The goal of the research reported in this thesis is to establish the feasibility of a novel optical architecture for an optical route & select circuit switch suitable for implementation as a photonic integrated circuit. The proposed architecture combines Optical Phased Array (OPA) switch elements implemented as multimode interference coupler based Generalised Mach-Zehnder Interferometers (GMZI) with a planar Lüneburg lens-based optical transpose interconnection network implemented using graded metamaterial waveguide slabs. The proposed switch is transparent to signal format and, in principle, can have zero excess insertion loss and scale to large port counts. These switches will enable the low-energy consumption high capacity communications network infrastructure needed to provide environmentally-friendly broadband access to all. The thesis first explains the importance of switch structures in optical communications networks and the difficulties of scaling to a large number of switch ports. The thesis then introduces the Talbot effect, i.e. the self-imaging of periodic field distributions in free space. It elaborates on a new approach to finding the phase relations between pairs of Talbot image planes at carefully selected positions. The free space Talbot effect is mapped to the waveguide Talbot effect which is fundamental to the operation of multimode interference couplers (MMI). Knowledge of the phase relation between the MMI ports is necessary to achieve correct operation of the GMZI OPA switch elements. An outline of the design procedures is given that can be applied to optimise the performance of MMI couplers and, as a consequence, the GMZI OPA switch elements. The Lüneburg Optical Transpose Interconnection System (LOTIS) is introduced as a potential solution to the problem of excessive insertion loss and cross-talk caused by the large number of crossovers in a switch fabric. Finally, the thesis explains how a Lüneburg lens may be implemented in a graded ‘metamaterial’, i.e. a composite material consisting of ‘atoms’ arranged on a regular lattice suspended in a host by nano-structuring of silicon waveguide slabs using a single etch-step. Furthermore, the propagation of light in graded almost-periodic structures is discussed. Detailed consideration is given to the calibration of the local homogenised effective index; in terms of the local parameters of the metamaterial microstructure in the plane and the corrections necessary to accommodate slab waveguide confinement in the normal to the plane. The concept and designs were verified by FDTD simulation. A 4×4 LOTIS structure showed correct routing of light with a low insertion loss of -0.25 dB and crosstalk of -24.12 dB. An -0.45 dB excess loss for 2D analysis and an -0.83 dB insertion excess loss for 3D analysis of two side by side metamaterial Lüneburg lenses with diameter of 15 μm was measured, which suggests that the metamaterial implementation produces minimal additional impairments to the switch.

The goal of the research reported in this thesis is to establish the feasibility of a novel optical architecture for an optical route & select circuit switch suitable for implementation as a photonic integrated circuit. The proposed architecture combines Optical Phased Array (OPA) switch elements implemented as multimode interference coupler based Generalised Mach-Zehnder Interferometers (GMZI) with a planar Lüneburg lens-based optical transpose interconnection network implemented using graded metamaterial waveguide slabs. The proposed switch is transparent to signal format and, in principle, can have zero excess insertion loss and scale to large port counts. These switches will enable the low-energy consumption high capacity communications network infrastructure needed to provide environmentally-friendly broadband access to all. The thesis first explains the importance of switch structures in optical communications networks and the difficulties of scaling to a large number of switch ports. The thesis then introduces the Talbot effect, i.e. the self-imaging of periodic field distributions in free space. It elaborates on a new approach to finding the phase relations between pairs of Talbot image planes at carefully selected positions. The free space Talbot effect is mapped to the waveguide Talbot effect which is fundamental to the operation of multimode interference couplers (MMI). Knowledge of the phase relation between the MMI ports is necessary to achieve correct operation of the GMZI OPA switch elements. An outline of the design procedures is given that can be applied to optimise the performance of MMI couplers and, as a consequence, the GMZI OPA switch elements. The Lüneburg Optical Transpose Interconnection System (LOTIS) is introduced as a potential solution to the problem of excessive insertion loss and cross-talk caused by the large number of crossovers in a switch fabric. Finally, the thesis explains how a Lüneburg lens may be implemented in a graded ‘metamaterial’, i.e. a composite material consisting of ‘atoms’ arranged on a regular lattice suspended in a host by nano-structuring of silicon waveguide slabs using a single etch-step. Furthermore, the propagation of light in graded almost-periodic structures is discussed. Detailed consideration is given to the calibration of the local homogenised effective index; in terms of the local parameters of the metamaterial microstructure in the plane and the corrections necessary to accommodate slab waveguide confinement in the normal to the plane. The concept and designs were verified by FDTD simulation. A 4×4 LOTIS structure showed correct routing of light with a low insertion loss of -0.25 dB and crosstalk of -24.12 dB. An -0.45 dB excess loss for 2D analysis and an -0.83 dB insertion excess loss for 3D analysis of two side by side metamaterial Lüneburg lenses with diameter of 15 μm was measured, which suggests that the metamaterial implementation produces minimal additional impairments to the switch.

The widespread adoption of photonic circuits requires the economics of volume manufacturing offered by integration technology. A Complementary Metal-Oxide Semiconductor compatible silicon material platform is particularly attractive because it leverages the huge investment that has been made in silicon electronics and its high index contrast enables tight confinement of light which decreases component footprint and energy consumption. Nevertheless, there remain challenges to the development of photonic integrated circuits. Although the density of integration is advancing steady and the integration of the principal components – waveguides, optical sources and amplifiers, modulators, and photodetectors – have all been demonstrated, the integration density is low and the device library far from complete. The integration density is low primarily because of the difficulty of confining light in structures small compared to the wavelength which measured in micrometers. The device library is incomplete because of the immaturity of hybridisation on silicon of other materials required by active devices such as III-V semiconductor alloys and ferroelectric oxides and the difficulty of controlling the coupling of light between disparate material platforms. Metamaterials are nanocomposite materials which have optical properties not readily found in Nature that are defined as much by their geometry as their constituent materials. This offers the prospect of the engineering of materials to achieve integrated components with enhanced functionality. Metamaterials are a class of photonic crystals includes subwavelength grating waveguides, which have already provided breakthroughs in component performance yet require a simpler fabrication process compatible with current minimum feature size limitations. The research reported in this PhD thesis advances our understanding of the structure-property relations of key planar light circuit components and the metamaterial engineering of these properties. The analysis and simulation of components featuring structures that are only just subwavelength is complicated and consumes large computer resources especially when a three dimensional analysis of components structured over a scale larger than the wavelength is desired. This obstructs the iterative design-simulate cycle. An abstraction is required that summarises the properties of the metamaterial pertinent to the larger scale while neglecting the microscopic detail. That abstraction is known as homogenisation. It is possible to extend homogenisation from the long-wavelength limit up to the Bragg resonance (band edge). It is found that a metamaterial waveguide is accurately modeled as a continuous medium waveguide provided proper account is taken of the emergent properties of the homogenised metamaterial. A homogenised subwavelength grating waveguide structure behaves as a strongly anisotropic and spatially dispersive material with a c-axis normal to the layers of a one dimensional multi-layer structure (Kronig-Penney) or along the axis of uniformity for a two dimensional photonic crystal in three dimensional structure. Issues with boundary effects in the near Bragg resonance subwavelength are avoided either by ensuring the averaging is over an extensive path parallel to boundary or the sharp boundary is removed by graded structures. A procedure is described that enables the local homogenised index of a graded structure to be determined. These finding are confirmed by simulations and experiments on test circuits composed of Mach-Zehnder interferometers and individual components composed of regular nanostructured waveguide segments with different lengths and widths; and graded adiabatic waveguide tapers. The test chip included Lüneburg micro-lenses, which have application to Fourier optics on a chip. The measured loss of each lens is 0.72 dB. Photonic integrated circuits featuring a network of waveguides, modulators and couplers are important to applications in RF photonics, optical communications and quantum optics. Modal phase error is one of the significant limitations to the scaling of multimode interference coupler port dimension. Multimode interference couplers rely on the Talbot effect and offer the best in-class performance. Anisotropy helps reduce the Talbot length but temporal and spatial dispersion is necessary to control the modal phase error and wavelength dependence of the Talbot length. The Talbot effect in a Kronig-Penny metamaterial is analysed. It is shown that the metamaterial may be engineered to provide a close approximation to the parabolic dispersion relation required by the Talbot effect for perfect imaging. These findings are then applied to the multimode region and access waveguide tapers of a multi-slotted waveguide multimode interference coupler with slots either in the transverse direction or longitudinal direction. A novel polarisation beam splitter exploiting the anisotropy provided by a longitudinally slotted structure is demonstrated by simulation. The thesis describes the design, verification by simulation and layout of a photonic integrated circuit containing metamaterial waveguide test structures. The test and measurement of the fabricated chip and the analysis of the data is described in detail. The experimental results show good agreement with the theory, with the expected errors due to fabrication process limitations. From the Scanning Electron Microscope images and the measurements, it is clear that at the boundary of the minimum feature size limit, the error increases but still the devices can function.