Abstract

We study, by means of full-electrodynamic calculations using the layer-multiple-scattering method, the effect of diffractive coupling on the enhancement of the local electromagnetic field in periodic arrays of nanolenses consisting of three silver spheres with progressively decreasing sizes and separations. The interaction between the hot-spot modes of an isolated nanolens with the Rayleigh–Wood anomalies of the periodic lattice leads to a further enhancement of the local field intensity, which can be controlled by an appropriate choice of the geometrical parameters involved.

© 2012 Optical Society of America

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  1. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
    [CrossRef]
  2. P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
    [CrossRef]
  3. K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint, Nano Lett. 11, 61 (2011).
    [CrossRef]
  4. K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
    [CrossRef]
  5. J. Dai, F. Čajko, I. Tsukerman, and M. I. Stockman, Phys. Rev. B 77, 115419 (2008).
    [CrossRef]
  6. S. V. Karpov, V. S. Gerasimov, I. L. Isaev, and V. A. Markel, Phys. Rev. B 72, 205425 (2005).
    [CrossRef]
  7. S. Toroghi and P. G. Kik, Appl. Phys. Lett. 100, 183105 (2012).
    [CrossRef]
  8. B. Ding, Z. Deng, H. Yan, S. Cabrini, R. N. Zuckermann, and J. Bokor, J. Am. Chem. Soc. 132, 3248 (2010).
    [CrossRef]
  9. D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, Nano Lett. 4, 153 (2004).
    [CrossRef]
  10. S. Zou and G. C. Schatz, Chem. Phys. Lett. 403, 62 (2005).
    [CrossRef]
  11. V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008).
    [CrossRef]
  12. B. Auguié and W. L. Barnes, Phys. Rev. Lett. 101, 143902 (2008).
    [CrossRef]
  13. N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998).
    [CrossRef]
  14. N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
    [CrossRef]
  15. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  16. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
    [CrossRef]

2012 (2)

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

S. Toroghi and P. G. Kik, Appl. Phys. Lett. 100, 183105 (2012).
[CrossRef]

2011 (1)

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint, Nano Lett. 11, 61 (2011).
[CrossRef]

2010 (2)

B. Ding, Z. Deng, H. Yan, S. Cabrini, R. N. Zuckermann, and J. Bokor, J. Am. Chem. Soc. 132, 3248 (2010).
[CrossRef]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

2008 (3)

J. Dai, F. Čajko, I. Tsukerman, and M. I. Stockman, Phys. Rev. B 77, 115419 (2008).
[CrossRef]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef]

B. Auguié and W. L. Barnes, Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef]

2005 (2)

S. V. Karpov, V. S. Gerasimov, I. L. Isaev, and V. A. Markel, Phys. Rev. B 72, 205425 (2005).
[CrossRef]

S. Zou and G. C. Schatz, Chem. Phys. Lett. 403, 62 (2005).
[CrossRef]

2004 (2)

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, Nano Lett. 4, 153 (2004).
[CrossRef]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

2003 (1)

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef]

2000 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

1998 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Aizpurua, J.

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Albella, P.

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Alonso-González, P.

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Ambekar, R.

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint, Nano Lett. 11, 61 (2011).
[CrossRef]

Arzubiaga, L.

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Auguié, B.

B. Auguié and W. L. Barnes, Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef]

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Barnes, W. L.

B. Auguié and W. L. Barnes, Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef]

Bergman, D. J.

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef]

Bokor, J.

B. Ding, Z. Deng, H. Yan, S. Cabrini, R. N. Zuckermann, and J. Bokor, J. Am. Chem. Soc. 132, 3248 (2010).
[CrossRef]

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Cabrini, S.

B. Ding, Z. Deng, H. Yan, S. Cabrini, R. N. Zuckermann, and J. Bokor, J. Am. Chem. Soc. 132, 3248 (2010).
[CrossRef]

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Cajko, F.

J. Dai, F. Čajko, I. Tsukerman, and M. I. Stockman, Phys. Rev. B 77, 115419 (2008).
[CrossRef]

Casanova, F.

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Chen, J.

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Dai, J.

J. Dai, F. Čajko, I. Tsukerman, and M. I. Stockman, Phys. Rev. B 77, 115419 (2008).
[CrossRef]

Deng, Z.

B. Ding, Z. Deng, H. Yan, S. Cabrini, R. N. Zuckermann, and J. Bokor, J. Am. Chem. Soc. 132, 3248 (2010).
[CrossRef]

Ding, B.

B. Ding, Z. Deng, H. Yan, S. Cabrini, R. N. Zuckermann, and J. Bokor, J. Am. Chem. Soc. 132, 3248 (2010).
[CrossRef]

Fang, N. X.

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint, Nano Lett. 11, 61 (2011).
[CrossRef]

Fung, K. H.

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint, Nano Lett. 11, 61 (2011).
[CrossRef]

García-Etxarri, A.

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Genov, D. A.

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, Nano Lett. 4, 153 (2004).
[CrossRef]

Gerasimov, V. S.

S. V. Karpov, V. S. Gerasimov, I. L. Isaev, and V. A. Markel, Phys. Rev. B 72, 205425 (2005).
[CrossRef]

Golmar, F.

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Grigorenko, A. N.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef]

Hillenbrand, R.

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Hueso, L. E.

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Huth, F.

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Isaev, I. L.

S. V. Karpov, V. S. Gerasimov, I. L. Isaev, and V. A. Markel, Phys. Rev. B 72, 205425 (2005).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Karpov, S. V.

S. V. Karpov, V. S. Gerasimov, I. L. Isaev, and V. A. Markel, Phys. Rev. B 72, 205425 (2005).
[CrossRef]

Kik, P. G.

S. Toroghi and P. G. Kik, Appl. Phys. Lett. 100, 183105 (2012).
[CrossRef]

Ko, K. D.

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint, Nano Lett. 11, 61 (2011).
[CrossRef]

Kravets, V. G.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef]

Kumar, A.

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint, Nano Lett. 11, 61 (2011).
[CrossRef]

Li, K.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef]

Liu, G. L.

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint, Nano Lett. 11, 61 (2011).
[CrossRef]

Markel, V. A.

S. V. Karpov, V. S. Gerasimov, I. L. Isaev, and V. A. Markel, Phys. Rev. B 72, 205425 (2005).
[CrossRef]

Modinos, A.

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

Nordlander, P.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Oubre, C.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Prodan, E.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Sarychev, A. K.

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, Nano Lett. 4, 153 (2004).
[CrossRef]

Schatz, G. C.

S. Zou and G. C. Schatz, Chem. Phys. Lett. 403, 62 (2005).
[CrossRef]

Schedin, F.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef]

Schnell, M.

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Shalaev, V. M.

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, Nano Lett. 4, 153 (2004).
[CrossRef]

Stefanou, N.

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

Stockman, M. I.

J. Dai, F. Čajko, I. Tsukerman, and M. I. Stockman, Phys. Rev. B 77, 115419 (2008).
[CrossRef]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef]

Toroghi, S.

S. Toroghi and P. G. Kik, Appl. Phys. Lett. 100, 183105 (2012).
[CrossRef]

Toussaint, K. C.

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint, Nano Lett. 11, 61 (2011).
[CrossRef]

Tsukerman, I.

J. Dai, F. Čajko, I. Tsukerman, and M. I. Stockman, Phys. Rev. B 77, 115419 (2008).
[CrossRef]

Wei, A.

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, Nano Lett. 4, 153 (2004).
[CrossRef]

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Yan, H.

B. Ding, Z. Deng, H. Yan, S. Cabrini, R. N. Zuckermann, and J. Bokor, J. Am. Chem. Soc. 132, 3248 (2010).
[CrossRef]

Yannopapas, V.

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

Zou, S.

S. Zou and G. C. Schatz, Chem. Phys. Lett. 403, 62 (2005).
[CrossRef]

Zuckermann, R. N.

B. Ding, Z. Deng, H. Yan, S. Cabrini, R. N. Zuckermann, and J. Bokor, J. Am. Chem. Soc. 132, 3248 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

S. Toroghi and P. G. Kik, Appl. Phys. Lett. 100, 183105 (2012).
[CrossRef]

Chem. Phys. Lett. (1)

S. Zou and G. C. Schatz, Chem. Phys. Lett. 403, 62 (2005).
[CrossRef]

Comput. Phys. Commun. (2)

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 113, 49 (1998).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, Comput. Phys. Commun. 132, 189 (2000).
[CrossRef]

J. Am. Chem. Soc. (1)

B. Ding, Z. Deng, H. Yan, S. Cabrini, R. N. Zuckermann, and J. Bokor, J. Am. Chem. Soc. 132, 3248 (2010).
[CrossRef]

Nano Lett. (3)

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, Nano Lett. 4, 153 (2004).
[CrossRef]

K. D. Ko, A. Kumar, K. H. Fung, R. Ambekar, G. L. Liu, N. X. Fang, and K. C. Toussaint, Nano Lett. 11, 61 (2011).
[CrossRef]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Nat. Commun. (1)

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, Nat. Commun. 3, 684 (2012).
[CrossRef]

Nat. Mater. (1)

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Phys. Rev. B (3)

J. Dai, F. Čajko, I. Tsukerman, and M. I. Stockman, Phys. Rev. B 77, 115419 (2008).
[CrossRef]

S. V. Karpov, V. S. Gerasimov, I. L. Isaev, and V. A. Markel, Phys. Rev. B 72, 205425 (2005).
[CrossRef]

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Phys. Rev. Lett. (3)

V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef]

B. Auguié and W. L. Barnes, Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef]

K. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic view of a square lattice of nanolenses in a glass matrix. Each nanolens consists of three silver spheres with decreasing radii R1=33.8nm, R2=13nm, and R3=5nm, and separations d12=7.8nm and d23=3nm.

Fig. 2.
Fig. 2.

Extinction spectra of square arrays (a=360nm) of silver nanospheres in a glass matrix, for p-polarized light incident at an angle θ=45°. Upper diagram: spheres of radius R1=33.8nm (solid line) or R2=13nm (dashed line). Middle diagram: nanosphere dimers (R1=33.8nm, R2=13nm, and d12=7.8nm). Lower diagram: complete nanolens motif (R1=33.8nm, R2=13nm, R3=5nm, d12=7.8nm, and d23=3nm). The vertical dashed lines mark the position of the RW anomalies RW3 and RW4. Next to the extinction diagrams we show corresponding field intensity plots at the resonance wavelengths indicated by the arrows.

Fig. 3.
Fig. 3.

Extinction spectra of square arrays of the nanolens motif under consideration in a glass matrix, for p-polarized light incident at an angle θ=45°, for lattice constants a varying from 270 to 300 nm. The vertical dashed lines indicate the position of RW2 in each case.

Fig. 4.
Fig. 4.

Dependence of the maximum hot-spot field intensity on the lattice constant for p-polarized light incident at an angle θ=45° on square arrays of the nanolens motif under consideration in a glass matrix. The vertical dashed lines denote the lattice constants at which RW anomalies coincide with the hot-spot resonance. A field intensity plot in the region between the medium and the smallest spheres at the hot-spot resonance, for a=250nm, is shown in the margin.

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