TY - JOUR
T1 - On Quasi-static cloaking due to anomalous localized resonance in R3
AU - Li, Hongjie
AU - Li, Jingzhi
AU - Liu, Hongyu
N1 - Funding information:
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, People?s Republic of China ([email protected]). This author’s work was supported by the NSF of China 11101033.
Department of Mathematics, South University of Science and Technology of China, Shenzhen 518055, People’s Republic of China ([email protected]). This author’s work was partially supported by the NSF of China 11201453 and the Shenzhen Research Program JCYJ20140509143748226.
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, and HKBU Institute of Research and Continuing Education, Virtual University Park, Shenzhen, People’s Republic of China ([email protected]). This author’s work was supported by the FRG and start-up grants of Hong Kong Baptist University, and the NSF grant of China 11371115.
Publisher copyright:
© 2015, Society for Industrial and Applied Mathematics
PY - 2015/6/11
Y1 - 2015/6/11
N2 - This work concerns the cloaking due to anomalous localized resonance (CALR) in the quasi-static regime. We extend the related two-dimensional studies in [H. Ammari et al., Arch. Ration. Mech. Anal., 208 (2013), pp. 667--692; R. V. Kohn et al., Comm. Math. Phys., 328 (2014), pp. 1--27] to the three-dimensional setting. CALR is shown not to take place for the plasmonic configuration considered in these two papers in the three-dimensional case. We give two different constructions which ensure the occurrence of CALR. There may be no core or an arbitrarily shaped core for the cloaking device. If there is a core, then the dielectric distribution inside it could be arbitrary.
AB - This work concerns the cloaking due to anomalous localized resonance (CALR) in the quasi-static regime. We extend the related two-dimensional studies in [H. Ammari et al., Arch. Ration. Mech. Anal., 208 (2013), pp. 667--692; R. V. Kohn et al., Comm. Math. Phys., 328 (2014), pp. 1--27] to the three-dimensional setting. CALR is shown not to take place for the plasmonic configuration considered in these two papers in the three-dimensional case. We give two different constructions which ensure the occurrence of CALR. There may be no core or an arbitrarily shaped core for the cloaking device. If there is a core, then the dielectric distribution inside it could be arbitrary.
KW - Anomalous localized resonance
KW - Invisibility cloaking
KW - Plasmonic material
UR - http://www.scopus.com/inward/record.url?scp=84937922872&partnerID=8YFLogxK
U2 - 10.1137/15M1009974
DO - 10.1137/15M1009974
M3 - Journal article
AN - SCOPUS:84937922872
SN - 0036-1399
VL - 75
SP - 1245
EP - 1260
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 3
ER -