We examine the effectiveness of the ground-plane invisibility cloak generated from quasiconformal mapping of electromagnetic space. This cloak without anisotropy will generally lead to a lateral shift of the scattered wave, whose value is comparable to the height of the cloaked object, making the object detectable. This can be explained by the fact that the corresponding virtual space is thinner and wider than it should be. Ray tracing on a concrete model shows that, for a bump with a maximum height of 0.2 units to be hidden, the lateral shift of a ray with 45° incidence is around 0.15 units.

Lateral Shift Makes a Ground-Plane Cloak Detectable

This letter presents a method to realize anisotropic two-dimensional designs with wideband operation. Glide symmetry has been proven to increase the bandwidth and equivalent refractive index of periodic structures. Here, two anisotropic glide-symmetric unit cells are proposed and characterized. Our simulated results prove that these unit cells follow the general behavior of periodic structures possessing glide symmetry. Moreover, we demonstrate that higher level of anisotropy can also be achieved by glide symmetry. Combining our proposed anisotropic glide-symmetric unit cell and transformation optics, a $\text{30}\%$ compressed Luneburg lens is designed. The lens operates from 1 to 13 GHz.

Ultrawideband Anisotropic Glide-Symmetric Metasurfaces

Plane-wave reflection and transmission in a planar interface between air and an axially chiral uniaxial medium whose axis is parallel to the interface is considered in the present study. By finding the reflection dyadic and its eigensolutions, we demonstrate that by dimensioning the uniaxial medium in a proper way, it is possible to make a reflection-transforming reflecting surface. The surface is able to transform the incident linear polarization into any other polarization with chosen axial ratio and handedness, and the reflected polarization can be continuously adjusted by rotating the surface around its normal direction. The reflected power is seen to be independent of the polarization of the reflected wave.

Plane-wave reflection from uniaxial chiral interface and its application to polarization transformation

Photonic crystal waveguide crossing based on transformation optics

A circular graded index lens is conformally transformed to an elliptical shape using a closed-form transformation. The proposed transformation is then employed to compress a Maxwell fish-eye and it ...

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Elliptical generalized Maxwell fish-eye lens using conformal mapping

We present a general method of designing optical devices based on optical conformal mapping and rescaling the optical path along a given bunch of rays. It provides devices with the same functionality as those based purely on conformal mapping, but enables to manipulate the refractive index to a great extent—for instance, eliminate superluminal regions of space as well as reduce the refractive index in other regions significantly. The method is illustrated in two examples, a waveguide coupler and a plasmonic bump cloak, and numerical simulations confirm its functionality.

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Controlling refractive index of transformation-optics devices via optical path rescaling.

Here, we demonstrate that transformation optics can be used to produce 2-D non-magnetic waveguide couplers with no reflections. Our approach consists of using a scaling function for reflection suppression and introducing an auxiliary function in the transformation optics formulation to achieve a non-magnetic medium for coupling the TM polarization. To demonstrate the potential of this method, two non-magnetic waveguide couplers are designed. The first one satisfies the Brewster angle condition for any arbitrary incidence angle (TMn modes), extending the performance of couplers previously reported in the literature that only operate for TEM (TM0 mode), i.e. waves with normal incidence. Our method can be applied to match any given dielectric constant. Our results demonstrate that for a given mode (angle), we achieve a perfect match to a defined dielectric constant. The second design removes the dependence of the reflectionless condition to the incident angle at the boundary. Hence, this coupler works for all incident angles (TMn modes). It is used to compress all the modes into a region with a higher predefined refractive index.

Transformation optics for perfect two-dimensional non-magnetic all-mode waveguide couplers

Design and realization of polarization splitting devices present several common challenges. Unwanted reflections from boundaries of the device and material anisotropy are among the major ones. We present a transformation electromagnetics-based method to design non-magnetic homogeneous polarization splitters that are reflectionless and have minimum anisotropy. This is accomplished by utilizing an area-preserving linear transformation with proper reflectionless conditions at the input and the output boundaries of the device. The condition of minimum anisotropy is determined analytically. This is done for the first time, to the best of our knowledge. The proposed devices enhance the performance of the optical systems by providing ideal transmission. The realizability of the device is also improved by minimization of the anisotropy. Several polarization splitters are designed which create an arbitrary deflection angle or lateral shift between TE and TM polarizations. In addition, the effective medium theory is employed to realize one of the designs by using equivalent dielectric layers. In order to verify the proposed methodology, the designed devices are simulated by the commercial software COMSOL Multiphysics.

Design of reflectionless non-magnetic homogeneous polarization splitters with minimum anisotropy based on transformation electromagnetics

In this paper, we propose a reflectionless design of an optical waveguide coupler that is nonmagnetic and homogeneous. The coupler is designed using the linear coordinate transformation of triangles from virtual space to physical space. The common problem of reflections from the boundaries of a nonmagnetic coupler is remedied by analytically specifying the common vertex of triangles in such a way that the Jacobian matrix determinant becomes equal for all transformed triangles. The device performs ideal transmission without distorting the beam profile. We employ the effective medium theory to demonstrate the realizability of the device by using consecutive dielectric layers. We present a procedure to specify the dielectric constants of the layers from common existing optical materials. Numerical finite-element simulations confirm the functionality and the reflectionless property of the proposed designs.

Hossein Eskandari

Papers

Elliptical generalized Maxwell fish-eye lens using conformal mapping

Controlling refractive index of transformation-optics devices via optical path rescaling.

Transformation optics for perfect two-dimensional non-magnetic all-mode waveguide couplers

Design of reflectionless non-magnetic homogeneous polarization splitters with minimum anisotropy based on transformation electromagnetics

Reflectionless design of a nonmagnetic homogeneous optical waveguide coupler based on transformation optics