标题： 一种微分几何方法研究光的非对称传输 显示英文标题

标题： A differential geometry approach to asymmetric transmission of light

摘要： 在过去十年中，微分几何技术已在引力物理中无处不在，并在光学领域找到了自己的位置。通过如今被称为“变换光学”的技术，它已被成功用于光学超材料的设计。 然而，这种方法仅适用于一类特定的超材料，即阻抗匹配材料，也就是说，材料的介电常数与其磁导率相等。在这种情况下，材料可以用时空度规来描述。 在本文中，我们将把变换光学的几何方法推广到材料未达到阻抗匹配的情况。在这种情况下，材料——更确切地说，其构成张量——不能仅用度规来描述。我们引入了第二个张量，具有Weyl张量的局部对称性，称为“$W$-张量”。 在几何光学近似下，我们展示了$W$-张量的性质与材料的非对称传输之间的关系。我们将这一特性应用于设计一组特别有趣的非对称材料。 这些材料当光线以某一方向接近时表现出双折射性，但当光线以相反方向且具有适当偏振（或在某些情况下，与偏振无关）时，它们的行为就像真空一样。 显示英文摘要

摘要： In the last ten years, the technology of differential geometry, ubiquitous in gravitational physics, has found its place in the field of optics. It has been successfully used in the design of optical metamaterials, through a technique now known as "transformation optics". This method, however, only applies for the particular class of metamaterials known as impedance matched, that is, materials whose electric permittivity is equal to their magnetic permeability. In that case, the material may be described by a spacetime metric. In the present work we will introduce a generalization of the geometric methods of transformation optics to situations in which the material is not impedance matched. In such situation, the material -or more precisely, its constitutive tensor- will not be described by a metric only. We bring in a second tensor, with the local symmetries of the Weyl tensor, the "$W$-tensor". In the geometric optics approximation we show how the properties of the $W$-tensor are related to the asymmetric transmission of the material. We apply this feature into the design of a particularly interesting set of asymmetric materials. These materials are birefringent when light rays approach the material in a given direction, but behave just like vacuum when the rays have the opposite direction with the appropriate polarization (or, in some cases, independently of the polarization).