INVISIBILITY CLOAKING AND TRANSFORMATION OPTICS FOR THREE DIMENSIONAL MANIFOLDS AND APPLICATIONS IN COSMOLOGY

We consider how transformation optics and invisibility cloaking can be used to construct models in subsets 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. Our model can be used in two ways. First, the model makes it possible to do mathematical analysis on a compact 3-manifold M by smoothly embedding the set M backslash L, where L is a finite union of closed curves, to an open subset of R-3. Second, the model 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 (R+ x M, -dt(2) + g), where (M, g) is a closed, orientable, C-infinity-smooth, 3-dimensional Riemannian manifold. Thus the obtained device could be used to simulate cosmological models using metamaterial devices.