Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the calculation of these material properties for coordinate transformations that describe spaces with spherical or cylindrical holes in them. The resulting material properties can then implement invisibility cloaks in flat space. We also describe a method for performing geometric ray tracing in these materials which are both inhomogeneous and anisotropic in their electric permittivity and magnetic permeability.
In this paper, we review the methodology of transformation optics, which can construct invisibility cloak through the transformation of coordinates based on the form invariance of Maxwell's equations. Three different ways to define the components of electromagnetic fields are compared for removing some ambiguities. The analytical expressions of light-ray and wave-normal ray are derived in spherical and cylindrical ideal invisibility cloaks created with any continuous radial transformation functions, and their physical interpretation is also given. Using the duality principle in anisotropic med…
Multiple light scattering hampers imaging objects in complex scattering media. Approaches used in real practices mainly aim to filter out multiple scattering obscuring the ballistic waves that travel straight through the scattering medium. Here, we propose a method that makes the deterministic use of multiple scattering for microscopic imaging of an object embedded deep within scattering media. The proposed method finds a stack of multiple complex phase plates that generate similar light trajectories as the original scattering medium. By implementing the inverse scattering using the identified…
Electromagnetic wave behaviour in an anisotropic medium with a two dimensional arbitrary geometry is studied. The aim is to trace the path of a ray in such a complex medium for the purpose of achieving cloaking (invisibility). A coordinate transformation is carried out for the formulation of an annular region at the centre of the structure whose topology is a scaled geometry of outer boundary of the structure.
It is well known that optical media create artificial geometry for light, and curved geometry acts as an effective optical medium. This correspondence originates from the form invariance of Maxwells equations, which recently has spawned a booming field called transformation optics. Here we investigate responses of three transformation media under electromagnetic pulses, and find that pulse radiation can induce unbalanced net force on transformation media, which will cause translation and rotation of transformation media although their final momentum can still be zero. Therefore, the transforma…
The Lorentz transformations for the optical constants (electric permittivity, magnetic permeability and index of refraction) of moving media are considered.
We present preliminary results on a novel numerical method describing wave propagation in non-uniform media. Following Huygens-Fresnel' principle, we model the wavefront as an array of point sources that emit wavelets, which interfere. We then identify a set of new points where the electric field has equal phase. In fact, without losing generality, we find zeros of the electric field, by means of the bisection method. This obviously corresponds to a specific phase-advance, but is easily generalized, e.g. by phase-shifting all sources. The points found form the new wavefront. One of the advanta…
Previous formulations of transformation optics have generally been restricted to transformations from relatively simple initial media, such as the vacuum, because of limitations due to their non-covariance. I show that a completely covariant approach enables arbitrary transformations from arbitrarily complex initial linear dielectrics.
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 geometrical interpretation of electromagnetism in transparent media (transformation optics) is extended to include media with isotropic, inhomogeneous, chirality. It is found that such media may be described through introducing the non-Riemannian geometrical property of torsion into the Maxwell equations, and shown how such an interpretation may be applied to the design of optical devices.
We show how transformation media can make a superantenna that is either completely invisible or focuses incoming light into a needle-sharp beam. Our idea is based on representating three-dimensional space as a foliage of sheets and performing two-dimensional conformal maps on each sheet
Conventional method for Gaussian beam collimation is to expand the beam waist to achieve a smaller divergence angle. Recent transformation optics offers an unconventional path to control the electromagnetic field. In this paper we show that a Gaussian beam can be converted into a plane wave-like beam by transformation media within the scale of several wavelengths. Design details and full-wave simulation results via finite element method are provided.
The technique of transformation optics (TO) is an elegant method for the design of electromagnetic media with tailored optical properties. In this paper, we focus on the formal structure of TO theory. By using a complete covariant formalism, we present a general transformation law that holds for arbitrary materials including bianisotropic, magneto-optical, nonlinear and moving media. Due to the principle of general covariance, the formalism is applicable to arbitrary space-time coordinate transformations and automatically accounts for magneto-electric coupling terms. The formalism is demonstra…
The advent of transformation optics has lead to the initiation of designing devices and applications associated to electromagnetic wave propagation in anisotropic media. Here, a method is suggested using a coordinate transformation with spherical coordinates for the purpose of designing a three dimensional cloak for a body having an arbitrary convex geometry. For the purpose of verification of the algorithm, a ray tracing process is carried out for an ellipsoid having axial symmetry.
Transformation-media designed by standard transformation-optics (TO) approaches, based on real-valued coordinate-mapping, cannot exhibit single-negative (SNG) character unless such character is already possessed by the domain that is being transformed. In this paper, we show that, for a given field polarisation, pseudo-SNG transformation media can be obtained by transforming a domain featuring double positive (or double-negative) character, via complex analytic continuation of the coordinate transformation rules. Moreover, we apply this concept to the TO-based interpretation of phenomena analo…
Based on the transformation media theory, the authors propose a way to replace a wide window with a narrow slit filled with designed metamaterial to achieve the same transmittance as the one of the window. Numerical simulations for a two dimensional case are given to illustrate the ideas and the performance of the design.
We propose a general method to evaluate the material parameters for arbitrary shape transformation media. By solving the original coordinates in the transformed region via Laplace's equations, we can obtain the deformation field numerically, in turn the material properties of the devices to be designed such as cloaks, rotators or concentrators with arbitrary shape. Devices which have non-fixed outer boundaries, such as beam guider, can also be designed by the proposed method. Examples with full wave simulation are given for illustration. In the end, wave velocity and energy change in the trans…
In this paper the interface between two transformation media or between a transformation medium and vacuum is studied. Strictly from the transformation optics point of view the consequences of the boundary conditions at such interfaces are addressed in two different ways. First, we analyze a restricted class of reflectionless interfaces, for which the tools of transformation optics allow to describe the electromagnetic fields on both sides of the interface by means of the same vacuum solution of the Maxwell equations. In a second step, we examine interfaces between two arbitrary transformation…
We suggest a way to manipulate electromagnetic wave by introducing a rotation mapping of coordinates that can be realized by a specific transformation of permittivity and permeability of a shell surrounding an enclosed domain. Inside the enclosed domain, the information from outside will appear as if it comes from a different angle. Numerical simulations were performed to illustrate these properties.
Via solution of appropriate variational problem it is shown that light beams with Gaussian spatial profile and sufficiently short duration provide maximal destruction of global coherence under nonlinear self-modulation.
The onset of transformation optics has opened avenues for designing of a plenitude of applications related to propagation of electromagnetic waves in anisotropic media. In this paper, an algorithm is proposed using a coordinate transformation and a piecewise function for the purpose of designing a three dimensional cloak having an arbitrary geometry which could be convex or non-convex in nature. The surfaces of the cloak as well as of the body under consideration are assumed to be conformal to each other. For an arbitrary geometry, the coordinate system needed to model the surface can be a non…
Starting from optical nihility media (ONM), we design several intriguing devices with transformation optics method in two dimensions, such as a wave splitter, a concave lens, a field rotator, a concentrator and an invisibility cloak. The extreme anisotropic property of ONM hinders the fabrication of these devices, which could be effectively realized by simplified materials with Fabry-Pérot resonances (FPs) at discrete frequencies. Moreover, we propose a reduced version of simplified materials with FPs to construct a concentrator and a rotator, which is feasible in experimental fabrications. Th…
We introduce a class of optical media based on adiabatically modulated, dielectric-only, and potentially extremely low-loss, photonic crystals. The media we describe represent a generalization of the eikonal limit of transformation optics (TO). The foundation of the concept is the possibility to fit frequency isosurfaces in the k-space of photonic crystals with elliptic surfaces, allowing them to mimic the dispersion relation of light in anisotropic effective media. Photonic crystal cloaks and other TO devices operating at visible wavelengths can be constructed from optically transparent subst…
We propose a scheme to controllably convert the wavefront of an arbitrary incident beam into a helical one by compact transformation slabs, thus enabling the output beam to carry desirable orbital angular momentum (OAM). First, based on transformation optics, a three-dimensional (3D) phase transformation between any two wavefronts by °at transformation media is established and then used to mold a wavefront of Gaussian beam into a helical one. Second, 3D FDTD simulations are performed to confirm the spiraling evolutions of the resultant field and phase, clearly demonstrating OAM generated. Furt…
Transformation optics offers an unconventional approach to the control of electromagnetic fields. A transformation optical structure is designed by first applying a form-invariant coordinate transform to Maxwell's equations, in which part of free space is distorted in some desired manner. The coordinate transformation is then applied to the permittivity and permeability tensors to yield the specification for a complex medium with desired functionality. The transformation optical structures proposed to date, such as electromagnetic "invisibility" cloaks and concentrators, are inherently reflect…
We present a way of exciting surface plasmon polaritons along non-patterned metallic surfaces by means of a flat squeezing slab designed with transformation optics. The slab changes the dispersion relation of incident light, enabling evanescent coupling to propagating surface plasmons. Unlike prism couplers, the proposed device does not introduce reflections at its input interface. Moreover, its compact geometry is suitable for integration. A feasible dielectric implementation of the coupler is suggested. Finally, we show that the angular response of the device can be engineered by using a non…
Based on operations prescribed under the paradigm of Complex Transformation Optics (CTO) [1-5], it was recently shown in [5] that a complex source point (CSP) can be mimicked by a parity-time ($\mathcal{PT}$) transformation media. Such coordinate transformation has a mirror symmetry for the imaginary part, and results in a balanced loss/gain metamaterial slab. A CSP produces a Gaussian beam and, consequently, a point source placed at the center of such metamaterial slab produces a Gaussian beam propagating away from the slab. Here, we extend the CTO analysis to non-symmetric complex coordinate…
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 thi…
The applications of vortex beam in biomedical field are always hindered by light scattering of biological tissues. Recently wavefront shaping technology has shown the potential in focusing a structured light field through scattering media. Herein we have proposed a novel theory to describe the field transformation property of the opaque lens. This theory makes it possible to generate foci with specified amplitude and phase profiles by well-designing the incident field. We verify the validity of this theory by experimentally generating doughnut-shaped foci with various topological charges, and …
It has been known that, keeping the outer boundary coordinates intact before and after a coordinate transformation is a sufficient condition for obtaining a reflectionless transformation medium. Here we prove that it is also a necessary condition for reflectionless transformation media in an isotropic and homogenous background. Our analytical results show that the outer boundary coordinates of a reflectionless transformation medium must be the same as the original coordinates with a combination of rotation and displacement, which is equivalent to situation that the boundary coordinates are kep…
In this letter first we show that the equation of null geodesics in spherically symmetric spacetimes in isotropic coordinates is identical to the equation of light ray trajectories in isotropic media in flat spacetime. Based on this analogy we introduce an exact simulation of the light ray trajectories both in these spacetimes and in their metamaterial analogs in terms of the spacetime index of refraction. As unstable light trajectories, the photon spheres form in these metamaterial analogs at {\it exactly} the same radial distances as expected from the corresponding black hole geometries. Usi…
Exact results concerning ray-tracing methods in Plebanski-Tamm media are derived. In particular, Hamilton equations describing the propagation of quasi-plane wave electromagnetic fields in the geometrical optics regime are explicitly written down in terms of the 3-metric representing the properties of the optical analogue, anisotropic medium. We exemplify our results by obtaining the trajectories of light in the resulting analogue medium recreating Gödel's universe.
We give a comprehensive study on regularized approximate electromagnetic cloaking via the transformation optics approach. The following aspects are investigated: (i) near-invisibility cloaking of passive media as well as active/radiating sources; (ii) the existence of cloak- busting inclusions without lossy medium lining; (iii) overcoming the cloaking-busts by employing a lossy layer outside the cloaked region; (iv) the frequency dependence of the cloaking performances. We address these issues and connect the obtained asymptotic results to singular ideal cloaking. Numerical verifications and d…
We introduce a new concept for the manipulation of fluid flow around three-dimensional bodies. Inspired by transformation optics, the concept is based on a mathematical idea of coordinate transformations and physically implemented with anisotropic porous media permeable to the flow of fluids. In two situations - for an impermeable object placed either in a free-flowing fluid or in a fluid-filled porous medium - we show that the object can be coated with an inhomogeneous, anisotropic permeable medium, such as to preserve the flow that would have existed in the absence of the object. The propose…
The author proposes the methodology of transformation optics in orthogonal coordinates to obtain the material parameters of the transformation media from the mapping in orthogonal coordinates. Several examples are given to show the applications of such a methodology by using the full-wave simulations.
In this work a transformation acoustics scheme for generic elastic media is developed. Our approach starts form the decomposition of the elasticity tensor in terms of its eigentensors, an idea previously used by Norris. While Norris' transformation acoustics is restricted to the special class of so-called pentamode materials, we show that a similar scheme can be defined for the most general elasticity tensor. As in case of Norris' model (and in sharp contrast to transformation optics), the compatibility equations of the transformation medium are not purely algebraic and it is not guaranteed th…
Despite the virtues of Jones and Mueller formalisms for the representation of the polarimetric properties, for some purposes in both Optics and SAR Polarimetry, the concept of coherency vector associated with a nondepolarizing medium has proven to be an useful mathematical structure that inherits certain symmetries underlying the nature of linear polarimetric transformations of the states of polarization of light caused by its interaction with material media. While the Jones and Mueller matrices of a serial combination of devices are given by the respective conventional matrix products, the co…
We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a finite period τ, as a phenomenologically realistic and sigmoidal change of the dielectric permittivity, an analytically exact solution to Maxwell's equations is derived for the electric displacement in terms of hypergeometric functions. Using this solution, we show the possibility of amplification and attenuation of waves and associate this with the decreas…
In this work, a plasmonic right-angled waveguide bend and divider are proposed. Using the Transformation Optics (TO) approach the transformation media of a bend and a T-shaped divider are obtained. Such media with continuous refractive index are realized with the help of graphene in the terahertz frequency range, key to effectively guiding the surface plasmon polariton (SPP) propagation on the 90 degree curves. Components with such capability are promising for THz device applications.
The coordinate transformation on the space that contains electromagnetic sources is studied. We find that, not only the permittivity and permeability tensors of the media, but also the sources inside the media will take another form in order to behave equivalently as the original case. It is demonstrated that, a source of arbitrary shape and position in the free space can be replaced by an appropriately designed metamaterial coating with current distributed on the inner surface and would not be detected by outer observers, because the emission of the source can be controlled at will in this wa…
While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance -- form invariance under general coordinate transformations, including between accelerating frames -- that led to general relativity. Several lines of inquiry over the past two decades, notably the development of metamaterial-based transformation optics, has spurred a greater interest in the role of geometry and space-time covariance for electrodynamics in ponderable media. I develop a generally covariant, coordinate-free framew…
In this paper various extensions of the design strategy of transformation media are proposed. We show that it is possible to assign different transformed spaces to the field strength tensor (electric field and magnetic induction) and to the excitation tensor (displacement field and magnetic field), resp. In this way, several limitations of standard transformation media can be overcome. In particular it is possible to provide a geometric interpretation of non-reciprocal as well as indefinite materials. We show that these transformations can be complemented by a continuous version of electric-ma…
One potentially realistic specification for devices designed with transformation optics is that they operate with high precision in curved space-time, such as Earth orbit. This raises the question of what, if any, role does space-time curvature play in determining transformation media? Transformation optics has been based on a three-vector representation of Maxwell's equations in flat Minkowski space-time. I discuss a completely covariant, manifestly four-dimensional approach that enables transformations in arbitrary space-times, and demonstrate this approach for stable circular orbits in the …
We experimentally show the results of the illusion device designed by the transformation optics (TO) technique. The coordinate transformation maps a zero thickness in virtual space to a finite region in physical space, yielding extreme material properties called optical null media (ONM). As a result, an object placed inside the core media will look larger to an outside observer. ONM media is realized using metal-dielectric layered structures in cylindrical coordinates. Also closed-form solutions for the scattering field from a cylindrical object are given in detail to prove illusion effect ana…
There is currently a great deal of interest in the invisibility cloaks recently proposed by Pendry et al. that are based in the transformation approach. They obtained their results using first order transformations. In recent papers Hendi et al. and Cai et al. considered invisibility cloaks with high order transformations. In this paper we study high order electromagnetic invisibility cloaks in transformation media obtained by high order transformations from general anisotropic media. We consider the case where there is a finite number of spherical cloaks located in different points in space. …
