Abstract

We unveil the relationship between two anomalous scattering processes known as Kerker conditions and the duality symmetry of Maxwell equations. We generalize these conditions and show that they can be applied to any particle with cylindrical symmetry, not only to spherical particles as the original Kerker conditions were derived for. We also explain the role of the optical helicity in these scattering processes. Our results find applications in the field of metamaterials, where new materials with directional scattering are being explored.

© 2013 Optical Society of America

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References

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  1. P. W. Merlin, Am. Inst. Aeronaut. Astronaut. Pap. 2009, 1522 (2009).
  2. M. Kerker, D.-S. Wang, and C. L. Giles, J. Opt. Soc. Am. 73, 765 (1983).
    [CrossRef]
  3. B. García-Cámara, F. González, F. Moreno, and J. M. Saiz, J. Opt. Soc. Am. A 25, 2875 (2008).
    [CrossRef]
  4. A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, Opt. Express 19, 4815 (2011).
    [CrossRef]
  5. A. Kuznetsov, A. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, Science Reports 2, 492 (2012).
  6. J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
    [CrossRef]
  7. S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, Nano Lett.13, 1806 (2013).
  8. Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, Nat. Commun. 4, 1527 (2013).
    [CrossRef]
  9. I. Fernandez-Corbaton, X. Zambrana-Puyalto, and G. Molina-Terriza, Phys. Rev. A 86, 042103 (2012).
    [CrossRef]
  10. I. Fernandez-Corbaton, X. Zambrana-Puyalto, N. Tischler, A. Minovich, X. Vidal, M. L. Juan, and G. Molina-Terriza, arXiv:1206.0868 (2012).
  11. X. Zambrana-Puyalto, X. Vidal, and G. Molina-Terriza, Opt. Express 20, 24536 (2012).
    [CrossRef]
  12. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  13. M. Nieto-Vesperinas, R. Gomez-Medina, and J. J. Saenz, J. Opt. Soc. Am. A 28, 54 (2011).
    [CrossRef]
  14. A. Alu and N. Engheta, J. Nanophoton. 4, 041590 (2010).
    [CrossRef]

2013 (1)

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, Nat. Commun. 4, 1527 (2013).
[CrossRef]

2012 (4)

I. Fernandez-Corbaton, X. Zambrana-Puyalto, and G. Molina-Terriza, Phys. Rev. A 86, 042103 (2012).
[CrossRef]

A. Kuznetsov, A. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, Science Reports 2, 492 (2012).

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

X. Zambrana-Puyalto, X. Vidal, and G. Molina-Terriza, Opt. Express 20, 24536 (2012).
[CrossRef]

2011 (2)

2010 (1)

A. Alu and N. Engheta, J. Nanophoton. 4, 041590 (2010).
[CrossRef]

2009 (1)

P. W. Merlin, Am. Inst. Aeronaut. Astronaut. Pap. 2009, 1522 (2009).

2008 (1)

1983 (1)

Aizpurua, J.

Albella, P.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

Alu, A.

A. Alu and N. Engheta, J. Nanophoton. 4, 041590 (2010).
[CrossRef]

Bohren, C. F.

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

Chantada, L.

Engheta, N.

A. Alu and N. Engheta, J. Nanophoton. 4, 041590 (2010).
[CrossRef]

Eyraud, C.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

Fernandez-Corbaton, I.

I. Fernandez-Corbaton, X. Zambrana-Puyalto, and G. Molina-Terriza, Phys. Rev. A 86, 042103 (2012).
[CrossRef]

I. Fernandez-Corbaton, X. Zambrana-Puyalto, N. Tischler, A. Minovich, X. Vidal, M. L. Juan, and G. Molina-Terriza, arXiv:1206.0868 (2012).

Froufe-Pérez, L.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

Froufe-Pérez, L. S.

Fu, Y. H.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, Nat. Commun. 4, 1527 (2013).
[CrossRef]

A. Kuznetsov, A. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, Science Reports 2, 492 (2012).

García-Cámara, B.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

B. García-Cámara, F. González, F. Moreno, and J. M. Saiz, J. Opt. Soc. Am. A 25, 2875 (2008).
[CrossRef]

García-Etxarri, A.

Geffrin, J.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

Giles, C. L.

Gomez-Medina, R.

Gómez-Medina, R.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, Opt. Express 19, 4815 (2011).
[CrossRef]

González, F.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

B. García-Cámara, F. González, F. Moreno, and J. M. Saiz, J. Opt. Soc. Am. A 25, 2875 (2008).
[CrossRef]

Huffman, D. R.

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

Jain, M.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, Nano Lett.13, 1806 (2013).

Juan, M. L.

I. Fernandez-Corbaton, X. Zambrana-Puyalto, N. Tischler, A. Minovich, X. Vidal, M. L. Juan, and G. Molina-Terriza, arXiv:1206.0868 (2012).

Kerker, M.

Kuznetsov, A.

A. Kuznetsov, A. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, Science Reports 2, 492 (2012).

Kuznetsov, A. I.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, Nat. Commun. 4, 1527 (2013).
[CrossRef]

Lapin, Z.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, Nano Lett.13, 1806 (2013).

Litman, A.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

López, C.

Luk’yanchuk, B.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, Nat. Commun. 4, 1527 (2013).
[CrossRef]

A. Kuznetsov, A. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, Science Reports 2, 492 (2012).

Merlin, P. W.

P. W. Merlin, Am. Inst. Aeronaut. Astronaut. Pap. 2009, 1522 (2009).

Minovich, A.

I. Fernandez-Corbaton, X. Zambrana-Puyalto, N. Tischler, A. Minovich, X. Vidal, M. L. Juan, and G. Molina-Terriza, arXiv:1206.0868 (2012).

Miroshnichenko, A.

A. Kuznetsov, A. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, Science Reports 2, 492 (2012).

Miroshnichenko, A. E.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, Nat. Commun. 4, 1527 (2013).
[CrossRef]

Molina-Terriza, G.

I. Fernandez-Corbaton, X. Zambrana-Puyalto, and G. Molina-Terriza, Phys. Rev. A 86, 042103 (2012).
[CrossRef]

X. Zambrana-Puyalto, X. Vidal, and G. Molina-Terriza, Opt. Express 20, 24536 (2012).
[CrossRef]

I. Fernandez-Corbaton, X. Zambrana-Puyalto, N. Tischler, A. Minovich, X. Vidal, M. L. Juan, and G. Molina-Terriza, arXiv:1206.0868 (2012).

Moreno, F.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

B. García-Cámara, F. González, F. Moreno, and J. M. Saiz, J. Opt. Soc. Am. A 25, 2875 (2008).
[CrossRef]

Nieto-Vesperinas, M.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

M. Nieto-Vesperinas, R. Gomez-Medina, and J. J. Saenz, J. Opt. Soc. Am. A 28, 54 (2011).
[CrossRef]

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, Opt. Express 19, 4815 (2011).
[CrossRef]

Novotny, L.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, Nano Lett.13, 1806 (2013).

Person, S.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, Nano Lett.13, 1806 (2013).

Saenz, J. J.

Sáenz, J. J.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, Opt. Express 19, 4815 (2011).
[CrossRef]

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, Nano Lett.13, 1806 (2013).

Saiz, J. M.

Scheffold, F.

Tischler, N.

I. Fernandez-Corbaton, X. Zambrana-Puyalto, N. Tischler, A. Minovich, X. Vidal, M. L. Juan, and G. Molina-Terriza, arXiv:1206.0868 (2012).

Vaillon, R.

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

Vidal, X.

X. Zambrana-Puyalto, X. Vidal, and G. Molina-Terriza, Opt. Express 20, 24536 (2012).
[CrossRef]

I. Fernandez-Corbaton, X. Zambrana-Puyalto, N. Tischler, A. Minovich, X. Vidal, M. L. Juan, and G. Molina-Terriza, arXiv:1206.0868 (2012).

Wang, D.-S.

Wicks, G.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, Nano Lett.13, 1806 (2013).

Yu, Y. F.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, Nat. Commun. 4, 1527 (2013).
[CrossRef]

Zambrana-Puyalto, X.

X. Zambrana-Puyalto, X. Vidal, and G. Molina-Terriza, Opt. Express 20, 24536 (2012).
[CrossRef]

I. Fernandez-Corbaton, X. Zambrana-Puyalto, and G. Molina-Terriza, Phys. Rev. A 86, 042103 (2012).
[CrossRef]

I. Fernandez-Corbaton, X. Zambrana-Puyalto, N. Tischler, A. Minovich, X. Vidal, M. L. Juan, and G. Molina-Terriza, arXiv:1206.0868 (2012).

Zhang, J.

A. Kuznetsov, A. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, Science Reports 2, 492 (2012).

Am. Inst. Aeronaut. Astronaut. Pap. (1)

P. W. Merlin, Am. Inst. Aeronaut. Astronaut. Pap. 2009, 1522 (2009).

J. Nanophoton. (1)

A. Alu and N. Engheta, J. Nanophoton. 4, 041590 (2010).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Nat. Commun. (2)

J. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, Nat. Commun. 3, 1171 (2012).
[CrossRef]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, Nat. Commun. 4, 1527 (2013).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (1)

I. Fernandez-Corbaton, X. Zambrana-Puyalto, and G. Molina-Terriza, Phys. Rev. A 86, 042103 (2012).
[CrossRef]

Science Reports (1)

A. Kuznetsov, A. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, Science Reports 2, 492 (2012).

Other (3)

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, Nano Lett.13, 1806 (2013).

I. Fernandez-Corbaton, X. Zambrana-Puyalto, N. Tischler, A. Minovich, X. Vidal, M. L. Juan, and G. Molina-Terriza, arXiv:1206.0868 (2012).

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

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Figures (1)

Fig. 1.
Fig. 1.

Sketch of the relations between Kerker conditions and cylindrical and duality symmetry. Large red helix pointing the scatterer represents an incident plane wave with well defined helicity. The other helices represent scattered plane waves. Small red helix has the same helicity as the incoming wave, while the small blue helix has the opposite helicity. (a) General scattering process with neither cylindrical nor dual symmetries is shown. In general, both back and forward scattering have contributions from both helicities. (b) Scattering from a cylindrically symmetric object. In this case, symmetry imposes that forward scattering is of the same helicity than the incident field, and backward scattering of opposite helicity. (c) Dual and cylindrically symmetric system. Only forward scattering is allowed with the same helicity. (d) Anti-dual system with cylindrical symmetry. Only back scattering is allowed with flipped helicity.

Equations (3)

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

Ajmz+=Ajmz(m)+iAjmz(e)2Ajmz=Ajmz(m)iAjmz(e)2.
Ei=j,mzαjmzpAjmzpEsca=j,mzαjmzp[aj+bj2Ajmzp+ajbj2Ajmzp]Eint=j,mzαjmzp[dj+cj2Ajmzp+djcj2Ajmzp],
εiμi=constΛconservation,

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