  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.
