Cost-Effective Additively-Manufactured Transformation Optics Luneburg Lens Design

This paper presents a 3D-printed Luneburg Lens designed using transformation optics for X-band applications. The lens is fabricated from polylactic acid (PLA) with embedded cubic air voids (5 mm unit cells) to create the required graded permittivity profile. With 2,928 unit cells forming an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$80 ~\text{mm} \times 80 ~\text{mm} \times 75 ~\text{mm}$</tex> structure, the lens achieves 16.65 dBi gain and wideangle beam steering capability (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\pm 42^{\circ}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\pm 31^{\circ}$</tex> in orthogonal planes) when fed by a WR90 waveguide. The additive manufacturing approach enables precise control of the dielectric distribution while maintaining cost-effectiveness. These performance characteristics, combined with the design's scalability, make the proposed lens suitable for advanced radar systems, satellite communication, and 5 G beamforming applications.