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 ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4 \lambda _{0}$ </tex-math></inline-formula> ), 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°. 

Wide-Angle Ceramic Retroreflective Luneburg Lens Based on Quasi-Conformal Transformation Optics for Mm-Wave Indoor Localization

Conformal transformation optics is employed to enhance an H-plane horn’s directivity by designing a graded-index all-dielectric lens. The transformation is applied so that the phase error at the aperture is gradually eliminated inside the lens, leading to a low-profile high-gain lens antenna. The physical space shape is modified such that singular index values are avoided, and the optical path inside the lens is rescaled to eliminate superluminal regions. A prototype of the lens is fabricated using three-dimensional printing. The measurement results show that the realized gain of an H-plane horn antenna can be improved by 1.5–2.4 dB compared to a reference H-plane horn.

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H-plane horn antenna with enhanced directivity using conformal transformation optics.

Abstract Using conformal transformation optics, a cylindrical shell made of an isotropic refractive index material is designed to improve the directivity of a wire antenna while making it unidirectionally invisible. If the incident wave comes from a specific direction, it is guided around the wire. Furthermore, when an electrical current is used to excite the wire, the dielectric shell transforms the radiated wave into two lateral beams, improving directivity. The refractive index of the dielectric shell is calculated using the transformation optics recipe after establishing a closed-form conformal mapping between an annulus and a circle with a slit. The refractive index is then modified and discretized using a hexagonal lattice. Ray-tracing and full-wave simulations with COMSOL Multiphysics are used to validate the functionality of the proposed shell. 

/pdf/strictly-conformal-transformation-optics-for-directivity-rwli9riw.pdf

Strictly conformal transformation optics for directivity enhancement and unidirectional cloaking of a cylindrical wire antenna

A two-dimensional half Maxwell fish-eye lens is compressed using a linear transformation that maps a half circle to a half ellipse. The focusing property of the lens is preserved while making the device more compact. The boundary reflections, investigated for both TE and TM polarizations, were suppressed for beams directed toward the optical axis of the lens. A designed prototype provided a scanning range of ±20° with negligible reflections. The design’s functionality was verified using COMSOL multiphysics.

A reflectionless compact elliptical half Maxwell fish-eye lens designed by transformation optics

Enhancing the directivity of a radiating array element for an optical true-time-delay network

A transformation-optical method is presented to enhance the directivity of a cylindrical wire antenna by using an all-dielectric graded index medium. The strictly conformal mapping between two doubly connected virtual and physical domains is established numerically. Multiple directive beams are produced, providing directive emission. The state-of-the-art optical path rescaling method is employed to mitigate the superluminal regions. The resulting transformation medium is all-dielectric and nondispersive, which can provide broadband functionality and facilitate the realization of the device using available fabrication technologies. The realization of the device is demonstrated by dielectric perforation based on the effective medium theory. The device's functionality is verified by carrying out both ray-tracing and full-wave simulations using finite-element-based software COMSOL Multiphysics.

/pdf/directivity-enhancement-of-a-cylindrical-wire-antenna-by-a-4zldqn91nd.pdf

Soorena Saviz

Papers

Directivity enhancement of a cylindrical wire antenna by a graded index dielectric shell designed using strictly conformal transformation optics.