Conformal carpet and grating cloaks

Multi-functional lens based on conformal mapping

Based on conformal mapping method, a two dimensional, multi-functional lens structure is proposed and designed in this work. The lens is an infinitely-long, gradient-index dielectric cylinder with a semi-elliptic cross-section. The lens can first be considered like a flattened Luneburg lens, which produces highly-directive electromagnetic waves by adjusting the feed position along the line connecting the two foci. It also functions like an Eaton lens. When an incoming beam impinges on the same line but outside the two foci, it will be guided through the lens structure and take a U-turn. Besides, if properly shaped, the structure can also be used as a waveguide bend. The lens can be realized using non-resonant metamaterials with inhomogeneous hole arrays. Simulation results demonstrate excellent performance of the lens and agree well with theoretical prediction. The designed lens can be used in the electromagnetic control. And it is especially useful in the real optical lens system.

Conceptual design of a beam steering lens through transformation electromagnetics

In this paper, based on transformation electromagnetics, the design procedure of a lens antenna, which steers the radiated beam of a patch array, is presented. Laplace's equation is adopted to construct the mapping between the virtual space and the physical space. The two dimensional (2D) design method can be extended to a potential three-dimensional (3D) realization, and with a proper parameter simplification, the lens can be further realized by common metamaterials or isotropic graded refractive index (GRIN) materials. Full wave simulations are performed to validate the proposed concept. It is observed that by placing the lens on a feeding source, we are able to steer the radiation emitted by the latter source.

Design of conformal lens by drilling holes materials using quasi-conformal transformation optics

In this paper, based on quasi-conformal transformation optics, a 3D conformal lens made of isotropic and non-resonant metamaterial is designed, which can make a cylindrical conformal array behave similarly to a uniform linear array. After discussion and simplification in the two-dimensional model, we realize the proposed lens by utilizing drilling-hole material in the three-dimensional structure. The ring-like shape and forward-only radiation make it possible to equip the lens on a cylindrical device.

Metamaterials beyond electromagnetism

Metamaterials are rationally designed man-made structures composed of functional building blocks that are densely packed into an effective (crystalline) material. While metamaterials are mostly associated with negative refractive indices and invisibility cloaking in electromagnetism or optics, the deceptively simple metamaterial concept also applies to rather different areas such as thermodynamics, classical mechanics (including elastostatics, acoustics, fluid dynamics and elastodynamics), and, in principle, also to quantum mechanics. We review the basic concepts, analogies and differences to electromagnetism, and give an overview on the current state of the art regarding theory and experiment-all from the viewpoint of an experimentalist. This review includes homogeneous metamaterials as well as intentionally inhomogeneous metamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics. Examples are laminates, transient thermal cloaks, thermal concentrators and inverters, 'space-coiling' metamaterials, anisotropic acoustic metamaterials, acoustic free-space and carpet cloaks, cloaks for gravitational surface waves, auxetic mechanical metamaterials, pentamode metamaterials ('meta-liquids'), mechanical metamaterials with negative dynamic mass density, negative dynamic bulk modulus, or negative phase velocity, seismic metamaterials, cloaks for flexural waves in thin plates and three-dimensional elastostatic cloaks.

Photorealistic rendering of unidirectional free-space invisibility cloaks

Carpet or ground-plane invisibility cloaks hide an object in reflection and inhibit transmission experiments by construction. This concept has significantly reduced the otherwise demanding material requirements and has hence enabled various experimental demonstrations. In contrast, free-space invisibility cloaks should work in both reflection and transmission. The fabrication of omnidirectional three-dimensional free-space cloaks still poses significant challenges. Recently, the idea of the carpet cloak has been carried over to experiments on unidirectional free-space invisibility cloaks that only work perfectly for one particular viewing direction and, depending on the design, also for one linear polarization of light only. Here, by using photorealistic ray tracing, we visualize the performance of four types of such unidirectional cloaks in three dimensions for different viewing directions and different polarizations of light, revealing virtues and limitations of these approaches in an intuitive manner.

Wide-angle scannable reflector design using conformal transformation optics

A flat reflector capable of scanning over wide angles is designed using a transformation optics approach. This reflector is derived from its virtual parabolic counterpart using a conformal coordinate transformation that determines the permittivity profile of the flat reflector. By changing the permittivity profile, the flat reflector is then capable of scanning up to 47° away from broadside while maintaining good beam characteristics across a wide frequency range. Moreover, its directivity is comparable to that of the virtual parabolic reflector, even at high scan angles. We use the Schwarz-Christoffel transformation as a versatile tool to produce perfect conformal mapping of coordinates between the virtual and flat reflectors, thereby avoiding the need to monitor the anisotropy of the material that results when employing quasi-conformal methods.

First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping

In the past years quasi-conformal mapping has been generally used to design broadband electromagnetic cloaks. However, this technique has some inherit practical limitations such as the lateral beam shift, rendering the device visible or difficult to hide a large object. In this work we circumvent these issues by using strict conformal mapping to build the first isotropic cloak. Microwave near-field measurement shows that our device (with dielectric constant larger than unity everywhere) has a very good cloaking performance and a broad frequency response. The present dielectric approach could be technically extended to the fabrication of other conformal devices at higher frequencies.

Photorealistic ray tracing of free-space invisibility cloaks made of uniaxial dielectrics

The design rules of transformation optics generally lead to spatially inhomogeneous and anisotropic impedance-matched magneto-dielectric material distributions for, e.g., free-space invisibility cloaks. Recently, simplified anisotropic non-magnetic free-space cloaks made of a locally uniaxial dielectric material (calcite) have been realized experimentally. In a two-dimensional setting and for in-plane polarized light propagating in this plane, the cloaking performance can still be perfect for light rays. However, for general views in three dimensions, various imperfections are expected. In this paper, we study two different purely dielectric uniaxial cylindrical free-space cloaks. For one, the optic axis is along the radial direction, for the other one it is along the azimuthal direction. The azimuthal uniaxial cloak has not been suggested previously to the best of our knowledge. We visualize the cloaking performance of both by calculating photorealistic images rendered by ray tracing. Following and complementing our previous ray-tracing work, we use an equation of motion directly derived from Fermat's principle. The rendered images generally exhibit significant imperfections. This includes the obvious fact that cloaking does not work at all for horizontal or for ordinary linear polarization of light. Moreover, more subtle effects occur such as viewing-angle-dependent aberrations. However, we still find amazingly good cloaking performance for the purely dielectric azimuthal uniaxial cloak.

Time-of-flight imaging of invisibility cloaks

As invisibility cloaking has recently become experimental reality, it is interesting to explore ways to reveal remaining imperfections. In essence, the idea of most invisibility cloaks is to recover the optical path lengths without an object (to be made invisible) by a suitable arrangement around that object. Optical path length is proportional to the time of flight of a light ray or to the optical phase accumulated by a light wave. Thus, time-of-flight images provide a direct and intuitive tool for probing imperfections. Indeed, recent phase-sensitive experiments on the carpet cloak have already made early steps in this direction. In the macroscopic world, time-of-flight images could be measured directly by light detection and ranging (LIDAR). Here, we show calculated time-of-flight images of the conformal Gaussian carpet cloak, the conformal grating cloak, the cylindrical free-space cloak, and of the invisible sphere. All results are obtained by using a ray-velocity equation of motion derived from Fermat's principle.

Newtonian photorealistic ray tracing of grating cloaks and correlation-function-based cloaking-quality assessment

Grating cloaks are a variation of dielectric carpet (or ground-plane) cloaks. The latter were introduced by Li and Pendry. In contrast to the numerical work involved in the quasi-conformal carpet cloak, the refractive-index profile of a conformal grating cloak follows a closed and exact analytical form. We have previously mentioned that finite-size conformal grating cloaks may exhibit better cloaking than usual finite-size carpet cloaks. In this paper, we directly visualize their performance using photorealistic ray-tracing simulations. We employ a Newtonian approach that is advantageous compared to conventional ray tracing based on Snell's law. Furthermore, we quantify the achieved cloaking quality by computing the cross-correlations of rendered images. The cross-correlations for the grating cloak are much closer to 100% (i.e., ideal) than those for the Gaussian carpet cloak.