Abstract

The influence of the degree of purity of a silicon nanoparticle on its resonances, either electric or magnetic, is assessed by using Mie theory as well as finite-element simulations. In particular, it is shown that the main effect of the increase of absorption due to the pollutants is observed in the magnetic resonances. Concerning Kerker’s conditions for the directionality of the scattering [J. Opt. Soc. Am. 73, 765 (1983)], it is found that both are strongly shifted when the material’s purity is varied. Resistive losses confirm the quenching of magnetic resonances, showing that the region of influence in the magnetic dipole resonance is much larger than in the electric one, although it has been found that losses are not critical for silicon content over 99.50%.

© 2014 Optical Society of America

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References

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  1. P. N. Prasad, Nanophotonics (Wiley, 2004).
  2. M. Kerker, D.-S. Wang, and C. L. Giles, J. Opt. Soc. Am. 73, 765 (1983).
    [CrossRef]
  3. J. M. 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]
  4. A. D. Yaghjian, in 3rd European Conference on Antennas and Propagation (IEEE, 2009), pp. 858–860.
  5. A. E. Miroshnichenko, B. Luk’yanchuk, S. A. Maier, and Y. S. Kivshar, ACS Nano 6, 837 (2012).
    [CrossRef]
  6. B. García-Cámara, R. Alcaraz de la Osa, J. M. Saiz, F. González, and F. Moreno, Opt. Lett. 36, 728 (2011).
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  7. L. Shi, J. T. Harris, R. Fenollosa, I. Rodriguez, X. Lu, B. A. Korgel, and F. Meseguer, Nat. Commun. 4, 1904 (2013).
    [CrossRef]
  8. Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, Nat. Commun. 4, 1527 (2013).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. Comsol Multiphysics 4.3a (Comsol Inc.), http://www.comsol.com .
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2013

L. Shi, J. T. Harris, R. Fenollosa, I. Rodriguez, X. Lu, B. A. Korgel, and F. Meseguer, Nat. Commun. 4, 1904 (2013).
[CrossRef]

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

2012

J. M. 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. E. Miroshnichenko, B. Luk’yanchuk, S. A. Maier, and Y. S. Kivshar, ACS Nano 6, 837 (2012).
[CrossRef]

2011

2010

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, Phys. Rev. B 82, 045404 (2010).
[CrossRef]

2008

2001

N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani, Prog. Photovoltaics 9, 203 (2001).
[CrossRef]

2000

H. Shi, L. Zhang, and W. Cai, J. Appl. Phys. 87, 1572 (2000).
[CrossRef]

1988

A. Forouhi and I. Bloomer, Phys. Rev. B 38, 1865 (1988).
[CrossRef]

1983

Abe, M.

N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani, Prog. Photovoltaics 9, 203 (2001).
[CrossRef]

Aizpurua, J.

Albella, P.

J. M. 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]

Alcaraz de la Osa, R.

Aratani, F.

N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani, Prog. Photovoltaics 9, 203 (2001).
[CrossRef]

Baba, H.

N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani, Prog. Photovoltaics 9, 203 (2001).
[CrossRef]

Bloomer, I.

A. Forouhi and I. Bloomer, Phys. Rev. B 38, 1865 (1988).
[CrossRef]

Bohren, C.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles, 2nd ed. (Wiley-VCH, 2010).

Bousmina, M.

A. Mejdoubi, M. Malki, M. Essone Mezeme, Z. Sekkat, M. Bousmina, and C. Brosseau, J. Appl. Phys. 110, 103105 (2011).
[CrossRef]

Brosseau, C.

A. Mejdoubi, M. Malki, M. Essone Mezeme, Z. Sekkat, M. Bousmina, and C. Brosseau, J. Appl. Phys. 110, 103105 (2011).
[CrossRef]

Cai, W.

H. Shi, L. Zhang, and W. Cai, J. Appl. Phys. 87, 1572 (2000).
[CrossRef]

Chantada, L.

Chichkov, B. N.

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, Phys. Rev. B 82, 045404 (2010).
[CrossRef]

Essone Mezeme, M.

A. Mejdoubi, M. Malki, M. Essone Mezeme, Z. Sekkat, M. Bousmina, and C. Brosseau, J. Appl. Phys. 110, 103105 (2011).
[CrossRef]

Evlyukhin, A. B.

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, Phys. Rev. B 82, 045404 (2010).
[CrossRef]

Eyraud, C.

J. M. 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]

Fenollosa, R.

L. Shi, J. T. Harris, R. Fenollosa, I. Rodriguez, X. Lu, B. A. Korgel, and F. Meseguer, Nat. Commun. 4, 1904 (2013).
[CrossRef]

Forcales, M.

Forouhi, A.

A. Forouhi and I. Bloomer, Phys. Rev. B 38, 1865 (1988).
[CrossRef]

Froufe-Perez, L. S.

Froufe-Pérez, L.

J. M. 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]

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]

García-Cámara, B.

J. M. 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, R. Alcaraz de la Osa, J. M. Saiz, F. González, and F. Moreno, Opt. Lett. 36, 728 (2011).
[CrossRef]

García-Etxarri, A.

Geffrin, J. M.

J. M. 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]

Giannini, V.

Giles, C. L.

Gómez Rivas, J.

Gómez-Medina, R.

J. M. 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-Perez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, Opt. Express 19, 4815 (2011).
[CrossRef]

González, F.

J. M. 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, R. Alcaraz de la Osa, J. M. Saiz, F. González, and F. Moreno, Opt. Lett. 36, 728 (2011).
[CrossRef]

Hanazawa, K.

N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani, Prog. Photovoltaics 9, 203 (2001).
[CrossRef]

Harris, J. T.

L. Shi, J. T. Harris, R. Fenollosa, I. Rodriguez, X. Lu, B. A. Korgel, and F. Meseguer, Nat. Commun. 4, 1904 (2013).
[CrossRef]

Hiwasa, S.

N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani, Prog. Photovoltaics 9, 203 (2001).
[CrossRef]

Huffman, D.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles, 2nd ed. (Wiley-VCH, 2010).

Kato, Y.

N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani, Prog. Photovoltaics 9, 203 (2001).
[CrossRef]

Kerker, M.

Kivshar, Y. S.

A. E. Miroshnichenko, B. Luk’yanchuk, S. A. Maier, and Y. S. Kivshar, ACS Nano 6, 837 (2012).
[CrossRef]

Korgel, B. A.

L. Shi, J. T. Harris, R. Fenollosa, I. Rodriguez, X. Lu, B. A. Korgel, and F. Meseguer, Nat. Commun. 4, 1904 (2013).
[CrossRef]

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]

Litman, A.

J. M. 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.

Lu, X.

L. Shi, J. T. Harris, R. Fenollosa, I. Rodriguez, X. Lu, B. A. Korgel, and F. Meseguer, Nat. Commun. 4, 1904 (2013).
[CrossRef]

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. E. Miroshnichenko, B. Luk’yanchuk, S. A. Maier, and Y. S. Kivshar, ACS Nano 6, 837 (2012).
[CrossRef]

Luk’yanchuk, B. S.

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, Phys. Rev. B 82, 045404 (2010).
[CrossRef]

Maier, S. A.

A. E. Miroshnichenko, B. Luk’yanchuk, S. A. Maier, and Y. S. Kivshar, ACS Nano 6, 837 (2012).
[CrossRef]

Malki, M.

A. Mejdoubi, M. Malki, M. Essone Mezeme, Z. Sekkat, M. Bousmina, and C. Brosseau, J. Appl. Phys. 110, 103105 (2011).
[CrossRef]

Mejdoubi, A.

A. Mejdoubi, M. Malki, M. Essone Mezeme, Z. Sekkat, M. Bousmina, and C. Brosseau, J. Appl. Phys. 110, 103105 (2011).
[CrossRef]

Meseguer, F.

L. Shi, J. T. Harris, R. Fenollosa, I. Rodriguez, X. Lu, B. A. Korgel, and F. Meseguer, Nat. Commun. 4, 1904 (2013).
[CrossRef]

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]

A. E. Miroshnichenko, B. Luk’yanchuk, S. A. Maier, and Y. S. Kivshar, ACS Nano 6, 837 (2012).
[CrossRef]

Moreno, F.

J. M. 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, R. Alcaraz de la Osa, J. M. Saiz, F. González, and F. Moreno, Opt. Lett. 36, 728 (2011).
[CrossRef]

Nakamura, N.

N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani, Prog. Photovoltaics 9, 203 (2001).
[CrossRef]

Nieto-Vesperinas, M.

J. M. 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-Perez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, Opt. Express 19, 4815 (2011).
[CrossRef]

Palik, E. D.

E. D. Palik,. Handbook of Optical Constants of Solids (Academic, 1998).

Prasad, P. N.

P. N. Prasad, Nanophotonics (Wiley, 2004).

Reinhardt, C.

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, Phys. Rev. B 82, 045404 (2010).
[CrossRef]

Rodriguez, I.

L. Shi, J. T. Harris, R. Fenollosa, I. Rodriguez, X. Lu, B. A. Korgel, and F. Meseguer, Nat. Commun. 4, 1904 (2013).
[CrossRef]

Sáenz, J. J.

J. M. 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-Perez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, Opt. Express 19, 4815 (2011).
[CrossRef]

Saiz, J. M.

Sakaguchi, Y.

N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani, Prog. Photovoltaics 9, 203 (2001).
[CrossRef]

Scheffold, F.

Seidel, A.

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, Phys. Rev. B 82, 045404 (2010).
[CrossRef]

Sekkat, Z.

A. Mejdoubi, M. Malki, M. Essone Mezeme, Z. Sekkat, M. Bousmina, and C. Brosseau, J. Appl. Phys. 110, 103105 (2011).
[CrossRef]

Shi, H.

H. Shi, L. Zhang, and W. Cai, J. Appl. Phys. 87, 1572 (2000).
[CrossRef]

Shi, L.

L. Shi, J. T. Harris, R. Fenollosa, I. Rodriguez, X. Lu, B. A. Korgel, and F. Meseguer, Nat. Commun. 4, 1904 (2013).
[CrossRef]

Vaillon, R.

J. M. 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]

Wang, D.-S.

Yaghjian, A. D.

A. D. Yaghjian, in 3rd European Conference on Antennas and Propagation (IEEE, 2009), pp. 858–860.

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]

Yuge, N.

N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani, Prog. Photovoltaics 9, 203 (2001).
[CrossRef]

Zhang, L.

H. Shi, L. Zhang, and W. Cai, J. Appl. Phys. 87, 1572 (2000).
[CrossRef]

Zhang, Y.

ACS Nano

A. E. Miroshnichenko, B. Luk’yanchuk, S. A. Maier, and Y. S. Kivshar, ACS Nano 6, 837 (2012).
[CrossRef]

J. Appl. Phys.

H. Shi, L. Zhang, and W. Cai, J. Appl. Phys. 87, 1572 (2000).
[CrossRef]

A. Mejdoubi, M. Malki, M. Essone Mezeme, Z. Sekkat, M. Bousmina, and C. Brosseau, J. Appl. Phys. 110, 103105 (2011).
[CrossRef]

J. Opt. Soc. Am.

Nat. Commun.

J. M. 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]

L. Shi, J. T. Harris, R. Fenollosa, I. Rodriguez, X. Lu, B. A. Korgel, and F. Meseguer, Nat. Commun. 4, 1904 (2013).
[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

Opt. Lett.

Phys. Rev. B

A. Forouhi and I. Bloomer, Phys. Rev. B 38, 1865 (1988).
[CrossRef]

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, Phys. Rev. B 82, 045404 (2010).
[CrossRef]

Prog. Photovoltaics

N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani, Prog. Photovoltaics 9, 203 (2001).
[CrossRef]

Other

Elkem AS Silicon Materials, http://www.elkem.com/Global/ESM/quality-safety/product-data-sheets/silicon-products/silgrain/Silgrain-pds.pdf .

E. D. Palik,. Handbook of Optical Constants of Solids (Academic, 1998).

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles, 2nd ed. (Wiley-VCH, 2010).

P. N. Prasad, Nanophotonics (Wiley, 2004).

A. D. Yaghjian, in 3rd European Conference on Antennas and Propagation (IEEE, 2009), pp. 858–860.

Comsol Multiphysics 4.3a (Comsol Inc.), http://www.comsol.com .

Supplementary Material (4)

» Media 1: MOV (678 KB)     
» Media 2: MOV (145 KB)     
» Media 3: MOV (720 KB)     
» Media 4: MOV (115 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Spectral extinction (top) and absorption (bottom) efficiencies ( λ [ 900 , 2100 ] nm ) for an isolated spherical particle of Si (radius a = 230 nm ) as the purity grade is reduced from 100.0% to 98.98%.

Fig. 2.
Fig. 2.

Spectral shifts in both the electric ( a 1 ) and magnetic ( b 1 ) dipole resonances as well as in Kerker’s conditions when varying the Si content.

Fig. 3.
Fig. 3.

Scattering patterns of Kerker’s conditions for an isolated Si particle when the purity grade varies from 98.98% to 100.0% (radial axis in logarithmic scale).

Fig. 4.
Fig. 4.

Maps of the near-field norm and resistive losses of the magnetic (top) [(Media 1) and (Media 2), respectively] and electric (bottom) [(Media 3) and (Media 4), respectively] dipole resonances at the wavelength they occur for several purity grades.

Tables (1)

Tables Icon

Table 1. Typical Silicon Powder wt. (%) Compositions (MG-Si and SG-Si from [13], Silgrain from Elkem [14])

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