Abstract

Using Lorentz reciprocity and power conservation, we prove that the extinction cross section of an arbitrarily shaped scatterer is always the same when illuminated from opposite directions and with the same polarization. For lossless and passive objects, this finding implies identical scattering cross sections for opposite excitations, with relevant implications on cloaking designs and scattering suppression schemes. This scattering symmetry can be broken by introducing absorption into the system, providing a path toward large scattering asymmetries when combined with Fano interference.

© 2014 Optical Society of America

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  1. N. Landy and D. R. Smith, Nat. Mater. 12, 25 (2012).
    [CrossRef]
  2. B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
    [CrossRef]
  3. X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, Nat. Commun. 2, 176 (2011).
    [CrossRef]
  4. Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
    [CrossRef]
  5. A. Mostafazadeh, Phys. Rev. A 87, 012103 (2013).
    [CrossRef]
  6. L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2012).
    [CrossRef]
  7. A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
    [CrossRef]
  8. Y. D. Chong, L. Ge, and A. D. Stone, Phys. Rev. Lett. 106, 093902 (2011).
    [CrossRef]
  9. X. Yin and X. Zhang, Nat. Mater. 12, 175 (2013).
    [CrossRef]
  10. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
    [CrossRef]
  11. A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2940 (2008).
  12. E. Plum, V. A. Fedotov, and N. I. Zheludev, Appl. Phys. Lett. 94, 131901 (2009).
    [CrossRef]
  13. C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
    [CrossRef]
  14. P. Grahn, A. Shevchenko, and M. Kaivola, Phys. Rev. B 86, 035419 (2012).
  15. P. Grahn, A. Shevchenko, and M. Kaivola, Opt. Express 21, 23471 (2013).
    [CrossRef]
  16. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  17. R. F. Harrington, Time Harmonic Electromagnetic Fields (Wiley, 2001).
  18. R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, Science 343, 516 (2014).
    [CrossRef]
  19. D. L. Sounas, C. Caloz, and A. Alù, Nat. Commun. 4, 2407 (2013).
    [CrossRef]
  20. If ε^i is the polarization vector of an elliptically polarized wave propagating in the n^i direction, ε^i* is the polarization vector of the same wave propagating in the −n^i direction. This can be easily understood by choosing a coordinate system where n^i=z^ and the x axis is parallel to the major axis of the polarization ellipse so that ε^i=ax^+iby^, where a and b are real numbers. A rotation of the coordinate system by 180° around the x axis results in a wave propagating in the −z^ direction with a polarization vector ε^i*=ax^−iby^.
  21. P.-S. Kildal, A. A. Kishk, and A. Tengs, IEEE Trans. Antennas Propag. 44, 1509 (1996).
    [CrossRef]
  22. S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2003).
  23. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
    [CrossRef]

2014 (1)

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, Science 343, 516 (2014).
[CrossRef]

2013 (4)

D. L. Sounas, C. Caloz, and A. Alù, Nat. Commun. 4, 2407 (2013).
[CrossRef]

X. Yin and X. Zhang, Nat. Mater. 12, 175 (2013).
[CrossRef]

A. Mostafazadeh, Phys. Rev. A 87, 012103 (2013).
[CrossRef]

P. Grahn, A. Shevchenko, and M. Kaivola, Opt. Express 21, 23471 (2013).
[CrossRef]

2012 (4)

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2012).
[CrossRef]

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

N. Landy and D. R. Smith, Nat. Mater. 12, 25 (2012).
[CrossRef]

P. Grahn, A. Shevchenko, and M. Kaivola, Phys. Rev. B 86, 035419 (2012).

2011 (4)

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
[CrossRef]

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, Nat. Commun. 2, 176 (2011).
[CrossRef]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Y. D. Chong, L. Ge, and A. D. Stone, Phys. Rev. Lett. 106, 093902 (2011).
[CrossRef]

2010 (2)

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

2009 (1)

E. Plum, V. A. Fedotov, and N. I. Zheludev, Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

2008 (1)

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2940 (2008).

2006 (1)

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef]

1996 (1)

P.-S. Kildal, A. A. Kishk, and A. Tengs, IEEE Trans. Antennas Propag. 44, 1509 (1996).
[CrossRef]

Almeida, V. R.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2012).
[CrossRef]

Alù, A.

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, Science 343, 516 (2014).
[CrossRef]

D. L. Sounas, C. Caloz, and A. Alù, Nat. Commun. 4, 2407 (2013).
[CrossRef]

Barbastathis, G.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
[CrossRef]

Bersch, C.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Caloz, C.

D. L. Sounas, C. Caloz, and A. Alù, Nat. Commun. 4, 2407 (2013).
[CrossRef]

Cao, H.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Chen, X.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, Nat. Commun. 2, 176 (2011).
[CrossRef]

Chen, Y.

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2940 (2008).

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef]

Chen, Y.-F.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2012).
[CrossRef]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Chong, Y. D.

Y. D. Chong, L. Ge, and A. D. Stone, Phys. Rev. Lett. 106, 093902 (2011).
[CrossRef]

Christodoulides, D. N.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Eichelkraut, T.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Fedotov, V. A.

E. Plum, V. A. Fedotov, and N. I. Zheludev, Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2940 (2008).

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef]

Fegadolli, W. S.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2012).
[CrossRef]

Feng, L.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2012).
[CrossRef]

Fleury, R.

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, Science 343, 516 (2014).
[CrossRef]

Ge, L.

Y. D. Chong, L. Ge, and A. D. Stone, Phys. Rev. Lett. 106, 093902 (2011).
[CrossRef]

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Grahn, P.

P. Grahn, A. Shevchenko, and M. Kaivola, Opt. Express 21, 23471 (2013).
[CrossRef]

P. Grahn, A. Shevchenko, and M. Kaivola, Phys. Rev. B 86, 035419 (2012).

Haberman, M. R.

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, Science 343, 516 (2014).
[CrossRef]

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Time Harmonic Electromagnetic Fields (Wiley, 2001).

Helgert, C.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Jiang, K.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, Nat. Commun. 2, 176 (2011).
[CrossRef]

Kaivola, M.

P. Grahn, A. Shevchenko, and M. Kaivola, Opt. Express 21, 23471 (2013).
[CrossRef]

P. Grahn, A. Shevchenko, and M. Kaivola, Phys. Rev. B 86, 035419 (2012).

Khardikov, V. V.

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2940 (2008).

Kildal, P.-S.

P.-S. Kildal, A. A. Kishk, and A. Tengs, IEEE Trans. Antennas Propag. 44, 1509 (1996).
[CrossRef]

Kishk, A. A.

P.-S. Kildal, A. A. Kishk, and A. Tengs, IEEE Trans. Antennas Propag. 44, 1509 (1996).
[CrossRef]

Kley, E.-B.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef]

Kottos, T.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Landy, N.

N. Landy and D. R. Smith, Nat. Mater. 12, 25 (2012).
[CrossRef]

Lederer, F.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef]

Lin, Z.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Liu, X.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
[CrossRef]

Lu, M.-H.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2012).
[CrossRef]

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Luo, Y.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
[CrossRef]

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, Nat. Commun. 2, 176 (2011).
[CrossRef]

Maier, S. A.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Menzel, C.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef]

Miri, M.-A.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

Mladyonov, P. L.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef]

Mostafazadeh, A.

A. Mostafazadeh, Phys. Rev. A 87, 012103 (2013).
[CrossRef]

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Oliveira, J. E. B.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2012).
[CrossRef]

Onishchukov, G.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

Pendry, J. B.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, Nat. Commun. 2, 176 (2011).
[CrossRef]

Pertsch, T.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef]

Peschel, U.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

Plum, E.

E. Plum, V. A. Fedotov, and N. I. Zheludev, Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

Prosvirnin, S. L.

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2940 (2008).

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef]

Ramezani, H.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Regensburger, A.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

Rockstuhl, C.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef]

Rogacheva, A. V.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef]

Scherer, A.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2012).
[CrossRef]

Schwanecke, A. S.

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2940 (2008).

Shevchenko, A.

P. Grahn, A. Shevchenko, and M. Kaivola, Opt. Express 21, 23471 (2013).
[CrossRef]

P. Grahn, A. Shevchenko, and M. Kaivola, Phys. Rev. B 86, 035419 (2012).

Sieck, C. F.

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, Science 343, 516 (2014).
[CrossRef]

Smith, D. R.

N. Landy and D. R. Smith, Nat. Mater. 12, 25 (2012).
[CrossRef]

Sounas, D. L.

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, Science 343, 516 (2014).
[CrossRef]

D. L. Sounas, C. Caloz, and A. Alù, Nat. Commun. 4, 2407 (2013).
[CrossRef]

Stone, A. D.

Y. D. Chong, L. Ge, and A. D. Stone, Phys. Rev. Lett. 106, 093902 (2011).
[CrossRef]

Tengs, A.

P.-S. Kildal, A. A. Kishk, and A. Tengs, IEEE Trans. Antennas Propag. 44, 1509 (1996).
[CrossRef]

Tretyakov, S.

S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2003).

Tünnermann, A.

C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef]

Xu, Y.-L.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2012).
[CrossRef]

Yin, X.

X. Yin and X. Zhang, Nat. Mater. 12, 175 (2013).
[CrossRef]

Zhang, B.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, Phys. Rev. Lett. 106, 033901 (2011).
[CrossRef]

Zhang, J.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, Nat. Commun. 2, 176 (2011).
[CrossRef]

Zhang, S.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, Nat. Commun. 2, 176 (2011).
[CrossRef]

Zhang, X.

X. Yin and X. Zhang, Nat. Mater. 12, 175 (2013).
[CrossRef]

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

E. Plum, V. A. Fedotov, and N. I. Zheludev, Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2940 (2008).

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

E. Plum, V. A. Fedotov, and N. I. Zheludev, Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

P.-S. Kildal, A. A. Kishk, and A. Tengs, IEEE Trans. Antennas Propag. 44, 1509 (1996).
[CrossRef]

Nano Lett. (1)

A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, Nano Lett. 8, 2940 (2008).

Nat. Commun. (2)

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, Nat. Commun. 2, 176 (2011).
[CrossRef]

D. L. Sounas, C. Caloz, and A. Alù, Nat. Commun. 4, 2407 (2013).
[CrossRef]

Nat. Mater. (4)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

N. Landy and D. R. Smith, Nat. Mater. 12, 25 (2012).
[CrossRef]

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If ε^i is the polarization vector of an elliptically polarized wave propagating in the n^i direction, ε^i* is the polarization vector of the same wave propagating in the −n^i direction. This can be easily understood by choosing a coordinate system where n^i=z^ and the x axis is parallel to the major axis of the polarization ellipse so that ε^i=ax^+iby^, where a and b are real numbers. A rotation of the coordinate system by 180° around the x axis results in a wave propagating in the −z^ direction with a polarization vector ε^i*=ax^−iby^.

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Figures (2)

Fig. 1.
Fig. 1.

Scattering by a hollow triangular and a rhombic PEC cylinder with l=0.3m and φ=30° under TM incidence. a, Integrated total scattering cross section versus frequency for opposite illumination directions; b, scattered magnetic field distribution (normal to the plane) at 2 GHz. Restoring the symmetry of the hollow cylinder leads to drastic scattering reduction.

Fig. 2.
Fig. 2.

Scattering cross section versus frequency for a dimer of gold nanospheres illuminated from opposite directions: a, assuming zero loss; b, accounting for real absorption in gold. Frequencies are normalized to the plasma frequency of gold fp, and scattering cross sections are normalized to the geometrical cross section of the largest nanoparticle. Extinction cross section is also plotted in the lossy case. The scattering patterns are calculated at the Fano dip, f=0.562fp. The nanosphere radiuses are r1=0.06λp and r1=0.09λp, where λp is the plasma wavelength of gold, and the distance between them d=1.1(r1+r2). In absence of loss, the structure exhibits exactly the same scattering cross section for the two illumination directions, a symmetry that can be largely broken at the Fano interference dip when loss is considered.

Equations (4)

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ε^i·f(ε^i,n^i,n^s)=ε^i·f(ε^i,n^i,n^s),
σext(ε^i,n^i)=σext(ε^i*,n^i).
Pscat=Z0c2k412π(|p1|2+|p2|2)+ωRe{p1p2*}Im{C},
Pext=ω2Im{α11+α21+2Ccos(kd)α11α21C2},

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