Bell-shaped quadratic spherical cloaks designed by a transformation-free method: Theory and optimization

Based on the concept of the cloak generating function, we propose a numerical method to compute the invisibility performance of various quadratic spherical cloaks and obtain optimal invisibility results. A non-ideal discrete model is used to calculate and optimize the total scattering cross-sections of different profiles of the generating function. A bell-shaped quadratic spherical cloak is found to be the best candidate, which is further optimized by controlling design parameters involved. Such improved invisibility is steady even when the model is highly discretized.