论文标题
用于与非平凡拓扑的宇宙中波的建模的转换光学器件
Transformation Optics for the Modelling of Waves in a Universe with Nontrivial Topology
论文作者
论文摘要
我们考虑如何使用转换光学和隐形套制造在子集中构建模型$ \ mathbb {r}^3 $带有不同度量的模型，其中给定的角度波数$ k $的时间谐波波在某些封闭的定向歧管中等同于波浪。原则上可以使用由超材料构建的设备实际实现所获得的模型。特别是，helmholtz源到解决方案操作员给出的超材料设备中的测量值等于$（\ Mathbb {r} _ +\ times m，-dt^2 +g）$（m，g）$（m，g）$（m，g）$（m，g）$（m，g）$（m，g）$（m，g）是$（m，g），$ c $ c $ c \ c \ c \ c^forty，里曼尼亚人的歧管。因此，获得的结构可用于使用超材料设备模拟宇宙学模型。
We consider how transformation optics and invisibility cloaking can be used to construct models in subsets $\mathbb{R}^3$ with a varying metric, where the time-harmonic waves for a given angular wavenumber $k$, are equivalent to the waves in some closed orientable manifold. The obtained models could in principle be physically implemented using a device built from metamaterials. In particular the measurements in the metamaterial device given by the Helmholtz source-to-solution operator are equivalent to Helmholtz source-to-solution measurements in a universe given by $(\mathbb{R}_+\times M, -dt^2 +g)$, where $(M,g)$ is a closed, orientable, $C^\infty$-smooth, 3-dimensional Riemannian manifold. Thus the obtained construction could be used to simulate cosmological models using metamaterial devices.
