Abstract

We present the design of an all-dielectric cloaking device at microwave frequencies. A gradient based topology optimization is employed to find a dielectric permittivity distribution that minimizes the diffracted field in free space. The layout is binary, i.e. made either of standard ABS plastic or air and is designed to reduce the scattering from an ABS cylinder excited by a line source for TE polarization. We study the performances of cloaks optimized for one, two and three frequencies in terms of scattering reduction and correlations with respect to the free space propagation case. Finally, a modal analysis is carried out providing physical insights on the resonant cloaking mechanism at stake.

© 2015 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] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [Crossref] [PubMed]
  3. A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
    [Crossref]
  4. A. Nicolet, F. Zolla, Y. O. Agha, and S. Guenneau, “Geometrical transformations and equivalent materials in computational electromagnetism,” COMPEL 27, 806–819 (2008).
    [Crossref]
  5. H. Chen, C. T. Chan, and P. Sheng, “Transformation Optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
    [Crossref] [PubMed]
  6. 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] [PubMed]
  7. B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
    [Crossref]
  8. Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3, 2182 (2013).
    [Crossref] [PubMed]
  9. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
    [Crossref] [PubMed]
  10. H. Chen and B. Zheng, “Broadband polygonal invisibility cloak for visible light,” Sci. Rep. 2, 255 (2012).
    [Crossref] [PubMed]
  11. J. Andkjær and O. Sigmund, “Topology optimized low-contrast all-dielectric optical cloak,” Appl. Phys. Lett. 98, 021112 (2011).
    [Crossref]
  12. J. Andkjær, N. Asger Mortensen, and O. Sigmund, “Towards all-dielectric, polarization-independent optical cloaks,” Appl. Phys. Lett. 100, 101106 (2012).
    [Crossref]
  13. L. Lan, F. Sun, Y. Liu, C. K. Ong, and Y. Ma, “Experimentally demonstrated a unidirectional electromagnetic cloak designed by topology optimization,” Appl. Phys. Lett. 103, 121113 (2013).
    [Crossref]
  14. B. Riddle, J. Baker-Jarvis, and J. Krupka, “Complex permittivity measurements of common plastics over variable temperatures,” IEEE Trans. Microw. Theory Techn. 51, 727–733 (2003).
    [Crossref]
  15. P. Deffenbaugh, R. Rumpf, and K. Church, “Broadband microwave frequency characterization of 3-d printed materials,” EEE Trans. Compon. Packag. Manuf. Techno. 3, 2147–2155 (2013).
    [Crossref]
  16. B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).
    [Crossref]
  17. J. Jin, The Finite Element Method in Electromagnetics (John Wiley & Sons, 2014).
  18. J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [Crossref]
  19. M. Lassas, J. Liukkonen, and E. Somersalo, “Complex Riemannian metric and absorbing boundary conditions,” J. Math. Pure. Appl. 80, 739–768 (2001).
    [Crossref]
  20. M. P. Bendsøe and O. Sigmund, “Material interpolation schemes in topology optimization,” Archive of Applied Mechanics 69, 635–654 (1999).
    [Crossref]
  21. F. Wang, B. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidiscip. O. 43, 767–784 (2011).
    [Crossref]
  22. R. Tapia, “Diagonalized multiplier methods and quasinewton methods for constrained optimization,” Journal of Optimization Theory and Applications 22, 135–194 (1977).
    [Crossref]
  23. J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high-bandwidth low-loss t-junction waveguide,” J. Opt. Soc. Am. B 22, 1191–1198 (2005).
    [Crossref]
  24. O. Schenk, A. Wachter, and M. Hagemann, “Matching-based preprocessing algorithms to the solution of saddle-point problems in large-scale nonconvex interior-point optimization,” Computational Optimization and Applications 36, 321–341 (2007).
    [Crossref]
  25. D. Bao, R. Mitchell-Thomas, K. Rajab, and Y. Hao, “Quantitative study of two experimental demonstrations of a carpet cloak,” IEEE Antennas Wireless Propag. Lett. 12, 206–209 (2013).
    [Crossref]
  26. C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
    [Crossref] [PubMed]
  27. M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
    [Crossref]
  28. A. Rahmani, M. J. Steel, and P. C. Chaumet, “Invisibility and supervisibility: Radiation dynamics in a discrete electromagnetic cloak,” Phys. Rev. B 87, 045430 (2013).
    [Crossref]
  29. P.-Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Advanced Materials 24, OP281–OP304 (2012).
    [PubMed]
  30. A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
    [Crossref]

2014 (1)

B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).
[Crossref]

2013 (6)

P. Deffenbaugh, R. Rumpf, and K. Church, “Broadband microwave frequency characterization of 3-d printed materials,” EEE Trans. Compon. Packag. Manuf. Techno. 3, 2147–2155 (2013).
[Crossref]

L. Lan, F. Sun, Y. Liu, C. K. Ong, and Y. Ma, “Experimentally demonstrated a unidirectional electromagnetic cloak designed by topology optimization,” Appl. Phys. Lett. 103, 121113 (2013).
[Crossref]

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3, 2182 (2013).
[Crossref] [PubMed]

D. Bao, R. Mitchell-Thomas, K. Rajab, and Y. Hao, “Quantitative study of two experimental demonstrations of a carpet cloak,” IEEE Antennas Wireless Propag. Lett. 12, 206–209 (2013).
[Crossref]

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref] [PubMed]

A. Rahmani, M. J. Steel, and P. C. Chaumet, “Invisibility and supervisibility: Radiation dynamics in a discrete electromagnetic cloak,” Phys. Rev. B 87, 045430 (2013).
[Crossref]

2012 (3)

P.-Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Advanced Materials 24, OP281–OP304 (2012).
[PubMed]

H. Chen and B. Zheng, “Broadband polygonal invisibility cloak for visible light,” Sci. Rep. 2, 255 (2012).
[Crossref] [PubMed]

J. Andkjær, N. Asger Mortensen, and O. Sigmund, “Towards all-dielectric, polarization-independent optical cloaks,” Appl. Phys. Lett. 100, 101106 (2012).
[Crossref]

2011 (3)

J. Andkjær and O. Sigmund, “Topology optimized low-contrast all-dielectric optical cloak,” Appl. Phys. Lett. 98, 021112 (2011).
[Crossref]

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

F. Wang, B. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidiscip. O. 43, 767–784 (2011).
[Crossref]

2010 (1)

H. Chen, C. T. Chan, and P. Sheng, “Transformation Optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref] [PubMed]

2009 (2)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
[Crossref]

2008 (1)

A. Nicolet, F. Zolla, Y. O. Agha, and S. Guenneau, “Geometrical transformations and equivalent materials in computational electromagnetism,” COMPEL 27, 806–819 (2008).
[Crossref]

2007 (1)

O. Schenk, A. Wachter, and M. Hagemann, “Matching-based preprocessing algorithms to the solution of saddle-point problems in large-scale nonconvex interior-point optimization,” Computational Optimization and Applications 36, 321–341 (2007).
[Crossref]

2006 (3)

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] [PubMed]

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

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

2005 (2)

2003 (1)

B. Riddle, J. Baker-Jarvis, and J. Krupka, “Complex permittivity measurements of common plastics over variable temperatures,” IEEE Trans. Microw. Theory Techn. 51, 727–733 (2003).
[Crossref]

2001 (1)

M. Lassas, J. Liukkonen, and E. Somersalo, “Complex Riemannian metric and absorbing boundary conditions,” J. Math. Pure. Appl. 80, 739–768 (2001).
[Crossref]

1999 (1)

M. P. Bendsøe and O. Sigmund, “Material interpolation schemes in topology optimization,” Archive of Applied Mechanics 69, 635–654 (1999).
[Crossref]

1996 (1)

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[Crossref]

1994 (1)

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

1977 (1)

R. Tapia, “Diagonalized multiplier methods and quasinewton methods for constrained optimization,” Journal of Optimization Theory and Applications 22, 135–194 (1977).
[Crossref]

Agha, Y. O.

A. Nicolet, F. Zolla, Y. O. Agha, and S. Guenneau, “Geometrical transformations and equivalent materials in computational electromagnetism,” COMPEL 27, 806–819 (2008).
[Crossref]

Alù, A.

P.-Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Advanced Materials 24, OP281–OP304 (2012).
[PubMed]

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

Andkjær, J.

J. Andkjær, N. Asger Mortensen, and O. Sigmund, “Towards all-dielectric, polarization-independent optical cloaks,” Appl. Phys. Lett. 100, 101106 (2012).
[Crossref]

J. Andkjær and O. Sigmund, “Topology optimized low-contrast all-dielectric optical cloak,” Appl. Phys. Lett. 98, 021112 (2011).
[Crossref]

Asger Mortensen, N.

J. Andkjær, N. Asger Mortensen, and O. Sigmund, “Towards all-dielectric, polarization-independent optical cloaks,” Appl. Phys. Lett. 100, 101106 (2012).
[Crossref]

Baker-Jarvis, J.

B. Riddle, J. Baker-Jarvis, and J. Krupka, “Complex permittivity measurements of common plastics over variable temperatures,” IEEE Trans. Microw. Theory Techn. 51, 727–733 (2003).
[Crossref]

Bao, D.

D. Bao, R. Mitchell-Thomas, K. Rajab, and Y. Hao, “Quantitative study of two experimental demonstrations of a carpet cloak,” IEEE Antennas Wireless Propag. Lett. 12, 206–209 (2013).
[Crossref]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Bendsøe, M. P.

M. P. Bendsøe and O. Sigmund, “Material interpolation schemes in topology optimization,” Archive of Applied Mechanics 69, 635–654 (1999).
[Crossref]

Berenger, J.-P.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation Optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref] [PubMed]

Chaumet, P. C.

A. Rahmani, M. J. Steel, and P. C. Chaumet, “Invisibility and supervisibility: Radiation dynamics in a discrete electromagnetic cloak,” Phys. Rev. B 87, 045430 (2013).
[Crossref]

Chen, H.

H. Chen and B. Zheng, “Broadband polygonal invisibility cloak for visible light,” Sci. Rep. 2, 255 (2012).
[Crossref] [PubMed]

H. Chen, C. T. Chan, and P. Sheng, “Transformation Optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref] [PubMed]

Chen, P.-Y.

P.-Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Advanced Materials 24, OP281–OP304 (2012).
[PubMed]

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

Church, K.

P. Deffenbaugh, R. Rumpf, and K. Church, “Broadband microwave frequency characterization of 3-d printed materials,” EEE Trans. Compon. Packag. Manuf. Techno. 3, 2147–2155 (2013).
[Crossref]

Commandré, M.

B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).
[Crossref]

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, 977–980 (2006).
[Crossref] [PubMed]

de Lustrac, A.

B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
[Crossref]

Deffenbaugh, P.

P. Deffenbaugh, R. Rumpf, and K. Church, “Broadband microwave frequency characterization of 3-d printed materials,” EEE Trans. Compon. Packag. Manuf. Techno. 3, 2147–2155 (2013).
[Crossref]

Engheta, N.

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

Enoch, S.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

Farhat, M.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

Germain, D.

B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
[Crossref]

Guenneau, S.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

A. Nicolet, F. Zolla, Y. O. Agha, and S. Guenneau, “Geometrical transformations and equivalent materials in computational electromagnetism,” COMPEL 27, 806–819 (2008).
[Crossref]

Hagemann, M.

O. Schenk, A. Wachter, and M. Hagemann, “Matching-based preprocessing algorithms to the solution of saddle-point problems in large-scale nonconvex interior-point optimization,” Computational Optimization and Applications 36, 321–341 (2007).
[Crossref]

Hao, Y.

D. Bao, R. Mitchell-Thomas, K. Rajab, and Y. Hao, “Quantitative study of two experimental demonstrations of a carpet cloak,” IEEE Antennas Wireless Propag. Lett. 12, 206–209 (2013).
[Crossref]

He, S.

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3, 2182 (2013).
[Crossref] [PubMed]

Hugonin, J. P.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref] [PubMed]

Jensen, J. S.

Jiang, W.

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3, 2182 (2013).
[Crossref] [PubMed]

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics (John Wiley & Sons, 2014).

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] [PubMed]

Kanté, B.

B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
[Crossref]

Krupka, J.

B. Riddle, J. Baker-Jarvis, and J. Krupka, “Complex permittivity measurements of common plastics over variable temperatures,” IEEE Trans. Microw. Theory Techn. 51, 727–733 (2003).
[Crossref]

Lalanne, P.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref] [PubMed]

Lan, L.

L. Lan, F. Sun, Y. Liu, C. K. Ong, and Y. Ma, “Experimentally demonstrated a unidirectional electromagnetic cloak designed by topology optimization,” Appl. Phys. Lett. 103, 121113 (2013).
[Crossref]

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3, 2182 (2013).
[Crossref] [PubMed]

Lassas, M.

M. Lassas, J. Liukkonen, and E. Somersalo, “Complex Riemannian metric and absorbing boundary conditions,” J. Math. Pure. Appl. 80, 739–768 (2001).
[Crossref]

Lazarov, B.

F. Wang, B. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidiscip. O. 43, 767–784 (2011).
[Crossref]

Lederer, F.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

Leonhardt, U.

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

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Liu, Y.

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3, 2182 (2013).
[Crossref] [PubMed]

L. Lan, F. Sun, Y. Liu, C. K. Ong, and Y. Ma, “Experimentally demonstrated a unidirectional electromagnetic cloak designed by topology optimization,” Appl. Phys. Lett. 103, 121113 (2013).
[Crossref]

Liukkonen, J.

M. Lassas, J. Liukkonen, and E. Somersalo, “Complex Riemannian metric and absorbing boundary conditions,” J. Math. Pure. Appl. 80, 739–768 (2001).
[Crossref]

Ma, Y.

L. Lan, F. Sun, Y. Liu, C. K. Ong, and Y. Ma, “Experimentally demonstrated a unidirectional electromagnetic cloak designed by topology optimization,” Appl. Phys. Lett. 103, 121113 (2013).
[Crossref]

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3, 2182 (2013).
[Crossref] [PubMed]

Maksymov, I. S.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref] [PubMed]

McPhedran, R.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

Mitchell-Thomas, R.

D. Bao, R. Mitchell-Thomas, K. Rajab, and Y. Hao, “Quantitative study of two experimental demonstrations of a carpet cloak,” IEEE Antennas Wireless Propag. Lett. 12, 206–209 (2013).
[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, 977–980 (2006).
[Crossref] [PubMed]

Nicolet, A.

B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).
[Crossref]

A. Nicolet, F. Zolla, Y. O. Agha, and S. Guenneau, “Geometrical transformations and equivalent materials in computational electromagnetism,” COMPEL 27, 806–819 (2008).
[Crossref]

Ong, C. K.

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3, 2182 (2013).
[Crossref] [PubMed]

L. Lan, F. Sun, Y. Liu, C. K. Ong, and Y. Ma, “Experimentally demonstrated a unidirectional electromagnetic cloak designed by topology optimization,” Appl. Phys. Lett. 103, 121113 (2013).
[Crossref]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 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, 977–980 (2006).
[Crossref] [PubMed]

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[Crossref]

Rahmani, A.

A. Rahmani, M. J. Steel, and P. C. Chaumet, “Invisibility and supervisibility: Radiation dynamics in a discrete electromagnetic cloak,” Phys. Rev. B 87, 045430 (2013).
[Crossref]

Rajab, K.

D. Bao, R. Mitchell-Thomas, K. Rajab, and Y. Hao, “Quantitative study of two experimental demonstrations of a carpet cloak,” IEEE Antennas Wireless Propag. Lett. 12, 206–209 (2013).
[Crossref]

Riddle, B.

B. Riddle, J. Baker-Jarvis, and J. Krupka, “Complex permittivity measurements of common plastics over variable temperatures,” IEEE Trans. Microw. Theory Techn. 51, 727–733 (2003).
[Crossref]

Rockstuhl, C.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

Rumpf, R.

P. Deffenbaugh, R. Rumpf, and K. Church, “Broadband microwave frequency characterization of 3-d printed materials,” EEE Trans. Compon. Packag. Manuf. Techno. 3, 2147–2155 (2013).
[Crossref]

Sauvan, C.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref] [PubMed]

Schenk, O.

O. Schenk, A. Wachter, and M. Hagemann, “Matching-based preprocessing algorithms to the solution of saddle-point problems in large-scale nonconvex interior-point optimization,” Computational Optimization and Applications 36, 321–341 (2007).
[Crossref]

Schurig, D.

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] [PubMed]

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

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation Optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref] [PubMed]

Sigmund, O.

J. Andkjær, N. Asger Mortensen, and O. Sigmund, “Towards all-dielectric, polarization-independent optical cloaks,” Appl. Phys. Lett. 100, 101106 (2012).
[Crossref]

J. Andkjær and O. Sigmund, “Topology optimized low-contrast all-dielectric optical cloak,” Appl. Phys. Lett. 98, 021112 (2011).
[Crossref]

F. Wang, B. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidiscip. O. 43, 767–784 (2011).
[Crossref]

J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high-bandwidth low-loss t-junction waveguide,” J. Opt. Soc. Am. B 22, 1191–1198 (2005).
[Crossref]

M. P. Bendsøe and O. Sigmund, “Material interpolation schemes in topology optimization,” Archive of Applied Mechanics 69, 635–654 (1999).
[Crossref]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 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, 977–980 (2006).
[Crossref] [PubMed]

Somersalo, E.

M. Lassas, J. Liukkonen, and E. Somersalo, “Complex Riemannian metric and absorbing boundary conditions,” J. Math. Pure. Appl. 80, 739–768 (2001).
[Crossref]

Soric, J.

P.-Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Advanced Materials 24, OP281–OP304 (2012).
[PubMed]

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] [PubMed]

Steel, M. J.

A. Rahmani, M. J. Steel, and P. C. Chaumet, “Invisibility and supervisibility: Radiation dynamics in a discrete electromagnetic cloak,” Phys. Rev. B 87, 045430 (2013).
[Crossref]

Sun, F.

L. Lan, F. Sun, Y. Liu, C. K. Ong, and Y. Ma, “Experimentally demonstrated a unidirectional electromagnetic cloak designed by topology optimization,” Appl. Phys. Lett. 103, 121113 (2013).
[Crossref]

Tapia, R.

R. Tapia, “Diagonalized multiplier methods and quasinewton methods for constrained optimization,” Journal of Optimization Theory and Applications 22, 135–194 (1977).
[Crossref]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Vial, B.

B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).
[Crossref]

Wachter, A.

O. Schenk, A. Wachter, and M. Hagemann, “Matching-based preprocessing algorithms to the solution of saddle-point problems in large-scale nonconvex interior-point optimization,” Computational Optimization and Applications 36, 321–341 (2007).
[Crossref]

Wang, F.

F. Wang, B. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidiscip. O. 43, 767–784 (2011).
[Crossref]

Ward, A. J.

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[Crossref]

Wu, T.

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3, 2182 (2013).
[Crossref] [PubMed]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Zheng, B.

H. Chen and B. Zheng, “Broadband polygonal invisibility cloak for visible light,” Sci. Rep. 2, 255 (2012).
[Crossref] [PubMed]

Zolla, F.

B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).
[Crossref]

A. Nicolet, F. Zolla, Y. O. Agha, and S. Guenneau, “Geometrical transformations and equivalent materials in computational electromagnetism,” COMPEL 27, 806–819 (2008).
[Crossref]

Advanced Materials (1)

P.-Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Advanced Materials 24, OP281–OP304 (2012).
[PubMed]

Appl. Phys. Lett. (3)

J. Andkjær and O. Sigmund, “Topology optimized low-contrast all-dielectric optical cloak,” Appl. Phys. Lett. 98, 021112 (2011).
[Crossref]

J. Andkjær, N. Asger Mortensen, and O. Sigmund, “Towards all-dielectric, polarization-independent optical cloaks,” Appl. Phys. Lett. 100, 101106 (2012).
[Crossref]

L. Lan, F. Sun, Y. Liu, C. K. Ong, and Y. Ma, “Experimentally demonstrated a unidirectional electromagnetic cloak designed by topology optimization,” Appl. Phys. Lett. 103, 121113 (2013).
[Crossref]

Archive of Applied Mechanics (1)

M. P. Bendsøe and O. Sigmund, “Material interpolation schemes in topology optimization,” Archive of Applied Mechanics 69, 635–654 (1999).
[Crossref]

COMPEL (1)

A. Nicolet, F. Zolla, Y. O. Agha, and S. Guenneau, “Geometrical transformations and equivalent materials in computational electromagnetism,” COMPEL 27, 806–819 (2008).
[Crossref]

Computational Optimization and Applications (1)

O. Schenk, A. Wachter, and M. Hagemann, “Matching-based preprocessing algorithms to the solution of saddle-point problems in large-scale nonconvex interior-point optimization,” Computational Optimization and Applications 36, 321–341 (2007).
[Crossref]

EEE Trans. Compon. Packag. Manuf. Techno. (1)

P. Deffenbaugh, R. Rumpf, and K. Church, “Broadband microwave frequency characterization of 3-d printed materials,” EEE Trans. Compon. Packag. Manuf. Techno. 3, 2147–2155 (2013).
[Crossref]

IEEE Antennas Wireless Propag. Lett. (1)

D. Bao, R. Mitchell-Thomas, K. Rajab, and Y. Hao, “Quantitative study of two experimental demonstrations of a carpet cloak,” IEEE Antennas Wireless Propag. Lett. 12, 206–209 (2013).
[Crossref]

IEEE Trans. Microw. Theory Techn. (1)

B. Riddle, J. Baker-Jarvis, and J. Krupka, “Complex permittivity measurements of common plastics over variable temperatures,” IEEE Trans. Microw. Theory Techn. 51, 727–733 (2003).
[Crossref]

J. Comput. Phys. (1)

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

J. Math. Pure. Appl. (1)

M. Lassas, J. Liukkonen, and E. Somersalo, “Complex Riemannian metric and absorbing boundary conditions,” J. Math. Pure. Appl. 80, 739–768 (2001).
[Crossref]

J. Mod. Opt. (1)

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[Crossref]

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

Journal of Optimization Theory and Applications (1)

R. Tapia, “Diagonalized multiplier methods and quasinewton methods for constrained optimization,” Journal of Optimization Theory and Applications 22, 135–194 (1977).
[Crossref]

Nat. Mater. (2)

H. Chen, C. T. Chan, and P. Sheng, “Transformation Optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref] [PubMed]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Phys. Rev. A (1)

B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).
[Crossref]

Phys. Rev. B (3)

B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
[Crossref]

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

A. Rahmani, M. J. Steel, and P. C. Chaumet, “Invisibility and supervisibility: Radiation dynamics in a discrete electromagnetic cloak,” Phys. Rev. B 87, 045430 (2013).
[Crossref]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (1)

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref] [PubMed]

Sci. Rep. (2)

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3, 2182 (2013).
[Crossref] [PubMed]

H. Chen and B. Zheng, “Broadband polygonal invisibility cloak for visible light,” Sci. Rep. 2, 255 (2012).
[Crossref] [PubMed]

Science (3)

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] [PubMed]

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

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

Struct. Multidiscip. O. (1)

F. Wang, B. Lazarov, and O. Sigmund, “On projection methods, convergence and robust formulations in topology optimization,” Struct. Multidiscip. O. 43, 767–784 (2011).
[Crossref]

Other (1)

J. Jin, The Finite Element Method in Electromagnetics (John Wiley & Sons, 2014).

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Figures (6)

Fig. 1
Fig. 1 Numerical setup for FEM simulations (Comsol). Only one half of the domain is modelled with Perfect Magnetic Conductor (PMC) boundary conduction on the symmetry plane (TE polarization). The domain is truncated by Perfectly Matched Layers (PML).
Fig. 2
Fig. 2 (a) Optimized permittivity map εc(x, y). (b) Square norm of the scattered electric field for the cloaked case, showing very weak diffraction in free space outside the cloak. Real part of the total electric field with cloak (c) and for the bare cylinder (d).
Fig. 3
Fig. 3 Study of cloaking performances. (a) Objective function ϕ1 as a function of wavelength λ for source point (solid red line) and plane wave (green dashed line) excitation. (b) Correlation coefficient ρ as a function of wavelength λ for source point excitation for the real part (orange solid line) and imaginary part (dashed blue line) of the scattered electric field.
Fig. 4
Fig. 4 Scattering reduction coefficient ϕ1 as a function of source position.
Fig. 5
Fig. 5 Multifrequency optimization for bandwidth enhancement. (Top) Optimized permittivity distributions for Nf = 2, 3 and 5 frequencies (from left to right). (Bottom) Objective function ϕ1 as a function of wavelength λ for various number of design frequencies Nf = 1 (red line), Nf = 2 (green line), Nf = 3 (orange line) and Nf = 5 (cyan line).
Fig. 6
Fig. 6 Convergence of the quasimodal expansion with the number of modes M. Reconstruction error err(M) (cyan solid line) and reconstructed objective function ϕ1(M) (orange solid line).

Equations (15)

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

( μ 1 E z ) + k 2 E z = δ ( r ) ,
W s = Ω B | E z d s | 2 d r , and W c = Ω B | E z d c | 2 d r ,
ϕ 1 ( ε c ) = W c / W s ,
ϕ 2 ( ε c ) = h m 2 S | ε c | 2 ,
ε c ( ξ ) = ε min + ξ p ( ε max ε min )
ξ ( s ) = tanh ( β ν ) + tanh ( β ( s ν ) ) tanh ( β ν ) + tanh ( β ( 1 ν ) ) ,
ϕ ( s ) = γ ϕ 1 ( s ) + ( 1 γ ) ϕ 2 ( s ) ,
ρ ( X , Y ) = E ( X Y ) E ( X ) E ( Y ) E ( X 2 ) E ( X ) 2 E ( Y 2 ) E ( Y ) 2
( μ 1 ψ n ) + k n 2 ε ψ n = 0.
ε ψ n | ψ n : = Ω ψ n ψ m d r .
E z c = n α n ψ n .
α n = ε E z c | ψ n = β n k 2 k n 2 ,
E z c E z c , rec ( M ) = n = 1 M ψ n ( r ) ψ n ( r ) k 2 k n 2 .
e r r ( M ) = Ω | E z c E c , rec ( M ) | 2 d r ,
ϕ 1 ( M ) = Ω B | E z d c , rec ( M ) | 2 d r .

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