GO Analysis of GRIN Lens Antennas by Combining in a Single ODE, Field and Wavefront-Curvature Transport to the Ray Tracing

A novel very efficient algorithm based on geometrical optics (GO) is presented for the analysis of graded index (GRIN) lens antennas, namely, dielectric inhomogeneous lenses with a 3-D arbitrary varying refractive index. A family of curved ray paths are traced starting from a set of points defined on the lens input interface, which is illuminated by a feed antenna, up to a corresponding set of points on the output interface, i.e., the lens radiating aperture. The ray tracing is numerically performed in combination with the field transportation along the ray by exploiting an additional wavefront-curvature transport equation, thus providing a single independent vector ordinary differential equation (ODE) for each ray. This scheme allows a complete parallelization of the algorithm by assigning any ray to a different thread. Crossing the lens input–output interfaces at the two end points of the curved ray is accomplished by augmenting the refraction Snell’s law and the Fresnel transmission coefficients with a novel compact closed-form dyadic formula for the transmitted wavefront curvature. The ODE output provides the field aperture distribution on the output lens interface, permitting the far-field calculation as a radiation integral. To this end, an ad hoc quadrature rule is exploited, which requires an aperture sampling rate corresponding to the slowly varying part of the integrand, while the rapid phase variation is accounted for analytically, thus resulting in an extremely efficient and frequency-independent scheme. The effectiveness and accuracy of the algorithm are shown by resorting to a couple of well-known analytical benchmarks and to two more general examples with real-life antennas: a spaceborne weather radar lens antenna and a feed antenna with a zero-focal lens.