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The localized surface plasmon resonance can be generated on the surface of the nano-metamaterial by the interaction between the nano-metamaterial and the light field, and also many plasmon oscillation modes can occur in the process of the hybridization between many infinitesimal composite structures, which is widely used for adjusting the resonant frequency in the optical frequency domain. Recently, analogue of the electromagnetically induced transparency（EIT) has been realized in the low-loss nano-metamaterial, and is well known as the plasmon induced transparency（PIT). In atomic physics, EIT is an effect which originates from the destructive quantum interference of two different excitation pathways. A sharp dip of nearly ideal transmission can arise within the broad absorption profile, which indicates that the EIT can be used in the fields of slow slight, delay lines and low-loss metamaterial. In this paper, a trimer consisting of a vertical nanorod（serving as a dipole antenna) and two parallel nanorods（used as a quadrupole antenna) is employed to investigate the process mechanism of the PIT in detail. It is found that the vertical nanorod with a large broad linewidth can be strongly coupled with the light. However, the parallel nanorods are weakly coupled with the light and their narrow linewidths are almost from the intrinsic metal loss（Drude damping) that is much smaller than the radiative damping of the dipole antenna. These two antennas can be strongly coupled due to their close similarities. Moreover, the absorption spectra of the trimer obtained by using three-dimensional finite element method vary with its coupling distance and geometry size, and the dipole bright mode corresponding to the dipole antenna splits under the action of the dark mode for the quadrupole antenna. Thus, a fresh physical interpretation is given:the PIT is mainly due to the coherent superposition after the splitting of the dipole oscillation mode in the vertical nanorod, rather than the parallel nanorods. Taking into consideration the phase correlation associated with coupling process of two oscillators, we introduce a modified Lorentzian oscillator model to investigate the effects of the coupling phase factor on the modulation of the absorption spectra and the coherent superposition between the splitting bright modes on the PIT. These findings will provide theoretical references for the applications of artificial atom, optical switching and slow light devices designed in the nanosize range.
[1] Brongersma M L, Kik P G 2007 Surface Plasmon Nanophotonics (Berlin:Springer)
[2] Pacifici D, Lezec H J, Atwater H A 2007 Nat. Photon. 1 402
[3] Linden S, Enkrich C, Wegener M, Zhou J, Koschny T, Soukoulis C M 2004 Science 306 1351
[4] Zhang S, Fan W, Panoiu N C, Malloy K J, Osgood R M, Brueck S R J 2005 Phys. Rev. Lett. 95 137404
[5] Ha T, Enderle T, Ogletree D F, Chemla D S, Selvin P R, Weiss S 1996 Proc. Natl. Acad. Sci. U S A 93 6264
[6] Nie S, Emory S R 1997 Science 275 1102
[7] Butet J, Martin O J F 2014 Opt. Express 22 29693
[8] Butet J, Dutta-Gupta S, Martin O J F 2014 Phys. Rev. B 89 245449
[9] Thyagarajan K, Butet J, Martin O J F 2013 Nano Lett. 13 1847
[10] Li J, Liu T, Zheng H, Dong J, He E, Gao W, Wu Y 2014 Plasmonics 9 1439
[11] Hao F, Sonnefraud Y, Dorpe P V, Maier S A, Halas N J, Nordlander P 2008 Nano Lett. 8 3983
[12] Jain P K, Huang X, El-Sayed I H, El-Sayed M A 2007 Plasmonics 2 107
[13] Dong Z G, Liu H, Cao J X, Li T, Wang S M, Zhu S N, Zhang X 2010 Appl. Phys. Lett. 97 114101
[14] Liu N, Weiss T, Mesch M, Langguth L, Eigenthaler U, Hirscher M, Giessen H 2009 Opt. Express 17 15372
[15] Artar A, Yanik A A, Altug H 2011 Nano Lett. 11 1685
[16] Sadeghi S M, Deng L, Li X, Huang W P 2009 Nanotechnology 20 365401
[17] Wang W, Li Y, Xu P, Chen Z, Chen J, Qian J, Xu J 2014 J. Opt. 16 125013
[18] Chen J, Wang P, Chen C, Lu Y, Ming H, Zhan Q 2011 Opt. Express 19 5970
[19] Harris S E 2008 Phys. Today 50 36
[20] Ham B S, Shahriar M S, Hemmer P R 1997 Opt. Lett. 22 1138
[21] Phillips M, Wang H 2002 Phys. Rev. Lett. 89 186401
[22] Maleki L, Matsko A B, Savchenkov A A, Ilchenko V S 2004 Opt. Lett. 29 626
[23] Ham B S, Hahn J 2009 Appl. Phys. Lett. 94 101110
[24] Gan Q, Fu Z, Ding Y J, Bartoli F J 2008 Phys. Rev. Lett 100 256803
[25] Wang G, Lu H, Liu X 2012 Appl. Phys. Lett. 101 013111
[26] Wei H, Wang Z, Tian X, Käll M, Xu H 2011 Nat. Commun. 2 387
[27] Totsuka K, Kobayashi N, Tomita M 2007 Phys. Rev. Lett. 98 213904
[28] Xu H, Ham B S 2008 Phys. Rev. Lett. 101 047401
[29] Johnson P B, Christy R W 1972 Phys. Rev. B 6 4370
[30] Liu T, Li J, Gao F, Han Q, Liu S 2013 Europhys. Lett. 104 47009
[31] Mhlschlegel P, Eisler H J, Martin O J F, Hecht, Pohl D W 2005 Science 308 1607
[32] Xu H, Lu Y, Lee Y, Ham B S 2010 Opt. Express 18 17736
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[1] Brongersma M L, Kik P G 2007 Surface Plasmon Nanophotonics (Berlin:Springer)
[2] Pacifici D, Lezec H J, Atwater H A 2007 Nat. Photon. 1 402
[3] Linden S, Enkrich C, Wegener M, Zhou J, Koschny T, Soukoulis C M 2004 Science 306 1351
[4] Zhang S, Fan W, Panoiu N C, Malloy K J, Osgood R M, Brueck S R J 2005 Phys. Rev. Lett. 95 137404
[5] Ha T, Enderle T, Ogletree D F, Chemla D S, Selvin P R, Weiss S 1996 Proc. Natl. Acad. Sci. U S A 93 6264
[6] Nie S, Emory S R 1997 Science 275 1102
[7] Butet J, Martin O J F 2014 Opt. Express 22 29693
[8] Butet J, Dutta-Gupta S, Martin O J F 2014 Phys. Rev. B 89 245449
[9] Thyagarajan K, Butet J, Martin O J F 2013 Nano Lett. 13 1847
[10] Li J, Liu T, Zheng H, Dong J, He E, Gao W, Wu Y 2014 Plasmonics 9 1439
[11] Hao F, Sonnefraud Y, Dorpe P V, Maier S A, Halas N J, Nordlander P 2008 Nano Lett. 8 3983
[12] Jain P K, Huang X, El-Sayed I H, El-Sayed M A 2007 Plasmonics 2 107
[13] Dong Z G, Liu H, Cao J X, Li T, Wang S M, Zhu S N, Zhang X 2010 Appl. Phys. Lett. 97 114101
[14] Liu N, Weiss T, Mesch M, Langguth L, Eigenthaler U, Hirscher M, Giessen H 2009 Opt. Express 17 15372
[15] Artar A, Yanik A A, Altug H 2011 Nano Lett. 11 1685
[16] Sadeghi S M, Deng L, Li X, Huang W P 2009 Nanotechnology 20 365401
[17] Wang W, Li Y, Xu P, Chen Z, Chen J, Qian J, Xu J 2014 J. Opt. 16 125013
[18] Chen J, Wang P, Chen C, Lu Y, Ming H, Zhan Q 2011 Opt. Express 19 5970
[19] Harris S E 2008 Phys. Today 50 36
[20] Ham B S, Shahriar M S, Hemmer P R 1997 Opt. Lett. 22 1138
[21] Phillips M, Wang H 2002 Phys. Rev. Lett. 89 186401
[22] Maleki L, Matsko A B, Savchenkov A A, Ilchenko V S 2004 Opt. Lett. 29 626
[23] Ham B S, Hahn J 2009 Appl. Phys. Lett. 94 101110
[24] Gan Q, Fu Z, Ding Y J, Bartoli F J 2008 Phys. Rev. Lett 100 256803
[25] Wang G, Lu H, Liu X 2012 Appl. Phys. Lett. 101 013111
[26] Wei H, Wang Z, Tian X, Käll M, Xu H 2011 Nat. Commun. 2 387
[27] Totsuka K, Kobayashi N, Tomita M 2007 Phys. Rev. Lett. 98 213904
[28] Xu H, Ham B S 2008 Phys. Rev. Lett. 101 047401
[29] Johnson P B, Christy R W 1972 Phys. Rev. B 6 4370
[30] Liu T, Li J, Gao F, Han Q, Liu S 2013 Europhys. Lett. 104 47009
[31] Mhlschlegel P, Eisler H J, Martin O J F, Hecht, Pohl D W 2005 Science 308 1607
[32] Xu H, Lu Y, Lee Y, Ham B S 2010 Opt. Express 18 17736
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