New theoretical tools for metamaterial design

Imagine that we could control light to the extent that we can control electrons. The modern computer was developed thanks to our ability to control the flow of electrons through a circuit, and the magnetism of electrons in a hard disk. If we had the same influence over the behaviour of light then this could produce a similar revolution in technology; many everyday optical devices could be improved - projectors, fiber optic cabling, telescopes, microscopes, medical imaging units, and DVD players, are all limited by our control over light. The problem is that while electrons interact with external fields and each other, in normal circumstances photons do not. It is the purpose of this research to increase our control over light through improving the tools used to design a new class of optical materials known as metamaterials.Metamaterials have optical properties that are not found in naturally occurring media. To make a metamaterial involves the manufacture of an intricate composite structure, made out of insulating and conducting materials. This technology has allowed for the construction of a lens that can overcome the diffraction limit, and even an invisibility cloak: so far both of these devices have been shown to work in the microwave region of the spectrum. How is this `intricate composite structure' of a metamaterial determined? The surprising answer is that often, as far as light is concerned, the region of space occupied by a metamaterial behaves as if it were free space, but with a modified definition of what can be considered as a straight line . The curved path the light follows through a metamaterial device can be considered to be formally equivalent to the curved axes of a non-Cartesian system of co-ordinates, and this modified geometry is immediately related to the physical properties of the material. Find a geometry that has the `right straight lines' for a given optical function, and the required `intricate composite structure' of the metamaterial can then be computed: this procedure is the theory of `transformation optics'. The aim of this research is to pursue the initial goal - `to control light as well as we can control electrons' - through extending the reach of transformation optics to include new physics and new geometry. The more powerful we can make transformation optics, the greater the scope we have for metamaterial design, and the greater influence we can have over the behaviour of light. First we introduce new geometry;(1) At present, the optical materials considered within transformation optics are only equivalent to spaces that are stretched or curved relative to free space. Although this is a powerful theory in itself, it does not allow for another geometric property; torsion. Torsion represents the way a space is twisted. The project will generalise transformation optics to include spaces with torsion. This will add chirality into metamaterial design. A metamaterial that is equivalent to a space that twists vectors as they move along a co-ordinate axis would be expected to twist the vector properties of light as it moves through the material. Therefore adding torsion into transformation optics should allow for the design of new materials that manipulate the polarization of light.The second step is to introduce new physics;(2) Transformation optics is a classical theory of light interacting with matter, that reduces the problem to one of geometry. However, it contains remarkably few approximations. So we might therefore wonder the extent to which this picture is useful when quantum mechanics becomes important. Can we use transformation optics to design single photon metamaterial devices? The project will use an approximate quantum mechanical model for a metamaterial interacting with a quantized light field, and attempt to extend the procedure of transformation optics to the design of a new generation of devices in quantum optics.

The non-academic beneficiaries of this work can be summarized as follows; (1) Photonics industry: Metamaterials are being used to create useful optical devices that are currently on the market (e.g. photonic crystal fibers). As the market grows it is expected that a much more general class of metamaterial based devices will be produced. The generalization of transformation optics obtained from this project will be a useful tool for designing devices that are sensitive to polarization. (2) Telecommunications infrastructure: With more efficient and effective optical components, the fiber optics based telecommunications infrastructure of the UK will be made more efficient. (3) Wider public: A more efficient communications network will mean that the cost of communication can be reduced, and that the energy required per unit of bandwidth will be lowered. Cheaper communication will benefit charities, businesses, government, and individuals, thus increasing the prosperity of the UK. The first substantial commercial applications of this project are most likely to be in the telecommunications industry. These applications would be expected to come after the diversification of the metamaterials market, which according to the report summarized in the Impact plan, is expected to be in around ten years. The communication of the project deliverables to the beneficiaries will be increased via, (1) Conferences & one day meetings with the involvement of knowledge transfer networks: Conferences, such as Photon10 (Photonics Knowledge Transfer Network), Metamaterials congress (IET Photonics Network), and one day meetings organised by the IoP groups detailed in the Dissemination & exploitation section conferences. (2) Publication: All pre-prints of academic publications will be made available to download. (3) Web material: A website will be produced that summarizes the research and makes the numerical work of the project available to use. I have experience as a first author, in presenting my work to a general audience, and in producing web pages. To increase the future impact of my work within industry I will also be, (4) Attending the industrial-academic interface postdoctoral workshops and training at St.Andrews.