Abstract
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.
Highlights
Conformal transformation optics is employed to enhance an H-plane horn’s directivity by designing a graded-index all-dielectric lens
Ever since transformation optics (TO) was proposed by Pendry[1] and L eonhardt[2] in 2006, it has been used in a plethora of applications, like carpet c loaking[3,4,5], polarization splitting and transforming[6,7,8,9,10], waveguide coupling[11,12,13,14,15,16,17], lens c ompression[18,19,20,21], lens flattening[22,23,24], and directivity e nhancement[25,26,27,28,29,30,31]
We address all of the above shortcomings to enhance the directivity of an H-plane horn antenna while keeping its refractive index at moderate, above-unity values
Summary
The 2D virtual and physical spaces are described by Cartesian coordinates (u,v) and (x,y), respectively. The throat’s width of the horn antenna in the physical space is similar to the virtual space’s one ( AB=A′B′ ) to get the refractive index close to one. The physical space’s final refractive index is derived by calculating the conformal mapping between the intermediate space and the physical space. This, combined with the known original optical path S along that ray, fully defines the rescaling S′(S) , which is shown in Fig. 2 for our case. We see that the superluminal regions have disappeared completely, which was our goal, and the entire refractive index profile ranges from unity to about 1.44
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