Eikonal equation for a general anisotropic or chiral medium: application to a negative-graded index-of-refraction lens with an anisotropic material

We discuss the numerical simulation of a graded refractive index (GRIN) lens with a general anisotropic medium and compare it with an equivalent nongraded positive-index-of-refraction-material (PIM) lens with an isotropic medium. To evaluate lens performance, we developed a modified eikonal equation valid for the most general form of an anisotropic or chiral medium. Our approach is more comprehensive than previous work in this area and is obtained from the dispersion relation of Maxwell's equations in the eikonal approximation. The software developed for the numerical integration of the modified eikonal equation is described. Subsequently, a full finite-difference time-dependent simulation was performed to verify the validity of the eikonal calculations. The performance of the GRIN lens is found to be improved over the equivalent PIM one. The GRIN lens is also five to ten times lighter than the equivalent PIM. A GRIN lens operating at 15 GHz is now under fabrication at Boeing, and the experimental results of this lens will be reported in a forthcoming paper.