Wavefront-aberration-free broadband dielectric window based on bipolar GRIN profile synthesis

This paper presents the design and full-wave analysis of a broadband gradient-index dielectric window that preserves wavefront integrity across curved interfaces without introducing boresight error or phase distortion. The proposed methodology combines bipolar coordinate mapping with the critical-angle theorem for the closed-form synthesis of the graded permittivity profile. Unlike prior applications of the critical-angle theorem to focusing lenses, where cylindrical wavefronts were transformed into plane waves, the present work enforces a straight-ray condition ( θ i = θ o ) for all oblique rays. This ensures that every ray traverses the curved window without angular deviation, eliminating wavefront aberration and boresight error. The synthesized spatial permittivity profile is inherently frequency-independent; the achievable operational bandwidth is ultimately limited by the constituent material dispersion and loss characteristics. Full-wave simulations over the 1–4 THz band confirm a 95% reduction in wavefront deviation compared to a homogeneous window while maintaining high transmission efficiency and minimal reflection across a wide range of incidence angles. The analytical design is material-agnostic and scalable, offering a robust solution for applications from microwave radomes to terahertz sensor systems.