Delivered by Ingenta to: Chinese University of Hong Kong IP: 191.101.54.129 On: Wed, 15 Jun 2016 13:44:54 Copyright: American Scientific Publishers RESEARCH ARTICLE Copyright © 2013 American Scientific Publishers All rights reserved Printed in the United States of America Journal of Nanoscience and Nanotechnology Vol. 13, 6627–6634, 2013 Longitudinal Plasmon Modes of Ag Nanorod Coupled with a Pair of Quantum Dots Jiunn-Woei Liaw 1 2 , Chun-Hui Huang 3 , and Mao-Kuen Kuo 3 ∗ 1 Department of Mechanical Engineering, Chang Gung University, 259 Wen-Hwa 1st Road, Kwei-Shan, Tao-Yuan 333, Taiwan 2 Center for Biomedical Engineering, Chang Gung University, 259 Wen-Hwa 1st Road, Kwei-Shan, Tao-Yuan 333, Taiwan 3 Institute of Applied Mechanics, National Taiwan University, 1 Sec. 4, Roosevelt Rd., Taipei 106, Taiwan The longitudinal plasmon modes of an elongated Ag nanorod induced by an obliquely incident plane wave were analyzed theoretically. Our results show that the proximities at the two apexes of the nanorod are the hotspots at the dipole (m = 1), quadrupole (m = 2), sextupole (m = 3), octupole (m = 4), decapole (m = 5) and duodecapole (m = 6) modes. This phenomenon implies that a pair of quantum dots (QDs) located at these hotspots might be excited simultaneously through these plasmon modes. Consequently, the coherent spontaneous emission of the paired QDs could be induced through these modes. Furthermore, the coherent emission of the pair of excited QDs was studied, where these QDs were modeled as two electric dipoles (bi-dipole) oscillating with anti-symmetric or symmetric configurations. The radiative and nonradiative powers show that the maximum Purcell factors occur at these modes; the odd modes enhance the emission of the anti- symmetric configuration, and the even modes the symmetric one. However, only those bi-dipoles emitting at the lower-order (e.g., dipole, quadrupole and sextupole) modes of Ag nanorod are with high apparent quantum yields. In addition, the correlation of these plasmon modes of Ag nanorod with the dispersion relation of Ag nanowire was discussed. Keywords: Ag Nanorod, Purcell Factor, Longitudinal Plasmon Modes, Radiative Power, Nonradiative Power, Dipole Mode, Quadrupole Mode, Sextupole Mode, Octupole Mode, Decapole Mode. 1. INTRODUCTION The longitudinal plasmon modes of Au nanorod have been studied by using the extinction spectrum, 1 2 and the near- field two-photon-induced photoluminescence imaging. 3 4 Recently, the electric energy loss spectroscopy has been used to investigate these longitudinal plasmon modes of nanorods. 5–9 In addition, the dispersion relations of the sur- face plasmon polariton (SPP) along Au or Ag nanowire have been extensively investigated in the past decade. 10–14 Moreover, the Fabry-Perot resonator of Ag nanorod 15 and the nanoantenna effect through these longitudinal plasmon modes have also been studied recently. 16–18 The SPP prop- agating along Ag nanowire leading to the fan-out of pho- ton from the end of nanowire has been studied. 12 Recently, using quantum dot (QD) incorporated with Ag nanowire to form an exciton-plasmon-photon system has attracted wide attentions. 19–25 In particular, a strong coupling of an ∗ Author to whom correspondence should be addressed. emitter (e.g., excited QD) to the SPP of Ag nanowire through the nanotip has been investigated. 24 25 In addition, a pair of QDs coupling to a plasmonic nanostructure has been studied. 26 27 The Purcell effect has also proven to be significantly enhanced utilizing the plasmon modes of metallic nanostructure. 28–30 In this paper, the near-field and far-field optical responses of an elongated Ag nanorod illuminated by a plane wave will be studied to identify the longitudinal plasmon modes. The locally enhanced electric fields in the proximity of the apexes of Ag nanorod at the longitudinal plasmon modes will be studied to identify what role the Ag nanorod plays to assist the simultaneous excitation of a pair of QDs near the apexes. Moreover, the emission of the paired emitting QDs, located at the two ends of nanorod, will be further investigated, where these QDs are modeled as two electric dipoles (bi-dipole). Two types of config- uration of the dipole moment are concerned: the anti- symmetric and symmetric bi-dipoles. The radiative and nonradiative powers of both bi-dipoles under the influence J. Nanosci. Nanotechnol. 2013, Vol. 13, No. 10 1533-4880/2013/13/6627/008 doi:10.1166/jnn.2013.7561 6627