Hemispherical Luneburg Lens Crafted via Non-Conformal Mapping: Advancing Towards Omnidirectional Beam Scanning

This report studies the differences and impacts of applying non-conformal and quasi-conformal mapping techniques in constructing flat-bottomed Luneburg lenses. In juxtaposition with quasi-conformal mapping, non-conformal mapping presents a more optimal gradient refractive index distribution during minor structural transformations. By utilizing this distinct mapping technique, we have designed a hemispherical Luneburg lens characterized by its ability for omnidirectional beam scanning with a relatively low refractive index. This pioneering design offers fresh perspectives and potentialities for forthcoming millimeter-wave and terahertz applications.