Strong anisotropic lifetime orientation distributions of a twolevel quantum emitter around a plasmonic nanorod
 JiaMing Liu^{1},
 JingFeng Liu^{2},
 YiCong Yu^{3},
 LingYu Zeng^{1} and
 XueHua Wang^{1}Email author
DOI: 10.1186/1556276X9194
© Liu et al.; licensee Springer. 2014
Received: 14 March 2014
Accepted: 17 April 2014
Published: 28 April 2014
Abstract
Spontaneous emission lifetime orientation distributions of a twolevel quantum emitter in metallic nanorod structures are theoretically investigated by the rigorous electromagnetic Green function method. It was found that spontaneous emission lifetime strongly depended on the transition dipole orientation and the position of the emitter. The anisotropic factor defined as the ratio between the maximum and minimum values of the lifetimes along different dipole orientations can reach up to 10^{3}. It is much larger than those in dielectric structures which are only several times usually. Our results show that the localized plasmonic resonance effect provides a new degree of freedom to effectively control spontaneous emission by the dipole orientation of the quantum emitters.
PACS: 78.67.Qa; 73.20.Mf; 42.50.p
Keywords
Surface plasmons Spontaneous emission Lifetime distribution NanorodBackground
Spontaneous emission (SE) control of quantum emitters (QEs) is of great importance in basic quantum optics researches and new type of quantum information devices design due to its diverse range of applications such as solar energy harvesting [1, 2], lightemitting diodes [3, 4], miniature lasers [5, 6], and singlephoton source for quantum information science [7, 8].
It is well known that, the spontaneous emission lifetime of QEs can be strongly modulated by the surrounding environment. So, various photonic systems, such as microcavities [9, 10] and photonic crystals [11–13], have been proposed to manipulate the lifetime of QEs. Recently, metallic nanostructures have attracted extensive of interest as they support surface plasmonic resonances, which are the collective oscillations of the electron gas in metals [14, 15]. Surface plasmons may greatly enhance the local electromagnetic field that leads to nanoscale ‘hot spots’ [16, 17]. Such local enhancement capability enables the quantum control of the SE process at nanoscale [18–23]. An important advantage of controlling SE of QEs is its wide range of application. In [24], the SE enhancement of a single quantum dot coupled to silver nanowire was successfully measured. Such measurements proved that the SE exhibits antibunching. This means that plasmonic nanowires can provide singlephoton sources, as has been demonstrated in [25] by using NV centers. Besides, alternative plasmonic systems have been presented to manipulate SE enhancement, such as hybrid waveguide [26] and plasmonic resonators [27]. Moreover, the efficient coupling between single emitter and the propagating plasmonic modes enables the realization of single photon transistor devices [28, 29]. However, the investigation of SE control with different transition dipole orientations of a QE is still a challenging task. To date, no clear picture has emerged of the orientationdependent characteristics around the metallic particles but it is of great importance in the research of interaction between light and matter [30].
In this paper, we investigate the SE lifetime of a twolevel QE with different dipole moment orientations around a plasmonic nanorod. Using the Finite Element Method, we calculate the SE lifetime, anisotropic factor and find that the SE lifetime has strongly orientation dependent character which is different from the structures reported before in photonic crystals and dielectric sphere structures [11, 31, 32].
Methods
where $\overrightarrow{\mathit{d}}\left(\overrightarrow{\mathit{r}},\mathit{\omega}\right)=\overrightarrow{\mathit{d}}\left(\mathit{\omega}\right)\mathit{\delta}\left(\overrightarrow{\mathit{r}}{\overrightarrow{\mathit{r}}}_{0}\right)$ is a dipole source at position ${\overrightarrow{\mathit{r}}}_{0}$. The whole elements of the Green tensor could be attained after setting the dipole source with x, y, and z polarizations in turn.
Results and discussion
Anisotropy factor η at different positions around gold nanorod
A  B  C  D  

Rectangular  206  386  361  60.1 
Cylinder  615  858  749  126 
Capsule  1,016  837  794  137 
Anisotropy factor η at different positions around Si nanorod
A  B  C  D  

Rectangular  4.18  3.47  3.02  1.87 
Cylinder  3.78  2.94  2.53  1.78 
Capsule  2.96  2.30  2.21  1.85 
Conclusions
In summary, we have studied the SE lifetime orientation distributions around a metallic nanorod by using the rigorous electromagnetic Green function method. Rectangular, cylinder, and capsule nanorods are considered. The anisotropic factor near the end of the gold capsule nanorod can reach up to 10^{3}. By comparing the results of a dielectric nanorod, we point out the importance of localized plasmonic resonance to the lifetime orientation anisotropy distributions. The factors of QEs position, frequency, and the length of nanorod are investigated in detail. Our results show that the localized plasmonic resonance effect provides a new degree of freedom to effectively control spontaneous emission by the dipole orientation of the QEs.
Abbreviations
 SE:

spontaneous emission
 QE:

quantum emitter.
Declarations
Acknowledgements
This work was financially supported by the National Basic Research Program of China (2010CB923200), the National Natural Science Foundation of China (Grant U0934002), and the Ministry of Education of China (Grant V200801). Jingfeng Liu thanks the National Natural Science Foundation of China (Grant 11204089, Grant 11334015) for their financial support.
Authors’ Affiliations
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