The 0 to R<inf>1</inf> cylinder radial coordinate transformation can not be used to induce cylinder layer EM invisible cloak and acoustic no scattering cloak

Abstract

In this paper, we discover and prove that the 0 to R 1 cylinder radial ρ transformation can not be used to induce cylinder layer EM invisible cloak and acoustic no scattering cloak. Because in the 0 to R 1 cylinder radial coordinate transformation, ρ q = R 1 + Q(ρ), Q(0) = 0, Q(R 2 ) = R 2 − R 1 , cylinder, ρ ≤ R 2 , |z| 1 ≤ ρ ≤ R 2 , |z| z (ρ,φ, z) and magnetic wave field H z (ρ,φ, z) and acoustic wave field u(ρ,φ, z) are invariant. When necessary condition of no scattering, i.e., wave and derivative continuous boundary condition are satisfied on r = R 2 , then E z (ρ q ,φ, z) = E z (ρ,φ, z), on the physical inner cylinder boundary, E z (ρ q = R 1 , ϕ, z) = E z (ρ = 0, ϕ, z) = 0, H z (ρ q = R 1 , ϕ, z) = H z (ρ = 0, ϕ, z) ≠ 0, and u(ρ q = R 1 , ϕ, z) = u(ρ = 0, ϕ, z) = 0 are not zero. The cylinder EM wave and cylinder acoustic field will propagation penetrate into the inner cylinder ρ 1 , and to become unbounded wave field without physics. The bounded solution requirement induces only zero wave in the inner cylinder ρ 1 , and make E z (ρ q = R 1 +, φ, z) = 0, that is contradiction with above E z (ρ q = R 1 , ϕ, z) = E z (ρ = 0, ϕ, z) = 0. The basic contradiction proved that the 0 to R 1 cylinder radial ρ transformation can not be used to induce cylinder layer EM invisible cloak and acoustic no scattering cloak. Inversely if the in the inner cylinder ρ 1 , is cloaked E z (ρ q = R 1 +,φ, z)= 0. we can prove that there exist scattering EM wave or scattering acoustic wave in outside of whole cylinder, ρ > R 2 to disturb incident wave in free space or in background space, the whole cylinder become no invisible and is detected or exposed. Moreover, the outside scattering is not satisfy radiation condition. The cloaked the inner cylinder ρ 1 , will cause the contradiction with No scattering condition on the outer boundary r = R 2 . In many published papers on EM and acoustic cylinder cloak, the 0 to R 1 cylinder radial transformation was wrong to use for their EM and acoustic cylinder layer cloak, for example [4], that should be reconsideration. We proved that the 0 to R 1 cylinder radial ρ transformation can not be used to induce cylinder layer EM invisible cloak and acoustic no scattering cloak that does cause the whole cylinder to be detected and exposed.