Abstract

Metallic hexamer, very much the plasmonic analog of benzene molecule, provides an ideal platform to mimic modes coupling and hybridization in molecular systems. To demonstrate this, we present a detailed study on radial breathing mode (RBM) coupling in a plasmonic dual-hexamers. We excite RBMs of hexamers by symmetrically matching the polarization state of the illumination with the distribution of electric dipole moments of the dual-hexamer. It is found that the RBM coupling exhibits a nonexponential decay when the inter-hexamer separation is increased, owing to the dark mode nature of RBM. When the outer hexamer is subjected to the in-plane twisting, resonant wavelengths of two coupled RBMs as well as the coupling constant show cosine variations with the twist angle, indicating the symmetry of hexamer structure plays a critical role in the coupling of RBMs. Moreover, it is demonstrated that the coupling of RBMs is dominated by the in-plane interaction as the outer hexamer is under an out-of-plane tilting, causing convergence of resonant wavelengths of the two coupled RBMs with increasing tilt angle. Our results not only provide an insight into the plasmonic RBM coupling mechanism, but also pave the way to systematically control the spectral response of plasmonic molecules.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (3)

2017 (3)

A. Campos, A. Arbouet, J. Martin, D. Gerard, J. Proust, J. Plain, and M. Kociak, “Plasmonic Breathing and Edge Modes in Aluminum Nanotriangles,” ACS Photonics 4(5), 1257–1263 (2017).
[Crossref]

M. Premaratne and M. I. Stockman, “Theory and technology of SPASERs,” Adv. Opt. Photonics 9(1), 79–128 (2017).
[Crossref]

C. Yi, P. D. Dongare, M. N. Su, W. Wang, D. Chakraborty, F. Wen, W. S. Chang, J. E. Sader, P. Nordlander, N. J. Halas, and S. Link, “Vibrational coupling in plasmonic molecules,” Proc. Natl. Acad. Sci. U.S.A. 114(44), 11621–11626 (2017).
[Crossref] [PubMed]

2016 (1)

S. D. Liu, E. S. P. Leong, G. C. Li, Y. Hou, J. Deng, J. H. Teng, H. C. Ong, and D. Y. Lei, “Polarization-Independent Multiple Fano Resonances in Plasmonic Nonamers for Multimode-Matching Enhanced Multiband Second-Harmonic Generation,” ACS Nano 10(1), 1442–1453 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (3)

F. Xiao, W. Zhu, M. Premaratne, and J. Zhao, “Controlling Fano resonance of ring/crescent-ring plasmonic nanostructure with Bessel beam,” Opt. Express 22(2), 2132–2140 (2014).
[Crossref] [PubMed]

A. Yanai, M. Grajower, G. M. Lerman, M. Hentschel, H. Giessen, and U. Levy, “Near- and far-field properties of plasmonic oligomers under radially and azimuthally polarized light excitation,” ACS Nano 8(5), 4969–4974 (2014).
[Crossref] [PubMed]

S. Panaro, A. Nazir, C. Liberale, G. Das, H. Wang, F. De Angelis, R. Proietti Zaccaria, E. Di Fabrizio, and A. Toma, “Dark to Bright Mode Conversion on Dipolar Nanoantennas: A Symmetry-Breaking Approach,” ACS Photonics 1(4), 310–314 (2014).
[Crossref]

2013 (6)

K. Liu, X. Hong, M. Wu, F. Xiao, W. Wang, X. Bai, J. W. Ager, S. Aloni, A. Zettl, E. Wang, and F. Wang, “Quantum-coupled radial-breathing oscillations in double-walled carbon nanotubes,” Nat. Commun. 4(1), 1375 (2013).
[Crossref] [PubMed]

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of Fano Resonances in Coupled Plasmonic Systems,” ACS Nano 7(5), 4527–4536 (2013).
[Crossref] [PubMed]

X. Zhang, Y. L. Chen, R. S. Liu, and D. P. Tsai, “Plasmonic photocatalysis,” Rep. Prog. Phys. 76(4), 046401 (2013).
[Crossref] [PubMed]

F. Shafiei, F. Monticone, K. Q. Le, X. X. Liu, T. Hartsfield, A. Alù, and X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nat. Nanotechnol. 8(2), 95–99 (2013).
[Crossref] [PubMed]

P. Ginzburg and A. V. Zayats, “Linewidth enhancement in spasers and plasmonic nanolasers,” Opt. Express 21(2), 2147–2153 (2013).
[Crossref] [PubMed]

S. Jäger, A. M. Kern, M. Hentschel, R. Jäger, K. Braun, D. Zhang, H. Giessen, and A. J. Meixner, “Au Nanotip as Luminescent Near-Field Probe,” Nano Lett. 13(8), 3566–3570 (2013).
[Crossref] [PubMed]

2012 (6)

R. P. Zaccaria, F. De Angelis, A. Toma, L. Razzari, A. Alabastri, G. Das, C. Liberale, and E. Di Fabrizio, “Surface plasmon polariton compression through radially and linearly polarized source,” Opt. Lett. 37(4), 545–547 (2012).
[Crossref] [PubMed]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2012).
[Crossref] [PubMed]

A. Polman and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11(3), 174–177 (2012).
[Crossref] [PubMed]

N. Liu, S. Mukherjee, K. Bao, Y. Li, L. V. Brown, P. Nordlander, and N. J. Halas, “Manipulating magnetic plasmon propagation in metallic nanocluster networks,” ACS Nano 6(6), 5482–5488 (2012).
[Crossref] [PubMed]

J. Ye, F. Wen, H. Sobhani, J. B. Lassiter, P. Van Dorpe, P. Nordlander, and N. J. Halas, “Plasmonic Nanoclusters: Near Field Properties of the Fano Resonance Interrogated with SERS,” Nano Lett. 12(3), 1660–1667 (2012).
[Crossref] [PubMed]

F. P. Schmidt, H. Ditlbacher, U. Hohenester, A. Hohenau, F. Hofer, and J. R. Krenn, “Dark plasmonic breathing modes in silver nanodisks,” Nano Lett. 12(11), 5780–5783 (2012).
[Crossref] [PubMed]

2011 (1)

L. Chuntonov and G. Haran, “Trimeric Plasmonic Molecules: The Role of Symmetry,” Nano Lett. 11(6), 2440–2445 (2011).
[Crossref] [PubMed]

2010 (4)

D. E. Gómez, K. C. Vernon, and T. J. Davis, “Symmetry effects on the optical coupling between plasmonic nanoparticles with applications to hierarchical structures,” Phys. Rev. B Condens. Matter Mater. Phys. 81(7), 075414 (2010).
[Crossref]

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano Resonances in Plasmonic Nanoclusters: Geometrical and Chemical Tunability,” Nano Lett. 10(8), 3184–3189 (2010).
[Crossref] [PubMed]

J. Nelayah, M. Kociak, O. Stéphan, N. Geuquet, L. Henrard, F. J. García de Abajo, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Two-Dimensional Quasistatic Stationary Short Range Surface Plasmons in Flat Nanoprisms,” Nano Lett. 10(3), 902–907 (2010).
[Crossref] [PubMed]

M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett. 10(7), 2721–2726 (2010).
[Crossref] [PubMed]

2009 (4)

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref] [PubMed]

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano Resonances in Individual Coherent Plasmonic Nanocavities,” Nano Lett. 9(4), 1663–1667 (2009).
[Crossref] [PubMed]

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
[Crossref]

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

2008 (5)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[Crossref]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-Induced Transparency in Metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

F. Hao, E. M. K. Larsson, T. A. Ali, D. S. Sutherland, and P. Nordlander, “Shedding light on dark plasmons in gold nanorings,” Chem. Phys. Lett. 458(4-6), 262–266 (2008).
[Crossref]

H. Lesnard, N. Lorente, and M. L. Bocquet, “Theoretical study of benzene and pyridine STM-induced reactions on copper surfaces,” J. Phys. Condens. Matter 20(22), 224012 (2008).
[Crossref]

2005 (1)

M. S. Dresselhaus, G. Dresselhaus, R. Saito, and A. Jorio, “Raman spectroscopy of carbon nanotubes,” Phys. Rep. 409(2), 47–99 (2005).
[Crossref]

2003 (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

2000 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B Condens. Matter Mater. Phys. 6(12), 4370–4379 (1972).
[Crossref]

Adato, R.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2012).
[Crossref] [PubMed]

Ager, J. W.

K. Liu, X. Hong, M. Wu, F. Xiao, W. Wang, X. Bai, J. W. Ager, S. Aloni, A. Zettl, E. Wang, and F. Wang, “Quantum-coupled radial-breathing oscillations in double-walled carbon nanotubes,” Nat. Commun. 4(1), 1375 (2013).
[Crossref] [PubMed]

Alabastri, A.

Ali, T. A.

F. Hao, E. M. K. Larsson, T. A. Ali, D. S. Sutherland, and P. Nordlander, “Shedding light on dark plasmons in gold nanorings,” Chem. Phys. Lett. 458(4-6), 262–266 (2008).
[Crossref]

Alivisatos, A. P.

M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett. 10(7), 2721–2726 (2010).
[Crossref] [PubMed]

Aloni, S.

K. Liu, X. Hong, M. Wu, F. Xiao, W. Wang, X. Bai, J. W. Ager, S. Aloni, A. Zettl, E. Wang, and F. Wang, “Quantum-coupled radial-breathing oscillations in double-walled carbon nanotubes,” Nat. Commun. 4(1), 1375 (2013).
[Crossref] [PubMed]

Altug, H.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2012).
[Crossref] [PubMed]

Alù, A.

F. Shafiei, F. Monticone, K. Q. Le, X. X. Liu, T. Hartsfield, A. Alù, and X. Li, “A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance,” Nat. Nanotechnol. 8(2), 95–99 (2013).
[Crossref] [PubMed]

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref] [PubMed]

Arbouet, A.

A. Campos, A. Arbouet, J. Martin, D. Gerard, J. Proust, J. Plain, and M. Kociak, “Plasmonic Breathing and Edge Modes in Aluminum Nanotriangles,” ACS Photonics 4(5), 1257–1263 (2017).
[Crossref]

Arju, N.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2012).
[Crossref] [PubMed]

Atwater, H. A.

A. Polman and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11(3), 174–177 (2012).
[Crossref] [PubMed]

Bai, X.

K. Liu, X. Hong, M. Wu, F. Xiao, W. Wang, X. Bai, J. W. Ager, S. Aloni, A. Zettl, E. Wang, and F. Wang, “Quantum-coupled radial-breathing oscillations in double-walled carbon nanotubes,” Nat. Commun. 4(1), 1375 (2013).
[Crossref] [PubMed]

Bao, K.

N. Liu, S. Mukherjee, K. Bao, Y. Li, L. V. Brown, P. Nordlander, and N. J. Halas, “Manipulating magnetic plasmon propagation in metallic nanocluster networks,” ACS Nano 6(6), 5482–5488 (2012).
[Crossref] [PubMed]

Bocquet, M. L.

H. Lesnard, N. Lorente, and M. L. Bocquet, “Theoretical study of benzene and pyridine STM-induced reactions on copper surfaces,” J. Phys. Condens. Matter 20(22), 224012 (2008).
[Crossref]

Braun, K.

S. Jäger, A. M. Kern, M. Hentschel, R. Jäger, K. Braun, D. Zhang, H. Giessen, and A. J. Meixner, “Au Nanotip as Luminescent Near-Field Probe,” Nano Lett. 13(8), 3566–3570 (2013).
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Brown, L. V.

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[Crossref] [PubMed]

A. Campos, A. Arbouet, J. Martin, D. Gerard, J. Proust, J. Plain, and M. Kociak, “Plasmonic Breathing and Edge Modes in Aluminum Nanotriangles,” ACS Photonics 4(5), 1257–1263 (2017).
[Crossref]

J. Nelayah, M. Kociak, O. Stéphan, N. Geuquet, L. Henrard, F. J. García de Abajo, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Two-Dimensional Quasistatic Stationary Short Range Surface Plasmons in Flat Nanoprisms,” Nano Lett. 10(3), 902–907 (2010).
[Crossref] [PubMed]

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F. P. Schmidt, A. Losquin, F. Hofer, A. Hohenau, J. R. Krenn, and M. Kociak, “How Dark Are Radial Breathing Modes in Plasmonic Nanodisks?” ACS Photonics 5(3), 861–866 (2018).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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F. Hao, E. M. K. Larsson, T. A. Ali, D. S. Sutherland, and P. Nordlander, “Shedding light on dark plasmons in gold nanorings,” Chem. Phys. Lett. 458(4-6), 262–266 (2008).
[Crossref]

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J. Ye, F. Wen, H. Sobhani, J. B. Lassiter, P. Van Dorpe, P. Nordlander, and N. J. Halas, “Plasmonic Nanoclusters: Near Field Properties of the Fano Resonance Interrogated with SERS,” Nano Lett. 12(3), 1660–1667 (2012).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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A. Yanai, M. Grajower, G. M. Lerman, M. Hentschel, H. Giessen, and U. Levy, “Near- and far-field properties of plasmonic oligomers under radially and azimuthally polarized light excitation,” ACS Nano 8(5), 4969–4974 (2014).
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[Crossref] [PubMed]

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N. Liu, S. Mukherjee, K. Bao, Y. Li, L. V. Brown, P. Nordlander, and N. J. Halas, “Manipulating magnetic plasmon propagation in metallic nanocluster networks,” ACS Nano 6(6), 5482–5488 (2012).
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S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-Induced Transparency in Metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
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A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of Fano Resonances in Coupled Plasmonic Systems,” ACS Nano 7(5), 4527–4536 (2013).
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S. Panaro, A. Nazir, C. Liberale, G. Das, H. Wang, F. De Angelis, R. Proietti Zaccaria, E. Di Fabrizio, and A. Toma, “Dark to Bright Mode Conversion on Dipolar Nanoantennas: A Symmetry-Breaking Approach,” ACS Photonics 1(4), 310–314 (2014).
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N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
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A. Campos, A. Arbouet, J. Martin, D. Gerard, J. Proust, J. Plain, and M. Kociak, “Plasmonic Breathing and Edge Modes in Aluminum Nanotriangles,” ACS Photonics 4(5), 1257–1263 (2017).
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S. Panaro, A. Nazir, C. Liberale, G. Das, H. Wang, F. De Angelis, R. Proietti Zaccaria, E. Di Fabrizio, and A. Toma, “Dark to Bright Mode Conversion on Dipolar Nanoantennas: A Symmetry-Breaking Approach,” ACS Photonics 1(4), 310–314 (2014).
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E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
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Ren, Y.

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F. P. Schmidt, A. Losquin, F. Hofer, A. Hohenau, J. R. Krenn, and M. Kociak, “How Dark Are Radial Breathing Modes in Plasmonic Nanodisks?” ACS Photonics 5(3), 861–866 (2018).
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[Crossref] [PubMed]

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J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
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Shvets, G.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2012).
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J. Ye, F. Wen, H. Sobhani, J. B. Lassiter, P. Van Dorpe, P. Nordlander, and N. J. Halas, “Plasmonic Nanoclusters: Near Field Properties of the Fano Resonance Interrogated with SERS,” Nano Lett. 12(3), 1660–1667 (2012).
[Crossref] [PubMed]

J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano Resonances in Plasmonic Nanoclusters: Geometrical and Chemical Tunability,” Nano Lett. 10(8), 3184–3189 (2010).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano Resonances in Individual Coherent Plasmonic Nanocavities,” Nano Lett. 9(4), 1663–1667 (2009).
[Crossref] [PubMed]

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J. Nelayah, M. Kociak, O. Stéphan, N. Geuquet, L. Henrard, F. J. García de Abajo, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Two-Dimensional Quasistatic Stationary Short Range Surface Plasmons in Flat Nanoprisms,” Nano Lett. 10(3), 902–907 (2010).
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F. Hao, E. M. K. Larsson, T. A. Ali, D. S. Sutherland, and P. Nordlander, “Shedding light on dark plasmons in gold nanorings,” Chem. Phys. Lett. 458(4-6), 262–266 (2008).
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S. D. Liu, E. S. P. Leong, G. C. Li, Y. Hou, J. Deng, J. H. Teng, H. C. Ong, and D. Y. Lei, “Polarization-Independent Multiple Fano Resonances in Plasmonic Nonamers for Multimode-Matching Enhanced Multiband Second-Harmonic Generation,” ACS Nano 10(1), 1442–1453 (2016).
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S. Panaro, A. Nazir, C. Liberale, G. Das, H. Wang, F. De Angelis, R. Proietti Zaccaria, E. Di Fabrizio, and A. Toma, “Dark to Bright Mode Conversion on Dipolar Nanoantennas: A Symmetry-Breaking Approach,” ACS Photonics 1(4), 310–314 (2014).
[Crossref]

R. P. Zaccaria, F. De Angelis, A. Toma, L. Razzari, A. Alabastri, G. Das, C. Liberale, and E. Di Fabrizio, “Surface plasmon polariton compression through radially and linearly polarized source,” Opt. Lett. 37(4), 545–547 (2012).
[Crossref] [PubMed]

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X. Zhang, Y. L. Chen, R. S. Liu, and D. P. Tsai, “Plasmonic photocatalysis,” Rep. Prog. Phys. 76(4), 046401 (2013).
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J. Ye, F. Wen, H. Sobhani, J. B. Lassiter, P. Van Dorpe, P. Nordlander, and N. J. Halas, “Plasmonic Nanoclusters: Near Field Properties of the Fano Resonance Interrogated with SERS,” Nano Lett. 12(3), 1660–1667 (2012).
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J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
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K. Liu, X. Hong, M. Wu, F. Xiao, W. Wang, X. Bai, J. W. Ager, S. Aloni, A. Zettl, E. Wang, and F. Wang, “Quantum-coupled radial-breathing oscillations in double-walled carbon nanotubes,” Nat. Commun. 4(1), 1375 (2013).
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K. Liu, X. Hong, M. Wu, F. Xiao, W. Wang, X. Bai, J. W. Ager, S. Aloni, A. Zettl, E. Wang, and F. Wang, “Quantum-coupled radial-breathing oscillations in double-walled carbon nanotubes,” Nat. Commun. 4(1), 1375 (2013).
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S. Panaro, A. Nazir, C. Liberale, G. Das, H. Wang, F. De Angelis, R. Proietti Zaccaria, E. Di Fabrizio, and A. Toma, “Dark to Bright Mode Conversion on Dipolar Nanoantennas: A Symmetry-Breaking Approach,” ACS Photonics 1(4), 310–314 (2014).
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C. Yi, P. D. Dongare, M. N. Su, W. Wang, D. Chakraborty, F. Wen, W. S. Chang, J. E. Sader, P. Nordlander, N. J. Halas, and S. Link, “Vibrational coupling in plasmonic molecules,” Proc. Natl. Acad. Sci. U.S.A. 114(44), 11621–11626 (2017).
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K. Liu, X. Hong, M. Wu, F. Xiao, W. Wang, X. Bai, J. W. Ager, S. Aloni, A. Zettl, E. Wang, and F. Wang, “Quantum-coupled radial-breathing oscillations in double-walled carbon nanotubes,” Nat. Commun. 4(1), 1375 (2013).
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S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-Induced Transparency in Metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
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N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
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C. Yi, P. D. Dongare, M. N. Su, W. Wang, D. Chakraborty, F. Wen, W. S. Chang, J. E. Sader, P. Nordlander, N. J. Halas, and S. Link, “Vibrational coupling in plasmonic molecules,” Proc. Natl. Acad. Sci. U.S.A. 114(44), 11621–11626 (2017).
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C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2012).
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K. Liu, X. Hong, M. Wu, F. Xiao, W. Wang, X. Bai, J. W. Ager, S. Aloni, A. Zettl, E. Wang, and F. Wang, “Quantum-coupled radial-breathing oscillations in double-walled carbon nanotubes,” Nat. Commun. 4(1), 1375 (2013).
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J. Ye, F. Wen, H. Sobhani, J. B. Lassiter, P. Van Dorpe, P. Nordlander, and N. J. Halas, “Plasmonic Nanoclusters: Near Field Properties of the Fano Resonance Interrogated with SERS,” Nano Lett. 12(3), 1660–1667 (2012).
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Figures (6)

Fig. 1
Fig. 1 (a) Schematic view of a plasmonic dual-hexamers structure. (b) Excitations of plasmonic radial breathing mode (RBM) with a tightly focused radially polarized beam. (c) Intensity distribution of the radially polarized beam at the top surface of hexamers, where the white arrows indicate the polarization states of beam.
Fig. 2
Fig. 2 (a) Scattering spectrum of inner hexamer. (b) Charge plot and (c) Electric field enhancement map of inner hexamer at wavelength of 690 nm. (d) Radiation pattern of the plasmonic RBM.
Fig. 3
Fig. 3 (a) Scattering spectrum of dual-hexamers with L1 = 400 nm and L2 = 620 nm, where red dots and the black solid line are simulation and fitting results, respectively. (b,c) Charge plots and (d,e) Electric field enhancement maps of coupled RBMs1 (b,d) and RBMs2 (c,e) in the dual-hexamers. (f) Charge distributions along the horizontal lines as labeled in (b) and (c). (g) Electric field enhancement along the horizontal lines as labeled in (d) and (e). The black and red solid lines in (f,g) are for coupled RBMs1 and RBMs2, respectively.
Fig. 4
Fig. 4 (a) Scattering spectra of dual-hexamer as a dependence of the gap between inner and outer hexamers. (b) Resonant wavelengths of RBMs as a function of the gap size, where red triangles represent the resonant wavelengths of coupled RBMs 1 (λ1) and coupled RBMs 2 (λ2), and black dashed lines are the intrinsic resonant wavelengths of individual inner (λ10) and outer hexamers (λ20). (c) Coupling constant between inner and outer RBMs versus the gap size, where the red dots and black solid line are theoretical results and the guide of the exponential decay, respectively.
Fig. 5
Fig. 5 (a) Schematics of in-plane twist of the dual hexamer with geometry parameters L1 = 400 nm and L2 = 620 nm. (b) Scattering spectra of dual-hexamer as a dependence of twist angle. Resonant wavelengths of (c) coupled RBMs 1, (d) coupled RBMs 2 and (e) coupling constant as a function of the twist angle, where the red dots are theoretical results and the black solid lines are guides to show cosine curves.
Fig. 6
Fig. 6 (a) Schematics of out-of-plane tilt of the dual hexamer with geometry parameters L1 = 400 nm and L2 = 620 nm. (b) Scattering spectra of dual-hexamer as a dependence of tilt angle. (c) Resonant wavelengths of RBMs as a function of the tilt angle, where red triangles represent the resonance wavelengths of coupled RBMs 1 (λ1) and coupled RBMs 2 (λ2), and black dashed lines are the intrinsic resonance wavelengths of individual inner (λ10) and tilted outer hexamers (λ20). (d) Coupling constant as a function of tilt angle, where the red dots are theoretical results and the black solid line is a guide to show the cosine trend.

Equations (3)

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P( θ )=exp[ β 2 ( sinθ sinα ) 2 ] J 1 ( 2βsinθ sinα ),
E r = A 0 0 α P( θ ) cos 1/2 θsin( 2θ ) J 1 ( krsinθ )exp( ikzcosθ )dθ E z =2i A 0 0 α P( θ ) cos 1/2 θ sin 2 θ J 0 ( krsinθ )exp( ikzcosθ )dθ .
d 2 x 1 d t 2 + γ 1 d x 1 dt + ω 1 2 x 1 +g x 2 = 1 2 ( η 1 d 3 x 1 d t 3 + η 2 d 3 x 2 d t 3 )+ η 1 E d 2 x 2 d t 2 + γ 2 d x 2 dt + ω 2 2 x 2 +g x 1 = 1 2 ( η 1 d 3 x 1 d t 3 + η 2 d 3 x 2 d t 3 )+ η 2 E .