Abstract

We investigate Fano resonances in planar two-dimensional periodic arrays of linear trimers of plasmonic nanoparticles that appear under plane wave incidence. The observed Fano resonances are associated to resonances belonging to the trimer (metamolecule) itself, where some are found to be strongly affected by the array periodicity. We observe that array-dependent resonances appearing for oblique incidence are resistant to losses, whereas narrow dipolar-like Fano resonances associated mainly to the metamolecule, which appear also under normal incidence, disappear when losses are too high. In particular, we prove the latter by theoretical (dipolar approximation) and full-wave simulations, in good agreement. We propose that the use of very low-loss plasmonic materials or the use of gain materials to mitigate plasmonic losses may lead to (high-quality factor) dipolar-like Fano resonances under normal incidence, exhibiting a certain degree of fabrication defect tolerance, which might be employed to improve sensors, lasing, switching, and nonlinear devices, for example.

© 2013 Optical Society of America

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2013 (2)

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alu, and X. Li, Nat. Nanotechnol. 8, 95 (2013).
[CrossRef]

B. S. Luk’yanchuk, A. E. Miroshnichenko, and S. K. Yu, J. Opt. 15, 073001 (2013).
[CrossRef]

2012 (6)

M. Gustafsson, I. Vakili, S. E. B. Keskin, D. Sjoberg, and C. Larsson, IEEE Trans. Antennas Propag. 60, 3818 (2012).
[CrossRef]

J. Jiao and Z. Wang, J. Mod. Opt. 59, 1434 (2012).
[CrossRef]

B. Gao, G. Arya, and A. R. Tao, Nat. Nanotechnol. 7, 433 (2012).
[CrossRef]

Y. Francescato, V. Giannini, and S. A. Maier, ACS Nano 6, 1830 (2012).
[CrossRef]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, Nat. Mater. 11, 69 (2012).
[CrossRef]

J. Ye, F. Wen, H. Sobhani, J. B. Lassiter, P. V. Dorpe, P. Nordlander, and N. J. Halas, Nano Lett. 12, 1660 (2012).
[CrossRef]

2011 (4)

A. Vallecchi, M. Albani, and F. Capolino, Opt. Express 19, 2754 (2011).
[CrossRef]

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, ACS Nano 5, 2042 (2011).
[CrossRef]

S. Campione, M. Albani, and F. Capolino, Opt. Mater. Express 1, 1077 (2011).
[CrossRef]

S. Steshenko, F. Capolino, P. Alitalo, and S. Tretyakov, Phys. Rev. E 84, 016607 (2011).
[CrossRef]

2010 (5)

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, Laser Photon. Rev. 4, 795 (2010).
[CrossRef]

R. Bardhan, N. K. Grady, T. Ali, and N. J. Halas, ACS Nano 4, 6169 (2010).
[CrossRef]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, Science 328, 1135 (2010).
[CrossRef]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

2009 (1)

J. H. Choi, S. M. Adams, and R. Ragan, Nanotechnology 20, 065301 (2009).
[CrossRef]

2008 (1)

2004 (1)

E. W. Edwards, M. F. Montague, H. H. Solak, C. J. Hawker, and P. F. Nealey, Adv. Mater. 16, 1315 (2004).
[CrossRef]

2002 (1)

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Moller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef]

2000 (1)

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

1995 (1)

W. H. Yang, G. C. Schatz, and R. P. Vanduyne, J. Chem. Phys. 103, 869 (1995).
[CrossRef]

1992 (1)

A. Van Blaaderen and A. Vrij, Langmuir 8, 2921 (1992).
[CrossRef]

1972 (1)

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

1965 (1)

1961 (1)

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Adams, S. M.

J. H. Choi, S. M. Adams, and R. Ragan, Nanotechnology 20, 065301 (2009).
[CrossRef]

Adato, R.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, Nat. Mater. 11, 69 (2012).
[CrossRef]

Albani, M.

Ali, T.

R. Bardhan, N. K. Grady, T. Ali, and N. J. Halas, ACS Nano 4, 6169 (2010).
[CrossRef]

Alitalo, P.

S. Steshenko, F. Capolino, P. Alitalo, and S. Tretyakov, Phys. Rev. E 84, 016607 (2011).
[CrossRef]

Altug, H.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, Nat. Mater. 11, 69 (2012).
[CrossRef]

Alu, A.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alu, and X. Li, Nat. Nanotechnol. 8, 95 (2013).
[CrossRef]

Arju, N.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, Nat. Mater. 11, 69 (2012).
[CrossRef]

Arya, G.

B. Gao, G. Arya, and A. R. Tao, Nat. Nanotechnol. 7, 433 (2012).
[CrossRef]

Bao, J.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, Science 328, 1135 (2010).
[CrossRef]

Bao, K.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, Science 328, 1135 (2010).
[CrossRef]

Bardhan, R.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, Science 328, 1135 (2010).
[CrossRef]

R. Bardhan, N. K. Grady, T. Ali, and N. J. Halas, ACS Nano 4, 6169 (2010).
[CrossRef]

Biswas, R.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Bohren, C. F.

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

Boltasseva, A.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, Laser Photon. Rev. 4, 795 (2010).
[CrossRef]

Cai, W.

Campione, S.

Capasso, F.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, Science 328, 1135 (2010).
[CrossRef]

Capolino, F.

Chettiar, U. K.

Choi, J. H.

J. H. Choi, S. M. Adams, and R. Ragan, Nanotechnology 20, 065301 (2009).
[CrossRef]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Christy, R. W.

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

Dorpe, P. V.

J. Ye, F. Wen, H. Sobhani, J. B. Lassiter, P. V. Dorpe, P. Nordlander, and N. J. Halas, Nano Lett. 12, 1660 (2012).
[CrossRef]

Drachev, V. P.

Dregely, D.

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, ACS Nano 5, 2042 (2011).
[CrossRef]

Dulkeith, E.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Moller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef]

Edwards, E. W.

E. W. Edwards, M. F. Montague, H. H. Solak, C. J. Hawker, and P. F. Nealey, Adv. Mater. 16, 1315 (2004).
[CrossRef]

El-Kady, I.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Emani, N. K.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, Laser Photon. Rev. 4, 795 (2010).
[CrossRef]

Fan, J. A.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, Science 328, 1135 (2010).
[CrossRef]

Fano, U.

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Feldmann, J.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Moller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

Francescato, Y.

Y. Francescato, V. Giannini, and S. A. Maier, ACS Nano 6, 1830 (2012).
[CrossRef]

Gao, B.

B. Gao, G. Arya, and A. R. Tao, Nat. Nanotechnol. 7, 433 (2012).
[CrossRef]

Giannini, V.

Y. Francescato, V. Giannini, and S. A. Maier, ACS Nano 6, 1830 (2012).
[CrossRef]

Giessen, H.

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, ACS Nano 5, 2042 (2011).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Gittins, D. I.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Moller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef]

Grady, N. K.

R. Bardhan, N. K. Grady, T. Ali, and N. J. Halas, ACS Nano 4, 6169 (2010).
[CrossRef]

Gustafsson, M.

M. Gustafsson, I. Vakili, S. E. B. Keskin, D. Sjoberg, and C. Larsson, IEEE Trans. Antennas Propag. 60, 3818 (2012).
[CrossRef]

Halas, N. J.

J. Ye, F. Wen, H. Sobhani, J. B. Lassiter, P. V. Dorpe, P. Nordlander, and N. J. Halas, Nano Lett. 12, 1660 (2012).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, Science 328, 1135 (2010).
[CrossRef]

R. Bardhan, N. K. Grady, T. Ali, and N. J. Halas, ACS Nano 4, 6169 (2010).
[CrossRef]

Hartsfield, T.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alu, and X. Li, Nat. Nanotechnol. 8, 95 (2013).
[CrossRef]

Hawker, C. J.

E. W. Edwards, M. F. Montague, H. H. Solak, C. J. Hawker, and P. F. Nealey, Adv. Mater. 16, 1315 (2004).
[CrossRef]

Hentschel, M.

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, ACS Nano 5, 2042 (2011).
[CrossRef]

Hessel, A.

Ho, K. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Huffman, D. R.

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

Ishii, S.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, Laser Photon. Rev. 4, 795 (2010).
[CrossRef]

Jiao, J.

J. Jiao and Z. Wang, J. Mod. Opt. 59, 1434 (2012).
[CrossRef]

Johnson, P. B.

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

Keskin, S. E. B.

M. Gustafsson, I. Vakili, S. E. B. Keskin, D. Sjoberg, and C. Larsson, IEEE Trans. Antennas Propag. 60, 3818 (2012).
[CrossRef]

Khanikaev, A. B.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, Nat. Mater. 11, 69 (2012).
[CrossRef]

Kildishev, A. V.

Kivshar, Y. S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

Klar, T. A.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Moller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef]

Larsson, C.

M. Gustafsson, I. Vakili, S. E. B. Keskin, D. Sjoberg, and C. Larsson, IEEE Trans. Antennas Propag. 60, 3818 (2012).
[CrossRef]

Lassiter, J. B.

J. Ye, F. Wen, H. Sobhani, J. B. Lassiter, P. V. Dorpe, P. Nordlander, and N. J. Halas, Nano Lett. 12, 1660 (2012).
[CrossRef]

Le, K. Q.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alu, and X. Li, Nat. Nanotechnol. 8, 95 (2013).
[CrossRef]

Levi, S. A.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Moller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef]

Li, X.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alu, and X. Li, Nat. Nanotechnol. 8, 95 (2013).
[CrossRef]

Liu, N.

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, ACS Nano 5, 2042 (2011).
[CrossRef]

Liu, X.-X.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alu, and X. Li, Nat. Nanotechnol. 8, 95 (2013).
[CrossRef]

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Luk’yanchuk, B. S.

B. S. Luk’yanchuk, A. E. Miroshnichenko, and S. K. Yu, J. Opt. 15, 073001 (2013).
[CrossRef]

Maier, S. A.

Y. Francescato, V. Giannini, and S. A. Maier, ACS Nano 6, 1830 (2012).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Manoharan, V. N.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, Science 328, 1135 (2010).
[CrossRef]

Miroshnichenko, A. E.

B. S. Luk’yanchuk, A. E. Miroshnichenko, and S. K. Yu, J. Opt. 15, 073001 (2013).
[CrossRef]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

Moller, M.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Moller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef]

Montague, M. F.

E. W. Edwards, M. F. Montague, H. H. Solak, C. J. Hawker, and P. F. Nealey, Adv. Mater. 16, 1315 (2004).
[CrossRef]

Monticone, F.

F. Shafiei, F. Monticone, K. Q. Le, X.-X. Liu, T. Hartsfield, A. Alu, and X. Li, Nat. Nanotechnol. 8, 95 (2013).
[CrossRef]

Morteani, A. C.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Moller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef]

Naik, G. V.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, Laser Photon. Rev. 4, 795 (2010).
[CrossRef]

Nealey, P. F.

E. W. Edwards, M. F. Montague, H. H. Solak, C. J. Hawker, and P. F. Nealey, Adv. Mater. 16, 1315 (2004).
[CrossRef]

Niedereichholz, T.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Moller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef]

Nordlander, P.

J. Ye, F. Wen, H. Sobhani, J. B. Lassiter, P. V. Dorpe, P. Nordlander, and N. J. Halas, Nano Lett. 12, 1660 (2012).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Sketch of a planar 2D periodic array of linear trimers of plasmonic nanoparticles.

Fig. 2.
Fig. 2.

Absorption efficiency Qa by the three nanoparticles in a unit cell of a 2D periodic array as in Fig. 1, via SDA method, as function of frequency and incidence angle. The permittivity of silver nanoparticles is modeled with (a) Drude formula [20] and (b) Palik data [22], with r=25, a=75, b=210, d=60 (in nanometer), and εh=2.25. Greater values are indicated by warmer colors.

Fig. 3.
Fig. 3.

(a), (c) Magnitude and (b), (d) phase of reflection R and transmission T versus frequency at normal incidence. Structure and material information are as in Fig. 2. The monochromatic time harmonic convention exp(iωt) is assumed.

Fig. 4.
Fig. 4.

As in Fig. 2 for b=240nm.

Fig. 5.
Fig. 5.

Absorption efficiency (from SDA) under normal incidence by a linear trimer (a) in a unit cell of the arrays with parameters as in Figs. 2 and 4 and (b) isolated metamolecule considering silver permittivity modeled with Drude formula [20].

Fig. 6.
Fig. 6.

(a) Magnitude and (b) phase of the nanoparticles’ induced dipole moments py,int and py,ext (from SDA) under normal incidence. (c) Vector field map (from full-wave simulation) for the Drude case in Fig. 2(a) representing the instantaneous electric field at a representative time, where the arrow colors denote its magnitude. The plots show only one fourth of the unit cell for clarity. The red and blue lines depict a perfect electric and magnetic conductor boundary condition, respectively, and the black dashed lines depict particles’ contours.

Fig. 7.
Fig. 7.

Extinction and absorption efficiencies versus frequency (from SDA) at normal incidence for an array of nanoshell trimers. The nanoshells are made of a dielectric core (glass-like filled with Rhodamine 800 fluorescent dyes modeled as in [20], with different dye concentrations) and gold shells whose permittivity is modeled using Palik data [22]. Array parameters: rcore=25, rshell=30, a=90, b=310, d=80 (in nanometer), and εh=2.25.

Fig. 8.
Fig. 8.

Robustness of the dipolar-like Fano resonance to representative geometrical perturbations, using SDA. Array parameters are as in Fig. 2(a) unless specified in the insets. Curve colors are matched to outline boxes of simulated clusters.

Equations (1)

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Qa=Caab=k[Im(αee1)+k36πε0εh]|E0|2ε0εhabcosθi=13|pi|2,

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