Volume 9, Issue 2
Maxwell Exterior Transmission Eigenvalue Problems and Their Applications to Electromagnetic Cloaking

Xiaofei Li, Jingzhi Li & Fang Zeng

East Asian J. Appl. Math., 9 (2019), pp. 312-329.

Published online: 2019-03

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  • Abstract

Maxwell exterior transmission eigenvalue problems arising in scattering problem for a penetrable cavity are considered. Properties of such eigenvalues for a weak formulation of the transmission problem in unbounded domains are studied and the Calderon operator for Maxwell's system is described. In particular, the absence of pure imaginary eigenvalues and the discreteness of the set of exterior transmission eigenvalues are established. Applications to exterior invisibility cloaking are also considered. Using the Maxwell-Herglotz approximation, we can generate nearly non-scattering waves corresponding to the exterior eigenvalues of an electromagnetic medium.

  • Keywords

Exterior transmission eigenvalue problem, Calderon operator, exterior invisibility cloaking.

  • AMS Subject Headings

35P25, 35Q60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-312, author = {}, title = {Maxwell Exterior Transmission Eigenvalue Problems and Their Applications to Electromagnetic Cloaking}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {2}, pages = {312--329}, abstract = {

Maxwell exterior transmission eigenvalue problems arising in scattering problem for a penetrable cavity are considered. Properties of such eigenvalues for a weak formulation of the transmission problem in unbounded domains are studied and the Calderon operator for Maxwell's system is described. In particular, the absence of pure imaginary eigenvalues and the discreteness of the set of exterior transmission eigenvalues are established. Applications to exterior invisibility cloaking are also considered. Using the Maxwell-Herglotz approximation, we can generate nearly non-scattering waves corresponding to the exterior eigenvalues of an electromagnetic medium.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.280418.190918}, url = {http://global-sci.org/intro/article_detail/eajam/13085.html} }
TY - JOUR T1 - Maxwell Exterior Transmission Eigenvalue Problems and Their Applications to Electromagnetic Cloaking JO - East Asian Journal on Applied Mathematics VL - 2 SP - 312 EP - 329 PY - 2019 DA - 2019/03 SN - 9 DO - http://doi.org/10.4208/eajam.280418.190918 UR - https://global-sci.org/intro/article_detail/eajam/13085.html KW - Exterior transmission eigenvalue problem, Calderon operator, exterior invisibility cloaking. AB -

Maxwell exterior transmission eigenvalue problems arising in scattering problem for a penetrable cavity are considered. Properties of such eigenvalues for a weak formulation of the transmission problem in unbounded domains are studied and the Calderon operator for Maxwell's system is described. In particular, the absence of pure imaginary eigenvalues and the discreteness of the set of exterior transmission eigenvalues are established. Applications to exterior invisibility cloaking are also considered. Using the Maxwell-Herglotz approximation, we can generate nearly non-scattering waves corresponding to the exterior eigenvalues of an electromagnetic medium.

Xiaofei Li, Jingzhi Li & Fang Zeng. (2019). Maxwell Exterior Transmission Eigenvalue Problems and Their Applications to Electromagnetic Cloaking. East Asian Journal on Applied Mathematics. 9 (2). 312-329. doi:10.4208/eajam.280418.190918
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