Supplementary information
Determination of coupling rate of light emitter to surface plasmon polaritons supported on
nanohole array
Z.L. Cao and H.C. Ong
Extension to localized SPPs
Our rate equation can be extended to localized SPPs, we follow the same formalism that
the energy from light emitters is coupled to [LSPP], which subsequently radiatively scatters to
far-field, resulting in LSPP mediated emission. However, the radiative decay channels in
LSPPs do not follow the phase-matching equation, which only allows several discrete decay
routes. In fact, the radiative decay behaves like a dipolar radiation and covers almost all
possible k in the half-space, yielding non-directional emission. The rate equation for [LSPP]
now is given as


d [ LSPP ]
  c [ EM ]    abs    krad dk  [ LSPP ] , which sums up all possible
dt
k


radiative decay channels.
Method of calculating far-field emission pattern from the near field data
Based on the surface equivalence theorem, if the electromagnetic fields on an infinite
single surface are replaced with suitable electric and magnetic current densities satisfying the
boundary conditions, then the far-field at any point above the surface can be obtained [1]. To
mimic an infinite surface, we expect the propagation distance for SPPs is a few microns and
thus set the simulation region to be 15.3  15.3 µm2, which is assumed to be sufficiently large
for SPPs to decay considerably. To calculate the far-field emission pattern, a power monitor is
placed at 41 nm above the nanostructure to record the electromagnetic fields for converting to
current densities. Finally, the emission pattern is projected to a hemisphere at a distance of 1 m,
expressed as a function of  and .
Sample preparation
The 2D nanohole array is fabricated by combining interference lithography and thin film
deposition [2, 3]. Basically, SU8 negative photoresist is spin-coated on glass substrate and is
then patterned by HeCd laser at 325 nm using a Lloyd’s mirror geometry. After development,
the SU8 template is transferred to a magnetron sputtering system for metallization. A gold film
with thickness of 150 nm is deposited on the substrate to form metallic array. Then, 0.02 mg of
styryl 8 dye is first dissolved in 15 ml methanol and a slight amount of polyvinyl alcohol
polymer is added into the dye solution. The polymer solution is spin-coated on the array. We
estimate the polymer is less than 80 nm.
Optical measurements
Angle-resolved orthogonal reflectivity mapping:
Angle-resolved reflectivity spectroscopy is performed by a home-built goniometer that
contains two motorized rotation stages so that both incident and detection angles can be
controlled independently [4]. The schematic of the optical setup is shown in Fig. 1. A
collimated white light from a quartz lamp is first passed through a 45° oriented polarizer so that
both p- and s-polarized lights are illuminated on the array at a particular incident angle. For
detection, the specular reflectivity spectrum is captured by a spectrometer-CCD detection
system. A detection analyzer is oriented at -45° to eliminate the non-resonant background [4].
We take the reflectivity spectra at different incident angles and then contour plot the spectra as
a function of incident angle to form angle-resolved mapping.
Fig. 1. The schematic of angle- and polarization-resolved reflectivity spectroscopy
Angle-resolved photoluminescence mapping:
The setup for photoluminescence mapping is shown in Fig. 2. The sample is kept at the
same goniometer but it is now illuminated by a p-polarized Ar+ 514 nm laser at a fixed incident
angle = 5°. Two notch filters are placed before the detector to eliminate the 514 nm laser line.
The detection angle is then varied from 0o to 80o. We take the photoluminescence spectra at
different detection angles and then contour plot the spectra as a function of detection angle.
Fig. 2. The schematic of angle-resolved photoluminescence spectroscopy
Calculations of Pd in half-space
We calculate the direct emission Pd in the entire half-space based on the information given
in -X direction. From the angle-dependent photoluminescence measurement taken in the -X
direction, as given in Fig. 4(c) of the main text, the background emission (i.e. the direct
emission) shows a cosine dependence indicating it is of Lambertian surface. We then assume
the emission has the function form of b cos , where b is the maximal power and  is the
detection polar angle. It has no azimuthal  dependence since the direct emission is expected
to possess full circular symmetry, as confirmed from the FDTD results in Fig. 2(b) of the main
text. To conduct the integration over the half-space, we define our system in Fig. 3 with the
sample being placed in the x-y plane at z = 0 and the -X direction is defined in the positive
x-direction. We find our optical detector covers  ~ 0.5o. Assume our detection is placed
along the z-axis, the small solid angle thus is determined as   
2
0

0.5 
2 180
0
sin  d d ~
π3/7202 steradian. For detector with a fixed aperture, the solid angle remains the same for
different arbitrary angles [5]. As a result, the maximum intensity is given as b/. The total
flux, i.e. the power Pd at a particular wavelength, can be calculated by performing the following
integration [5]:

2
b
Pd   
cos  d   
S 
0
2
b
b
  cos sin  d d  
0
Fig. 3 Illustration for calculating Pd
Ref:
1. A. Taflove, Computational Electromagnetics: The Finite-Difference Time-Domain Method.
(Artech House, Boston , 2000).
2. J. Li, H. lu, W.C. Luk, J.T.K. Wan and H.C. Ong, Appl. Phys. Lett. 92, 213106 (2008).
3. J. Li, H. lu, D.Y. Lei, J.T.K. Wan, J.B. Xu, H.P. Ho, M.Y. Waye and H.C. Ong, Appl. Phys.
Lett. 94, 183112 (2009).
4. Z.L. Cao, H.Y. Lo, and H.C. Ong, Opt. Lett. 37, 5166 (2012).
5. F.L. Pedrotti, L.S. Pedrotti, Introduction to Optics. (Prentice Hall, 1993)