Non-Euclidean cloaking for light waves

Non-Euclidean geometry combined with transformation optics has recently led to the proposal of an invisibility cloak that avoids optical singularities and therefore can work, in principle, in a broad band of the spectrum [U. Leonhardt and T. Tyc, Science 323, 110 (2009)]. Such a cloak is perfect in the limit of geometrical optics, but not in wave optics. Here we analyze, both analytically and numerically, full wave propagation in non-Euclidean cloaking. We show that the cloaking device performs remarkably well even in a regime beyond geometrical optics where the device is comparable in size with the wavelength. In particular, the cloak is nearly perfect for a spectrum of frequencies that are related to spherical harmonics. We also show that for increasing wavenumber the device works increasingly better, approaching perfect behavior in the limit of geometrical optics.