Simulation of a discrete Luneburg lens fed by a conformal printed antenna

Because of their simplicity, slot fed circular microstrip antennas (MA) are popular. Even more popular are MAs conformally printed on curved surfaces, such as spherical-circular MAs because of their higher degree of freedom. A very attractive candidate is a discrete Luneburg lens, which is a layered dielectric sphere. To simulate the antenna, we use the Method of Analytical Regularization (MAR), sometimes called the semi-inversion method. Generally, it converts a first-kind singular integral or series equation to a well-conditioned second-kind Fredholm matrix equation, and therefore serves as a perfect pre-conditioner of an ill-posed problem. Both numerical convergence and efficiency are achieved and matrix-truncation error is controlled.