Abstract

A fully three-dimensional carpet cloak presenting invisibility in all viewing angles is theoretically demonstrated. The design is developed using transformation optics and three-dimensional quasi-conformal mapping. Parametrization strategy and numerical optimization of the coordinate transformation deploying a quasi-Newton method is applied. A discussion about the minimum achievable anisotropy in the 3D transformation optics is presented. The method allows to reduce the anisotropy in the cloak and an isotropic medium could be considered. Numerical simulations confirm the strategy employed enabling the design of an isotropic reflectionless broadband carpet cloak independently of the incident light direction and polarization.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  4. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
    [Crossref] [PubMed]
  5. M. A. F. C. Junqueira, L. H. Gabrielli, and D. H. Spadoti, “Anisotropy minimization via least squares method for transformation optics,” Opt. Express 22(15), 18490–18498 (2014).
    [Crossref] [PubMed]
  6. D. Liu, L. H. Gabrielli, M. Lipson, and S. G. Johnson, “Transformation inverse design,” Opt. Express 21(12), 14223–14243 (2013).
    [Crossref] [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]
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    [Crossref] [PubMed]
  9. Z. Chang, X. Zhou, J. Hu, and G. Hu, “Design method for quasi-isotropic transformation materials based on inverse Laplace’s equation with sliding boundaries,” Opt. Express 18(6), 6089–6096 (2010).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2017 (1)

M. H. Fakheri, A. Abdolali, S. Hashemi, and B. Noorbakhsh, ‘Three-dimensional ultra-wideband carpet cloak using multi-layer dielectrics,” Microw. Opt. Technol. Lett. 59(6), 1284–1288 (2017).
[Crossref]

2016 (1)

2015 (1)

2014 (3)

C. García-Meca, R. Ortuno, J. Martí, and A. Martínez, “Full three-dimensional isotropic transformation media,” New J. Phys. 16(2), 023030 (2014).
[Crossref]

M. Yin, X. Yong Tian, L. Ling Wu, and D. Chen Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
[Crossref]

M. A. F. C. Junqueira, L. H. Gabrielli, and D. H. Spadoti, “Anisotropy minimization via least squares method for transformation optics,” Opt. Express 22(15), 18490–18498 (2014).
[Crossref] [PubMed]

2013 (1)

2011 (1)

2010 (5)

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105(19), 193902 (2010).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
[Crossref] [PubMed]

Z. Chang, X. Zhou, J. Hu, and G. Hu, “Design method for quasi-isotropic transformation materials based on inverse Laplace’s equation with sliding boundaries,” Opt. Express 18(6), 6089–6096 (2010).
[Crossref] [PubMed]

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt. 13(2), 024002 (2010).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

2009 (1)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[Crossref]

2008 (1)

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

2006 (2)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(23), 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]

Abdolali, A.

M. H. Fakheri, A. Abdolali, S. Hashemi, and B. Noorbakhsh, ‘Three-dimensional ultra-wideband carpet cloak using multi-layer dielectrics,” Microw. Opt. Technol. Lett. 59(6), 1284–1288 (2017).
[Crossref]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[Crossref]

Chang, Z.

Chen Li, D.

M. Yin, X. Yong Tian, L. Ling Wu, and D. Chen Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
[Crossref]

Cui, T. J.

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
[Crossref] [PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

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]

Ergin, T.

Fakheri, M. H.

M. H. Fakheri, A. Abdolali, S. Hashemi, and B. Noorbakhsh, ‘Three-dimensional ultra-wideband carpet cloak using multi-layer dielectrics,” Microw. Opt. Technol. Lett. 59(6), 1284–1288 (2017).
[Crossref]

Fischer, J.

Gabrielli, L. H.

García-Meca, C.

C. García-Meca, R. Ortuno, J. Martí, and A. Martínez, “Full three-dimensional isotropic transformation media,” New J. Phys. 16(2), 023030 (2014).
[Crossref]

Hashemi, S.

M. H. Fakheri, A. Abdolali, S. Hashemi, and B. Noorbakhsh, ‘Three-dimensional ultra-wideband carpet cloak using multi-layer dielectrics,” Microw. Opt. Technol. Lett. 59(6), 1284–1288 (2017).
[Crossref]

Hu, G.

Hu, J.

Johnson, S. G.

Junqueira, M. A. F. C.

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]

Kundtz, N.

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105(19), 193902 (2010).
[Crossref]

Kundtz, N. B.

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt. 13(2), 024002 (2010).
[Crossref]

Landy, N. I.

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105(19), 193902 (2010).
[Crossref]

Li, J.

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

Ling Wu, L.

M. Yin, X. Yong Tian, L. Ling Wu, and D. Chen Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
[Crossref]

Lipson, M.

D. Liu, L. H. Gabrielli, M. Lipson, and S. G. Johnson, “Transformation inverse design,” Opt. Express 21(12), 14223–14243 (2013).
[Crossref] [PubMed]

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[Crossref]

Liu, D.

Ma, H. F.

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
[Crossref] [PubMed]

Martí, J.

C. García-Meca, R. Ortuno, J. Martí, and A. Martínez, “Full three-dimensional isotropic transformation media,” New J. Phys. 16(2), 023030 (2014).
[Crossref]

Martínez, A.

C. García-Meca, R. Ortuno, J. Martí, and A. Martínez, “Full three-dimensional isotropic transformation media,” New J. Phys. 16(2), 023030 (2014).
[Crossref]

Mejía, F. B.

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]

Noorbakhsh, B.

M. H. Fakheri, A. Abdolali, S. Hashemi, and B. Noorbakhsh, ‘Three-dimensional ultra-wideband carpet cloak using multi-layer dielectrics,” Microw. Opt. Technol. Lett. 59(6), 1284–1288 (2017).
[Crossref]

Ortuno, R.

C. García-Meca, R. Ortuno, J. Martí, and A. Martínez, “Full three-dimensional isotropic transformation media,” New J. Phys. 16(2), 023030 (2014).
[Crossref]

Pendry, J. B.

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt. 13(2), 024002 (2010).
[Crossref]

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(23), 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]

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[Crossref]

Qiu, M.

W. Yan, M. Yan, and M. Qiu, “Necessary and sufficient conditions for reflectionless transformation media in an isotropic and homogenous background,” arXiv preprint arXiv:0806.3231 (2008).

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(23), 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]

Smith, D. R.

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt. 13(2), 024002 (2010).
[Crossref]

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105(19), 193902 (2010).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(23), 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]

Spadoti, D. H.

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]

Urzhumov, Y. A.

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt. 13(2), 024002 (2010).
[Crossref]

Wegener, M.

Yan, M.

W. Yan, M. Yan, and M. Qiu, “Necessary and sufficient conditions for reflectionless transformation media in an isotropic and homogenous background,” arXiv preprint arXiv:0806.3231 (2008).

Yan, W.

W. Yan, M. Yan, and M. Qiu, “Necessary and sufficient conditions for reflectionless transformation media in an isotropic and homogenous background,” arXiv preprint arXiv:0806.3231 (2008).

Yin, M.

M. Yin, X. Yong Tian, L. Ling Wu, and D. Chen Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
[Crossref]

Yong Tian, X.

M. Yin, X. Yong Tian, L. Ling Wu, and D. Chen Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
[Crossref]

Zhou, X.

Appl. Phys. Lett. (1)

M. Yin, X. Yong Tian, L. Ling Wu, and D. Chen Li, “All-dielectric three-dimensional broadband Eaton lens with large refractive index range,” Appl. Phys. Lett. 104(9), 094101 (2014).
[Crossref]

J. Opt. (1)

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt. 13(2), 024002 (2010).
[Crossref]

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

Microw. Opt. Technol. Lett. (1)

M. H. Fakheri, A. Abdolali, S. Hashemi, and B. Noorbakhsh, ‘Three-dimensional ultra-wideband carpet cloak using multi-layer dielectrics,” Microw. Opt. Technol. Lett. 59(6), 1284–1288 (2017).
[Crossref]

Nat. Commun. (2)

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
[Crossref] [PubMed]

Nat. Photonics (1)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[Crossref]

New J. Phys. (1)

C. García-Meca, R. Ortuno, J. Martí, and A. Martínez, “Full three-dimensional isotropic transformation media,” New J. Phys. 16(2), 023030 (2014).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. Lett. (2)

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105(19), 193902 (2010).
[Crossref]

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

Science (2)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(23), 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]

Other (1)

W. Yan, M. Yan, and M. Qiu, “Necessary and sufficient conditions for reflectionless transformation media in an isotropic and homogenous background,” arXiv preprint arXiv:0806.3231 (2008).

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Figures (3)

Fig. 1
Fig. 1 Simulation results for 3D carpet cloak with p = q = r = 3: (a) optimized coordinate transformation, and (b) refractive index profile in perspective view, and x = 0 and y = 0 planes.
Fig. 2
Fig. 2 Instantaneous normalized electric field plot in perspective view, x = 0, y = 0 and z = 2.31 µm planes, and electromagnetic power flow in the z = 2.31 µm plane, respectively, for (a) a perfectly flat mirror, (b) deformed mirror without cloak, and (c) deformed mirror with cloak whose limits are indicated by the dashed lines.
Fig. 3
Fig. 3 Instantaneous normalized electric field plot for c = 0.4 µm in perspective view, x = 0, y = 0 and z = 2.31 µm planes, and electromagnetic power flow in z = 2.31 µm plane, respectively, for (a) deformed mirror without cloak, and (b) deformed mirror with cloak whose limits are defined by the dashed lines.

Equations (3)

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

x = x + b ( x , y , z ) i = 0 p j = 0 q k = 0 r A i j k x i y j z k y = y + b ( x , y , z ) i = 0 p j = 0 q k = 0 r B i j k x i y j z k z = z + c ( 1 z h ) cos ( π x w 1 ) cos ( π y w 2 ) + b ( x , y , z ) i = 0 p j = 0 q k = 0 r C i j k x i y j z k
b ( x , y , z ) = ( x 2 + y 2 + z ) ( z h ) c o s ( π x w 1 ) c o s ( π y w 2 )
n ( x , y , z ) = n b ( x x ) 2 + ( y x ) 2 + ( z x ) 2

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