Logarithm conformal mapping brings the cloaking effect

Transformation Metamaterials

Based on the form-invariance of Maxwell's equations under coordinate transformations, mathematically smooth deformation of space can be physically equivalent to inhomogeneous and anisotropic electromagnetic (EM) medium (called a transformation medium). It provides a geometric recipe to control EM waves at will. A series of examples of achieving transformation media by artificially structured units from conventional materials is summarized here. Such concepts are firstly implemented for EM waves, and then extended to other wave dynamics, such as elastic waves, acoustic waves, surface water waves, and even stationary fields. These shall be cataloged as transformation metamaterials. In addition, it might be conceptually attractive and practically useful to control diverse waves for multi-physics designs.

Designing conformal cloaks by manipulating structures directly in the physical space

The method to elaborately design the refractive index profile in the lower Riemann sheet of Zhukovski transformation plays an important role in the performance of this kind of conformal cloaks. However, for most proposed schemes, the mathematical calculations are complex. Here, we propose a more convenient method to design conformal cloaks by manipulating structures directly in the physical space. The designed cloak only needs symmetrical metal boundaries filled with normal dielectrics (refractive index ranges from 1 to 2) in the 'circular branch cut', which would be more feasible for future experimental implementation. Numerical simulations are performed by using the finite element method to validate our theoretical analysis.

Conformal optical devices based on geodesic lenses

Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann sheets, hence compromising the functionalities. To deal with that, we present a special method for conformal transformation optics based on geodesic lenses with special closed surfaces. The requirement is a continuous refractive index profile of dielectrics, which shows the almost perfect performance of designed devices. We demonstrate such a proposal by achieving conformal transparency (invisibility without cloaking region) and reflection. We can further achieve conformal invisible cloaks by two methods with perfect conductors. The conformal transformation optics method based on geodesic lenses may also find applications in other waves that obey the Helmholtz wave equation in two dimensions.

Self-Focusing and the Talbot Effect in Conformal Transformation Optics

Transformation optics has been used to propose various novel optical devices. With the help of metamaterials, several intriguing designs, such as invisibility cloaks, have been implemented. However, as the basic units should be much smaller than the working wavelengths to achieve the effective material parameters, and the sizes of devices should be much larger than the wavelengths of illumination to work within the light-ray approximation, it is a big challenge to implement an experimental system that works simultaneously for both geometric optics and wave optics. In this Letter, by using a gradient-index microstructured optical waveguide, we realize a device of conformal transformation optics (CTO) and demonstrate its self-focusing property for geometry optics and the Talbot effect for wave optics. In addition, the Talbot effect in such a system has a potential application to transfer digital information without diffraction. Our findings demonstrate the photon controlling ability of CTO in a feasible experiment system.

Optical implementation of Riemann sheets: an analogy to an electromagnetic 'wormhole'

Inspired by the branch cut that can link two Riemann sheets in complex function theory, we utilize the branch cut to mimic an electromagnetic 'wormhole' linking two 2D 'parallel spaces' in a reference space. With the help of optical conformal mapping, we design a time-varying inhomogeneous medium that can effectively perform like an electromagnetic 'wormhole' in the real space. Based on this method, we can simulate the evolutionary process of an electromagnetic 'wormhole' and the wave propagation from one space to another in a laboratory environment. The proposed device may also be applied in light capture, light modulators, and absorption with directional dependence.

Optimized invisibility cloaks from the Logarithm conformal mapping

Invisibility cloaks designed from the coordinate transformation method have attracted increasing interest recently. Conformal transformation optics scheme leads to cloaks that possess isotopic media, thus provides a prospective way to facilitate easier realization. Reducing the maximum value of the refractive index required by the cloaks is very important in practical imple- mentation. This letter studies on how the parameters in the logarithm conformal mapping control the cloaking effect. The optimized invisibility cloaks are designed. The maximum values of the refractive index required from the first kind and the second kind of logarithm conformal mappings are reduced to 9.779 and 12.936, respectively.