A GL Double Layer EM Cloaks In Broad Frequency Band And Reciprocal Law

We have proved that there exists no Maxwell wavefield can be excited by sources inside the single layer cloaked concealment with normal materials [1]. For covering this difficulty, we proposed a GL double layer cloak [2]. Its outer layer has invisibility from the exterior light and EM wave field, never disturb the exterior field, and cloak the Local inner layer and concealment from the Global exterior wavefield. Its inner layer cloak absorbs the internal wave field, such that the internal wave field, which is excited from the sources inside the concealment, can not propagate outside of the inner layer. Our GL double layer cloak is proposed by the GL EM modeling and inversion [3]. The GL double layer cloak overcomes the following difficulties of the single layer PS cloak by Pendry [4]. (1) The PS cloak damaged the EM environment of its concealment, such that there exists no EM wavefield can be excited inside the concealment of the PS cloak, the concealment of the PS cloak is blind. Our GL double layer cloak recovered the normal EM environment in its concealment, such that the EM wave field can be excited inside the concealment of the GL double layer cloak. (2) The two sources reciprocal law is very important principle in the electromagnetic theory and application. The reciprocal law is satisfied in our GL double cloak media. However, the reciprocal law is damaged by the PS cloak. The PS cloak is strong dispersive cloak material, in which the ε r ε θ = R 2 3 (r -R 2 ) 2 /r 2 /(R 3 -R 2 ) 2 , when r → R 2 ε r ε θ ≈ (r -R 2 ) 2 → 0. such that the EM wave velocity exceed the light speed in some part of the PS cloak that is violated to the physical principle. The PS cloak has invisibility only in very narrow frequency band. In the GL outer layer cloak [2] [5] [6], the weak dispersion is obtained, when r → R 2 ε r ε θ ≈ (r -R 2 ) 1.5 → 0. In this paper, we obtain very significant progress to overcome the difficulty. very pefect weak dispersive and degenerative rate, ε r ε θ ≈ 1/ log(r -R 2 ) → 0, is obtained. Chen et al proposed an analytical method for analysis of the PS cloak [7].

Finding and exploration is inverse problem; Hiding and cloaking is other inverse problem. They have close relationship. Based on the 3D GL EM modeling simulations [3] and GL Metre Carlo inversion [5], We propose a novel GL double layer cloak in the broad frequency band.

The President Professor Yuesheng Li in Sun Yat-Sen University very concerns and encourages our research works on the GL EM modeling method and the GL double cloak. Our paper is for celebrating his great scientific computational carrier in 60 years and his 80 birthday.

The description order of this paper is as follows. We have introduced single layer cloak and our GL double layer cloak and main content and research cue path in Section 1. In Section 2, we propose a novel GL double layer cloak in the broad frequency band The EM wave propagation simulations in our wide frequency band GL double layer cloak are presented in Section 3. The important reciprocal law in the cloak media is presented in Section 4. In Section 5, we will conclude our paper.

For overcoming the weakness of the single layer cloak, we proposed the GL double layer cloak in broad frequency band, in short it is called GLWF, which consists of the inner layer cloak and outer layer cloak

On the inner sphere annular layer domain, Ω GLI = {r : R 1 ≤ r ≤ R 2 } , by the GL EM modeling and inversion [3][5], we propose an anisotropic metamaterial as follows,

(

The Ω GLI is called as GL inner layer cloak, the materials, (1), are the anisotropic GL inner layer cloak metamaterials. Where the subscript GLI means the GL inner layer, the symbol diag denotes the diagonal matrix, [D] GLI is 6 × 6 diagonal matrix, εi is 3 × 3 dielectric diagonal matrix in the inner layer, the subscript i denotes the inner layer, μi is 3 × 3 magnetic permeability diagonal matrix in the inner layer, ε r,i is the relative dielectric cloak metamaterial which is formulated by the fourth sub equation in (1), the subscript index r, i denotes the dielectric is in r direction and in the inner layer, ε θ,i is the relative dielectric cloak metamaterial in θ direction and in the inner layer which is formulated by the fifth sub equation in (1), The µ r,i is the relative permeability cloak metamaterial which is formulated by the fourth sub equation in (1), ε b is the basic dielectric in free space, ε b = 0.88541878176 . . . × 10 -11 F/m, µ b is the basic magnetic permeability in free space, µ b = 1.25663706 × 10 -6 mkgs -2 A -2 , other symbols in (1) have similar explanation.

The EM wavefield of sources located inside inner layer or the cloaked concealment is completely absorbed by the inner layer and never reaches the outside boundary of the inner layer, also, the EM wavefield excited in concealment is not disrupted by the cloak. The inner layer metamaterial, in equation ( 1), cloaks outer space from the local field excited in the inner layer and

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