volume | PIER Journals

Abstract

Three-dimensional (3D) axisymmetric invisibility cloaks with arbitrary shaped in layered-media background are presented using the transformation optics. The inner and outer boundaries of the cloaks can be non-conformal with arbitrary shapes, which considerably improve the flexibility of the cloaking applications. However, such kinds of 3D cloaks cannot be simulated using the commercial softwares due to the tremendous memory requirements and CPU time. By taking advantage of the rotationally symmetrical property, we propose an efficient finite-element method (FEM) to simulate and analyze the 3D cloaks, which can greatly reduce the CPU time and memory requirements. The method is based on the electric-field formulation, in which the transverse fields are expanded in terms of second-order edge-based vector basis functions and the azimuth components are expanded using second-order nodal-based scalar basis functions. The FEM mesh is truncated using the absorbing boundary condition. Excellent cloaking performance of the 3D cloaks in layered-media background has been verified by the proposed method.

1. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, No. 5781, 1780-1782, 2006.
doi:10.1126/science.1125907 Google Scholar

2. Schurig, D., J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express, Vol. 14, 9794-9804, 2006.
doi:10.1364/OE.14.009794 Google Scholar

3. Cummer, S. A., B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E,, Vol. 74, 2006. Google Scholar

4. Schurig, D., 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, 977-980, 2006.
doi:10.1126/science.1133628 Google Scholar

5. Chen, H., B. I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interactions with a metamaterial cloak," Phys. Rev. Lett., Vol. 99, 2007. Google Scholar

6. Andrey, N., W. Q. Cheng, and S. Zouhdi, "Transformation-based spherical cloaks designed by an implicit transformation-independent method: Theory and optimization," New J. Phys., Vol. 11, 2009. Google Scholar

7. Luo, Yu., H. S. Chen, J. J. Zhang, L. Ran, and J. A. Kong, "Design and analytically full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations," Phys. Rev. B., Vol. 77, 2008. Google Scholar

8. Rahm, M., 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," Photo. Nanos. Fund. Appl., Vol. 6, 87-95, 2008.
doi:10.1016/j.photonics.2007.07.013 Google Scholar

9. Chen, H. and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett., Vol. 90, 2007. Google Scholar

10. Tsang, M. and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B, Vol. 77, 2008. Google Scholar

11. Kildishev, A. V. and E. E. Narimanov, "Impedance-matched hyperlens," Opt. Lett., Vol. 32, 3432-3434, 2007.
doi:10.1364/OL.32.003432 Google Scholar

12. Zhang, J. J., F. Huang, T. Jiang, Y. Luo, H. S. Chen, J. A. Kong, and B. I. Wu, "Cloak for multilayered and gradually changing media," Phys. Rev. B, Vol. 77, 2008. Google Scholar

13. Li, C., K. Yao, and F. Li, "Invisibility cloaks with arbitrary geometries for layered and gradually changing backgrounds," J. Phys. D: Appl. Phys., Vol. 42, 2009. Google Scholar

14. You, Y., G. W. Kattawar, P. W. Zhai, and P. Yang, "Zero-backscatter cloak for aspherical particles using a generalized DDA formalism," Opt. Express, Vol. 16, 2068-2079, 2008.
doi:10.1364/OE.16.002068 Google Scholar

15. You, Y., G. W. Kattawar, P. W. Zhai, and P. Yang, "Invisibility cloaks for irregular particles using coordinate transformations," Opt. Express, Vol. 16, 6134-6145, 2008.
doi:10.1364/OE.16.006134 Google Scholar

16. Ping, X. W., T. J. Cui, and W. B. Lu, "The combination of Bcgstab with multifrontal algorithm to solve Febi-MLFMA linear systems arising from inhomogeneous electromagnetic scattering problems," Progress In Electromagnetics Research, Vol. 93, 91-105, 2009.
doi:10.2528/PIER09050604 Google Scholar

17. Sun, X. Y. and Z. P. Nie, "Vector finite element analysis of multicomponent induction response in anisotropic formations," Progress In Electromagnetics Research, Vol. 81, 21-39, 2008.
doi:10.2528/PIER07121502 Google Scholar

18. Greenwood, A. D. and J. M. Jin, "A novel efficient algorithm for scattering from a complex BOR using mixed finite elements and cylindrical PML," IEEE Trans. Antennas Propgat., Vol. 47, 1260-1266, 1999.
doi:10.1109/8.791941 Google Scholar

19. Ding, D. Z. and R. S. Chen, "Electromagnetic scattering by conducting bodies of revolution (BOR) coated with homogeneous chiral media above a lossy half-space," Progress In Electromagnetics Research, Vol. 104, 385-401, 2010.
doi:10.2528/PIER10021004 Google Scholar

20. Zhai, Y. B., X. W. Ping, W. X. Jiang, and T. J. Cui, "Finite-element analysis of three-dimensional axisymmetrical invisibility cloaks and other metamaterial devices," Commun. Comput. Phys., Vol. 8, 823-834, 2010. Google Scholar

21. Jin, J. M., The Finite Element Method in Electromagnetics, Wiley, New York, 1993.

22. Chew, W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York, 1990.

23. Webb, J. P. and S. McFee, "The use of hierarchical triangles in finite-element analysis of microwave and optical devical," IEEE Transactions on Magnetics, Vol. 27, 4040-4043, 1991.
doi:10.1109/20.104988 Google Scholar

24. Andersen, L. S. and J. L. Volakis, "Development and application of a novel class of hierarchical tangential vector finite elements for electromagnetics," IEEE Trans. Antennas Propagat., Vol. 47, 112-120, 1999.
doi:10.1109/8.753001 Google Scholar

25. Chen, R. S., D. X. Wang, E. K. N. Yung, and J. M. Jin, "Application of the multifrontal method to the vector FEM for analysis of microwave filters," Microw. Opt. Tech. Lett., Vol. 31, 465-470, 2001.
doi:10.1002/mop.10064 Google Scholar

Dr. Yong-Bo Zhai

Professor Tie-Jun Cui