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 can, therefore, work, in principle, in a broadband of the spectrum [U. Leonhardt and T. Tyc, Science, vol. 323, pp. 110-112, 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.