The 0 to R<inf>1</inf> spherical radial transformation can not be used to induce acoustic no scattering cloak but some can be for EM invisible cloak

Abstract

In part 1 of this paper, we propose a new GLHUA 0 to R 1 sphere radial transformation for EM invisible cloak. We theoretically prove that some 0 to R 1 spherical radial continuous transformation can be to induce EM invisible cloak. In part 2 of this paper, we discover and prove that the 0 to R 1 spherical radial transformation method can not be used to induce acoustic no scattering cloak. Because in the 0 to R 1 radial spherical coordinate transformation, the value range of the acoustic field is invariant, p(r q ) = p(r) the p(R 2 −) = p i (R 2 +), R 2 (R 2 − R 1 ) p(R− 2 ) = R2 2 p i (R 2 +), on boundary r = R 2 , both are necessary conditions for boundary no scattering. Then on the physical inner spherical surface boundary r = R 1 , p(R 1 ) is nonzero. p(R 1 ) = −eikrs/4πr s . In inner sphere r ≤ R 1 , relative background parameters 1 are sited. For infinite countable angular frequency ω m and wave number k m = ω m /c b > 0, j 1 (ω m R 1 /c b ) = 0, the acoustic field p(R 1 ) = −eikrs/4πr s will propagation penetrate into the inner spherer 1 , with bounded physical wave field (for other ωj 1 (ωR 1 /c b ) ≠ 0, penetrated wave field will be unbounded and unphysical). Moreover, if inner sphere r ≤ R 1 is cloaked, the zero wave field in the inner sphere r 1 causes p(R 1 +) = 0, that is contradiction with p(R 1 ) = −eikrs/4πr s on inner boundary r = R 1 . Inversely if the the inner sphere r 1 is cloaked, that causes p(R 2 ) = p i (R 2 ), that is contradiction with no scattering boundary conditions on the outer boundary r = R 2 . Therefore, the 0 to R 1 spherical radial transformation can not be used to induce acoustic no scattering cloak. In some published papers on acoustic cloak, for example [7], the 0 to R 1 spherical radial transformation is used to induce their acoustic cloak that should be reconsideration. For wave number k = 0, the static field will propagation penetrate into the inner sphere r 1 , with constant field as same as incident field, inner sphere can not be cloaked. Inversely, if force field p(r) = 0, in inner sphere, the field will scattering back to outside sphere r > R 2 to disturb incident field. Same problem for source field. Therefore, authors claim “no scattering cloak” in paper [14] is wrong.