Design method for quasi-isotropic transformation materials based on inverse Laplace's equation with sliding boundaries

The deformation method of transformation optics has been demonstrated to be a useful tool, especially in designing arbitrary and nonsingular transformation materials. Recently, there are emerging demands for isotropic material parameters, arising from the broadband requirement of the designed devices. In this work, the deformation method is further developed to design quasi-isotropic/isotropic transformation materials. The variational functional of the inverse Laplace's equation is investigated and found to involve the smooth and quasi-conformal nature of coordinate transformation. Together with the sliding boundary conditions, the inverse Laplace's equation can be utilized to give transformations which are conformal or quasi-conformal, depending on functionalities of interest. Examples of designing an arbitrary carpet cloak and a waveguide with arbitrary cross sections are given to validate the proposed idea. Compared with other quasi-conformal methods based on grid generation tools, the proposed method unifies the design and validation of transformation devices, and thus is much convenient.Comment: 8 pages, 4 figure

Carpet cloaking on a dielectric half-space

Carpet cloaking is proposed to hide an object on a dielectric half-space from electromagnetic (EM) detection. A two-dimensional conformal transformation specified by an analytic function is utilized for the design. Only one nonsingular material parameter distribution suffices for the characterization. The cloaking cover situates on the dielectric half-space, and consists of a lossless upper part for EM wave redirection and an absorbing bottom layer for inducing correct reflection coefficient and absorbing transmission. Numerical simulations with Gaussian beam incidence are performed for verification.Comment: 6 pages, 3 figure

Conformal carpet and grating cloaks

We introduce a class of conformal versions of the previously introduced quasi-conformal carpet cloak, and show how to construct such conformal cloaks for different cloak shapes. Our method provides exact refractive-index profiles in closed mathematical form for the usual carpet cloak as well as for other shapes. By analyzing their asymptotic behavior, we find that the performance of finite-size cloaks becomes much better for metal shapes with zero average value, e.g., for gratings.Comment: added Ref. 12; added 2 figures; reformatte

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.Comment: 11 pages, 6 figures, journal pape

Homogeneous optical cloak constructed with uniform layered structures

The prospect of rendering objects invisible has intrigued researchers for centuries. Transformation optics based invisibility cloak design is now bringing this goal from science fictions to reality and has already been demonstrated experimentally in microwave and optical frequencies. However, the majority of the invisibility cloaks reported so far have a spatially varying refractive index which requires complicated design processes. Besides, the size of the hidden object is usually small relative to that of the cloak device. Here we report the experimental realization of a homogenous invisibility cloak with a uniform silicon grating structure. The design strategy eliminates the need for spatial variation of the material index, and in terms of size it allows for a very large obstacle/cloak ratio. A broadband invisibility behavior has been verified at near-infrared frequencies, opening up new oppotunities for using uniform layered medium to realize invisibility at any frequency ranges, where high-quality dielectrics are available

Approaches to Three-Dimensional Transformation Optical Media Using Quasi-Conformal Coordinate Transformations

We introduce an approach to the design of three-dimensional transformation optical (TO) media based on a generalized quasi-conformal mapping approach. The generalized quasi-conformal TO (QCTO) approach enables the design of media that can, in principle, be broadband and low-loss, while controlling the propagation of waves with arbitrary angles of incidence and polarization. We illustrate the method in the design of a three-dimensional "carpet" ground plane cloak and of a flattened Luneburg lens. Ray-trace studies provide a confirmation of the performance of the QCTO media, while also revealing the limited performance of index-only versions of these devices

Cloaking and anamorphism for light and mass diffusion

We first review classical results on cloaking and mirage effects for electromagnetic waves. We then show that transformation optics allows the masking of objects or produces mirages in diffusive regimes. In order to achieve this, we consider the equation for diffusive photon density in transformed coordinates, which is valid for diffusive light in scattering media. More precisely, generalizing transformations for star domains introduced in [Diatta and Guenneau, J. Opt. 13, 024012, 2011] for matter waves, we numerically demonstrate that infinite conducting objects of different shapes scatter diffusive light in exactly the same way. We also propose a design of external light-diffusion cloak with spatially varying sign-shifting parameters that hides a finite size scatterer outside the cloak. We next analyse non-physical parameter in the transformed Fick's equation derived in [Guenneau and Puvirajesinghe, R. Soc. Interface 10, 20130106, 2013], and propose to use a non-linear transform that overcomes this problem. We finally investigate other form invariant transformed diffusion-like equations in the time domain, and touch upon conformal mappings and non-Euclidean cloaking applied to diffusion processes.Comment: 42 pages, Latex, 14 figures. V2: Major changes : some formulas corrected, some extra cases added, overall length extended from 21 pages (V1) to 42 pages (present version V2). The last version will appear at Journal of Optic

Hidden progress: broadband plasmonic invisibility

The key challenge in current research into electromagnetic cloaking is to achieve invisibility over an extended bandwidth. There has been significant progress towards this using the idea of cloaking by sweeping under the carpet of Li and Pendry, with dielectric structures superposed on a mirror. Here, we show that we can harness surface plasmon polaritons at a metal surface structured with a dielectric material to obtain a unique control of their propagation. We exploit this to control plasmonic coupling and demonstrate both theoretically and experimentally cloaking over an unprecedented bandwidth (650-900 nm). Our non-resonant plasmonic metamaterial allows a curved reflector to mimic a flat mirror. Our theoretical predictions are validated by experiments mapping the surface light intensity at the wavelength 800 nm