Transformation Optics for the Modelling of Waves in a Universe with Nontrivial Topology
| Autor: | Balehowsky, Tracey, Lassas, Matti, Pankka, Pekka, Sirviö, Ville |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 42 pages. Added 3 figures. Layout of chapter 3 changed for clarity. More motivation and a new subsection on cloaking and black holes added to the introduction. Additional references added. Typos fixed |
| Databáze: | arXiv |
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