Nearly cloaking the full Maxwell equations: Cloaking active contents with general conducting layers

被引:40
作者
Bao, Gang [1 ,2 ]
Liu, Hongyu [3 ]
Zou, Jun [4 ]
机构
[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China
[2] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA
[3] Univ N Carolina, Dept Math & Stat, Charlotte, NC 28223 USA
[4] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
来源
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2014年 / 101卷 / 05期
基金
美国国家科学基金会;
关键词
Electromagnetic scattering; Maxwell's equations; Invisibility cloaking; Transformation optics; Asymptotic estimates; INVERSE PROBLEMS; INVISIBILITY; ENHANCEMENT; DEVICES;
D O I
10.1016/j.matpur.2013.10.010
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The regularized near-cloak via the transformation optics approach in the time-harmonic electromagnetic scattering is considered. This work extends the existing studies mainly in two aspects. First, it presents a near-cloak construction by incorporating a much more general conducting layer between the cloaked and cloaking regions. This might be of significant practical importance when production fluctuations occur. Second, it allows the cloaked contents to be both passive and active with an applied current inside. In assessing the near-cloaking performance, comprehensive and sharp estimates are derived for the scattering amplitude in terms of the asymptotic regularization parameter and the material tensors of the conducting layer. The scattering estimates are independent of the passive/active contents being cloaked, which implies that one could nearly cloak arbitrary contents by using the proposed near-cloak construction. (C) 2013 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码:716 / 733
页数:18
相关论文
共 48 条
[1]   Achieving transparency with plasmonic and metamaterial coatings -: art. no. 016623 [J].
Alù, A ;
Engheta, N .
PHYSICAL REVIEW E, 2005, 72 (01)
[2]   Low-frequency electromagnetic scattering [J].
Ammari, H ;
Nédélec, JC .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2000, 31 (04) :836-861
[3]   Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. The full Maxwell equations [J].
Ammari, H ;
Vogelius, MS ;
Volkov, D .
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2001, 80 (08) :769-814
[4]  
Ammari H., PREPRINT
[5]  
Ammari H., 2004, LECT NOTES MATH, V1846, DOI DOI 10.1007/B98245
[6]   Music-type electromagnetic imaging of a collection of small three-dimensional inclusions [J].
Ammari, Habib ;
Iakovleva, Ekaterina ;
Lesselier, Dominique ;
Perrusson, Gaele .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2007, 29 (02) :674-709
[7]   Spectral Theory of a Neumann-Poincar,-Type Operator and Analysis of Cloaking Due to Anomalous Localized Resonance [J].
Ammari, Habib ;
Ciraolo, Giulio ;
Kang, Hyeonbae ;
Lee, Hyundae ;
Milton, Graeme W. .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2013, 208 (02) :667-692
[8]   Enhancement of Near-Cloaking. Part II: The Helmholtz Equation [J].
Ammari, Habib ;
Kang, Hyeonbae ;
Lee, Hyundae ;
Lim, Mikyoung .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2013, 317 (02) :485-502
[9]   Enhancement of Near Cloaking Using Generalized Polarization Tensors Vanishing Structures. Part I: The Conductivity Problem [J].
Ammari, Habib ;
Kang, Hyeonbae ;
Lee, Hyundae ;
Lim, Mikyoung .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2013, 317 (01) :253-266
[10]   Enhancement of near-cloaking. Part III: Numerical simulations, statistical stability, and related questions [J].
Ammari, Habib ;
Garnier, Josselin ;
Jugnon, Vincent ;
Kang, Hyeonbae ;
Lee, Hyundae ;
Lim, Mikyoung .
MULTI-SCALE AND HIGH-CONTRAST PDE: FROM MODELLING, TO MATHEMATICAL ANALYSIS, TO INVERSION, 2011, 577 :1-+