Conformal mappings to achieve simple material parameters for transformation optics devices

The transformation optics technique for designing novel electromagnetic and optical devices offers great control over wave behavior, but is difficult to implement primarily due to limitations in current metamaterial design and fabrication techniques. This paper demonstrates that restricting the spatial transformation to a conformal mapping can lead to much simpler material parameters for more practical implementation. As an example, a flat cylindrical-to-plane-wave conversion lens is presented and its performance validated through numerical simulations. It is shown that the lens dimensions and embedded source location can be adjusted to produce one, two, or four highly directive planar beams. Two metamaterial designs for this lens that implement the required effective medium parameters are proposed and their behavior analyzed.