Spherical cloaking with homogeneous isotropic multilayered structures

Abstract

We propose a practical realization of electromagnetic spherical cloaking by layered structure of homogeneous isotropic materials. By mimicking the classic anisotropic cloak by many alternating thin layers of isotropic dielectrics, the permittivity and permeability in each isotropic layer can be properly determined by effective medium theory in order to achieve invisibility. The model greatly facilitates modeling by Mie theory and realization by multilayer coating of dielectrics. Eigenmode analysis is also presented to provide insights of the discretization in multilayers. DOI: 10.1103/PhysRevE.79.047602 PACS number͑s͒: 41.20.Jb, 42.25.Fx, 41.20.Ϫq Recently, invisibility cloaks ͓1-4͔ have received great attention since Pendry et al. ͓5͔ suggested that an object coated by an inhomogeneous anisotropic shell becomes invisible to electromagnetic waves. The electromagnetic wave interaction with such a cloak was analyzed ͓6͔. In addition to the common method of geometric transformation, various approaches have been proposed to create invisibility cloaks, such as plasmonic resonances ͓7͔, scattering cancellation ͓8͔, negative index material ͓9͔, and stationary Schrödinger equation ͓10͔. Attempts to realize the cloaking idea have been initiated with encouraging results ͓11͔.Conventional cloaks need to be anisotropic and their parameters are functions of position. Although this restriction can be bypassed with the simplified material parameters ͓11͔, later it was found that the coating established by simplified parameters cannot perfectly shield the targeted object inside without electromagnetic perturbation to external EM fields ͓12͔. However, the cylindrical invisibility cloak is still difficult to realize due to the limited resource of natural materials exhibiting radial anisotropy ͓13͔, not to mention that those tensorial parameters are spatially varying. In this connection, Cai et al. ͓14͔ investigated a multilayered cylindrical cloak by discretizing the conventional position-dependent cloak into many layered coatings, and the material in each layer is position independent but still anisotropic. Huang et al. ͓15͔ proposed a cylindrical cloak by replacing one anisotropic coating with a multilayered structure in which each layer is constructed with a certain homogeneous isotropic medium. Some recent works on cylindrical acoustic cloaks were also reported ͓16,17͔. When each layer is thin enough, the effective medium theory can be employed to find out the required permittivity for each layer ͓18͔. More recently, this idea was further applied to three-dimensional acoustic cloak by multilayered isotropic materials ͓19͔.As for electromagnetic spherical invisibility cloaks, material parameters for the perfect cloak are suggested ͓5͔:where the cloak occupies the spherical region ͑a Ͻ r Ͻ b͒ and its constitutive material parameters are given bywhere the unit dyad is I = rr + + and the subscripts r and t denote the parameters along radial ͑r͒ and tangential direction ͑ or ͒, respectively. The anisotropic cloaking proposed b...

Neutral shielding and cloaking of magnetic fields using isotropic media

“…The recursive formula can be used to design the cloaks, which is a stationary case of the general cloaking problem for the particular geometry. The solutions are exact and thereby different from approximation methods such as homogenization [35,36] or numerical optimization [37] of multilayered structures. However, to include every multipole field in the solution we have to let k turn to infinity, resulting in an infinite series of Figure 11.…”

Optimization Towards Broadband Cylindrical Cloaks With Layered Magnetic Materials

“…Therefore, in higher frequency band, where greater N is required, we need to use more optimization parameters to increase the dynamic range of f n in order to find the optimal result. This can be done by increasing M [23,24] or increase optimization parameters. Consider the following example: targeting at bandwidth of 80 MHz, and optimizing an equally discretized 20-layer cloak with center frequencies f c (with wavelength λ c ) of 0.5 GHz and 2 GHz respectively.…”

“…Since BFGS is not a global optimization algorithm, the initial guess was found to play a vital role in the performance of the optimized cloak. Aiming at minimized total scattering, an optimized cloak comprised of a few anisotropic layers can be designed, by using a global optimization algorithm such as the genetic algorithm (GA) [20,24], or the particle swarm optimization (PSO) algorithm [21,22]. In such optimized cloaks, the extreme values in the original cloak can be avoided and the results from [21] indicated a trade-off between the operating frequency band and the RCS reduction.…”

“…Yao et al applied this conversion to the optimized 3-layer cloak presented in [19] and studied the impact of the conversion parameters, such as the thickness and the number of repetition [23]. By applying Mie theory, physical insights of the scattering from the isotropic multilayered cloaks were obtained through eigenmode analysis [24]. The relationship of the invisibility with the number of layers of the isotropic cloaks was extensively investigated [24], and a minimum number of layers of spherical cloak was suggested by using optimization [26].…”

“…By applying Mie theory, physical insights of the scattering from the isotropic multilayered cloaks were obtained through eigenmode analysis [24]. The relationship of the invisibility with the number of layers of the isotropic cloaks was extensively investigated [24], and a minimum number of layers of spherical cloak was suggested by using optimization [26]. In [27,28], the bi-layered non-magnetic isotropic cloak with minimum number of layers was directly optimized.…”