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Efficient Higher Order Full-Wave Numerical Analysis of 3-D Cloaking Structures

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Abstract

Highly efficient and versatile computational electromagnetic analysis of 3-D transformation-based metamaterial cloaking structures based on a hybridization of a higher order finite element method for discretization of the cloaking region and a higher order method of moments for numerical termination of the computational domain is proposed and demonstrated. The technique allows for an effective modeling of the continuously inhomogeneous anisotropic cloaking region, for cloaks based on both linear and nonlinear coordinate transformations, using a very small number of large curved finite elements with continuous spatial variations of permittivity and permeability tensors and high-order p-refined field approximations throughout their volumes, with a very small total number of unknowns. In analysis, there is no need for a discretization of the permittivity and permeability profiles of the cloak, namely for piecewise homogeneous (layered) approximate models, with material tensors replaced by appropriate piecewise constant approximations. Numerical results show a very significant reduction (three to five orders of magnitude for the simplest possible 6-element model and five to seven orders of magnitude for an h-refined 24-element model) in the scattering cross section of a perfectly conducting sphere with a metamaterial cloak, in a broad range of wavelengths. Given the introduced explicit approximations in modeling of the spherical geometry and continuous material tensor profiles (both by fourth-order Lagrange interpolating functions), and inherent numerical approximations involved in the finite element and moment method techniques and codes, the cloaking effects are shown to be predicted rather accurately by the full-wave numerical analysis method.

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References

  1. Alù A, Engheta N (2011) Optical metamaterials based on optical nanocircuits. Proc IEEE 99(10):1669–1681. doi:10.1109/JPROC.2011.2160834

    Article  Google Scholar 

  2. Engheta N, Ziolkowski RW (eds) (2006) Metamaterials: physics and engineering explorations, 1st edn. Wiley-IEEE Press, New York

    Google Scholar 

  3. Christophe C, Tatsuo I (2005) Electromagnetic metamaterials: transmission line theory and microwave applications, 1st edn. Wiley-IEEE Press, New York

    Google Scholar 

  4. Capolino F (2009) Metamaterials handbook, 1st edn. CRC Press, New York

    Google Scholar 

  5. Cai W, Shalaev VM (2010) Optical metamaterials: fundamentals and applications, 1st edn. Springer, New York

    Google Scholar 

  6. Pendry JB (2004) Negative refraction. Contemp Phys 45(3):191–202. doi:10.1080/00107510410001667434

    Article  CAS  Google Scholar 

  7. Scherer A, Painter O, Vuckovic J, Loncar M, Yoshie T (2002) Photonic crystals for confining, guiding, and emitting light. IEEE Trans Nanotechnol 1(1):4–11. doi:10.1109/TNANO.2002.1005421

    Article  Google Scholar 

  8. Pendry JB, Schurig D, Smith DR (2006) Controlling electromagnetic fields. Science 312(5781):1780–1782. doi:10.1126/science.1125907

    Article  CAS  Google Scholar 

  9. Schurig D, Pendry JB, Smith DR (2006) Calculation of material properties and ray tracing in transformation media. Opt Express 14(21):9794–9804. doi:10.1364/OE.14.009794

    Article  CAS  Google Scholar 

  10. Cummer SA, Popa B-I, Schurig D, Smith DR, Pendry J (2006) Full-wave simulations of electromagnetic cloaking structures. Phys Rev E 74(3):036621. doi:10.1103/PhysRevE.74.036621

    Article  Google Scholar 

  11. Zolla F, Guenneau S, Nicolet A, Pendry JB (2007) Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect. Opt Lett 32(9):1069–1071. doi:10.1364/OL.32.001069

    Article  Google Scholar 

  12. Ni Y, Gao L, Qiu C-W (2010) Achieving invisibility of homogeneous cylindrically anisotropic cylinders. Plasmonics 5(3):251–258. doi:10.1007/s11468-010-9145-8

    Article  Google Scholar 

  13. Farhat M, Guenneau S, Movchan AB, Enoch S (2008) Achieving invisibility over a finite range of frequencies. Opt Express 16(8):5656–5661. doi:10.1364/OE.16.005656

    Article  CAS  Google Scholar 

  14. Huang Y, Feng Y, Jiang T (2007) Electromagnetic cloaking by layered structure of homogeneous isotropic materials. Opt Express 15(18):11133–11141. doi:10.1364/oe.15.011133

    Article  Google Scholar 

  15. Schurig D, Mock JJ, Justice BJ, Cummer SA, Pendry JB, Starr AF, Smith DR (2006) Metamaterial electromagnetic cloak at microwave frequencies. Science 314(5801):977–980. doi:10.1126/science.1133628

    Article  CAS  Google Scholar 

  16. Yan M, Yan W, Qiu M (2009) Invisibility cloaking by coordinate transformation. In: Emil W (ed) Progress in optics, vol 52., pp 261–304. doi:10.1016/s0079-6638(08)00006-1

    Google Scholar 

  17. Kwon D-H, Werner DH (2010) Transformation electromagnetics: an overview of the theory and applications. IEEE Antenn Propag Mag 52(1):24–46. doi:10.1109/MAP.2010.5466396

    Article  Google Scholar 

  18. Maci S (2010) A cloaking metamaterial based on an inhomogeneous linear field transformation. IEEE Trans Antenn Propag 58(4):1136–1143. doi:10.1109/TAP.2010.2041272

    Article  Google Scholar 

  19. Xie Y, Chen H, Xu Y, Zhu L, Ma H, Dong J-W (2011) An invisibility cloak using silver nanowires. Plasmonics 6(3):477–481. doi:10.1007/s11468-011-9226-3

    Article  CAS  Google Scholar 

  20. Chen H, Wu B-I, Zhang B, Kong JA (2007) Electromagnetic wave interactions with a metamaterial cloak. Phys Rev Lett 99(6):063903. doi:10.1103/PhysRevLett.99.063903

    Article  Google Scholar 

  21. Qiu C, Hu L, Zhang B, Wu B-I, Johnson SG, Joannopoulos JD (2009) Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coatings. Opt Express 17(16):13467–13478. doi:10.1364/OE.17.013467

    Article  CAS  Google Scholar 

  22. Furlani EP, Baev A (2009) Optical nanotrapping using cloaking metamaterial. Phys Rev E 79(2):026607. doi:10.1103/PhysRevE.79.026607

    Article  Google Scholar 

  23. Alù A, Engheta N (2007) Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights. Opt Express 15(6):3318–3332. doi:10.1364/OE.15.003318

    Article  Google Scholar 

  24. Ilić MM, Notaroš BM (2003) Higher order hierarchical curved hexahedral vector finite elements for electromagnetic modeling. IEEE Trans Microw Theor Tech 51(3):1026–1033. doi:10.1109/TMTT.2003.808680

    Article  Google Scholar 

  25. Djordjević M, Notaroš BM (2004) Double higher order method of moments for surface integral equation modeling of metallic and dielectric antennas and scatterers. IEEE Trans Antenn Propag 52(8):2118–2129. doi:10.1109/TAP.2004.833175

    Article  Google Scholar 

  26. Ilić MM, Djordjević M, Ilić AŽ, Notaroš BM (2009) Higher order hybrid FEM-MoM technique for analysis of antennas and scatterers. IEEE Trans Antenn Propag 57(5):1452–1460. doi:10.1109/TAP.2009.2016725

    Article  Google Scholar 

  27. Ilić MM, Ilić AŽ, Notaroš BM (2009) Continuously inhomogeneous higher order finite elements for 3-D electromagnetic analysis. IEEE Trans Antenn Propag 57(9):2798–2803. doi:10.1109/TAP.2009.2027350

    Article  Google Scholar 

  28. Guild MD, Haberman MR, Alù A (2011) Plasmonic cloaking and scattering cancelation for electromagnetic and acoustic waves. Wave Motion 48(6):468–482. doi:10.1016/j.wavemoti.2011.02.006

    Article  Google Scholar 

  29. Notaroš BM (2008) Higher order frequency-domain computational electromagnetics. IEEE Trans Antenn Propag 56(8):2251–2276. doi:10.1109/TAP.2008.926784

    Article  Google Scholar 

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Acknowledgments

This work was supported by the National Science Foundation under grants ECCS-0650719 and ECCS-1002385 and by the Serbian Ministry of Science and Technological Development under grant TR-32005.

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Authors and Affiliations

  1. School of Electrical Engineering, University of Belgrade, Belgrade, 11120, Serbia

    Slobodan V. Savić & Milan M. Ilić

  2. Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, 80523-1373, USA

    Ana B. Manić, Milan M. Ilić & Branislav M. Notaroš

Authors
  1. Slobodan V. Savić
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  2. Ana B. Manić
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  3. Milan M. Ilić
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  4. Branislav M. Notaroš
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Correspondence to Branislav M. Notaroš.

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Savić, S.V., Manić, A.B., Ilić, M.M. et al. Efficient Higher Order Full-Wave Numerical Analysis of 3-D Cloaking Structures. Plasmonics 8, 455–463 (2013). https://doi.org/10.1007/s11468-012-9410-0

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