## Abstract

Mie theory and genetic algorithms are used to determine the parameters and performance of cloaks made of homogeneous isotropic metamaterials that would hide a spherical dielectric object of size comparable to the incident radiation wavelength. A single-layer (SL) cover with negative permittivity and permeability can produce a much greater reduction in the extinction efficiency than one with the permittivity and permeability of positive or opposite signs. Minimization of the extinction efficiency in the former case leads to both nonresonant and resonant solutions. Adding a second layer to the cover can lead to a significant enhancement of the bandwidth, but only to a modest reduction in the extinction efficiency at the design wavelength. In the SL case, Debye’s scattering series is used to show that the nonresonant and resonant minima of the extinction efficiency correspond to scattering phase shifts approximately equal to zero and $-\pi $, respectively, and to understand the simple approximate expressions for the cloak parameters of the nonresonant solutions. The series also explains the value of the outer radius of a multilayer cloak, provides a link to a previously studied isotropic approximation to a transformation optics cloak, and indicates that a cloak consisting of an odd number of alternate double-negative and double-positive layers will probably give the best possible performance.

© 2015 Optical Society of America

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