Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations

Abstract

The technique of applying form-invariant, spatial coordinate transformations of Maxwell's equations can facilitate the design of structures with unique electromagnetic or optical functionality. Here, we illustrate the transformation-optical approach in the designs of a square electromagnetic cloak and an omni-directional electromagnetic field concentrator. The transformation equations are described and the functionality of the devices is numerically confirmed by two-dimensional finite element simulations. The two devices presented demonstrate that the transformation optic approach leads to the specification of complex, anisotropic and inhomogeneous materials with well directed and distinct electromagnetic behavior.

Manipulating DC Currents with Bilayer Bulk Natural Materials

“…On the basis of the invariance of Maxwell's equations where equivalence is established between metric transformations and changes in material parameters, transformation optics [3] and conformal mapping [4] have been 2 developed to manipulate EM wave propagation in a practically arbitrary manner. Besides making objects invisible [1][2][3][4] , many other novel devices are rapidly emerging, with a representative one being a concentrator [5,6] that can enhance the energy density of incident waves in a given area. In addition to manipulation of EM waves [1][2][3][4][5][6] , the theoretical tool of coordinate transformation has been extended to other areas of physics (such as acoustic waves [7] , matter waves [8] and elastic waves [9] ).…”

“…Besides making objects invisible [1][2][3][4] , many other novel devices are rapidly emerging, with a representative one being a concentrator [5,6] that can enhance the energy density of incident waves in a given area. In addition to manipulation of EM waves [1][2][3][4][5][6] , the theoretical tool of coordinate transformation has been extended to other areas of physics (such as acoustic waves [7] , matter waves [8] and elastic waves [9] ).Recently, many significant achievements have been made in the manipulation of magnetostatic field [10][11][12][13][14][15] , thermal conduction [16][17][18][19] , and electrostatic field [20][21][22][23][24] . In 2007, Wood and Pendry proposed a dc metamaterial that pointed the way towards the design of static magnetic cloak [10] , and the dc metamaterial was experimentally verified soon afterwards [11] .…”

Dc Magnetic Concentrator and Omnidirectional Cascaded Cloak by Using Only One or Two Homogeneous Anisotropic Materials of Positive Permeability

“…By designing the coordinates of transformations or the geometry of the reference space, one can obtain a different distribution of special materials in the real space, which can allow for many predesigned functions (e.g., invisibility, optical illusions, subwavelength focusing, and etc.). The basic idea in this paper is the space compression transformation, which has been used for optical energy concentration [18,19]. For simplicity, we consider a two-dimensional (2D) structure in this paper.…”

Transformation Optics Methodology for Changing the Appearance of an Object

“…And the metric tensors of the transformed space that contains the desired electromagnetic properties can also be derived simultaneously [3][4][5]. Transformation optics has become a fundamental tool for exploring a diverse set of devices with novel properties, such as cloaks [6,7], concentrators [8], lenses [9][10][11][12], waveguide bends and transitions [13][14][15][16][17], antennas [18][19][20][21][22][23][24][25][26], and so on. Generally speaking, the generated materials are inhomogeneous and anisotropic by transformation optics methodology.…”