM), a second-order accurate interpolation scheme. The CDM theory is discussed and applied to numerical examples employing the FDTD and ADI-FDTD methods

The High-Order Symplectic Finite-Difference Time-Domain Scheme

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Optimized operator-splitting methods in numerical integration of Maxwell's equations

Optimized operator splitting methods for numerical integration of the time domain Maxwell's equations in computational electromagnetics (CEM) are proposed for the first time. The methods are based on splitting the time domain evolution operator of Maxwell's equations into suboperators, and corresponding time coefficients are obtained by reducing the norm of truncation terms to a minimum. The general high-order staggered finite difference is introduced for discretizing the three-dimensional curl operator in the spatial domain. The detail of the schemes and explicit iterated formulas are also included. Furthermore, new high-order Padé approximations are adopted to improve the efficiency of the proposed methods. Theoretical proof of the stability is also included. Numerical results are presented to demonstrate the effectiveness and efficiency of the schemes. It is found that the optimized schemes with coarse discretized grid and large Courant-Friedrichs-Lewy (CFL) number can obtain satisfactory numerical results, which in turn proves to be a promising method, with advantages of high accuracy, low computational resources and facility of large domain and long-time simulation. In addition, due to the generality, our optimized schemes can be extended to other science and engineering areas directly. © 2012 Z. X. Huang et al.published_or_final_versio

Super-resolution from Quantum Metamaterials

Negative refraction and sub-wavelength resolution have been demonstrated with metamaterials throughout the past decade. This thesis introduces a quantum metamaterial, based on quantum mechanical principles, which exhibits negative refraction and sub-wavelength resolution with reduced absorption compared to non-quantum metamaterials. In particular, this thesis introduces a novel method of achieving sub-wavelength resolution using the quantum metamaterial. This method of superresolution does not require a negative permittivity or permeability, as the predecessors require, but is instead based on a dispersion curve with a high elliptical eccentricity. This thesis uses an effective medium approach to calculate the quantum metamaterial’s permittivity, which is then used to model super-resolution and negative refraction. After considerable design, optimisation and epitaxial growths, a GaAs based quantum metamaterial is fabricated into a superlens. A scanning near-field optical microscope is used to measure the sub-wavelength imaging capability of the quantum metamaterial superlens.Open Acces

Implementation of the Finite Difference Time Domain algorithm for the analysis of terahertz waves

The aim of this report is to present results related to the application of the Finite Difference Time Domain (FDTD) method for the study of various devices at terahertz frequencies. The FDTD method has emerged as one of the most widely used numerical analysis methods used for electromagnetic simulations. The FDTD method can be used to solve numerous types of problems ranging from modelling the behaviour of microwave circuits, waveguides, and photonics to simulating terahertz devices and plasmas. In this study the FDTD approach is derived from first principles (finite differences) and explicit equations are shown based on Maxwell's equations. Furthermore, absorbing boundary conditions (ABCs) are discussed for the FDTD method. The algorithm is tested against a range of problems to ensure its validity and accuracy. The FDTD method is then applied for the numerical analysis of a range of devices at terahertz frequencies. The numerical results obtained from the application of the FDTD method to examine a microstrip circuit with filter loading and a Multi-mode Interference (MMI) coupler at terahertz frequencies are discussed in detail. Moreover, the results of the application of the FDTD method for the calculation of the dispersion characteristics of plasmonic waveguides are also presented. Finally, a summary of the work carried out is presented and an outline is given for future research which can be carried out by using the FDTD method for the study of terahertz frequency devices

High Speed Switching in Magnetic Recording Thin-Film Heads

There has always been an increasing demand for high density data storage. However, the increased areal storage densities of hard disk drives require a level of miniturisation of the recording heads where the micromagnetic details and switching mechanisms can no longer be ignored. Furthermore, theoretical and numerical studies on thin-film recording heads tend to separate the micromagnetics from the electromagnetic aspects of the head during switching and hence ignore the lossy nature of head materials. This project was aimed to develop a numerical simulation approach that simultaneously incorporates the fundamental micromagnetic and electromagnetic details of magnetic materials to study the fast switching process in soft magnetic materials in general, and in thin-film inductive writers in particular. The project also was aimed at establishing an impedance measurement system to characterise losses in magnetic recording heads, and to allow comparison with the simulations. This project successfully met all its original objectives. A numerical technique to simulate the dynamic behaviour of magnetic materials and devices has been developed, and applied to study the switching process in thin-film recording heads. Two-dimensional simulations of complete commercial head structures including the coils and pole regions were carried out and parameters such as gap field rise times, gap field distributions, and core inductances, which are important for head designers, were predicted. Moreover, the role of eddy currents delaying the magnetisation switching was elucidated. Furthermore, it was found that the gradient of the recording fields were sharper near the conrner regions of the poles when considering magnetic details. A high precision, high bandwidth impedance measurement system was established to characterise losses in magnetic heads. Fittings of measured core inductances to a proposed equivalent circuit model of the core’s relaxation processes revealed the switching times of heads (of the order 0.1 to 1.0ns)