Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics
Abstract
We describe recent theoretical and experimental progress on making objects invisible to detection by electromagnetic waves. Ideas for devices that would once have seemed fanciful may now be at least approximately implemented physically using a new class of artificially structured materials called metamaterials. Maxwell's equations have transformation laws that allow for the design of electromagnetic material parameters that steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was being hidden. An object contained in the hidden region, which would have no shadow, is said to be cloaked. Proposals for, and even experimental implementations of, such cloaking devices have received the most attention, but other designs having striking effects on wave propagation are possible. All of these designs are initially based on the transformation laws of the equations that govern wave propagation but, due to the singular parameters that give rise to the desired effects, care needs to be taken in formulating and analyzing physically meaningful solutions. We recount the recent history of the subject and discuss some of the mathematical and physical issues involved.
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Submitted: 27 February 2008
Accepted: 5 September 2008
Published online: 5 February 2009
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- On Electromagnetic Scattering from a Penetrable CornerSIAM Journal on Mathematical Analysis, Vol. 49, No. 6 | 21 December 2017
- Full and Partial Cloaking in Electromagnetic ScatteringArchive for Rational Mechanics and Analysis, Vol. 223, No. 1 | 20 August 2016
- Quantum metamaterials in the microwave and optical rangesEPJ Quantum Technology, Vol. 3, No. 1 | 20 February 2016
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- Metamaterials and imagingNano Convergence, Vol. 2, No. 1 | 9 November 2015
- Invisibility and Cloaking: Origins, Present, and Future PerspectivesPhysical Review Applied, Vol. 4, No. 3 | 1 September 2015
- Some a priori estimates of solutions to the Maxwell equationsMathematical Methods in the Applied Sciences, Vol. 38, No. 11 | 14 July 2014
- Regularized Transformation-Optics Cloaking for the Helmholtz Equation: From Partial Cloak to Full CloakCommunications in Mathematical Physics, Vol. 335, No. 2 | 18 February 2015
- Total Reflection and Cloaking by Triangular Defects Embedded in Zero Index MetamaterialsAdvances in Applied Mathematics and Mechanics, Vol. 7, No. 2 | 23 March 2015
- Accurate Simulation of Circular and Elliptic Cylindrical Invisibility CloaksCommunications in Computational Physics, Vol. 17, No. 3 | 24 March 2015
- Inverse problems and invisibility cloaking for FEM models and resistor networksMathematical Models and Methods in Applied Sciences, Vol. 25, No. 02 | 24 November 2014
- Uniqueness and Nonuniqueness in Inverse Problems for Elliptic Partial Differential Equations and Related Medical ImagingAdvances in Mathematical Physics, Vol. 2015 | 1 Jan 2015
- On the Existence of Weak Optimal Controls in the Coefficients for a Degenerate Anisotropic p-LaplacianContinuous and Distributed Systems II | 5 June 2015
- Well-posedness study for a time-domain spherical cloaking modelComputers & Mathematics with Applications, Vol. 68, No. 12 | 1 Dec 2014
- Perfect cloaking of ellipsoidal regionsQuarterly of Applied Mathematics, Vol. 72, No. 4 | 25 September 2014
- Towards a Piecewise-Homogeneous Metamaterial Model of the Collision of Two Linearly Polarized Gravitational Plane WavesIEEE Transactions on Antennas and Propagation, Vol. 62, No. 12 | 1 Dec 2014
- Controlling Cherenkov Radiation with Transformation-Optical MetamaterialsPhysical Review Letters, Vol. 113, No. 16 | 16 October 2014
- An efficient plate heater with uniform surface temperature engineered with effective thermal materialsOptics Express, Vol. 22, No. 14 | 3 July 2014
- Inverse problems: seeing the unseenBulletin of Mathematical Sciences, Vol. 4, No. 2 | 5 June 2014
- An analogy strategy for transformation opticsNew Journal of Physics, Vol. 16, No. 6 | 5 June 2014
- Nearly cloaking the full Maxwell equations: Cloaking active contents with general conducting layersJournal de Mathématiques Pures et Appliquées, Vol. 101, No. 5 | 1 May 2014
- Analysis of an approximate cloaking for acoustic scattering problems in R3Applied Mathematics and Computation, Vol. 232 | 1 Apr 2014
- Enhanced approximate cloaking by optimal change of variablesInverse Problems, Vol. 30, No. 3 | 21 February 2014
- Estimates of scattered electromagnetic fieldsMathematical Methods in the Applied Sciences, Vol. 37, No. 2 | 19 August 2013
- Nearly Cloaking the Electromagnetic FieldsSIAM Journal on Applied Mathematics, Vol. 74, No. 3 | 3 June 2014
- Mathematical Analysis and Time-Domain Finite Element Simulation of Carpet CloakSIAM Journal on Applied Mathematics, Vol. 74, No. 4 | 31 July 2014
- Invisibility Regions and Regular MetamaterialsApplications of Mathematics and Informatics in Science and Engineering | 29 March 2014
- An adaptive edge finite element method for electromagnetic cloaking simulationJournal of Computational Physics, Vol. 249 | 1 Sep 2013
- Fluid-structure effects of cloaking a submerged spherical shellThe Journal of the Acoustical Society of America, Vol. 134, No. 3 | 1 Sep 2013
- Spectral Theory of a Neumann–Poincaré-Type Operator and Analysis of Cloaking Due to Anomalous Localized ResonanceArchive for Rational Mechanics and Analysis, Vol. 208, No. 2 | 7 March 2013
- Numerical simulations of cloaking problems using a DPG methodComputational Mechanics, Vol. 51, No. 5 | 22 June 2012
- Regular scattering patterns from near-cloaking devices and their implications for invisibility cloakingInverse Problems, Vol. 29, No. 4 | 22 March 2013
- Optical contrast analysis and reflectance optimization of photonic clusters: an analytical approachJournal of Optics, Vol. 15, No. 3 | 16 January 2013
- On near-cloak in acoustic scatteringJournal of Differential Equations, Vol. 254, No. 3 | 1 Feb 2013
- Enhancement of Near Cloaking for the Full Maxwell EquationsSIAM Journal on Applied Mathematics, Vol. 73, No. 6 | 12 November 2013
- Introduction to MetamaterialsTime-Domain Finite Element Methods for Maxwell's Equations in Metamaterials | 20 October 2012
- Introduction to Finite Element MethodsTime-Domain Finite Element Methods for Maxwell's Equations in Metamaterials | 20 October 2012
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- Enhancement of Near Cloaking Using Generalized Polarization Tensors Vanishing Structures. Part I: The Conductivity ProblemCommunications in Mathematical Physics, Vol. 317, No. 1 | 11 November 2012
- Enhancement of Near-Cloaking. Part II: The Helmholtz EquationCommunications in Mathematical Physics, Vol. 317, No. 2 | 11 November 2012
- Enhanced near-cloak by FSH liningJournal de Mathématiques Pures et Appliquées, Vol. 99, No. 1 | 1 Jan 2013
- On an Optimal -Control Problem in Coefficients for Linear Elliptic Variational InequalityAbstract and Applied Analysis, Vol. 2013 | 1 Jan 2013
- Recovering boundary shape and conductivity in electrical impedance tomographyInverse Problems & Imaging, Vol. 7, No. 1 | 1 Jan 2013
- Transformation Elastodynamics and Active Exterior Acoustic CloakingAcoustic Metamaterials | 1 Jan 2013
- A Matlab Edge Element Code for MetamaterialsTime-Domain Finite Element Methods for Maxwell's Equations in Metamaterials | 20 October 2012
- Perfectly Matched LayersTime-Domain Finite Element Methods for Maxwell's Equations in Metamaterials | 20 October 2012
- Discontinuous Galerkin Methods for MetamaterialsTime-Domain Finite Element Methods for Maxwell's Equations in Metamaterials | 20 October 2012
- A Posteriori Error EstimationTime-Domain Finite Element Methods for Maxwell's Equations in Metamaterials | 20 October 2012
- Superconvergence Analysis for MetamaterialsTime-Domain Finite Element Methods for Maxwell's Equations in Metamaterials | 20 October 2012
- Comparison of tunneling times in isotropic and anisotropic mediaApplied Physics A, Vol. 109, No. 4 | 14 November 2012
- Refractive properties of metamaterial composed of InGaAs layers with alternating doping densitiesJournal of Electromagnetic Waves and Applications, Vol. 26, No. 17-18 | 10 October 2012
- Invisibility and Cloaking Based on Scattering CancellationAdvanced Materials, Vol. 24, No. 44 | 19 October 2012
- Special transformations for pentamode acoustic cloakingThe Journal of the Acoustical Society of America, Vol. 132, No. 4 | 3 October 2012
- Enhanced approximate cloaking by SH and FSH liningInverse Problems, Vol. 28, No. 7 | 26 June 2012
- Cloaked electromagnetic, acoustic, and quantum amplifiers via transformation opticsProceedings of the National Academy of Sciences, Vol. 109, No. 26 | 14 June 2012
- Inverse Problems With Partial Data for a Magnetic Schrödinger Operator in an Infinite Slab and on a Bounded DomainCommunications in Mathematical Physics, Vol. 312, No. 1 | 16 February 2012
- Developing a time-domain finite-element method for modeling of electromagnetic cylindrical cloaksJournal of Computational Physics, Vol. 231, No. 7 | 1 Apr 2012
- Creating electromagnetic cavities using transformation opticsNew Journal of Physics, Vol. 14, No. 3 | 6 March 2012
- Toward a cylindrical cloak via inverse homogenizationJournal of the Optical Society of America A, Vol. 29, No. 3 | 9 February 2012
- Mathematical Simulation of Cloaking Metamaterial StructuresAdvances in Applied Mathematics and Mechanics, Vol. 4, No. 1 | 3 June 2015
- On the Existence and Uniqueness of a Solution for Some Frequency-Dependent Partial Differential Equations Coming from the Modeling of MetamaterialsSIAM Journal on Mathematical Analysis, Vol. 44, No. 6 | 6 November 2012
- An inverse problem for the wave equation with one measurement and the pseudorandom sourceAnalysis & PDE, Vol. 5, No. 5 | 29 December 2012
- Inverse Problems: Visibility and InvisibilityJournées équations aux dérivées partielles | 2 December 2013
- All-dielectric invisibility cloaks made of BaTiO 3 -loaded polyurethane foamNew Journal of Physics, Vol. 13, No. 10 | 19 October 2011
- Broadband optimization of a pentamode-layered spherical acoustic waveguideWave Motion, Vol. 48, No. 6 | 1 Sep 2011
- Exterior cloaking with active sources in two dimensional acousticsWave Motion, Vol. 48, No. 6 | 1 Sep 2011
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- Generalized transformation optics of linear materialsJournal of Optics, Vol. 13, No. 5 | 7 April 2011
- Ray trajectories for Alcubierre spacetimeJournal of Optics, Vol. 13, No. 5 | 15 April 2011
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- Acoustically invisible gatewaysInverse Problems and Imaging, Vol. 5, No. 1 | 1 Feb 2011
- On Approximate Electromagnetic Cloaking by Transformation MediaSIAM Journal on Applied Mathematics, Vol. 71, No. 1 | 8 February 2011
- Effective constitutive parameters of linear nanocomposites in the long-wavelength regimeJournal of Nanophotonics, Vol. 5, No. 1 | 1 Jan 2011
- Generation of adaptive coordinates and their use in the Fourier Modal MethodOptics Express, Vol. 18, No. 22 | 20 October 2010
- Ray trajectories for a spinning cosmic string and a manifestation of self-cloakingPhysics Letters A, Vol. 374, No. 46 | 1 Oct 2010
- Electromagnetic cloaking by change of variables2010 URSI International Symposium on Electromagnetic Theory | 1 Aug 2010
- A General Procedure for Introducing Structured Nonorthogonal Discretization Grids Into High-Order Finite-Difference Time-Domain MethodsIEEE Transactions on Microwave Theory and Techniques, Vol. 58, No. 7 | 1 Jul 2010
- A general cloak to shift the scattering of different objectsJournal of Physics D: Applied Physics, Vol. 43, No. 24 | 1 June 2010
- Towards a metamaterial simulation of a spinning cosmic stringPhysics Letters A, Vol. 374, No. 23 | 1 May 2010
- Acoustic cloaking and transformation acousticsJournal of Physics D: Applied Physics, Vol. 43, No. 11 | 4 March 2010
- Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensorsNew Journal of Physics, Vol. 12, No. 3 | 23 March 2010
- Impedance Imaging, Inverse Problems, and Harry Potter's CloakSIAM Review, Vol. 52, No. 2 | 6 May 2010
- On Acoustic Cloaking Devices by Transformation Media and Their SimulationSIAM Journal on Applied Mathematics, Vol. 70, No. 8 | 14 October 2010
- Cloaking via change of variables for the Helmholtz equationCommunications on Pure and Applied Mathematics, Vol. 72 | 1 Jan 2010
- Electrical impedance tomography and Calderón's problemInverse Problems, Vol. 25, No. 12 | 3 December 2009
- Nearly perfect nonmagnetic invisibility cloaking: Analytic solutions and parametric studiesPhysical Review B, Vol. 80, No. 12 | 18 September 2009
- Active Exterior Cloaking for the 2D Laplace and Helmholtz EquationsPhysical Review Letters, Vol. 103, No. 7 | 11 August 2009