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 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.
