Design of a planar gradient-index dielectric lens for arbitrary point-to-point beam focusing using critical-angle theory

This paper presents a novel analytical design method for a planar gradient-index (GRIN) dielectric lens based on the critical-angle theorem, capable of focusing electromagnetic waves between two arbitrarily located points. Unlike conventional curved lenses, the proposed flat lens structure enables flexible beam pointing and precise wavefront control without mechanical movement. The refractive index profile is derived analytically to ensure phase matching and minimal internal reflection. The design is validated through full-wave numerical simulations in COMSOL Multiphysics, demonstrating effective beam focusing, and improved impedance matching. The proposed lens, validated here in the 4-7 THz band, exhibits significant potential for frequency-scalable applications ranging from Terahertz imaging to 5G/6G communications, satellite links, and radar systems where versatile beam alignment is required.