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A special lattice resonance can be observed when the array period of a metal nanoparticle array matches the resonant wavelength of the localized plasmon resonance of an isolated particle. The lattice resonance is sharper and its linewidth is narrower than the localized plasmonics resonance of a single particle. According to the modified long wavelength approximation approach, we discuss the extinction cross-section of the rectangular array in terms of the array factor and the particle polarizability. In this paper we emphasize the polarization characteristics of the regular array when the laser is incident vertically under different polarizations, and we also discuss in detail the variation of the array factor with the direction of electric dipole, and its influence on extinction cross section of the particle array. The square lattice with big size is polarization independent, while the rectangular lattice is polarization dependent. The coupling between the neighboring particle dipoles along the two lattice vectors of the regular array gives rise to a maximum value of its array factor, which determines a minimum value of the extinction cross section. When the incident light is polarized along one of the lattice vectors, the dipole coupling along that direction can be ignored since the particles are located in the far field of its neighboring particles, and the relevant peak in the array factor disappears.
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Keywords:
- scattering /
- plasmonics /
- nanoparticles
[1] Ekmel O 2006 Science 311 189
[2] Stefan A M, Harry A A 2005 J. Appl. Phys. 98 011101
[3] Katherine A W, Richard V D 2007 Annu. Rev. Phys. Chem. 58 267
[4] Xu D, Wang X Y, Huang Y G, Ouyang S L, He H L, He H 2015 Chin. Phys. B 24 024205
[5] Huang Q, Zhang X D, Zhang H, Xiong S Z, Geng W D, Geng X H, Zhao Y 2010 Chin. Phys. B 19 047304
[6] Guo Y N, Xue W R, Zhang W M 2009 Acta Phys. Sin. 58 4168 (in Chinese) [郭亚楠, 薛文瑞, 张文梅 2009 物理学报 58 4168]
[7] Stefan A M, Mark L B, Pieter G K, Sheffer M, Ari A G R, Harry A A 2001 Adv. Mater. 13 1501
[8] Huang Q, Xiong S Z, Zhao Y, Zhang X D 2012 Acta Phys. Sin. 61 157801 (in Chinese) [黄茜, 熊绍珍, 赵颖, 张晓丹 2012 物理学报 61 157801]
[9] Huang Q, Cao L R, Sun J, Zhang X D, Geng W D, Xiong S Z, Zhao Y, Wang J 2009 Acta Phys. Sin. 58 1980 (in Chinese) [黄茜, 曹丽冉, 孙建, 张晓丹, 耿卫东, 熊绍珍, 赵颖, 王京 2009 物理学报 58 1980]
[10] Eleonora P, Ulrich J K 2011 Anal. Chim. Acta 706 8
[11] Craig F B, Donald R H 1998 Absorption and Scattering of Light by Small Particles (New York: John Wiley & Sons) p136
[12] Alexander M 2009 JOSA B 26 517
[13] García de Abajo F J 2007 Rev. Mod. Phys. 79 1267
[14] Kravets V G, Schedin F, Grigorenko A N 2008 Phys. Rev. Lett. 22 087403
[15] Rodriguez S, Schaafsma M, Berrier A, Rivas J G 2012 Physica B 407 4081
[16] Väkeväinen A I, Moerland R J, Rekola H T, Eskelinen A P, Martikainen J P, Kim D H, Törmä P 2014 Nano Lett. 14 1721
[17] Palik E D 1985 Handbook of Optical Constants of Solids (New York: Academic Press) p275
[18] Hulst H C 1981 Light Scattering by Small Particles (New York: Dover Publications, Inc) p4
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[1] Ekmel O 2006 Science 311 189
[2] Stefan A M, Harry A A 2005 J. Appl. Phys. 98 011101
[3] Katherine A W, Richard V D 2007 Annu. Rev. Phys. Chem. 58 267
[4] Xu D, Wang X Y, Huang Y G, Ouyang S L, He H L, He H 2015 Chin. Phys. B 24 024205
[5] Huang Q, Zhang X D, Zhang H, Xiong S Z, Geng W D, Geng X H, Zhao Y 2010 Chin. Phys. B 19 047304
[6] Guo Y N, Xue W R, Zhang W M 2009 Acta Phys. Sin. 58 4168 (in Chinese) [郭亚楠, 薛文瑞, 张文梅 2009 物理学报 58 4168]
[7] Stefan A M, Mark L B, Pieter G K, Sheffer M, Ari A G R, Harry A A 2001 Adv. Mater. 13 1501
[8] Huang Q, Xiong S Z, Zhao Y, Zhang X D 2012 Acta Phys. Sin. 61 157801 (in Chinese) [黄茜, 熊绍珍, 赵颖, 张晓丹 2012 物理学报 61 157801]
[9] Huang Q, Cao L R, Sun J, Zhang X D, Geng W D, Xiong S Z, Zhao Y, Wang J 2009 Acta Phys. Sin. 58 1980 (in Chinese) [黄茜, 曹丽冉, 孙建, 张晓丹, 耿卫东, 熊绍珍, 赵颖, 王京 2009 物理学报 58 1980]
[10] Eleonora P, Ulrich J K 2011 Anal. Chim. Acta 706 8
[11] Craig F B, Donald R H 1998 Absorption and Scattering of Light by Small Particles (New York: John Wiley & Sons) p136
[12] Alexander M 2009 JOSA B 26 517
[13] García de Abajo F J 2007 Rev. Mod. Phys. 79 1267
[14] Kravets V G, Schedin F, Grigorenko A N 2008 Phys. Rev. Lett. 22 087403
[15] Rodriguez S, Schaafsma M, Berrier A, Rivas J G 2012 Physica B 407 4081
[16] Väkeväinen A I, Moerland R J, Rekola H T, Eskelinen A P, Martikainen J P, Kim D H, Törmä P 2014 Nano Lett. 14 1721
[17] Palik E D 1985 Handbook of Optical Constants of Solids (New York: Academic Press) p275
[18] Hulst H C 1981 Light Scattering by Small Particles (New York: Dover Publications, Inc) p4
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