Supplementary Information:
Manipulating Nonlinear Emission and Cooperative effect of
CdSe/ZnS Quantum Dots by Coupling to a Silver Nanorod
Complex Cavity
Fan Nan1,‡, Zi-Qiang Cheng1,‡, Ya-Lan Wang1, Qing Zhang2, Li Zhou1,2,*, Zhong-Jian
Yang3, Yu-Ting Zhong1, Shan Liang1, Qihua Xiong2,4,*, Qu-Quan Wang1,*
1Department
2Division
of Physics, Wuhan University, Wuhan 430072, P. R. China
of Physics and Applied Physics, School of Physical and Mathematical
Sciences, Nanyang Technological University, Singapore 637371
3Beijing
Computational Science Research Center, Beijing 100084, P. R. China
4NOVITAS,
Nanoelectronics Centre of Excellence, School of Electrical and Electronic
Engineering, Nanyang Technological University, Singapore 639798
‡
These authors contributed this manuscript equally.
*To whom correspondence should be addressed. Email addresses: qihua@ntu.edu.sg,
zhouli@whu.edu.cn, or qqwang@whu.edu.cn
1
1. Experimental methods
a
b
SQD/AgNR:AAO
CCD
PL
f = 100 mm
 = 35 mm
Laser
80o
80o
SQD/AgNR:AAO
Figure S1. Experimental set-up of (a) extinction spectra measurement and (b)
reflective PL measurement.
2. AFM images of barrier layer surface of AAO cavity with and without SQDs
Figure S2. Tapping-mode AFM images of AAO cavity. (a) (b) AFM images of barrier
layer surface of the bare AAO cavity. The average fluctuation of the surface reaches a
height of 10.5 nm. (c) (d) AFM images of the backside of the AAO cavity coated with
CdSe/ZnS SQDs. The fluctuation of the surface is 13.95 nm in elevation on average.
The thickness of the coated CdSe/ZnS SQDs is approximately one monolayer.
2
3. SEM images of silver nanostructured film (AgNF) sputtered on the backside of
AAO cavity
Figure S3. SEM images of AgNF sputtered on the backside of AAO cavity. The average
silver thickness is 3.9 nm (a), 7.1 nm (b), 10.5 nm (c), and 16.4 nm (d). The nanopores
of AAO template are covered when the silver thickness is larger than 10 nm.
3
4. Spectral modulations of the complex cavity by tuning AgNF thickness and
excitation power
a
Normalized extinction
13.5 nm (dAgNF)
10.3 nm
7.5 nm
4.5 nm
3.2 nm
2.1 nm
0 nm
700
720
740
760
780
800
Wavelength (nm)
0.4
3/2
0.3
Phase shift
0.2
/2

Reflectivity

c 594
0.1
0
0
2
4
6
8
10
dAgNF (nm)
12
14
0.0
Envelope center(nm)
2
b
592
SQD/AgNR:AAO
590
588
SQD/AAO
586
584
0
2
4
6
8
Excitation power (mW)
10
Figure S4. (a) Normalized extinction spectra of the AAO/AgNF cavity. The silver
thickness is 0, 2.1, 3.2, 4.5, 7.5, 10.3, and 13.5 nm. The oscillation period varies very
little but the peak positions shift after deposition of AgNF. (b) Phase shift and
reflectivity as a function of dAgNF for the sample SQD/AgNR:AAO/AgNF. As dAgNF
increases to 13.5 nm, the reflectivity of the back surface of the cavity increases from
~0.03 to ~0.36 and the phase shift measured by PL spectra reaches ~3/2. (c) PL
central wavelength of the spectral envelope as a function of P (without AgNF). The
central wavelength of the PL envelope shifts from 586 to 596 nm for SQD/AgNR:AAO,
while the central wavelength stays unchange for SQD/AAO.
4
5. Power-dependent PL spectra and TRPL decay traces of the bare AAO and
AgNR:AAO cavities.
a
0.30
AAO
in= 80
0.25
d
0
0.8
AgNR:AAO
0.7
in= 80
0.20
Extinction
Extinction
0.6
0.15
0.10
0.5
0.4
0.3
in= 0
0.2
in= 0
0.05
300
400
500
600
700
0.0
300
900
400
AAO
16000
P
14000
12000
10000
8000
6000
4000
e
5500
Photon counts (a.u.)
PL intensity (a.u.)
20000
18000
4500
2000
450
5000
700
800
900
AgNR:AAO
P
4000
3500
3000
2500
2000
1500
1000
500
550
600
650
700
0
750
450
500
10000
f
Photon counts (a.u.)
AAO
P
1000
0
2
4
6
550
8
600
650
700
750
Wavelength (nm)
Wavelength (nm)
Photon counts (a.u.)
600
500
0
c
500
Wavelength (nm)
Wavelength (nm)
b
0
0.1
0
800
0
10
AgNR:AAO
P
1000
100
0
12
2
4
6
8
10
Time Delay (ns)
Time delay (ns)
Figure S5. Extinction and PL spectra and TRPL of bare AAO and AgNR/AAO cavities. (a)
(d) Extinction spectra. (b) (e) PL spectra. (c) (f) TRPL decay traces. (a), (b), and (c) for
bare AAO cavity. (d), (e), and (f) for AgNR/AAO cavity with weak PL of AgNRs.
5
6. PL spectra of SQD/AgNR:AAO recorded by transmittance geometry
a
b 18000
16000
CCD
PL intensity
14000
PL
12000
Excitation Power P
1 mW
3 mW
6 mW
8 mW
10000
Laser
8000
6000
4000
2000
SQD/AgNR:AAO
450
500
550
600
650
700
750
Wavelength (nm)
Figure S6. Power-dependent PL spectra of SQD/AgNR:AAO recorded by using
transmittance geometry. The peak also shifts to the longer wavelength at higher
excitation power.
7. Power-dependent spectra of SQDs on quartz substrate and empty AAO cavity
30
7.5 mW
7.0 mW
6.5 mW
exc=400 nm
3
25
b
SQD/Quartz
PL intensity (10 , a.u.)
3
PL intensity (10 , a.u.)
a
20
P
15
10
1.5 mW
1.0 mW
0.5 mW
5
21
18
15
P
12
9
1.5 mW
1.0 mW
0.5 mW
6
3
0
0
450
500
550
600
650
700
450
750
500
d
SQD/Quartz
SQD/AAO
600
650
700
750
36
SQD/Quartz
SQD/AAO
35
25
FWHM (nm)
3
PL intensity (10 , a.u.)
30
550
Wavelength (nm)
Wavelength (nm)
c
8.0 mW
7.5 mW
7.0 mW
SQD/AAO
exc=400 nm
20
15
10
34
33
32
31
5
0
1
2
3
4
5
6
7
30
8
1
P (mW)
2
3
4
5
6
7
8
P (mW)
Figure S7. Power-dependent spectra of CdSe/ZnS SQDs on quartz substrate and
empty AAO cavity. (a) (b) PL spectra obtained from SQDs on quartz substrate and
empty AAO cavity at different pumping power. (c) Power dependences of the PL peak
intensity of the SQDs. (d) Power dependences of the spectral width of the SQDs.
6
8. Power-dependent spectra of SQDs on AAO/AgNF cavity without Ag nanorods
b
0.9
AAO/AgNF
AAO
0.8
0.7
Extinction
4
3.0x10
SQD/AAO/AgNF
exc= 400 nm
4
PL intensity (a.u.)
a
0.6
0.5
0.4
0.3
2.5x10
2.0x10
4
P
1.5x10
0.5 mW
0.3 mW
0.1 mW
4
1.0x10
3
5.0x10
0.2
0.1
300
400
500
600
700
800
450
900
500
d
575 nm
600 nm
22
FWHM (nm)
4
3.0x10
600
650
700
750
575 nm
600 nm
4
PL intensity (a.u.)
24
550
Wavelength (nm)
Wavelength (nm)
c
8.0 mW
7.5 mW
7.0 mW
4
20
18
2.5x10
4
2.0x10
4
1.5x10
4
1.0x10
3
5.0x10
16
0.0
0
2
4
6
0
8
2
4
6
8
P (mW)
P (mW)
Figure S8. Power-dependent spectra of SQDs on the cavity of AAO/AgNF without Ag
nanorods. (a) Extinction spectra of the cavity before and after deposition of AgNF
(incident angle in = 0). (b) Power-dependent spectra of SQD/AAO/AgNF. Power
dependences of (c) the spectral width and (d) the peak PL intensity of the emissions
at 575 nm and 600 nm.
9. Multi-peak fitting of emission spectrum with multimode oscillations
b 35
PL intensity (x10 , a.u.)
12
3
10
3
PL Intensity (x10 , a.u.)
a 14
8
6
4
2
0
500
550
600
650
Wavelength (nm)
700
30
25
20
15
10
5
0
500
550
600
650
Wavelength (nm)
700
Figure S9. Multi-peak fitting of emission spectrum with multi-mode oscillations. (a)
The central frequencies of three main oscillating modes are approximately 575, 596,
and 618 nm, respectively. (b) The central frequencies of five oscillating modes are
approximately 570, 585, 600, 616, and 636 nm, respectively.
7
10. Emission spectra width and slope for multi-mode oscillations of the SQDs
coupled to a AgNR:AAO/AgNF cavity (in Fig. 3a)
b
14
Weak excitation
Strong excitation
1.4
606 nm
1.2
13
Slope
Spectral width (nm)
a
12
588 nm
0.8
11
10
1.0
0.6
0
2
4
6
Excitation power (mW)
8
0.4
10
560
580
600
620
Wavelength (nm)
640
Figure S10. (a) Spectral width as a function of excitation power at 606 nm and 588
nm. (b) The slope index of six emission peaks at weak and strong excitation. Three
emission peaks with wavelength longer than SQD,0 shows nonlinear amplifications.
11. Power-dependent emission spectra with three-mode oscillations of the SQDs
coupled to a AgNR:AAO cavity
Cavity
b
SQD/AgNR:AAO
3
PL intensity ( 10 , a.u.)
a 16 SQDs
6.0
5.5
5.0
3
PL intensity ( 10 , a.u.)
12
P
(mW)
8
c
PL spectral width (nm)
4
450
500
550
600
650
700
SQD/AgNR:AAO
12
596 nm
9
6
575 nm
3
630 nm
0
SQD/AAO 590 nm
40
0.5
0.3
0.1
0
15
750
Wavelength (nm)
35
30
SQD/AgNR:AAO
596 nm
25
20
0
1
2
3
4
5
Excitation power (mW)
6
Figure S11. Power-dependent three-mode oscillations and amplifications of the
ensemble CdSe/ZnS SQDs coupled with complex cavities. (a) Power-dependent
emission spectra with three-mode oscillations of the SQDs coupled to a AgNR:AAO
cavity (cav  0.98SQD,0, L-SPR  610 nm). (b) Power dependences of PL peak
intensity at three modes at 575, 596, and 630 nm. Two emission peaks with
wavelengths of ~ 596 nm and ~ 630 nm (> SQD,0) are nonlinearly amplified with slope
8
index  increasing from 0.95 to 1.35, while the emission peak with wavelength of ~
575 nm (< SQD,0) shows a saturated-like behavior and the corresponding slope index
is decreased from 0.9 to 0.3. (c) Spectral width of the emissions at 596 nm as a
function of excitation power. The spectral width is prominently decreased from 38.5
nm to 24.5 nm when the excitation power is larger than Pc.
12. Theoretical relationship of PL emission spectrum
The PL electric field (E()) of the SQDs can be assumed to be the sum of the
uncoupled and coupled field (labeled by Eu() and Ec(), respectively). When the
excitation power is not very strong and the saturation effect can be neglected, the
uncoupled emission field Eu() is proportional to (f()P)1/2, where f() is the spectral
function of emissions for the ensemble SQDs. For the complex cavity with a low
Q-factor, the emission field coupled to the cavity is approximately written as
Ec ( )  ( f ( ) P)1/2 (1  r2 eG e j ) ,
(S1)
where r2 is the reflective coefficient of the back surface of the complex cavity, and
e G and e j
represents the variations of amplitude and phase of the PL
electromagnetic field travelling a circle in the cavity.  = 2nd/ + , nd is optical
thickness of the cavity and  is the phase shift induced by the reflection on the AgNF
surface. G is equivalent “gain” factor of the cavity and e G includes all factors
inducing variation of electromagnetic field amplitude, such as gain, propagation loss,
and the excitation energy transfer and relaxation from the higher levels to the lower.
Then, the modulated PL spectrum I() of the SQDs/cavity nanosystem with a low
Q-factor can be approximately expressed as,
I PL ( P,  )  Pf ( )[1  (kr2 eG ) 2  2kr2 eG cos(2nd /    )] ,
9
(S2)
where k is a coupling factor of the SQDs and the complex cavity, the modulating
factor of the PL spectrum is,
I PL,max ( P, max )  I PL,min ( P, min )
4kr2 eG
 

.
I PL,max ( P, max )
(1  kr2 eG ) 2
(S3)
Then, we define a normalized PL spectrum I PL,nor ( P,  ) and the differential
normalized PL spectrum I PL,nor ( P,  ) as,
I PL,nor ( P,  )  I PL ( P,  ) / P ,
(S4)
For simplification of calculation, the PL spectrum is normalized by the peak PL
intensity.
I PL,nor ( P,  )  I PL,nor ( P  P,  )  I PL,nor ( P,  ) ,
(S5)
From Eqs. (S2, S4, and S5), we obtain,
I PL,nor ( P,  )  f ( )(kr2 ) 2{exp 2 [G ( P  P,  )]  exp 2 [G ( P,  )]}
 2 f ( )kr2 cos(2 nd /    ){exp[G ( P  P,  )]  exp[G ( P,  )]}
(S6)
By using the weak “gain” approximation, exp{G}  1 + G, the differential normalized
PL spectrum has a relationship,
I PL,nor ( P,  )  2G( P,  ) f ( )[(kr2 )2  kr2 cos  ] ,
where G ( P,  )  G ( P  P,  )  G ( P,  ) is differential “gain”.
10
(S7)
13.
Power-dependent
spectra
of the ensemble SQDs
coupled with a
AgNR:AAO/AgNF complex cavity and SQDs on quartz substrate (in Fig. 4)
9000
8000
SQD/AgNRs:AAO/AgNF
exc = 400 nm
PL intensity (a.u.)
7000
30000
6000
5000
4000
3000
0.3 mW
9 mW
20000
15000
10000
5000
0.3 mW
1000
450
500
550
SQD/Quartz
exc = 400 nm
25000
9 mW
2000
b
PL intensity (a.u.)
a
600
650
700
750
450
500
Wavelength (nm)
550
600
650
700
750
Wavelength (nm)
Figure S12. Power-dependent spectra of (a) the ensemble SQDs coupled with a
AgNR:AAO/AgNF complex cavity and (b) SQDs on quartz substrate (in Fig. 4).
14. Radiative rate enhancement for superradiance of two dipoles coupled with
AgNRs
Total enhancements
30
25
20
Superradiance
Subradiance
One dipole
15
10
5
0
400
500
600
700
Wavelength (nm)
800
Figure S13. Enhancement of radiative rate of the two dipoles coupled with the AgNRs.
Solid and dashed lines represent the calculated results of the AgNRs with rod-lengths
of 30 nm and 32 nm, respectively.
11