Nearly Cloaking the Electromagnetic Fields

The approximate cloaking is investigated for time-harmonic Maxwell's equations via the approach of transformation optics. The problem is reduced to certain boundary effect estimates due to an inhomogeneous electromagnetic inclusion with an asymptotically small support but an arbitrary content enclosed by a thin high-conducting layer. Sharp estimates are established in terms of the asymptotic parameter, which are independent of the material tensors of the small electromagnetic inclusion. The result implies that the “blow-up-a-small-region” construction via the transformation optics approach yields a near-cloak for the electromagnetic waves. A novelty lies in the fact that the geometry of the cloaking construction of this work can be very general. Moreover, by incorporating the conducting layer developed in the present paper right between the cloaked region and the cloaking region, arbitrary electromagnetic contents can be nearly cloaked. Our mathematical technique extends the general one developed in [H. Y...

[1]  A. Norris.  Acoustic cloaking theory , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[2]  Matti Lassas,et al.  Anisotropic conductivities that cannot be detected by EIT. , 2003, Physiological measurement.

[3]  Habib Ammari,et al.  Low-Frequency Electromagnetic Scattering , 2000, SIAM J. Math. Anal..

[4]  Ilker Kocyigit,et al.  Regular scattering patterns from near-cloaking devices and their implications for invisibility cloaking , 2013 .

[5]  Gunther Uhlmann,et al.  Visibility and invisibility , 2009 .

[6]  M. Vogelius,et al.  Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogen , 2000 .

[7]  H. Ammari,et al.  Reconstruction of Small Inhomogeneities from Boundary Measurements , 2005 .

[8]  Matti Lassas,et al.  Invisibility and Inverse Problems , 2008, 0810.0263.

[9]  Habib Ammari,et al.  Enhancement of near-cloaking , 2012 .

[10]  Xavier Antoine,et al.  Far Field Modeling of Electromagnetic Time Reversal and Application to Selective Focusing on Small Scatterers , 2008, SIAM J. Appl. Math..

[11]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[12]  L. B. Slichter.  An Inverse Boundary Value Problem in Electrodynamics , 1933 .

[13]  G. Uhlmann,et al.  Isotropic transformation optics: approximate acoustic and quantum cloaking , 2008, 0806.0085.

[14]  Robert V. Kohn,et al.  Cloaking via change of variables for the Helmholtz equation , 2010 .

[15]  Martin Costabel,et al.  On the Kleinman-Martin Integral Equation Method for Electromagnetic Scattering by a Dielectric Body , 2009, SIAM J. Appl. Math..

[16]  P. Grisvard.  Elliptic Problems in Nonsmooth Domains , 1985 .

[17]  M. Qiu,et al.  Ideal cylindrical cloak: perfect but sensitive to tiny perturbations. , 2007, Physical review letters.

[18]  H. Ammari,et al.  Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. The full Maxwell equations , 2001 .

[19]  J. Conoir,et al.  Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles , 2006 .

[20]  G. Uhlmann,et al.  Full-Wave Invisibility of Active Devices at All Frequencies , 2006, math/0611185.

[21]  David R. Smith,et al.  Controlling Electromagnetic Fields , 2006, Science.

[22]  Habib Ammari,et al.  Enhancement of Near Cloaking Using Generalized Polarization Tensors Vanishing Structures. Part I: The Conductivity Problem , 2011, Communications in Mathematical Physics.

[23]  J. Lions,et al.  Non-homogeneous boundary value problems and applications , 1972 .

[24]  G. Uhlmann,et al.  Improvement of cylindrical cloaking with the SHS lining. , 2007, Optics express.

[25]  J. Nédélec.  Acoustic and Electromagnetic Equations : Integral Representations for Harmonic Problems , 2001 .

[26]  Huanyang Chen,et al.  Acoustic cloaking and transformation acoustics , 2010 .

[27]  Hongyu Liu,et al.  Enhanced near-cloak by FSH lining , 2011 .

[28]  U. Leonhardt.  Optical Conformal Mapping , 2006, Science.

[29]  Jingzhi Li,et al.  Enhanced approximate cloaking by SH and FSH lining , 2012 .

[30]  阿部 剛久,et al.  R. Leis: Initial Boundary Value Problems in Mathematical Physics, John Wiley & Sons, New York, 1986, viii+266ページ, 24×16cm, 11,690円. , 1987 .

[31]  Matti Lassas,et al.  On nonuniqueness for Calderón’s inverse problem , 2003 .

[32]  Habib Ammari,et al.  Communications in Mathematical Physics Enhancement of Near-Cloaking . Part II : The Helmholtz Equation , 2013 .

[33]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[34]  George Dassios,et al.  Low Frequency Scattering , 2000 .

[35]  Ralf Schweizer,et al.  Integral Equation Methods In Scattering Theory , 2016 .

[36]  Michael E. Taylor,et al.  Partial Differential Equations II , 1996 .

[37]  Petri Ola,et al.  Electromagnetic Inverse Problems and Generalized Sommerfeld Potentials , 1996, SIAM J. Appl. Math..

[38]  R. Kohn,et al.  Cloaking via change of variables in electric impedance tomography , 2008 .

[39]  Hongyu Liu,et al.  Virtual reshaping and invisibility in obstacle scattering , 2008, 0811.1308.

[40]  D. Griffel,et al.  Initial Boundary Value Problems in Mathematical Physics , 1986 .

[41]  M. Qiu,et al.  Invisibility Cloaking by Coordinate Transformation , 2009 .

[42]  Michael E. Taylor,et al.  Partial Differential Equations II: Qualitative Studies of Linear Equations , 1996 .

[43]  Ting Zhou,et al.  On Approximate Electromagnetic Cloaking by Transformation Media , 2010, SIAM J. Appl. Math..

[44]  W. McLean.  Strongly Elliptic Systems and Boundary Integral Equations , 2000 .

[45]  Josselin Garnier,et al.  Enhancement of near-cloaking. Part III: Numerical simulations, statistical stability, and related questions , 2011 .

[46]  Matti Lassas,et al.  Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics , 2009, SIAM Rev..