System-by-design method for efficient linear array miniaturisation through low-complexity isotropic lenses

The design of miniaturised linear arrays by using isotropic lenses with reduced complexity is addressed. The problem at hand is formulated as a global optimisation one, then solved by means of a computationally-efficient customisation of the system-by-design (SbD) paradigm suitably integrated with the quasi-conformal transformation optics method. To yield arbitrary transformation geometries with a limited set of degrees-of-freedom and to reduce the lens complexity, while guaranteeing the same radiation performance of a larger reference aperture, a spline-based description of the lens shape is adopted. Representative numerical results are reported to assess the effectiveness as well as the computational efficiency of the proposed SbD-based approach.