Theory and optimization of transformation-based quadratic spherical cloaks

TL;DR

This paper introduces a numerical method to evaluate and optimize the invisibility performance of quadratic spherical cloaks, identifying a bell-shaped profile as the most effective design for steady invisibility.

Contribution

It presents a new computational approach for optimizing quadratic spherical cloaks based on the cloak generating function concept, improving invisibility performance.

Findings

Bell-shaped quadratic spherical cloak offers optimal invisibility.

Optimized design parameters enhance steady invisibility.

Performance remains robust under high discretization.

Abstract

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.