Abstract

The design of an arbitrary polygonal invisible cloak is introduced in this paper by considering the different transformation orders. The transformation order is considered as a design variable to achieve the allowable constitutive parameters for a practical cloak with the optimum performance. In the proposed method, a thin layer is removed from the inner cloak boundary to avoid the inevitable singularity at this boundary. Then the transformation order is optimized to achieve the best performance in this truncated cloak. Also, the effect of transformation order in choosing the cloak shield thickness is investigated to design a truncated cloak with better performance.

© 2012 Optical Society of America

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References

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic Fields,” Science 312, 1780–1782 (2006).
    [CrossRef]
  2. Y. Luo, J. J. Zhang, H. S. Chen, B. I. Wu, and L. X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178 (2009).
  3. D. H. Kwon and D. H. Werner, “Transformation electromagnetics, An overview of the theory and applications,” IEEE Antennas Propag. Mag. 52(1), 24–46 (2010).
    [CrossRef]
  4. B. L. Zhang, H. S. Chen, and B. I. Wu, “Practical limitations of an invisibility cloak,” Prog. Electromagn. Res. 97, 407–416 (2009).
    [CrossRef]
  5. H. Ma, S. Qu, Z. Xu, and J. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E 78, 036608 (2008).
    [CrossRef]
  6. A. Shahzad, F. Qasim, S. Ahmed, and Q. A. Naqvi, “Cylindrical invisibility cloak incorporating PEMC at perturbed void region,” Prog. Electromagn. Res. M 21, 61–76 (2011).
    [CrossRef]
  7. S. Taravati and A. Abdolali, “A new three-dimensional conical grounded plane cloak with homogeneous materials,” Prog. Electromagn. Res. M 19, 91–104 (2011).
    [CrossRef]
  8. S. H. Sedighy and M. K. Amirhosseini, “Design of an arbitrary shaped invisible cloak using coordinate transformation,” Int. Rev. Model. Simul. 3, 1167–1171 (2010).
  9. J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson’s equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).
  10. 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,” in Photonics and Nanostructures—Fundamentals and Applications (Elsevier, 2008), pp. 87–95.
  11. Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
    [CrossRef]
  12. S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
    [CrossRef]
  13. 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, 977–980 (2006).
    [CrossRef]
  14. M. Yan, Z. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
    [CrossRef]
  15. L. Zhang, M. Yan, and M. Qiu, “The effect of transformation order on the invisibility performance of a practical cylindrical cloak,” J. Opt. A 10, 095001 (2008).
    [CrossRef]
  16. S. H. Sedighy and M. Khalaj-Amirhosseini, “Arbitrary n-sided irregular polygonal electromagnetic transformed media,” J. Opt. Soc. Am. A 29, 1549–1555 (2012).
    [CrossRef]

2012 (1)

2011 (2)

A. Shahzad, F. Qasim, S. Ahmed, and Q. A. Naqvi, “Cylindrical invisibility cloak incorporating PEMC at perturbed void region,” Prog. Electromagn. Res. M 21, 61–76 (2011).
[CrossRef]

S. Taravati and A. Abdolali, “A new three-dimensional conical grounded plane cloak with homogeneous materials,” Prog. Electromagn. Res. M 19, 91–104 (2011).
[CrossRef]

2010 (2)

S. H. Sedighy and M. K. Amirhosseini, “Design of an arbitrary shaped invisible cloak using coordinate transformation,” Int. Rev. Model. Simul. 3, 1167–1171 (2010).

D. H. Kwon and D. H. Werner, “Transformation electromagnetics, An overview of the theory and applications,” IEEE Antennas Propag. Mag. 52(1), 24–46 (2010).
[CrossRef]

2009 (3)

B. L. Zhang, H. S. Chen, and B. I. Wu, “Practical limitations of an invisibility cloak,” Prog. Electromagn. Res. 97, 407–416 (2009).
[CrossRef]

Y. Luo, J. J. Zhang, H. S. Chen, B. I. Wu, and L. X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178 (2009).

J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson’s equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).

2008 (2)

H. Ma, S. Qu, Z. Xu, and J. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E 78, 036608 (2008).
[CrossRef]

L. Zhang, M. Yan, and M. Qiu, “The effect of transformation order on the invisibility performance of a practical cylindrical cloak,” J. Opt. A 10, 095001 (2008).
[CrossRef]

2007 (2)

M. Yan, Z. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
[CrossRef]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef]

2006 (3)

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

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, 977–980 (2006).
[CrossRef]

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

Abdolali, A.

S. Taravati and A. Abdolali, “A new three-dimensional conical grounded plane cloak with homogeneous materials,” Prog. Electromagn. Res. M 19, 91–104 (2011).
[CrossRef]

Ahmed, S.

A. Shahzad, F. Qasim, S. Ahmed, and Q. A. Naqvi, “Cylindrical invisibility cloak incorporating PEMC at perturbed void region,” Prog. Electromagn. Res. M 21, 61–76 (2011).
[CrossRef]

Amirhosseini, M. K.

S. H. Sedighy and M. K. Amirhosseini, “Design of an arbitrary shaped invisible cloak using coordinate transformation,” Int. Rev. Model. Simul. 3, 1167–1171 (2010).

Cao, X. Y.

J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson’s equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).

Chen, H. S.

Y. Luo, J. J. Zhang, H. S. Chen, B. I. Wu, and L. X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178 (2009).

B. L. Zhang, H. S. Chen, and B. I. Wu, “Practical limitations of an invisibility cloak,” Prog. Electromagn. Res. 97, 407–416 (2009).
[CrossRef]

Cummer, S. A.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

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, 977–980 (2006).
[CrossRef]

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,” in Photonics and Nanostructures—Fundamentals and Applications (Elsevier, 2008), pp. 87–95.

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, 977–980 (2006).
[CrossRef]

Khalaj-Amirhosseini, M.

Kwon, D. H.

D. H. Kwon and D. H. Werner, “Transformation electromagnetics, An overview of the theory and applications,” IEEE Antennas Propag. Mag. 52(1), 24–46 (2010).
[CrossRef]

Liu, T.

J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson’s equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).

Luo, Y.

Y. Luo, J. J. Zhang, H. S. Chen, B. I. Wu, and L. X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178 (2009).

Ma, H.

H. Ma, S. Qu, Z. Xu, and J. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E 78, 036608 (2008).
[CrossRef]

Ma, J. J.

J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson’s equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).

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, 977–980 (2006).
[CrossRef]

Naqvi, Q. A.

A. Shahzad, F. Qasim, S. Ahmed, and Q. A. Naqvi, “Cylindrical invisibility cloak incorporating PEMC at perturbed void region,” Prog. Electromagn. Res. M 21, 61–76 (2011).
[CrossRef]

Neff, C. W.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef]

Pendry, J.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[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, 977–980 (2006).
[CrossRef]

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

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,” in Photonics and Nanostructures—Fundamentals and Applications (Elsevier, 2008), pp. 87–95.

Popa, B. I.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Qasim, F.

A. Shahzad, F. Qasim, S. Ahmed, and Q. A. Naqvi, “Cylindrical invisibility cloak incorporating PEMC at perturbed void region,” Prog. Electromagn. Res. M 21, 61–76 (2011).
[CrossRef]

Qiu, M.

L. Zhang, M. Yan, and M. Qiu, “The effect of transformation order on the invisibility performance of a practical cylindrical cloak,” J. Opt. A 10, 095001 (2008).
[CrossRef]

M. Yan, Z. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
[CrossRef]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef]

Qu, S.

H. Ma, S. Qu, Z. Xu, and J. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E 78, 036608 (2008).
[CrossRef]

Rahm, M.

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,” in Photonics and Nanostructures—Fundamentals and Applications (Elsevier, 2008), pp. 87–95.

Ran, L. X.

Y. Luo, J. J. Zhang, H. S. Chen, B. I. Wu, and L. X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178 (2009).

Roberts, D. A.

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,” in Photonics and Nanostructures—Fundamentals and Applications (Elsevier, 2008), pp. 87–95.

Ruan, Z.

M. Yan, Z. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
[CrossRef]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef]

Schurig, D.

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

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, 977–980 (2006).
[CrossRef]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

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,” in Photonics and Nanostructures—Fundamentals and Applications (Elsevier, 2008), pp. 87–95.

Sedighy, S. H.

S. H. Sedighy and M. Khalaj-Amirhosseini, “Arbitrary n-sided irregular polygonal electromagnetic transformed media,” J. Opt. Soc. Am. A 29, 1549–1555 (2012).
[CrossRef]

S. H. Sedighy and M. K. Amirhosseini, “Design of an arbitrary shaped invisible cloak using coordinate transformation,” Int. Rev. Model. Simul. 3, 1167–1171 (2010).

Shahzad, A.

A. Shahzad, F. Qasim, S. Ahmed, and Q. A. Naqvi, “Cylindrical invisibility cloak incorporating PEMC at perturbed void region,” Prog. Electromagn. Res. M 21, 61–76 (2011).
[CrossRef]

Smith, D. R.

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

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

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, 977–980 (2006).
[CrossRef]

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,” in Photonics and Nanostructures—Fundamentals and Applications (Elsevier, 2008), pp. 87–95.

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, 977–980 (2006).
[CrossRef]

Taravati, S.

S. Taravati and A. Abdolali, “A new three-dimensional conical grounded plane cloak with homogeneous materials,” Prog. Electromagn. Res. M 19, 91–104 (2011).
[CrossRef]

Wang, J.

H. Ma, S. Qu, Z. Xu, and J. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E 78, 036608 (2008).
[CrossRef]

Werner, D. H.

D. H. Kwon and D. H. Werner, “Transformation electromagnetics, An overview of the theory and applications,” IEEE Antennas Propag. Mag. 52(1), 24–46 (2010).
[CrossRef]

Wu, B. I.

Y. Luo, J. J. Zhang, H. S. Chen, B. I. Wu, and L. X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178 (2009).

B. L. Zhang, H. S. Chen, and B. I. Wu, “Practical limitations of an invisibility cloak,” Prog. Electromagn. Res. 97, 407–416 (2009).
[CrossRef]

Xu, Z.

H. Ma, S. Qu, Z. Xu, and J. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E 78, 036608 (2008).
[CrossRef]

Yan, M.

L. Zhang, M. Yan, and M. Qiu, “The effect of transformation order on the invisibility performance of a practical cylindrical cloak,” J. Opt. A 10, 095001 (2008).
[CrossRef]

M. Yan, Z. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
[CrossRef]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef]

Yu, K. M.

J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson’s equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).

Zhang, B. L.

B. L. Zhang, H. S. Chen, and B. I. Wu, “Practical limitations of an invisibility cloak,” Prog. Electromagn. Res. 97, 407–416 (2009).
[CrossRef]

Zhang, J. J.

Y. Luo, J. J. Zhang, H. S. Chen, B. I. Wu, and L. X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178 (2009).

Zhang, L.

L. Zhang, M. Yan, and M. Qiu, “The effect of transformation order on the invisibility performance of a practical cylindrical cloak,” J. Opt. A 10, 095001 (2008).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

D. H. Kwon and D. H. Werner, “Transformation electromagnetics, An overview of the theory and applications,” IEEE Antennas Propag. Mag. 52(1), 24–46 (2010).
[CrossRef]

Int. Rev. Model. Simul. (1)

S. H. Sedighy and M. K. Amirhosseini, “Design of an arbitrary shaped invisible cloak using coordinate transformation,” Int. Rev. Model. Simul. 3, 1167–1171 (2010).

J. Opt. A (1)

L. Zhang, M. Yan, and M. Qiu, “The effect of transformation order on the invisibility performance of a practical cylindrical cloak,” J. Opt. A 10, 095001 (2008).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Phys. Rev. E (2)

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, “Numerical method for designing approximate cloaks with arbitrary shapes,” Phys. Rev. E 78, 036608 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef]

Prog. Electromagn. Res. (2)

B. L. Zhang, H. S. Chen, and B. I. Wu, “Practical limitations of an invisibility cloak,” Prog. Electromagn. Res. 97, 407–416 (2009).
[CrossRef]

Y. Luo, J. J. Zhang, H. S. Chen, B. I. Wu, and L. X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178 (2009).

Prog. Electromagn. Res. M (3)

A. Shahzad, F. Qasim, S. Ahmed, and Q. A. Naqvi, “Cylindrical invisibility cloak incorporating PEMC at perturbed void region,” Prog. Electromagn. Res. M 21, 61–76 (2011).
[CrossRef]

S. Taravati and A. Abdolali, “A new three-dimensional conical grounded plane cloak with homogeneous materials,” Prog. Electromagn. Res. M 19, 91–104 (2011).
[CrossRef]

J. J. Ma, X. Y. Cao, K. M. Yu, and T. Liu, “Determination the material parameters for arbitrary cloak based on Poisson’s equation,” Prog. Electromagn. Res. M 9, 177–184 (2009).

Science (2)

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

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, 977–980 (2006).
[CrossRef]

Other (1)

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,” in Photonics and Nanostructures—Fundamentals and Applications (Elsevier, 2008), pp. 87–95.

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Figures (8)

Fig. 1.
Fig. 1.

Arbitrary cloak cross section. (a) An arbitrary polygonal cloak divided into n-triangles. (b) A triangular unit of the arbitrary cloak.

Fig. 2.
Fig. 2.

Y-intercept transformation function versus the transformation order, n.

Fig. 3.
Fig. 3.

Cross section of three computational domains for a square, octagon, and 4-sided arbitrary cloaks for a 3.5 GHz TE uniform incident plane wave. First (a)–(c) and second (d)–(f) columns are corresponding to n=1/4 and 1, respectively.

Fig. 4.
Fig. 4.

Constitutive parameters (εxx,εxy,εyy,εzz) of the designed ideal square cloak for n=1/4 (first column) and n=2 (second column).

Fig. 5.
Fig. 5.

Maximum value of the εxx in the truncated designed square cloak for different removed layer thicknesses.

Fig. 6.
Fig. 6.

Reflection coefficients versus the transformation order, n, for different removed layer thicknesses.

Fig. 7.
Fig. 7.

Electric field distribution for different cloak thicknesses: (a) 20, (b) 10, and (c) 5 cm.

Fig. 8.
Fig. 8.

Reflection coefficients versus the transformation order n for t=20cm, t=10cm, and t=5cm; Δ=1mm.

Equations (13)

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

εr=μr=AATdet(A),
μr=εr=[A112+A122A11A21+A12A220A11A21+A12A22A212+A2220001]/|A|,
y=mx+δ,
δ=f(δ),
y=yxx,
δ=ymx.
δ=babnδn+a.
x=xδymx=xymx(babn(ymx)n+a),
y=yδymx=yymx(babn(ymx)n+a).
A11=babn(ymx)n1+babnmx(1n)(ymx)n2+ay(ymx)2,
A12=babnx(n1)(ymx)n2ax(ymx)2,
A21=mybabn(1n)(ymx)n2+amy(ymx)2,
A22=babn(ymx)n1+babny(n1)(ymx)n2max(ymx)2.

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