This paper presents a quasi-conformal transformation optics (QCTO) based three-dimensional (3D) retroreflective flattened Luneburg lens for wide-angle millimeter-wave radio-frequency indoor localization. The maximum detection angle and radar cross-section (RCS) are investigated, including an impedance matching layer (IML) between the lens antenna and the free-space environment. The 3D QCTO Luneburg lenses are fabricated in alumina by lithography-based ceramic manufacturing, a 3D printing process. The manufactured structures have a diameter of 29.9 mm (4 𝜆 0 ), showing a maximum realized gain of 16.51 dBi and beam steering angle of ±70° at 40 GHz. The proposed QCTO Luneburg lens with a metallic reflective layer achieves a maximum RCS of -20.05 dBsqm at 40 GHz with a wide-angle response over ±37°, while the structure with an IML between the lens and air improves these values to a maximum RCS of -15.78 dBsqm and operating angular response between ±50°.

A circular graded index lens is conformally transformed to an elliptical shape using a closed-form transformation. The proposed transformation is then employed to compress a Maxwell fish-eye and its generalized version. Since the transformation is conformal, the electromagnetic properties of the device are perfectly preserved after the transformation with fully isotropic and dielectriconly materials. Ray-tracing and full-wave simulations are carried out for several cases to verify the functionality of the optically transformed lenses in geometrical optics and wave optics regimes.

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We present a general method of designing optical devices based on optical conformal mapping and rescaling the optical path along a given bunch of rays. It provides devices with the same functionality as those based purely on conformal mapping, but enables to manipulate the refractive index to a great extent—for instance, eliminate superluminal regions of space as well as reduce the refractive index in other regions significantly. The method is illustrated in two examples, a waveguide coupler and a plasmonic bump cloak, and numerical simulations confirm its functionality.

The design of an optical waveguide coupler has several challenges, such as reflection losses at the interfaces of the coupler, material complexity for optical applications, and the coupling between arbitrary materials at the input and the output of the coupler. In this paper, for the first time to the best of our knowledge, we propose a solution to overcome the above difficulties. For this purpose, we introduce an auxiliary transformation function and an impedance scaling function. The auxiliary function specifies the matched dielectric materials at the input and output interfaces of the coupler, and the scaling function suppresses the reflections and makes the material nonmagnetic for transverse magnetic (TM) polarization. As a result, an optical waveguide coupler is designed that can ideally couple two waveguides with arbitrary dielectric materials and arbitrary cross sections using a nonmagnetic material. Validation of the design method is done by using COMSOL Multiphysics.