Conformal Singularities and Topological Defects from Inverse Transformation Optics

The conventional approach in transformation optics (TO) starts with a virtual space and determines a complicated material profile in physical space to achieve unconventional phenomena, such as invisibility cloaks. We demonstrate that complicated materials can be effectively fabricated by virtual space based on the reversed process of TO in two dimensions. We first show that a conformal singularity of a refractive-index profile, with either zero or infinity resulting from a power conformal mapping w=zα, is equivalent to a topological defect with positive charge or negative charge. The splitting effect and illusion effect are induced by the conformal singularities and related to the two-dimensional topological defects. Based on the equivalence, we fabricate a device of such a topological defect with a positive charge in experiments. Moreover, we observe its related light-bending functionality with laser beams. It has potential important applications in designing on-chip optical devices.