Implementation of transformed lenses in bed of nails reducing refractive index maximum value and sub-unity regions

Transformation optics with quasi-conformal mapping is applied to design a Generalized Maxwell Fish-eye Lens (GMFEL) which can be used as a power splitter. The flattened focal line obtained as a result of the transformation allows the lens to adapt to planar antenna feeding systems. Moreover, sub-unity refraction index regions are reduced because of the space compression effect of the transformation, reducing the negative impact of removing those regions when implementing the lens. A technique to reduce the maximum value of the refractive index is presented to compensate for its increase because of the transformation. Finally, the lens is implemented with the bed of nails technology, employing a commercial dielectric slab to improve the range of the effective refractive index. The lens was simulated with a 3D full-wave simulator to validate the design, obtaining an original and feasible power splitter based on a dielectric lens.