Abstract

The existence of non-radiating sources is of fundamental importance for inverse scattering problems and the design of invisible objects. However, the excitation of such radiationless sources is quite challenging. We present a method based on which the anapole mode of a high-index isotropic dielectric nanosphere can be excited but radiationless. We show that this radiationless anapole is attributed to the destructive interference of the Cartesian dipole and toroidal moment of the induced current by our proposed focused radially polarized beam illumination. Further, with a standing-wave illumination formed by two counter-propagating focused radially polarized beams under 4π configuration, the ideal radiationless anapole can be excited. This result illustrates a case where the reciprocity condition is not violated, and yet, a radiationless mode can be excited by external illumination.

© 2016 Optical Society of America

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References

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  9. G. H. Goedecke, Phys. Rev. 135, B281 (1964).
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  13. U. Leonhardt, Science 312, 1777 (1993).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  27. P. l. Wozniak, P. Banzer, and G. Leuchs, Laser Photon. Rev. 12, 231 (2012).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  32. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Oxford, 1960).

2016 (1)

2015 (4)

T. Das, P. P. Iyer, R. A. DeCrescent, and J. A. Schuller, Phys. Rev. B 92, 241110 (2015).
[Crossref]

W. Liu, B. Lei, J. H. Shi, H. J. Hu, and A. E. Miroschnichenko, J. Nanomater. 2015, 672957 (2015).

S. Lannebere and M. G. Silveirinha, Nat. Commun. 6, 8766 (2015).
[Crossref]

A. E. Miroschnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, Nat. Commun. 6, 8069 (2015).
[Crossref]

2014 (1)

M. G. Silveirinha, Phys. Rev. A 89, 23813 (2014).
[Crossref]

2013 (2)

C. M. Ho and R. J. Scherrer, Phys. Lett. B 722, 341 (2013).
[Crossref]

V. A. Fedotov, V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zhueludev, Sci. Rep. 3, 2967 (2013).
[Crossref]

2012 (5)

P. l. Wozniak, P. Banzer, and G. Leuchs, Laser Photon. Rev. 12, 231 (2012).

T. X. Hoang, X. Chen, and C. J. R. Sheppard, J. Opt. Soc. Am. A 29, 32 (2012).
[Crossref]

T. X. Hoang, X. Chen, and C. J. R. Sheppard, Phys. Rev. A 86, 33817 (2012).
[Crossref]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, Sci. Rep. 2, 492 (2012).
[Crossref]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, Nano Lett. 12, 3749 (2012).
[Crossref]

2010 (1)

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zhueludev, Science 330, 1510 (2010).
[Crossref]

2007 (1)

1997 (1)

1995 (1)

G. N. Afanasiev and Y. U. P. Stepanovsky, J. Phys. A 28, 4565 (1995).
[Crossref]

1993 (2)

U. Leonhardt, Science 312, 1777 (1993).
[Crossref]

E. Wolf and T. Habashy, J. Mod. Opt. 40, 785 (1993).
[Crossref]

1990 (1)

V. M. Dubovik and V. V. Tugushev, Phys. Rep. 187, 145 (1990).
[Crossref]

1986 (1)

K. Kim and E. Wolf, Opt. Commun. 59, 1 (1986).
[Crossref]

1975 (1)

M. Kerker, J. Opt. Soc. Am. B 65, 376 (1975).
[Crossref]

1973 (1)

A. J. Devaney and E. Wolf, Phys. Rev. D 8, 1044 (1973).

1964 (1)

G. H. Goedecke, Phys. Rev. 135, B281 (1964).
[Crossref]

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London A 253, 358 (1959).
[Crossref]

1957 (1)

Y. A. B. Zel’dovich, Zh. Eksp. Teor. Fiz 33, 1531 (1957).

1933 (1)

G. A. Schott, Philos. Mag. 15(100), 752 (1933).
[Crossref]

1910 (1)

P. Ehrenfest, Phys. Z 11, 708 (1910).

Adam, A. J. L.

Afanasiev, G. N.

G. N. Afanasiev and Y. U. P. Stepanovsky, J. Phys. A 28, 4565 (1995).
[Crossref]

Bakker, R. M.

A. E. Miroschnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, Nat. Commun. 6, 8069 (2015).
[Crossref]

Banzer, P.

P. l. Wozniak, P. Banzer, and G. Leuchs, Laser Photon. Rev. 12, 231 (2012).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).

Bozhevolnyi, S. I.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, Nano Lett. 12, 3749 (2012).
[Crossref]

Chen, X.

T. X. Hoang, X. Chen, and C. J. R. Sheppard, J. Opt. Soc. Am. A 29, 32 (2012).
[Crossref]

T. X. Hoang, X. Chen, and C. J. R. Sheppard, Phys. Rev. A 86, 33817 (2012).
[Crossref]

Chichkov, B. N.

A. E. Miroschnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, Nat. Commun. 6, 8069 (2015).
[Crossref]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, Nano Lett. 12, 3749 (2012).
[Crossref]

Chipouline, A.

A. E. Miroschnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, Nat. Commun. 6, 8069 (2015).
[Crossref]

Das, T.

T. Das, P. P. Iyer, R. A. DeCrescent, and J. A. Schuller, Phys. Rev. B 92, 241110 (2015).
[Crossref]

DeCrescent, R. A.

T. Das, P. P. Iyer, R. A. DeCrescent, and J. A. Schuller, Phys. Rev. B 92, 241110 (2015).
[Crossref]

Devaney, A. J.

A. J. Devaney and E. Wolf, Phys. Rev. D 8, 1044 (1973).

Dubovik, V. M.

V. M. Dubovik and V. V. Tugushev, Phys. Rep. 187, 145 (1990).
[Crossref]

Ehrenfest, P.

P. Ehrenfest, Phys. Z 11, 708 (1910).

Eriksen, R. L.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, Nano Lett. 12, 3749 (2012).
[Crossref]

Evlyukhin, A. B.

A. E. Miroschnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, Nat. Commun. 6, 8069 (2015).
[Crossref]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, Nano Lett. 12, 3749 (2012).
[Crossref]

Fedotov, V. A.

V. A. Fedotov, V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zhueludev, Sci. Rep. 3, 2967 (2013).
[Crossref]

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zhueludev, Science 330, 1510 (2010).
[Crossref]

Fu, Y. H.

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, Sci. Rep. 2, 492 (2012).
[Crossref]

Gbur, G.

G. Gbur, “Non-radiating sources and the inverse source problem,” Ph.D. thesis (University of Rochester, 2001).

Goedecke, G. H.

G. H. Goedecke, Phys. Rev. 135, B281 (1964).
[Crossref]

Habashy, T.

E. Wolf and T. Habashy, J. Mod. Opt. 40, 785 (1993).
[Crossref]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University, 2012).

Ho, C. M.

C. M. Ho and R. J. Scherrer, Phys. Lett. B 722, 341 (2013).
[Crossref]

Hoang, T. X.

T. X. Hoang, X. Chen, and C. J. R. Sheppard, J. Opt. Soc. Am. A 29, 32 (2012).
[Crossref]

T. X. Hoang, X. Chen, and C. J. R. Sheppard, Phys. Rev. A 86, 33817 (2012).
[Crossref]

Hoenders, B. J.

Hu, H. J.

W. Liu, B. Lei, J. H. Shi, H. J. Hu, and A. E. Miroschnichenko, J. Nanomater. 2015, 672957 (2015).

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).

Iyer, P. P.

T. Das, P. P. Iyer, R. A. DeCrescent, and J. A. Schuller, Phys. Rev. B 92, 241110 (2015).
[Crossref]

Kaelberer, T.

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zhueludev, Science 330, 1510 (2010).
[Crossref]

Kerker, M.

M. Kerker, J. Opt. Soc. Am. B 65, 376 (1975).
[Crossref]

Kim, K.

K. Kim and E. Wolf, Opt. Commun. 59, 1 (1986).
[Crossref]

Kivshar, Y. S.

A. E. Miroschnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, Nat. Commun. 6, 8069 (2015).
[Crossref]

Kuznetsov, A. I.

A. E. Miroschnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, Nat. Commun. 6, 8069 (2015).
[Crossref]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, Sci. Rep. 2, 492 (2012).
[Crossref]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Oxford, 1960).

Lannebere, S.

S. Lannebere and M. G. Silveirinha, Nat. Commun. 6, 8766 (2015).
[Crossref]

Lei, B.

W. Liu, B. Lei, J. H. Shi, H. J. Hu, and A. E. Miroschnichenko, J. Nanomater. 2015, 672957 (2015).

Leonhardt, U.

U. Leonhardt, Science 312, 1777 (1993).
[Crossref]

Leuchs, G.

P. l. Wozniak, P. Banzer, and G. Leuchs, Laser Photon. Rev. 12, 231 (2012).

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Oxford, 1960).

Liu, W.

W. Liu, B. Lei, J. H. Shi, H. J. Hu, and A. E. Miroschnichenko, J. Nanomater. 2015, 672957 (2015).

Luk’yanchuk, B.

A. E. Miroschnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, Nat. Commun. 6, 8069 (2015).
[Crossref]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, Sci. Rep. 2, 492 (2012).
[Crossref]

Miroschnichenko, A. E.

W. Liu, B. Lei, J. H. Shi, H. J. Hu, and A. E. Miroschnichenko, J. Nanomater. 2015, 672957 (2015).

A. E. Miroschnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, Nat. Commun. 6, 8069 (2015).
[Crossref]

Miroshnichenko, A. E.

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, Sci. Rep. 2, 492 (2012).
[Crossref]

Novikov, S. M.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, Nano Lett. 12, 3749 (2012).
[Crossref]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University, 2012).

Papasimakis, N.

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zhueludev, Science 330, 1510 (2010).
[Crossref]

Reinhardt, C.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, Nano Lett. 12, 3749 (2012).
[Crossref]

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London A 253, 358 (1959).
[Crossref]

Rogacheva, V.

V. A. Fedotov, V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zhueludev, Sci. Rep. 3, 2967 (2013).
[Crossref]

Savinov, V.

V. A. Fedotov, V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zhueludev, Sci. Rep. 3, 2967 (2013).
[Crossref]

Scherrer, R. J.

C. M. Ho and R. J. Scherrer, Phys. Lett. B 722, 341 (2013).
[Crossref]

Schott, G. A.

G. A. Schott, Philos. Mag. 15(100), 752 (1933).
[Crossref]

Schuller, J. A.

T. Das, P. P. Iyer, R. A. DeCrescent, and J. A. Schuller, Phys. Rev. B 92, 241110 (2015).
[Crossref]

Sheppard, C. J. R.

T. X. Hoang, X. Chen, and C. J. R. Sheppard, Phys. Rev. A 86, 33817 (2012).
[Crossref]

T. X. Hoang, X. Chen, and C. J. R. Sheppard, J. Opt. Soc. Am. A 29, 32 (2012).
[Crossref]

Shi, J. H.

W. Liu, B. Lei, J. H. Shi, H. J. Hu, and A. E. Miroschnichenko, J. Nanomater. 2015, 672957 (2015).

Silveirinha, M. G.

S. Lannebere and M. G. Silveirinha, Nat. Commun. 6, 8766 (2015).
[Crossref]

M. G. Silveirinha, Phys. Rev. A 89, 23813 (2014).
[Crossref]

Stepanovsky, Y. U. P.

G. N. Afanasiev and Y. U. P. Stepanovsky, J. Phys. A 28, 4565 (1995).
[Crossref]

Tsai, D. P.

V. A. Fedotov, V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zhueludev, Sci. Rep. 3, 2967 (2013).
[Crossref]

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zhueludev, Science 330, 1510 (2010).
[Crossref]

Tugushev, V. V.

V. M. Dubovik and V. V. Tugushev, Phys. Rep. 187, 145 (1990).
[Crossref]

Urbach, H. P.

Wachters, A. J. H.

Wei, L.

Wei, X. H.

Wolf, E.

E. Wolf and T. Habashy, J. Mod. Opt. 40, 785 (1993).
[Crossref]

K. Kim and E. Wolf, Opt. Commun. 59, 1 (1986).
[Crossref]

A. J. Devaney and E. Wolf, Phys. Rev. D 8, 1044 (1973).

B. Richards and E. Wolf, Proc. R. Soc. London A 253, 358 (1959).
[Crossref]

Wozniak, P. l.

P. l. Wozniak, P. Banzer, and G. Leuchs, Laser Photon. Rev. 12, 231 (2012).

Xi, Z.

Yu, Y. F.

A. E. Miroschnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, Nat. Commun. 6, 8069 (2015).
[Crossref]

Zel’dovich, Y. A. B.

Y. A. B. Zel’dovich, Zh. Eksp. Teor. Fiz 33, 1531 (1957).

Zhang, J. B.

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, Sci. Rep. 2, 492 (2012).
[Crossref]

Zhueludev, N. I.

V. A. Fedotov, V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zhueludev, Sci. Rep. 3, 2967 (2013).
[Crossref]

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zhueludev, Science 330, 1510 (2010).
[Crossref]

Zywietz, U.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, Nano Lett. 12, 3749 (2012).
[Crossref]

J. Mod. Opt. (1)

E. Wolf and T. Habashy, J. Mod. Opt. 40, 785 (1993).
[Crossref]

J. Nanomater. (1)

W. Liu, B. Lei, J. H. Shi, H. J. Hu, and A. E. Miroschnichenko, J. Nanomater. 2015, 672957 (2015).

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

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

M. Kerker, J. Opt. Soc. Am. B 65, 376 (1975).
[Crossref]

J. Phys. A (1)

G. N. Afanasiev and Y. U. P. Stepanovsky, J. Phys. A 28, 4565 (1995).
[Crossref]

Laser Photon. Rev. (1)

P. l. Wozniak, P. Banzer, and G. Leuchs, Laser Photon. Rev. 12, 231 (2012).

Nano Lett. (1)

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, Nano Lett. 12, 3749 (2012).
[Crossref]

Nat. Commun. (2)

A. E. Miroschnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, Nat. Commun. 6, 8069 (2015).
[Crossref]

S. Lannebere and M. G. Silveirinha, Nat. Commun. 6, 8766 (2015).
[Crossref]

Opt. Commun. (1)

K. Kim and E. Wolf, Opt. Commun. 59, 1 (1986).
[Crossref]

Opt. Lett. (1)

Philos. Mag. (1)

G. A. Schott, Philos. Mag. 15(100), 752 (1933).
[Crossref]

Phys. Lett. B (1)

C. M. Ho and R. J. Scherrer, Phys. Lett. B 722, 341 (2013).
[Crossref]

Phys. Rep. (1)

V. M. Dubovik and V. V. Tugushev, Phys. Rep. 187, 145 (1990).
[Crossref]

Phys. Rev. (1)

G. H. Goedecke, Phys. Rev. 135, B281 (1964).
[Crossref]

Phys. Rev. A (2)

T. X. Hoang, X. Chen, and C. J. R. Sheppard, Phys. Rev. A 86, 33817 (2012).
[Crossref]

M. G. Silveirinha, Phys. Rev. A 89, 23813 (2014).
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Figures (4)

Fig. 1.
Fig. 1. (a) Dielectric nanosphere of refractive index n=3.5 and radius r0=100  nm is illuminated by a focused radially polarized beam in an optical system with numerical aperture NA=0.86. (b) Normalized energy inside the particle and the scattering power for a dielectric nanosphere at the focus of a radially polarized beam.
Fig. 2.
Fig. 2. (a) Amplitude and (b) phase of Cartesian dipole moment Pz and toroidal moment ikTz of the induced current inside the particle at focus. The left inserted figure in (a) shows the induced current distribution at wavelength λ=464  nm where the anapole mode is excited. The right inserted figure in (a) shows the pure dipole mode.
Fig. 3.
Fig. 3. Radiation pattern (radiation power in arbitrary units) of the particle illuminated by a focused radially polarized beam in xz plane at the wavelengths of (a) anapole mode and (b) electric dipole mode.
Fig. 4.
Fig. 4. (a) 4π illumination configuration, where the two counter-propagating radially polarized beams have exactly the same intensity but π phase difference. (b) The normalized internal energy, the scattering power spectrum of the particle excited under the 4π configuration calculated by FEM and the scattering power spectrum of a pure electric dipole and octupole by the Lorenz–Mie theory. (c) The focal electrical field of the 4π configuration. (d) Total electric field of the particle excited by the focal field in (c) at the radiating anapole condition λ=464  nm. (e) Total field subtracted by the illumination field.

Equations (6)

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Ef(r)=l=1[pEl0Nl0(r)+pMl0Ml0(r)],
J=iω(n21)E,
P=iωsphJdr,
T=110csph[(r·J)r2r2J]dr.
pEl0=ilπ(2l+1)l(l+1)[0θmA(α)Pl(cosα)αsinαdαππθmA(πα)Pl(cosα)αsinαdα],
sphEf4π·Jdr=VJf4π·Esdr.

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