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A body-of-revolution finite-difference time-domain (BOR-FDTD) method was developed and employed to rigorously analyze axisymmetric transformation optics (TO) lenses. The novelty of the proposed BOR-FDTD technique is that analytical expressions were derived and presented to introduce obliquely incident plane waves into the total-field/scattered-field formulation, allowing for accurate simulation of BOR objects in layered media illuminated by obliquely incident waves. The accuracy of the proposed method was verified by comparing numerical results with analytical solutions. The developed code was further utilized to study the imaging properties of a cylindrical TO Luneburg lens on a substrate, demonstrating the desired focusing of light onto a flat plane.

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.