In the field of transformation optics, metamaterials mimic the effect of
coordinate transformations on electromagnetic waves, creating the illusion that
the waves are propagating through a virtual space. Transforming space by
appropriately designed materials makes devices possible that have been deemed
impossible. In particular, transformation optics has led to the demonstration
of invisibility cloaking for microwaves, surface plasmons and infrared light.
Here we report the achievement of another "impossible task". We implement, for
microwaves, a device that would normally require a dielectric singularity, an
infinity in the refractive index. We transmute a singularity in virtual space
into a mere topological defect in a real metamaterial. In particular, we
demonstrate an omnidirectional retroreflector, a device for faithfully
reflecting images and for creating high visibility, from all directions. Our
method is robust, potentially broadband and similar techniques could be applied
for visible light