Adjoint Sensitivity Optimization of Three-Dimensional Directivity-Enhancing, Size-Reducing GRIN Lenses

Gradient Index (GRIN) lenses have the potential to tailor the radiation behavior of existing antennas for improved gain performance. Conventional methods such as transformation optics have mainly focused on two-dimensional (2-D) problems (e.g., axisymmetric or sectoral horn lenses), and often produce designs with unrealistic material parameters or poor impedance matching. In this letter, we propose a new method of designing freeform GRIN lenses using adjoint sensitivities to rapidly find optimal solutions within feasible material bounds that achieve desired performance goals. A proof-of-concept 3-D GRIN lens that achieves comparable performance to a larger 20 dB standard gain horn albeit with considerable size reduction is optimized, fabricated, and tested in order to highlight the effectiveness of the proposed approach.