Abstract

We propose to use morphing algorithms to deduce some approximate wave pictures of scattering by cylindrical invisibility cloaks of various shapes deduced from the exact computation (e.g. using a finite element method) of scattering by cloaks of two given shapes, say circular and elliptic ones, thereafter called the source and destination images. The error in L2 norm between the exact and approximate solutions deduced via morphing from the source and destination images is typically less than 2 percent if control points are judiciously chosen. Our approach works equally well for rotators and concentrators, and also unveils some device which we call rotacon since it both rotates and concentrates electromagnetic fields. However, it breaks down for superscatterers (deduced from non-monotonic transforms): the error in L2 norm is about 25 percent. We stress that our approach might greatly accelerate numerical studies of 2D and 3D cloaks.

© 2014 Optical Society of America

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References

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  1. D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, “Elastically deformable models,” Comput. Graph. 21(4), 205–214 (1987).
    [Crossref]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref] [PubMed]
  3. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [Crossref] [PubMed]
  4. U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover Publications, 2012).
  5. 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]
  6. N.-A. P. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B Condens. Matter 49(12), 8479–8482 (1994).
    [Crossref] [PubMed]
  7. G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. Lond. A 461(2064), 3999–4034 (2005).
    [Crossref]
  8. G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lond. A 462(2074), 3027–3059 (2006).
    [Crossref]
  9. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [Crossref] [PubMed]
  10. J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003).
    [Crossref]
  11. http://www.xiberpix.net/SqirlzMorph.html
  12. S.-Y. Lee, K.-Y. Chwa, J. Hahn, and S. Y. Shin, “Image morphing using deformation techniques,” J. Visual. Comp. Animat. 7(1), 3–23 (1996).
    [Crossref]
  13. A. Nicolet, F. Zolla, and S. Guenneau, “Finite element analysis of cylindrical invisibility cloaks of elliptical cross section,” IEEE Trans. Magn. 44(6), 1150–1153 (2008).
    [Crossref]
  14. G. Bouchitté and R. Petit, “On the concepts of a perfectly conducting material and of a perfectly conducting and infinitely thin screen,” Radio Sci. 24(1), 13–26 (1989).
    [Crossref]
  15. T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatter: enhancement of scattering with complementary media,” Opt. Express 16, 618545 (2008).
  16. 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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
    [Crossref]
  17. Y. Luo, J. Zhang, J. Wu, and H. Chen, “Interaction of an electromagnetic wave with a cone-shaped invisibility cloak and polarization rotator,” Phys. Rev. B 78(12), 125108 (2008).
    [Crossref]
  18. Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
    [Crossref]
  19. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
    [Crossref]
  20. A. Nicolet, F. Zolla, and S. Guenneau, “Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section,” Opt. Lett. 33(14), 1584–1586 (2008).
    [Crossref] [PubMed]
  21. G. Dolling, M. Wegener, S. Linden, and C. Hormann, “Photorealistic images of objects in effective negative-index materials,” Opt. Express 14(5), 1842–1849 (2006).
    [Crossref] [PubMed]

2008 (6)

A. Nicolet, F. Zolla, and S. Guenneau, “Finite element analysis of cylindrical invisibility cloaks of elliptical cross section,” IEEE Trans. Magn. 44(6), 1150–1153 (2008).
[Crossref]

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatter: enhancement of scattering with complementary media,” Opt. Express 16, 618545 (2008).

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Y. Luo, J. Zhang, J. Wu, and H. Chen, “Interaction of an electromagnetic wave with a cone-shaped invisibility cloak and polarization rotator,” Phys. Rev. B 78(12), 125108 (2008).
[Crossref]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

A. Nicolet, F. Zolla, and S. Guenneau, “Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section,” Opt. Lett. 33(14), 1584–1586 (2008).
[Crossref] [PubMed]

2007 (1)

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

2006 (4)

G. Dolling, M. Wegener, S. Linden, and C. Hormann, “Photorealistic images of objects in effective negative-index materials,” Opt. Express 14(5), 1842–1849 (2006).
[Crossref] [PubMed]

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

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lond. A 462(2074), 3027–3059 (2006).
[Crossref]

2005 (2)

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. Lond. A 461(2064), 3999–4034 (2005).
[Crossref]

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)

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

1996 (1)

S.-Y. Lee, K.-Y. Chwa, J. Hahn, and S. Y. Shin, “Image morphing using deformation techniques,” J. Visual. Comp. Animat. 7(1), 3–23 (1996).
[Crossref]

1994 (1)

N.-A. P. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B Condens. Matter 49(12), 8479–8482 (1994).
[Crossref] [PubMed]

1989 (1)

G. Bouchitté and R. Petit, “On the concepts of a perfectly conducting material and of a perfectly conducting and infinitely thin screen,” Radio Sci. 24(1), 13–26 (1989).
[Crossref]

1987 (1)

D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, “Elastically deformable models,” Comput. Graph. 21(4), 205–214 (1987).
[Crossref]

Alù, A.

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]

Barr, A.

D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, “Elastically deformable models,” Comput. Graph. 21(4), 205–214 (1987).
[Crossref]

Bouchitté, G.

G. Bouchitté and R. Petit, “On the concepts of a perfectly conducting material and of a perfectly conducting and infinitely thin screen,” Radio Sci. 24(1), 13–26 (1989).
[Crossref]

Chan, C. T.

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

Chen, H.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

Y. Luo, J. Zhang, J. Wu, and H. Chen, “Interaction of an electromagnetic wave with a cone-shaped invisibility cloak and polarization rotator,” Phys. Rev. B 78(12), 125108 (2008).
[Crossref]

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatter: enhancement of scattering with complementary media,” Opt. Express 16, 618545 (2008).

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

Chwa, K.-Y.

S.-Y. Lee, K.-Y. Chwa, J. Hahn, and S. Y. Shin, “Image morphing using deformation techniques,” J. Visual. Comp. Animat. 7(1), 3–23 (1996).
[Crossref]

Cummer, S. 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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Dolling, G.

Engheta, N.

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]

Fleischer, K.

D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, “Elastically deformable models,” Comput. Graph. 21(4), 205–214 (1987).
[Crossref]

Guenneau, S.

A. Nicolet, F. Zolla, and S. Guenneau, “Finite element analysis of cylindrical invisibility cloaks of elliptical cross section,” IEEE Trans. Magn. 44(6), 1150–1153 (2008).
[Crossref]

A. Nicolet, F. Zolla, and S. Guenneau, “Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section,” Opt. Lett. 33(14), 1584–1586 (2008).
[Crossref] [PubMed]

Hahn, J.

S.-Y. Lee, K.-Y. Chwa, J. Hahn, and S. Y. Shin, “Image morphing using deformation techniques,” J. Visual. Comp. Animat. 7(1), 3–23 (1996).
[Crossref]

Hormann, C.

Kong, J. A.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

Lee, S.-Y.

S.-Y. Lee, K.-Y. Chwa, J. Hahn, and S. Y. Shin, “Image morphing using deformation techniques,” J. Visual. Comp. Animat. 7(1), 3–23 (1996).
[Crossref]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Linden, S.

Luo, X.

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatter: enhancement of scattering with complementary media,” Opt. Express 16, 618545 (2008).

Luo, Y.

Y. Luo, J. Zhang, J. Wu, and H. Chen, “Interaction of an electromagnetic wave with a cone-shaped invisibility cloak and polarization rotator,” Phys. Rev. B 78(12), 125108 (2008).
[Crossref]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

Ma, H.

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatter: enhancement of scattering with complementary media,” Opt. Express 16, 618545 (2008).

McPhedran, R. C.

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. Lond. A 461(2064), 3999–4034 (2005).
[Crossref]

N.-A. P. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B Condens. Matter 49(12), 8479–8482 (1994).
[Crossref] [PubMed]

Milton, G. W.

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lond. A 462(2074), 3027–3059 (2006).
[Crossref]

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. Lond. A 461(2064), 3999–4034 (2005).
[Crossref]

N.-A. P. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B Condens. Matter 49(12), 8479–8482 (1994).
[Crossref] [PubMed]

Nicolet, A.

A. Nicolet, F. Zolla, and S. Guenneau, “Finite element analysis of cylindrical invisibility cloaks of elliptical cross section,” IEEE Trans. Magn. 44(6), 1150–1153 (2008).
[Crossref]

A. Nicolet, F. Zolla, and S. Guenneau, “Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section,” Opt. Lett. 33(14), 1584–1586 (2008).
[Crossref] [PubMed]

Nicorovici, N.-A. P.

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lond. A 462(2074), 3027–3059 (2006).
[Crossref]

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. Lond. A 461(2064), 3999–4034 (2005).
[Crossref]

N.-A. P. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B Condens. Matter 49(12), 8479–8482 (1994).
[Crossref] [PubMed]

Pendry, J. B.

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

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

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003).
[Crossref]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Petit, R.

G. Bouchitté and R. Petit, “On the concepts of a perfectly conducting material and of a perfectly conducting and infinitely thin screen,” Radio Sci. 24(1), 13–26 (1989).
[Crossref]

Platt, J.

D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, “Elastically deformable models,” Comput. Graph. 21(4), 205–214 (1987).
[Crossref]

Podolskiy, V. A.

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. Lond. A 461(2064), 3999–4034 (2005).
[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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Ramakrishna, S. A.

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003).
[Crossref]

Ran, L.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Schurig, D.

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

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

Shin, S. Y.

S.-Y. Lee, K.-Y. Chwa, J. Hahn, and S. Y. Shin, “Image morphing using deformation techniques,” J. Visual. Comp. Animat. 7(1), 3–23 (1996).
[Crossref]

Smith, D. R.

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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

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

Terzopoulos, D.

D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, “Elastically deformable models,” Comput. Graph. 21(4), 205–214 (1987).
[Crossref]

Wegener, M.

Wu, J.

Y. Luo, J. Zhang, J. Wu, and H. Chen, “Interaction of an electromagnetic wave with a cone-shaped invisibility cloak and polarization rotator,” Phys. Rev. B 78(12), 125108 (2008).
[Crossref]

Yang, T.

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatter: enhancement of scattering with complementary media,” Opt. Express 16, 618545 (2008).

Zhang, J.

Y. Luo, J. Zhang, J. Wu, and H. Chen, “Interaction of an electromagnetic wave with a cone-shaped invisibility cloak and polarization rotator,” Phys. Rev. B 78(12), 125108 (2008).
[Crossref]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

Zolla, F.

A. Nicolet, F. Zolla, and S. Guenneau, “Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section,” Opt. Lett. 33(14), 1584–1586 (2008).
[Crossref] [PubMed]

A. Nicolet, F. Zolla, and S. Guenneau, “Finite element analysis of cylindrical invisibility cloaks of elliptical cross section,” IEEE Trans. Magn. 44(6), 1150–1153 (2008).
[Crossref]

Appl. Phys. Lett. (1)

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

Comput. Graph. (1)

D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, “Elastically deformable models,” Comput. Graph. 21(4), 205–214 (1987).
[Crossref]

IEEE Trans. Magn. (1)

A. Nicolet, F. Zolla, and S. Guenneau, “Finite element analysis of cylindrical invisibility cloaks of elliptical cross section,” IEEE Trans. Magn. 44(6), 1150–1153 (2008).
[Crossref]

J. Phys. Condens. Matter (1)

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003).
[Crossref]

J. Visual. Comp. Animat. (1)

S.-Y. Lee, K.-Y. Chwa, J. Hahn, and S. Y. Shin, “Image morphing using deformation techniques,” J. Visual. Comp. Animat. 7(1), 3–23 (1996).
[Crossref]

Opt. Express (2)

G. Dolling, M. Wegener, S. Linden, and C. Hormann, “Photorealistic images of objects in effective negative-index materials,” Opt. Express 14(5), 1842–1849 (2006).
[Crossref] [PubMed]

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatter: enhancement of scattering with complementary media,” Opt. Express 16, 618545 (2008).

Opt. Lett. (1)

Photon. Nanostruct. Fundam. Appl. (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,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Phys. Rev. B (2)

Y. Luo, J. Zhang, J. Wu, and H. Chen, “Interaction of an electromagnetic wave with a cone-shaped invisibility cloak and polarization rotator,” Phys. Rev. B 78(12), 125108 (2008).
[Crossref]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

Phys. Rev. B Condens. Matter (1)

N.-A. P. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B Condens. Matter 49(12), 8479–8482 (1994).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (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]

Phys. Rev. Lett. (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A (2)

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. Lond. A 461(2064), 3999–4034 (2005).
[Crossref]

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lond. A 462(2074), 3027–3059 (2006).
[Crossref]

Radio Sci. (1)

G. Bouchitté and R. Petit, “On the concepts of a perfectly conducting material and of a perfectly conducting and infinitely thin screen,” Radio Sci. 24(1), 13–26 (1989).
[Crossref]

Science (2)

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

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Other (2)

U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover Publications, 2012).

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Figures (14)

Fig. 1
Fig. 1 Case of morphing from (a) to (b) and from (c) to (d) with too few control points in (a) and (b) and too many control points in (c) and (d), with also some control points aligned and close to other ones in (c) and (d). One can see that the control point numbers “1”, “2”, “3”, “4” in (c) correspond to the same control points in (d), with however a stretch along the vertical axis.
Fig. 2
Fig. 2 Obtained intermediate result (image half-way from the final image) in the case of morphing with a few number of control points in (a), and with too many control points in (b). The result of a direct computation in (c) is quite close from the morphing result in (b).
Fig. 3
Fig. 3 Rectangular (warp) meshing example in (a) and triangular (Delaunay) meshing example in (b).
Fig. 4
Fig. 4 Morphing example with a mapping from the leftmost into the rightmost photos, with intermediate images obtained with respectively 33% and 66% of morphing. One should note that both shapes and colors are interpolated.
Fig. 5
Fig. 5 Comparison by difference (c), in gradation of grey, between a calculated result (a) and a morphing result (b).
Fig. 6
Fig. 6 Test of L2 norm for image comparison’s function (f) with black and white images with respectively 0% (a), 25% (b), 50% (c), 75% (d), and 100% (e) of white.
Fig. 7
Fig. 7 Scatter cloaks in transverse magnetic (TM) polarization with inner radii R1 = 0.25m (a) and R1 = 0.1m (b) and outer radii R2 = 0.4m (a) and R2 = 0.2m (b). The inner discs are filled with infinite conducting material. Obtained intermediate result (image half-way from the final image) in the case of morphing in (c), and a direct computation in (d) for a scatter cloak with inner radius R1 = 0.175m and outer radius R2 = 0.3m. In (e) we show the difference image between (c) and (d).
Fig. 8
Fig. 8 Infinite conducting obstacles in transverse magnetic (TM) polarization (with two different radii R3 = 0.64m and R3 = 0.4m) with almost the same scattered fields as in (a) and (b). Obtained intermediate result (image half-way from the final image) in the case of morphing in (c), and calculated intermediate result in (d) for an infinite conducting obstacle of radius R3 = 0.5142857m. In (e) we show the difference image between (c) and (d).
Fig. 9
Fig. 9 Scatter cloaks in transverse electric (TE) polarization with inner radii R1 = 0.25m (a) and R1 = 0.1m (b) and outer radii R2 = 0.4m (a) and R2 = 0.2m (b). The inner discs are filled with infinite conducting material. Obtained intermediate result (image half-way from the final image) in the case of morphing in (c), and a direct computation in (d) for a scatter cloak with inner radius R1 = 0.175m and outer radius R2 = 0.3m. In (e) we show the difference image between (c) and (d).
Fig. 10
Fig. 10 Infinite conducting obstacle in transverse electric (TE) polarization of radii 0.64m (a) and 0.4m (b). Obtained intermediate result (image half-way from the final image) in the case of morphing in (c), and a direct computation in (d). In (e) we show the difference image between (c) and (d). One notes that the scattered fields in (a)-(d) are identical to that in (a)-(d) in Fig. 9. On the contrary, panel (e) in Figs. 9 and 10 are much different.
Fig. 11
Fig. 11 External cloaks in transverse magnetic polarization (TM) with inner radii R1 = 0.25m (a) and R1 = 0.1m (b) and outer radii R2 = 0.4m (a) and R2 = 0.2m (b). The inner discs are filled with a material with ε ' = ε ( R 2 ) 4 / R 1 4 , μ ' = μ
Fig. 12
Fig. 12 Non Circular cloak’s shape concentrating (a) and rotating (b) the electric field, with their control points.
Fig. 13
Fig. 13 Morphing result in (c) at 20%, in (d) at 40%, in (e) at 60%, and in (f) at 80%, of a combination of a rotator in (a) with a concentrator in (b) keeping the special cloak’s shape of Fig. 12 (boundaries are not shown as they are not useful in the morphing algorithm here).
Fig. 14
Fig. 14 Morphing result in (a) without boundary, in (b) with boundary of a combination of a rotator with a concentrator keeping the special cloak’s shape of Fig. 12, and numerical result in (c) without boundary, in (d) with boundary of a combination of a rotator with a concentrator keeping the special cloak’s shape of Fig. 12.

Equations (4)

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f : ( r , θ ) ( r , θ ) = ( α r + β , θ ) , w h e r e 0 < r < R 2 = a 2 2 cos 2 θ + b 2 2 sin 2 θ α = ( R 2 - β ) / R 2 , w i t h β = a 1 2 cos 2 θ + b 1 2 sin 2 θ ,
. ( T T ε 1 H z ) + ω 2 T z z 1 μ H z = 0 , . ( T T μ 1 E z ) + ω 2 T z z 1 ε E z = 0
( r , θ ) f I ( r ' , θ ' ) f i = { α i r + β i = r ' θ + γ i r + Κ i = θ ' } i = I I , I I I 0 < r < R 2 ( θ ) f I I / α I I = R 1 ( θ ) R 2 ( θ ) , β I I = 0 , γ I I = 0 , Κ I I = 0 R 2 ( θ ) < r < R 3 ( θ ) f I I I / α I I I = R 3 ( θ ) R 1 ( θ ) R 3 ( θ ) R 2 ( θ ) , β I I I = R 3 ( θ ) ( R 1 ( θ ) R 2 ( θ ) ) R 3 ( θ ) R 2 ( θ ) , γ I I I = θ 0 R 2 ( θ ) R 3 ( θ ) , Κ I I I = R 3 ( θ ) θ 0 R 3 ( θ ) R 2 ( θ ) f i / i = I : α I = 1 , β I = 0 , γ I = 0 , Κ I = 0
R 1 ( θ ) = 0.4 R ( 1 + 0.2 sin ( 3 θ ) ) ; R 2 ( θ ) = 0.6 R ( 1 + 0.2 sin ( 3 θ ) ) ; R 3 ( θ ) = R ( 1 + 0.2 ( sin ( 3 θ ) + cos ( 4 θ ) ) ;

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