Mitigating optical singularities in coordinate-based metamaterial waveguides

Transformation optics has revolutionized our approach to material design in several scientific disciplines by determining the material properties that implement the desired effects of a coordinate transformation. Unfortunately, the performance of several coordinate-based devices, such as beam splitters and invisibility cloaks, suffers from the necessary implementation of singularities with extreme material parameters. Here, we make use of transformation optics to eliminate these singularities in an isotropic way for the improvement of coordinate-based metamaterial waveguides. In particular, singularities that lead to vanishing material properties are softened with a global rescaling of the coordinates, while singular terms that lead to infinite material properties are strategically replaced by well-behaved curve factors. Detailed full-wave simulations confirm that the resulting waveguide devices are as efficient as their singular counterparts despite the fact that they consist of materials with much more moderate optical properties.