Abstract

Since the first studies made by Kerker in the 1970s stating the conditions for null light scattering in certain directions by particles, such conditions have remained unquestioned. The increasing interest in scattering directionality by tuning the optical properties of materials demands a new analysis of this problem. In addition, as has been shown recently, one of Kerker’s statements does not comply with the optical theorem. We propose corrected expressions for the null-scattering conditions that satisfy the optical theorem.

© 2011 Optical Society of America

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2010 (4)

H. Chen, C. T. Chan, and P. Sheng, Nat. Mater. 9, 387 (2010).
[CrossRef] [PubMed]

B. García-Cámara, J. M. Saiz, F. González, and F. Moreno, Opt. Commun. 283, 490 (2010).
[CrossRef]

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

B. García-Cámara, F. González, F. Moreno, and J. M. Saiz, J. Opt. Soc. Am. A 25, 2875 (2010).
[CrossRef]

2009 (2)

A. Alù and N. Engheta, Phys. Rev. Lett. 102, 233901 (2009).
[CrossRef] [PubMed]

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolsky, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (2)

V. M. Shalaev, Nat. Photon. 1, 41 (2007).
[CrossRef]

N. Engheta, Science 317, 1698 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (2)

S. A. Ramakrishna and O. J. F. Martin, Opt. Lett. 30, 2626 (2005).
[CrossRef] [PubMed]

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

1994 (1)

1983 (1)

1979 (1)

1978 (1)

Alexopoulos, N. G.

Alù, A.

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

A. Alù and N. Engheta, Phys. Rev. Lett. 102, 233901 (2009).
[CrossRef] [PubMed]

Atkinson, R.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolsky, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, Nat. Mater. 9, 387 (2010).
[CrossRef] [PubMed]

Chen, H.

H. Chen, C. T. Chan, and P. Sheng, Nat. Mater. 9, 387 (2010).
[CrossRef] [PubMed]

Draine, B. T.

Engheta, N.

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

A. Alù and N. Engheta, Phys. Rev. Lett. 102, 233901 (2009).
[CrossRef] [PubMed]

N. Engheta, Science 317, 1698 (2007).
[CrossRef] [PubMed]

Evans, P.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolsky, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Firsov, A. A.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Flatau, P. J.

García-Cámara, B.

Geim, A. K.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Giles, C. L.

Gleeson, H. F.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

González, F.

Grigorenko, A. N.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Hendren, W.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolsky, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Hess, O.

O. Hess, Nature 455, 299 (2008).
[CrossRef] [PubMed]

Kabashin, A. V.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolsky, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Kerker, M.

Khrushchev, I. Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Lagendijk, A.

Martin, O. J. F.

Moreno, F.

Mosk, A. P.

Park, W.

Q. Wu and W. Park, Appl. Phys. Lett. 92, 153114 (2008).
[CrossRef]

Pastkovsky, S.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolsky, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Petrovic, J.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Podolsky, V. A.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolsky, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Pollard, R.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolsky, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Ramakrishna, S. A.

Saiz, J. M.

Shalaev, V. M.

V. M. Shalaev, Nat. Photon. 1, 41 (2007).
[CrossRef]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, Nat. Mater. 9, 387 (2010).
[CrossRef] [PubMed]

Uzunoglu, N. K.

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles(Dover, 1981).

van der Molen, K. L.

Videen, G.

Wang, D.-S.

Wu, Q.

Q. Wu and W. Park, Appl. Phys. Lett. 92, 153114 (2008).
[CrossRef]

Wurtz, G. A.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolsky, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Zayats, A. V.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolsky, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Zhang, Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

Zijlstra, P.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

Q. Wu and W. Park, Appl. Phys. Lett. 92, 153114 (2008).
[CrossRef]

J. Nanophoton. (1)

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Nat. Mater. (2)

H. Chen, C. T. Chan, and P. Sheng, Nat. Mater. 9, 387 (2010).
[CrossRef] [PubMed]

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolsky, and A. V. Zayats, Nat. Mater. 8, 867 (2009).
[CrossRef] [PubMed]

Nat. Photon. (1)

V. M. Shalaev, Nat. Photon. 1, 41 (2007).
[CrossRef]

Nature (2)

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef] [PubMed]

O. Hess, Nature 455, 299 (2008).
[CrossRef] [PubMed]

Opt. Commun. (1)

B. García-Cámara, J. M. Saiz, F. González, and F. Moreno, Opt. Commun. 283, 490 (2010).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

A. Alù and N. Engheta, Phys. Rev. Lett. 102, 233901 (2009).
[CrossRef] [PubMed]

Science (1)

N. Engheta, Science 317, 1698 (2007).
[CrossRef] [PubMed]

Other (1)

H. C. Van de Hulst, Light Scattering by Small Particles(Dover, 1981).

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Figures (3)

Fig. 1
Fig. 1

Scattering patterns of a spherical scatterer with R = 4.96 nm , such that their optical constants satisfy either the new zero-forward (4) [ ( ε r , μ r ) = ( 2 , 0.4 3.88 × 10 5 i ) ] or the zero-backward (3) [ ( ε r , μ r ) = ( 2 , 2 ) ] conditions. The arrow represents the direction of the incident field.

Fig. 2
Fig. 2

Real (continuos line, scale on the left) and imaginary (curves with symbols, scale on the right) part of the relative magnetic permeability as a function of the electric permittivity, following Eq. (4), for several particle sizes. For comparison, the values of μ r following the original Kerker’s zero-forward condition are included.

Fig. 3
Fig. 3

Evolution of the scattering, ab sorption (amplification), and extinction cross sections of a spherical particle ( R 5 nm ) as a function of ε when the magnetic permeability is fixed ( μ r = 0.4 3.88 × 10 5 i ). The pair ( ε r , μ r ) = ( 2 , 0.4 3.88 × 10 5 i ) satisfies the “new” zero- forward condition (4).

Equations (6)

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α CM = 3 V ε r 1 ε r + 2 ,
α CR = 6 π V ( ε r 1 ) 2 π ( ε r + 2 ) i V k 3 ( ε r 1 ) ,
zero-backward ε r = μ r ,
zero-forward ε r = π ( 4 μ r ) i V k 3 ( μ r 1 ) π ( 2 μ r + 1 ) i V k 3 ( μ r 1 ) ,
ε r = μ r = 4 π + i V k 3 2 π + i V k 3 .
C ext = 4 π k 2 Re { S ( 0 ° ) } .

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