Supporting information for
Enhanced single-molecule spontaneous emission in an
optimized nanoantenna with plasmonic gratings
Hongming Shen, Guowei Lu*, Tianyue Zhang, Jie Liu and Qihuang Gong*
Near-to-far-field calculation method. For the simulations, we place an oriented
dipole (λ0=670 nm) in the center of the slit cavity. Here, we give a brief procedure for
NTFF transformation. A 14 μm wide line, at a surface 250 nm above the metal/water
interface, is used to record the near-field data. In our 2-D FDTD simulations, we only
need to record the complex field components ( E x (t ), H y (t )) . According to the
frequency domain analysis method, we set the initial frequency  0  2 / 0 and then
obtain field quantities ( E x ( x,  0 ), H y ( x, 0 )) by performing Fourier transform. Based
on the surface equivalence theorem, we calculate the surface equivalent electric and
magnetic currents ( J x   H y , M y   E x ) . For   0 , we compute the integrations of
N   J x cos  exp( ik ( x sin   z 0 cos )dx and L   M y  exp( ik ( x sin   z 0 cos )dx ,
respectively. Finally, the far-field radiation pattern as a function of angle θ can be
easily investigated by calculating the angular radiation power density P(θ), which can
be written as: P( ) 
L
k 2
 (| N  ) |2 ) . Here,  is the impedance of free space.
2

32
Noted that all the equations above have already been simplified corresponding to our
2-D geometry.
 Corresponding author.
Email: guowei.lu @pku.edu.cn (G. Lu); qhgong@pku.edu.cn (Q. Gong)
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Supplementary figures
Figure Captions
Fig. 7 Influences of various geometric features on the far-field angular distribution of
an oriented dipole (λ0=670 nm) placed in the center of the slit cavity. In all cases,
N is fixed to be 6 and the mesh pitch is 2 nm. (a) Groove periodicity G: We
increase G from 300 to 500 nm, setting H=270 nm, W=100 nm, d=40 nm and
a=G/2. (c) Groove depth d: H=270 nm, W=100 nm, G=400 nm and a=G/2. Only
certain groove structure (G, d) can produce a collimated beam normal to the
metal surface for a fixed wavelength. Additionally, we are able to realize
beaming or splitting light by tuning parameters of G and d. (b) Slit thickness H
(W=100 nm, d=40 nm, G=400 nm and a=G/2) and (d) Slit width W (H=270 nm,
d=30 nm, G=400 nm and a=G/2): Both of them do not affect on the far-field
directivity, but affect the values of power density. (e) Groove width a: It is
confirmed from our calculations that a close to half the period is appropriate
(H=270 nm, W=50 nm, d=30 nm and G=400 nm).
Fig. 8 Normalized (a) transmission and (b) absorption spectrums for a single slit
without gratings (black dashed line) and with symmetric metal gratings (red solid
line), respectively. A Gaussian-pulse line source illuminates from upside of the
metal. In the case of a slit-grooves nanostructure, the resonant wavelength
corresponding to the absorption maximum is about 650 nm with FWHM around
50 nm. As we can see, both the transmission and absorption enhancements of the
slit-grooves nanostructure are much higher than the bare-slit nanostructure.
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Fig.7 H. Shen
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Fig.8
H. Shen
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