Abstract

In this paper, we demonstrate the design of a low-scattering metamaterial shell with strong backward scattering reduction and a wide bandwidth at microwave frequencies. Low echo is achieved through cylindrical wave expanding theory, and such shell only contains one metamaterial layer with simultaneous low permittivity and permeability. Cut-wire structure is selected to realize the low electromagnetic (EM) parameters and low loss on the resonance brim region. The full-model simulations show good agreement with theoretical calculations, and illustrate that near −20dB reduction is achieved and the −10 dB bandwidth can reach up to 0.6 GHz. Compared with the cloak based on transformation electromagnetics, the design possesses advantage of simpler requirement of EM parameters and is much easier to be implemented when only backward scattering field is cared.

© 2015 Optical Society of America

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References

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  1. E. F. Knott, J. F. Shaeffer, and M. T. Tuley, Radar Cross Section, 2nd ed. (SciTech Publishing, Inc. 2004).
  2. G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Plenum, 1970).
  3. C. Y. Chin and C. F. Jou, “Improvement on RCS reduction using flat lossy focusing reflectors,” Opt. Express 21(26), 32534–32548 (2013).
    [Crossref] [PubMed]
  4. E. H. Kerner, “The elastic and thermoelastic properties of composite media,” Proc. Phys. Soc. B 69(8), 808–813 (1956).
    [Crossref]
  5. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref] [PubMed]
  6. P. Y. Chen, J. Soric, and A. Alù, “Invisibility and Cloaking Based on Scattering Cancellation,” Adv. Mater. 24(44), OP281–OP304 (2012).
    [PubMed]
  7. 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 314(5801), 977–980 (2006).
    [Crossref] [PubMed]
  8. W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
    [Crossref]
  9. J. J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a non-magnetic cloak,” Appl. Phys. Lett. 96(11), 113511 (2010).
    [Crossref]
  10. R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
    [Crossref] [PubMed]
  11. T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
    [Crossref] [PubMed]
  12. A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
    [Crossref] [PubMed]
  13. W. Yan, M. Yan, and M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93(2), 021909 (2008).
    [Crossref]
  14. A. Alù and N. Engheta, “Cloaking and transparency for collections of particles with metamaterial and plasmonic covers,” Opt. Express 15(12), 7578–7590 (2007).
    [Crossref] [PubMed]
  15. X. Zhou and G. Hu, “Design for electromagnetic wave transparency with metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026607 (2006).
    [Crossref] [PubMed]
  16. C. Li and Z. Shen, “Electromagnetic scattering by a conducting cylinder coated with metamaterials,” PIER 42, 91–105 (2003).
    [Crossref]
  17. H. Oraizi and A. Abdolali, “Ultra wide band RCS optimization of multilayered cylindrical structures for arbitrarily polarized incident plane waves,” PIER 78, 129–157 (2008).
    [Crossref]
  18. J. H. Richmond, “Efficient recursive solutions for plane and cylindrical multilayers,” DTIC Document 1968.
  19. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists Sixth Edition (Elsevier Academic 2005).
  20. H. E. Bussey and J. H. Richmond, “Scattering by a Lossy Dielectric Circular Cylindrical Multilayer, Numerical Values,” IEEE Trans. Antenn. Propag. 23(5), 723–725 (1975).
    [Crossref]
  21. J. F. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006).
    [Crossref]
  22. S. A. Ramakrishna and T. M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (CRC 2009).

2014 (2)

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
[Crossref] [PubMed]

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (1)

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and Cloaking Based on Scattering Cancellation,” Adv. Mater. 24(44), OP281–OP304 (2012).
[PubMed]

2010 (1)

J. J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a non-magnetic cloak,” Appl. Phys. Lett. 96(11), 113511 (2010).
[Crossref]

2008 (2)

H. Oraizi and A. Abdolali, “Ultra wide band RCS optimization of multilayered cylindrical structures for arbitrarily polarized incident plane waves,” PIER 78, 129–157 (2008).
[Crossref]

W. Yan, M. Yan, and M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93(2), 021909 (2008).
[Crossref]

2007 (2)

A. Alù and N. Engheta, “Cloaking and transparency for collections of particles with metamaterial and plasmonic covers,” Opt. Express 15(12), 7578–7590 (2007).
[Crossref] [PubMed]

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

2006 (4)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

X. Zhou and G. Hu, “Design for electromagnetic wave transparency with metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026607 (2006).
[Crossref] [PubMed]

J. F. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006).
[Crossref]

2005 (1)

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[Crossref] [PubMed]

2003 (1)

C. Li and Z. Shen, “Electromagnetic scattering by a conducting cylinder coated with metamaterials,” PIER 42, 91–105 (2003).
[Crossref]

1975 (1)

H. E. Bussey and J. H. Richmond, “Scattering by a Lossy Dielectric Circular Cylindrical Multilayer, Numerical Values,” IEEE Trans. Antenn. Propag. 23(5), 723–725 (1975).
[Crossref]

1956 (1)

E. H. Kerner, “The elastic and thermoelastic properties of composite media,” Proc. Phys. Soc. B 69(8), 808–813 (1956).
[Crossref]

Abdolali, A.

H. Oraizi and A. Abdolali, “Ultra wide band RCS optimization of multilayered cylindrical structures for arbitrarily polarized incident plane waves,” PIER 78, 129–157 (2008).
[Crossref]

Alù, A.

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and Cloaking Based on Scattering Cancellation,” Adv. Mater. 24(44), OP281–OP304 (2012).
[PubMed]

A. Alù and N. Engheta, “Cloaking and transparency for collections of particles with metamaterial and plasmonic covers,” Opt. Express 15(12), 7578–7590 (2007).
[Crossref] [PubMed]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[Crossref] [PubMed]

Bückmann, T.

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
[Crossref] [PubMed]

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

Bussey, H. E.

H. E. Bussey and J. H. Richmond, “Scattering by a Lossy Dielectric Circular Cylindrical Multilayer, Numerical Values,” IEEE Trans. Antenn. Propag. 23(5), 723–725 (1975).
[Crossref]

Cai, W. S.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Chen, P. Y.

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and Cloaking Based on Scattering Cancellation,” Adv. Mater. 24(44), OP281–OP304 (2012).
[PubMed]

Chettiar, U. K.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Chin, C. Y.

Cummer, S. A.

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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Engheta, N.

A. Alù and N. Engheta, “Cloaking and transparency for collections of particles with metamaterial and plasmonic covers,” Opt. Express 15(12), 7578–7590 (2007).
[Crossref] [PubMed]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[Crossref] [PubMed]

Hu, G.

X. Zhou and G. Hu, “Design for electromagnetic wave transparency with metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026607 (2006).
[Crossref] [PubMed]

Jou, C. F.

Justice, B. J.

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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Kadic, M.

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
[Crossref] [PubMed]

Kerner, E. H.

E. H. Kerner, “The elastic and thermoelastic properties of composite media,” Proc. Phys. Soc. B 69(8), 808–813 (1956).
[Crossref]

Kildishev, A. V.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Koschny, T.

J. F. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006).
[Crossref]

Li, C.

C. Li and Z. Shen, “Electromagnetic scattering by a conducting cylinder coated with metamaterials,” PIER 42, 91–105 (2003).
[Crossref]

Luo, Y.

J. J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a non-magnetic cloak,” Appl. Phys. Lett. 96(11), 113511 (2010).
[Crossref]

Mock, J. J.

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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Mortensen, N. A.

J. J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a non-magnetic cloak,” Appl. Phys. Lett. 96(11), 113511 (2010).
[Crossref]

Oraizi, H.

H. Oraizi and A. Abdolali, “Ultra wide band RCS optimization of multilayered cylindrical structures for arbitrarily polarized incident plane waves,” PIER 78, 129–157 (2008).
[Crossref]

Pendry, J. B.

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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Qiu, M.

W. Yan, M. Yan, and M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93(2), 021909 (2008).
[Crossref]

Richmond, J. H.

H. E. Bussey and J. H. Richmond, “Scattering by a Lossy Dielectric Circular Cylindrical Multilayer, Numerical Values,” IEEE Trans. Antenn. Propag. 23(5), 723–725 (1975).
[Crossref]

Schittny, R.

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
[Crossref] [PubMed]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Shalaev, V. M.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Shen, Z.

C. Li and Z. Shen, “Electromagnetic scattering by a conducting cylinder coated with metamaterials,” PIER 42, 91–105 (2003).
[Crossref]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Soric, J.

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and Cloaking Based on Scattering Cancellation,” Adv. Mater. 24(44), OP281–OP304 (2012).
[PubMed]

Soukoulis, C. M.

J. F. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006).
[Crossref]

Starr, A. F.

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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Thiel, M.

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

Tuttle, G.

J. F. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006).
[Crossref]

Wegener, M.

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
[Crossref] [PubMed]

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

Yan, M.

W. Yan, M. Yan, and M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93(2), 021909 (2008).
[Crossref]

Yan, W.

W. Yan, M. Yan, and M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93(2), 021909 (2008).
[Crossref]

Zhang, J. J.

J. J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a non-magnetic cloak,” Appl. Phys. Lett. 96(11), 113511 (2010).
[Crossref]

Zhang, L.

J. F. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006).
[Crossref]

Zhou, J. F.

J. F. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006).
[Crossref]

Zhou, X.

X. Zhou and G. Hu, “Design for electromagnetic wave transparency with metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026607 (2006).
[Crossref] [PubMed]

Adv. Mater. (1)

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and Cloaking Based on Scattering Cancellation,” Adv. Mater. 24(44), OP281–OP304 (2012).
[PubMed]

Appl. Phys. Lett. (2)

J. J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a non-magnetic cloak,” Appl. Phys. Lett. 96(11), 113511 (2010).
[Crossref]

W. Yan, M. Yan, and M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93(2), 021909 (2008).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

H. E. Bussey and J. H. Richmond, “Scattering by a Lossy Dielectric Circular Cylindrical Multilayer, Numerical Values,” IEEE Trans. Antenn. Propag. 23(5), 723–725 (1975).
[Crossref]

Nat. Commun. (1)

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

Opt. Express (2)

Phys. Rev. B (1)

J. F. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

X. Zhou and G. Hu, “Design for electromagnetic wave transparency with metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026607 (2006).
[Crossref] [PubMed]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[Crossref] [PubMed]

PIER (2)

C. Li and Z. Shen, “Electromagnetic scattering by a conducting cylinder coated with metamaterials,” PIER 42, 91–105 (2003).
[Crossref]

H. Oraizi and A. Abdolali, “Ultra wide band RCS optimization of multilayered cylindrical structures for arbitrarily polarized incident plane waves,” PIER 78, 129–157 (2008).
[Crossref]

Proc. Phys. Soc. B (1)

E. H. Kerner, “The elastic and thermoelastic properties of composite media,” Proc. Phys. Soc. B 69(8), 808–813 (1956).
[Crossref]

Science (3)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345(6195), 427–429 (2014).
[Crossref] [PubMed]

Other (5)

J. H. Richmond, “Efficient recursive solutions for plane and cylindrical multilayers,” DTIC Document 1968.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists Sixth Edition (Elsevier Academic 2005).

S. A. Ramakrishna and T. M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (CRC 2009).

E. F. Knott, J. F. Shaeffer, and M. T. Tuley, Radar Cross Section, 2nd ed. (SciTech Publishing, Inc. 2004).

G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook (Plenum, 1970).

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Figures (6)

Fig. 1
Fig. 1 (a) Whole frame of designed shell. (b) The backward RCS of the model presented in Fig. 1(a) with different ε1 and μ1.
Fig. 2
Fig. 2 RCS of PEC cylinder (black dashed line) and PEC cylinder with shell presented in Fig. 1(a) (red line).
Fig. 3
Fig. 3 (a) Unit cell for the achievement of small electromagnetic parameters (b) the S-parameters for the unit cell of the short metal wires structure (c) the effective permittivity and (d) the effective permeability of the unit cell displayed in Fig. 3(a) retrieval by the effective medium theory.
Fig. 4
Fig. 4 (a) Platform of the whole model used in full wave simulation and (b) the side view of metamaterial layer (i.e. the middle two layers).
Fig. 5
Fig. 5 (a) RCS of PEC (black dashed line) and PEC with cylindrical shell (red line) in Descartes coordinates at the optimal frequency 15.9GHz, (b) the magnetic distribution in the propagation plane is given for PEC cylinder (upper) and PEC with cylindrical shell (lower).
Fig. 6
Fig. 6 RCS of different frequency for the whole-model.

Tables (1)

Tables Icon

Table 1 The EM parameters variety of different structure parameters

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

E z = n=0 [ e n j n J n ( k 0 R )+ C n H n ( 2 ) ( k 0 R ) ] cosnφoutsidethecylinder
E z,m = n=0 [ A mn J n ( k m R )+ B mn Y n ( k m R ) ] cosnφinsidethecylinder
H m =( k m / jω μ m ) n=0 [ A mn J n ' ( k m r )+ B mn Y n ' ( k m r ) ]cosnϕ
A m+1,n = U mn A mn + W mn B mn B m+1,n = V mn A mn + X mn B mn
U mn =( π R m / 2 μ m )[ μ m+1 k m J n ' ( k m R m ) Y n ( k m+1 R m )+ μ m k m+1 J n ( k m R m ) Y n ' ( k m+1 R m ) ] V mn =( π R m / 2 μ m )[ μ m+1 k m J n ' ( k m R m ) J n ( k m+1 R m ) μ m k m+1 J n ( k m R m ) J n ' ( k m+1 R m ) ] W mn =( π R m / 2 μ m )[ μ m+1 k m Y n ' ( k m R m ) Y n ( k m+1 R m )+ μ m k m+1 Y n ( k m R m ) Y n ' ( k m+1 R m ) ] X mn =( π R m / 2 μ m )[ μ m+1 k m Y n ' ( k m R m ) J n ( k m+1 R m ) μ m k m+1 Y n ( k m R m ) J n ' ( k m+1 R m ) ]
σ( φ )= 2λ π | n=0 e n B M+1,n B M+1,n +i A M+1.n cosnφ | 2 .

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