• Yanglu Xuan
  • Xinhe Xu



Complementary media, Coordinate transformation theory, Multilayered structure, Radar cross section (RCS)


We investigate a three-dimensional (3D) reciprocal invisibility cloak with a multilayered structure based on coordinate transformation theory and complementary media. There has been considerable research on invisibility cloaks such as the external cloak, which requires complex "anti-objects``, and closed cloaks of different shapes, in which the object enclosed is blind. Because all these are hard to realize in actual application, we apply a uniform layer to the whole construct into several parts in efforts to replace the ideal cloak with the aim to reduce complexity in actual fabrication. This multilayered cloak allows exchange of information without requiring "anti-objects``. All results were simulated and calculated in the Cartesian coordinate system and with the Comsol Multiphysics software. Electrical field simulations verified the efficiency of the designed cloak and the computed radar cross section (RCS) to illustrate the validity of this method and its efficiency in replacing the ideal cloak.


[1] J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science, vol. 312, no. 5781, pp. 1780-
1782, 2006.
[2] D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial
electromagnetic cloak at microwave frequencies,” Science, vol. 314, no. 5801, pp. 977-980, 2006.
[3] H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Applied Physics Letters, vol. 90, no.
24, 241105, 2007.
[4] W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, “Arbitrarily elliptical-cylindrical invisible
cloaking,” Journal of Physics D: Applied Physics, vol. 41, no. 19, 199801, 2008.
[5] D. H. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Applied Physics Letters,
vol. 92, no. 1, 013505, 2008.
[6] K. Yao, C. Li, and F. Li, “Electromagnetic invisibility of elliptic cylinder cloaks,” Chinese Physics Letters, vol. 25, no.
5, pp. 1657-1660, 2008.
[7] H. Ma, S. B. Qu, Z. Xu, J. Q. Zhang, B. Chen, and J. F. Wang, “Material parameter equation for elliptical cylindrical
cloaks,” Physical Review A, vol. 77, no. 1, 013825, 2008.
[8] C. Li and F. Li, “Two-dimensional electromagnetic cloaks with arbitrary geometries,” Optics Express, vol. 16, no. 17,
pp. 13414-13420, 2008.
[9] J. J. Zhang, Y. Luo, H. S. Chen, and B. I. Wu, “Cloak of arbitrary shape,” Journal of the Optical Society America B,
vol. 25, no. 11, pp. 1776-1779, 2008.
[10] H. Ma, S. B. Qu, Z. Xu, and J. F. Wang, “Approximation approach of designing practical cloaks with arbitrary shapes,”
Optics Express, vol. 16, no. 20, pp. 15449-15454, 2008.
[11] G. X. Yu, T. J. Cui, and W. X. Jiang, “Design of transparent structure using metamaterial,” Journal of Infrared
Millimeter and Terahertz Waves, vol. 30, no. 6, pp. 633-641, 2009.
[12] M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks
and concentrators using form-invariant coordinate transformations of Maxwell's equations,” Photonics and
Nanostructures-Fundamentals and Applications, vol. 6, no. 1, pp. 87-95, 2008.
[13] H. Ma, S. B. Qu, Z. Xu, and J. F. Wang, “The open cloak,” Applied Physics Letters, vol. 94, no. 10, 103501, 2009.
[14] Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a
distance outside the cloaking shell,” Physical Review Letters, vol. 102, no. 9, 093901, 2009.
[15] Y. Luo, S. Z. Zhu, L. X. He, and Y. Wang, “Arbitrary polygonal cloaks with multiple invisible regions,” Journal of
Modern Optics, vol. 58, no. 1, pp. 14-20, 2011.
[16] J. J. Yang, M. Huang, C. F. Yang, and J. Yu, “Reciprocal invisibility cloak based on complementary media,” European
Physical Journal D, vol. 61, no. 3, pp. 731-736, 2011.
[17] C. F. Yang, J. J. Yang, M. Huang, Z. Xiao, and J. H. Peng, “An external cloak with arbitrary cross section based on
complementary medium and coordinate transformation,” Optics Express, vol. 19, no. 2, pp. 1147-1157, 2011.
[18] Y. Urzhumov, N. Landy, T. Driscoll, D. Basov, and D. R. Smith, “Thin low-loss dielectric coatings for free-space
cloaking,” Optics Letters, vol. 38, no. 10, pp. 1606-1608, 2013.
[19] R. Dehbashi and M. Shahabadi, “External cylindrical invisibility cloaks with small material dynamic range,” IEEE
Transaction on Antennas and Propagation, vol. 62, no. 4, pp. 2187-2191, 2014.
[20] Y. Tian, C. Lu, R. F. Wang, and Z. L. Mei, “An exterior anti-cloak,” Plasmonics, Vol. 11, No. 5, 1213-1217, 2016.
[21] P. Vura, A. Rajput, and K. V. Srivastava, “Composite-shaped external cloaks with homogeneous material properties,”
IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 282-285, 2016.
[22] J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” Journal of Physics: Comdensed Matter,
vol. 15, no. 37, pp. 6345-6364, 2003.




How to Cite

Xuan, Y. ., & Xu, X. (2020). THREE-DIMENSIONAL RECIPROCAL INVISIBILITY CLOAK WITH MULTILAYERED STRUCTURE. Journal of Microwaves, Optoelectronics and Electromagnetic Applications (JMOe), 18(2), 184–195.



Regular Papers