New theoretical tools for metamaterial design

想象一下，我们可以控制光到我们可以控制电子的程度。现代计算机的发展要归功于我们控制电子在电路中流动的能力，以及硬盘中电子的磁性。如果我们对光的行为有同样的影响，那么这可能会产生类似的技术革命;许多日常光学设备可以得到改进-投影仪，光纤电缆，望远镜，显微镜，医学成像单元和DVD播放器，都受到我们对光的控制的限制。问题是，虽然电子与外部场相互作用，但在正常情况下光子不会。这项研究的目的是通过改进用于设计一类新的光学材料（称为超材料）的工具来增加我们对光的控制。超材料具有自然存在的介质中没有的光学特性。制造超材料涉及到制造一种复杂的复合结构，由绝缘和导电材料制成。这项技术已经允许建造一个可以克服衍射极限的透镜，甚至是一个隐形斗篷：到目前为止，这两种设备都被证明可以在频谱的微波区域工作。超材料的这种“复杂的复合结构”是如何确定的？令人惊讶的答案是，就光而言，超材料所占据的空间区域通常表现得就像自由空间一样，但对可以被视为直线的定义进行了修改。光通过超材料器件的弯曲路径可以被认为在形式上等同于非笛卡尔坐标系的弯曲轴，并且这种修改的几何形状与材料的物理特性直接相关。找到一种几何形状，它具有给定光学函数的“正确直线”，然后就可以计算出超材料所需的“复杂复合结构”：这个过程就是“变换光学”理论。这项研究的目的是追求最初的目标-"控制光，就像我们控制电子一样“-通过扩大变换光学的范围，使之包括新的物理学和新的几何学。我们能制造的转换光学器件越强大，超材料设计的范围就越大，我们对光的行为的影响就越大。首先，我们引入新的几何：（1）目前，在变换光学中考虑的光学材料仅等价于相对于自由空间拉伸或弯曲的空间。虽然这本身是一个强大的理论，但它不考虑另一个几何性质：挠率。Torsion表示空间扭曲的方式。该项目将推广变换光学，包括扭转空间。这将在超材料设计中增加手性。当矢量沿沿着坐标轴移动时，等效于扭曲矢量的空间的超材料将被期望在光移动通过材料时扭曲光的矢量属性。第二步是引入新的物理学;（2）变换光学是光与物质相互作用的经典理论，它将光与物质相互作用的问题简化为几何问题。然而，它包含的近似值非常少。因此，我们可能想知道，当量子力学变得重要时，这幅图在多大程度上是有用的。我们能用转换光学设计单光子超材料器件吗？该项目将使用一个近似的量子力学模型与量子光场相互作用的超材料，并试图将变换光学的过程扩展到量子光学中新一代器件的设计。

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.