Development, Fabrication and Characterization of Hyperbolic Flat Lensing in the X-Band using 3D Printing and Quasi-Conformal Transformation Optics

Transformation optics is a well-established technique that can be used to design many novel electromagnetic and optical devices; some include cloaking, integrated optical components, focusing devices, and antennas. The method relies on the form-invariance of Maxwell's equations under a spatial coordinate transformation. Consequently, this approach can be difficult to implement in fabrication due to the complex material properties imposed, often requiring anisotropic lossy metamaterials. In this work, we restrict the transformation to a quasi-conformal mapping, requiring only dielectric isotropic materials. This allows for flat lens designs with varying focal lengths and thicknesses to be fabricated through 3D printing, experimentally tested, and compared with FEM numerical simulations.<br/><br/>Various flat hyperbolic lenses with controlled thicknesses and focal lengths have been designed for fabrication and experimental characterization in the X-band microwave regime. Standard Polymaker PLA 3D-printer filament has been optically characterized, allowing the refractive index to be modeled as a function of infill percentage. Quasi-Conformal transformation optics is used to transform modeled hyperbolic canonical lenses of various focal lengths into a planar lens of controlled thickness with variable refractive index. The varying refractive index regions of the flat lens are controlled through the 3D-printed infill percentage. After FEM numerical simulations verify the desired optical properties of this transformation, the lenses are fabricated using 3D printing. Both the flat lens and hyperbolic lens are created for experimental comparison. It is verified through this process that these flat lens variants are in excellent agreement with the FEM simulations and the experimental results from their hyperbolic canonical lens counterparts.