1：Experimental Design and Method Selection:

The study employed a quasi-conformal transformation optics (QCTO) approach to modify a spherical Luneburg lens into a geometry with a flat surface, followed by fabrication using Fused Deposition Modeling (FDM) with space-filling curves to achieve graded permittivity. Full-wave electromagnetic simulations were conducted using COMSOL Multiphysics to validate the design.

2：Sample Selection and Data Sources:

A modified Luneburg lens was designed for operation in the Ka-band (26-40 GHz), with a radius of 30 mm. Calibration samples were fabricated to characterize the effective permittivity of the space-filling curve geometries.

3：List of Experimental Equipment and Materials:

Equipment includes an nScrypt 3Dn-300 additive manufacturing system, Agilent PNA E83684B vector network analyzer, polycarbonate thermoplastic (εr = 2.68), WR28 open-ended waveguide, standard gain horn antenna, and radar absorbing material (RAM). Materials used are polycarbonate for printing and air as the background.

4：68), WR28 open-ended waveguide, standard gain horn antenna, and radar absorbing material (RAM). Materials used are polycarbonate for printing and air as the background. Experimental Procedures and Operational Workflow:

4. Experimental Procedures and Operational Workflow: The QCTO mapping was implemented using COMSOL to design the lens. FDM printing was performed with specific parameters (nozzle temperature 295°C, bed temperature 130°C, filament diameter 0.3 mm, layer height 0.125 mm, unit-cell size 3.0 mm). Antenna performance was measured by placing waveguide feeds at different positions on the flat surface and rotating the lens to measure gain patterns and S-parameters.

5：3 mm, layer height 125 mm, unit-cell size 0 mm). Antenna performance was measured by placing waveguide feeds at different positions on the flat surface and rotating the lens to measure gain patterns and S-parameters. Data Analysis Methods:

5. Data Analysis Methods: Full-wave simulations in COMSOL were used to predict antenna performance. Experimental data were analyzed using the vector network analyzer to measure reflection coefficients and gain patterns, with comparisons to simulations.