Plasmonic Amplification with Ultra-High Optical Gain at
Room Temperature
Ning Liu,1 Hong Wei,1 Jing Li,1 Zhuoxian Wang,1 Xiaorui Tian,1 Anlian Pan,2
Hongxing Xu1*
1
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics,
Chinese academy of Sciences, Beijing 100190, China
2
College of Physics and Microelectronics Science, Hunan University, Changsha,
410082, China
1. Characterize the roughness of the Ag film
Figure S1: AFM image showing the quality of the thermally evaporated 40 nm Ag
film on glass substrate. RMS of the height along the line marked in the AFM image is
1.065 nm.
2. Life time measurements with time correlated single photon counting (TCSPC)
and the deconvolution of the decay curve:
The spontaneous emission lifetime of the CdSe film, a CdSe NB, and the composite
plasmonic waveguide were measured with TCSPC method, and their decay curves are
given in Fig. S2. To measure the life time of the photoluminescence, the scattered
photons from the end of the NB, which is highlighted by the dashed circles in Fig. 2
1
and Fig. 4, is directed into the SPAD, as illustrated in Fig. 1c. The induced electric
pulses will then be sent to the counting unit PicoHarp 300 for processing. After
certain accumulation time, the time trace of an optical pulse is reconstructed with a
time resolution of 4 picoseconds.
To obtain the best estimation of the spontaneous emission rate, we try to fit our
measured decay curves with the convolution of the excitation laser profile, including
the instrumental response, with an exponential decay function, whose time constant
will give us the estimated spontaneous emission life time. The decay curve is
calculated with the equation:
t
g (t )  A f (t ')e
0
t ' t

dt '
where A is a scaling factor, f(t) the excitation laser profile, and τ is the time constant.
By varying τ, we get the g(t) that will fit the best with our measured decay curve, as
shown in Fig. S2. The fitted τ for the plasmonic composite structure is 50 ps, and τ for
the photonic NB is 113 ns.
These two values are substantially shorter than that of the CdSe material itself,
which is about 0.7 ns. As discussed in references 1-4, the decrease of lifetime is
attributed to the Purcell effect (in other words the increased density of state per
frequency per volume) of the hybrid plasmonic modes and the resonant cavity formed
by the two ends of the NB. Surface states may also contribute to the reduction of the
lifetime for the CdSe NBs on glass as no alumina layer was deposited on them 1. Nonradiative decay rate does not play a dominant role in these cases.
Figure S2: (a) Fit to the measured spontaneous emission decay curve from the
plasmonic composite structure. (b) Fit to the measured spontaneous emission decay
curve from the CdSe NB on glass substrate.
3. Gain measurements with TCSPC method:
As stated in the main texts, by changing the optical delay line, the probe and pump
pulses can be overlapped in both space and time. Fig. S3 shows two sets of time traces.
The time traces were obtained from the scattered photons at the end of the plasmonic
structure, corresponding to waveguided probe signal (dashed red), spontaneously
decayed surface plasmon modes from pump only (black), and total output when both
probe and pump light are present (blue). The wavelength of the light collected is
limited by the F3 (7305 nm). Using TCSPC, we can easily determine the relative
time difference between the probe signal and the pump. In Fig. S3(a), the time of the
probe light and pump light are overlapped, while in Fig. S3(b) the probe signal
2
preceds the pump. It is quite clear from the plots that only when the probe and pump
signals overlap in time, the amplification of probe signal through stimulated emission
takes place. To calculate the gain G (dB), we used the equation (1) in the paper. Same
G (dB) was obtained from either the intensity reading of the CCD camera or the
counts in the time trace.
Figure S3: Time traces of photons scattered out from the end of the composite
plasmonic structure. The red dashed curves correspond to the waveguided probe light;
the black curves are the PL from the pump only and the blue ones are the total output
when both probe and pump are present. All time traces were recorded after passing
through the same 7305 nm filter. Panel (a) shows that the probe signal got magnified
when the probe and pump were overlapped in time. Panel (b) illustrates that no
amplification was found when probe preceds the pump.
4. Evaluate the multi-path gain in the hybrid plasmonic waveguide
In a simple mode, the electric field intensity transmitting through a cavity can be
written as:
(1  R)2 e L I in ( )
It 
1  R 2e2 L  2 Re L cos 
Where R is intensity reflectivity,  is the propagation loss coefficient, L is the length
of the cavity and =2k0nL (n is the refractive index), assuming R is the same for both
ends. When cos = 1, It is maximum, corresponding to the resonant peak in the
spectrum. When cos = -1, It is minimum, corresponding to the resonant trough in the
spectrum. Therefore, we have:
(1  R ) 2 e  L I in
(1  R ) 2 e  L I in
I t (max) 
and
I

t (min)
(1  R ') 2
(1  R ') 2
I t (min) (1  R ') 2

I t (max) (1  R ') 2
where R '  Re  L . From the intensity difference at different wavelength in the probe
spectra after passing through the waveguide cavity, we can estimate the value of R’.
From Fig. 2c, however, we can hardly distinguish any cavity mode. We can only
estimate that the R’ is less than 0.32 %. Given measured  = 6230 cm-1 and L =8.6 μm
for the current waveguide, we can estimate that the intensity reflectivity R is less than
3
68 %. Because the R’ is quite small in our case, the transmitted intensity over the
entire wavelength span can be approximated to be:
I t  (1  R) 2 e  L (1  R 2e 2 L ) I in
When gain is present in the cavity, the transmitted electric field intensity becomes:
(1  R) 2 e  L  gL I in ( )
g
I t
1  R 2 e 2 L  2 gL  2 Re  L  gL cos 
(1  R) 2 e  L I in gL
(1  R) 2 e  L I in gL
g
and I g t (max) 
e
and
I

e
t (min)
(1  R ' e gL ) 2
(1  R ' e gL ) 2
When cos =1, the gain coefficient is slightly higher than the single path gain
coefficient g. When cos = -1, the gain coefficient is slightly lower than g. If we
assume the R ' e gL is still much smaller than 1, then the averaged transmitted intensity
over the full wavelength when the gain is present can be estimated to be:
I tg  (1  R)2 e L (1  R 2e2 L 2 gL ) I in e gL
and
I tg 1  R 2e2 L 2 gL gL

e  e gL
2 2 L
It
1 R e
Given R’ is around 0.32 %, the measured gain coefficient g is just 0.5 % less than the
single path gain coefficient, literally the same as the single path gain.
5. Rate equations, carrier dynamics, and additional information on the PL and
gain measurements
As partially mentioned in the main texts, the carriers in semiconductor materials
can be in the form of free excitons, bound excitons, biexcitons, or free carriers
(electrons and holes). The bonding energy of exctions in bulk CdSe is about 15 meV.5
At room temperature, the carriers mostly exist as free carriers. The carrier
recombination rate equations then can be simply written as:
dn
I
I
 R  ksp(1) n  k sp(2) np  k st(1) n  k st(2) np  ka n 2 p
(1)
dt
hv
hv
dp
I
I
 R  ksp(1) p  ksp(2) np  k st(1) n  k st(2) np  ka n 2 p
(2)
dt
hv
hv
dI
 hvcef (ksp(1) n  k sp(2) np)  Icef (k sp(1) n  k sp(2) np )
(3)
dt
where n is the electron density in the conduction band, p the hole density in the
valence band, ksp(1) and ksp(2) the 1st and 2nd order spontaneous recombination rate
constants, k st(1) and k st(2) the 1st and 2nd order stimulated emission rate constants, and ka
the Auger recombination rate constant. R is the carrier generation rate, which is
usually expressed as R  I exc ab / hvexc . In this simple model, we ignore the defect
states recombination, which may play important roles at the low pump intensity.
To get a better understanding of the carrier dynamics, we investigated both the
spontaneous decay rate into the waveguided plasmonic modes as well as the measured
gain as a function of the pump intensity. Fig. S4 shows the intensity of waveguided
plasmonic modes, generated from the spontaneous carrier recombination, with the
increase of pump intensity. It is apparent from the figure that the monotonic increase
4
is not linear. If we fit the intensity as a power law of the pump Im, at pump intensity
lower than 50 W/cm2, m = 1.69. At stronger pump power, m reduces to less than one
and at pump intensity higher than 1 kW/cm2, the intensity plateaus. This behaviour
can be well explained by the rate equations (1) to (3). In the simplified consideration,
we treat n  p (in reality, electron and hole masses depend on the band structures and
are quite different. They also behave differently in defeat recombination.) When only
spontaneously radiative recombination is concerned, the above equations can be
simplified to:
dn
 R  k sp(1) n  k sp(2) n 2  ka n3
(4)
dt
dI
 hvcef (ksp(2) n 2 +k sp(1) n)
(5)
dt
dn
 R . With pulsed pumping, n  R.
At lower pump intensity, equation (4) becomes
dt
Since ksp(2) is usually much smaller than ksp(1) for crystallized semiconductor due to the
momentum conservation, we get Isp  R from equation (5). At very high pump
intensity, the nonradiative Auger recombination can no longer be neglected. At steady
state, equation (4) is then approximated as R  ka n3 0 , n  R1/3. In this case, the Isp 
R1/3~2/3, becoming sublinear. At highest pump intensity, the Auger recombination
dominates the carrier dynamics and the spontaneous decay channel saturates.
However, the above analysis can not explain the fast increase of spontaneously
decayed scattered light intensity at pump intensity lower than 50 W/cm2 with m =
1.69. Stated in the paper, we attribute this superlinear increase to the electron transfer
across the metal-insulator-semiconductor interface. R is no longer linearly dependent
on the pump intensity at low pump intensity, but larger than I exc ab / hvexc .
Figure S4: Spontaneous decay intensity .vs. the pump intensity for the plasmonic
structure presented in Fig. 2. Black and blue curves are fits to power function Im at
different ranges of pump intensity.
Figure S5 shows the intensity of spontaneous decay into the waveguided
plasmonic modes as well as the measured gain G (dB) as a function of the pump
intensity for another hybrid plasmonic structure. For this structure, the power law fit
to the gain yields better agreement with the data than the logarithmic fit. In addition,
we notice that at the same pump intensity, the intensity of spontaneous decay
increases faster than that of the gain of the stimulated emission. This can be explained
by the nature of the pump-probe technique. As shown in Fig. S3, in order to overlap
the pump and probe signals in time domain, we deliberately make the arriving time of
5
the probe signal few tens of picoseconds after the advent of the pump light. This
means that the carrier density already builds up to a certain level close to steady state
when the probe signal arrives, which give rise to a dependence G(dB)  R or G(dB) 
R2/3. Because of the time delay, the probe signal also lasts few tens of picoseconds
without the pump light. The carrier density is then determined by the dominant decay
channel. This further slows down the increase of gain as a function of pump. These
are the reasons accounting for the sublinear dependence of the gain with respect to the
pump intensity. The same trend was observed on the main plasmonic structure
discussed in the paper.
Figure S5: (a) Optical images of another plasmonic structure. Panel I is the wide field
optical image; II corresponds to probe signal being launched from one end of the NB
and emitting from the other; III shows the PL when the structure is being pumped
from the middle. (b) Gain G (dB) ‘■’ and PL ‘’ scattered out from the end of the NB,
as marked in (a), as a function of the pump intensity. The continuous curves are the
fits to the data.
6. Coupling efficiency of the probe beam and Gain .vs. probe intensity
To estimate the coupling efficiency of the input laser beam to the waveguided
plasmonic mode, we calculated the ratio of the waveguided hybrid plasmonic mode
intensity integrated over a cross section of the waveguide (4 μm away from the input
end of the waveguide) with respect to the power of the input laser beam. Since we
know the simulated propagation loss (5624 cm-1 for the TM mode, detailed in section
8 of SI), we can work out the ratio of the power of the excited hybrid plasmonic mode
with the total input laser power at the input end of the waveguide, hence the coupling
coefficient, which is about 12% of the total power of input probe beam.
In general, at a fixed pump rate, the gain G (dB) depends on the intensity of the
probe signal. Usually, the highest gain is obtained with a weak probe signal, which is
called the small signal gain. When the probe signal increases, the gain drops as a
result of the decreased carrier density. Once the probe intensity reaches the so called
saturation intensity, the gain coefficient drops to ½ of the small signal value. Fig. S6
shows the plots of the gain G (dB) as a function of the probe intensity, in two
polarization directions, as described in Fig. 2. As we cannot determine experimentally
how much the input laser beam is coupled into the waveguided plasmonic modes
using the edge coupling method with good accuracy, the intensity of the probe light is
only given in a relative unit. A rough estimation of the maximum intensity of the
input laser beam is about 1 % of the pump intensity, about 22 W/cm2.
6
As we can see clearly from the plots, the gain only decreased 16 % and 7.4 % in
these two polarization directions when the probe signal intensity was increased by 50
times. This means that the probe intensity we used in our experiment is much less
than the saturation intensity and the gains we obtained in our experiments are close to
the value of small signal gain.
Figure S6: Gain G (dB) as a function of probe signal intensity. The input laser beam
was polarized along (left) and perpendicular to the waveguide (right).
7. Additional information on the polarization of the PL from the plasmonic
structure:
90
120
1.0
PL from pump
Pump
60
0.8
30
150
0.6
0.4
0.2
0.0
180
0
0.2
0.4
0.6
330
210
0.8
1.0
240
300
270
Figure S7: Polar plot of the emission intensity as a function of polarization angle .
From the plot we can clearly see that the pump is linearly polarized in 90 degrees, but
the PL from the pump produces the same results as shown in Fig. 2f.
8. Estimation of the propagation loss of two perpendicularly polarized hybrid
plasmonic modes
7
Figure S8: FDTD simulation of electric field intensity distribution on XZ plane at
Y=0 μm for hybrid plasmonic modes excited by input field polarized in Z and X
direction for panel (a) and (b) respectively. The intensities as a function of Z position
along the dashed lines are plotted at the bottom of the panels. Simple exponential
decay fit to part of the curve gives an estimation of the propagation loss, which is
5624 cm-1 and 10309 cm-1 for modes in (a) and (b) respectively.
9. Simulation of optical modes excited in photonic waveguides below critical
dimension
Figure S9: FDTD simulation of the photonic modes excited by the probe light
polarized in Z direction in the photonic waveguide of the same dimensions as the
hybrid plasmonic waveguide presented in Fig. 2. (a) is the E-intensity distribution on
XY plane at Z = 2 μm, with scale bar 200 nm. It is quite obvious that the mode is
mostly distributed outside the CdSe NB, and the intensity is extremely small. (b) is
the E-intensity distribution in log scale on YZ plane at X=0, with Y from -1 μm to
1μm and Z from -3 μm to 3 μm. It is plotted asymmetrically to show the distribution
of E-field in Y direction better. It is confirmed again that most part of the field is
outside the NB.
8
10. Lasing from the CdSe NBs on glass substrate and estimation of the
reflectivity of the cavity:
The lasing threshold of the CdSe NBs strongly depends on the thickness of the NBs.
NBs that are thinner than 160 nm do not exhibit lasing behaviour even at our highest
available pump intensity 2.2 kW/cm2, due to the weak mode overlap with the gain
material. For NBs thicker than 180 nm, the lasing threshold varies from one to another,
but mostly within the range of 500 to 800 W/cm2. Occasionally, a lasing threshold as
high as 1.5 kW/cm2 is required. The emission spectra and corresponding optical
images of these photonic NBs as a function of pump intensity are given in Fig. S10.
Cavity modes are clearly distinguishable even at low pump power (I). The
corresponding optical image, obtained with the 7305 nm filter, shows the
spontaneous emission into the scattering mode (at the middle of the NB) and
waveguided modes, which scatter out at both ends of the NB. With higher pump
energy (II), the full width at half maximum (FWHM) of the cavity modes starts to
narrow, indicating the onset of the amplified spontaneous emission (ASE). The
corresponding image exhibits stronger emission intensity at the ends of the NB than
that at the middle. At relatively high pump intensity (III, 1.03 kW/cm2), strongly
enhanced emission intensity and resonant peak width narrowing are observed at
specific cavity modes, which are clear signatures of lasing. The optical image shows
strong emission from the ends of the NB and considerably suppressed spontaneous
emission from the pumping area. Fig. S10 (b) plots the emission intensity at the
bottom end of the NB as a function of pump intensity. The figure clearly shows the
characteristic kink, which indicates the transition from spontaneous emission to lasing.
Given the gain value at lasing threshold, we can roughly estimate the upper limit
of averaged reflectivity at both ends of the NB by R=e-gD, where g is the gain
coefficient, and D is the pump beam diameter. Since the measured gain for these
photonic waveguides below lasing threshold is in the range of 1.1 dB to 3.8 dB (with
gain coefficients from 870 cm-1 to 2900 cm-1), R is roughly 42% to 75%. In this
estimation, we neglected the internal loss from the NBs.
Figure S10: (a) shows the emission spectra at the bottom end of NB at three different
pump intensities: (I) 22 W/cm2, (II) 0.52 kW/cm2, and (III) 1.03 kW/cm2 and the
corresponding optical image (recorded with filter F3). (b). Emission intensity at the
bottom end of the NB .vs. pump intensity.
11. Simple model to evaluate the multiple-path gain in the photonic amplifiers
Interestingly, we found that some photonic NBs exhibit unusually high gain as well as
a very abrupt transition from low-to-high gain in a short range of pump intensity. One
9
of the examples is illustrated in Fig. S11 (NB dimension 245 nm 186 nm  9.4 μm).
Fig S11a and S11b show the optical images and a corresponding time trace of the
emission intensity in the high gain regime. To understand the origin of this gain
increase, we recorded the spectra of the emission light from the area highlighted by
the dashed circles in Fig. S11a at three different pump intensities I1, I2, and I3. The
results are displayed in Fig. S11d, with the red curves corresponding to the probe
signal only; the blue curves the PL emissions from the pump, and the green ones the
spectra of the total output when both input and pump lights are present. Compared to
the spectra obtained from the plasmonic waveguides, cavity resonant modes are
clearly discerned from all three types of spectra at all pump intensities in this photonic
cases. (Fig.S11d) This means that instead of a single path amplification, the probe
signal is also amplified through multiple paths in this situation. At low pump energy
I1, where the ASE can be neglected, the FWHM of the resonant peaks is determined
by the transmittance of light through a multi-path reflective cavity. The FWHM of
resonant peaks in the total output is the same as that in the probe and PL spectra. With
the increase of pump power, at the pump intensity I2 and I3, the FWHM of the
resonant peaks in the PL spectra starts to decrease, suggesting the onset of ASE, even
though the lasing threshold is not yet reached due to the transmission loss at two ends
of the NB. At pump intensity I2, the FWHM of the total output is still similar to that of
the corresponding PL, but narrower than that of the input signal, showing the obvious
effect of loss compensation from the gain materials. At slightly higher pump intensity
I3, specific cavity mode is magnified substantially, leading to an abrupt jump in the
optical gain. The resultant FWHM of the selected cavity mode is further narrowed
compared to that in the PL spectrum.
The spectra clearly reveal the evolution of total output light from the simple
amplification of the broadband probe signal to lasing at specific wavelengths within
the probe light bandwidth with the increase of pump intensity. Given these, we tried
to fit the sudden increase in the gain data with a simple mode of multi-path
amplification, which also take into account the broadband wavelengths allowed by the
filter. The transition from low to high gain indicates the onset of probe signal induced
lasing.
In this model, we skip the detailed analysis of rate equations. Using the
conclusions obtained from section 5, at the pump intensity we are interested in, we
0.6
assuming the gain coefficient g  I exc
. However, in the case of multiple-path
amplification, we need to consider gain saturation caused by the intensity of the
stimulated light Ist. In this case, the gain coefficient g is related to Ist by equation:
gunsat
g
, where gunsat is the small signal gain and Isat the saturation intensity.
1  I st / I sat
Since the filter we used allows light of wavelength 7305 nm passing through and the
wavelength difference between two adjacent cavity modes is only around 5 nm or less,
we have to take into account the destructive interferences at some wavelength when
transmitting through the cavity. Therefore, the electric field transmits through the
cavity after passing the cavity once is: E1 ( )  tEin e1/ 2 gD ik0 (  ) nl , where Ein is the input
probe field, t the transmittance, D the diameter of the pump beam, n the refractive
index (neglects the variation with the wavelength), and l the length of the cavity.
Similarly, the transmitted field after passing the cavity 2m+1 time would be:
E2 m1 ( )  tr 2 m Ein e(2 m1)[1/ 2 gD ik0 (  ) nl ] . The total intensity transmitted through is then
10
Itrans   |  tr 2 m Ein e(2 m1)[1/ 2 gD ik0 (  ) nl ] |2

and
the
gain
G
(dB)
=
m
10log[ |  r 2 me(2 m1)[1/ 2 gD ik0 (  ) nl ] |2 /  |  r 2 me(2 m1)[ ik0 (  ) nl ] |2 ] . The fitted result to

m

m
the measured gains is given in Fig. S11c and our simulation yields good agreement
with the experimental results.
Figure S11: Characterization of a photonic amplifier with abrupt gain increase. a The
first panel is a wide field optical image of a CdSe NB on glass (with cross section 245
nm  182 nm). Images I to III were obtained with 7305 nm band pass filter,
corresponding to a probe signal launched from one end of the NB and emitted from
the other (I), PL with the pump only (II), and the amplification of the probe signal
when both pump and probe are present (III). b Time trace of the output intensity at the
emission end of the photonic amplifier. The dashed circles in a mark the area where
the time trace was obtained. BK indicates the background dark counts. c Gain (dB) .vs.
pump intensity. ‘■’ corresponds to the measured gain and the red curve is the fit to a
multi-path gain model. d Three sets of emission spectra, obtained at three different
pump intensities I1, I2 and I3 indicated in c. Red, blue, and green spectra represent the
probe signal, PL, and total output, respectively.
12. Current-Voltage measurements across Ag-Al2O3-Ag junction:
The current through Ag-Al2O3-Ag junction is measured with Keithley 4200-scs
parameter analyzer. The bottom Ag electrode and the ultrathin Al2O3 layer were
prepared the same way as our hybrid plasmonic waveguides. To avoid the damage to
the Al2O3 film during wire bonding, we added the top electrode with silver elargol.
The size of the top electrode ranges from 150  150 μm2 to 400  400 μm2. Fig. S12
shows the measured current .vs. applied voltage across two junctions. The
corresponding resistances are 4.89 ohm and 6.38 ohm for the 4 nm and 3 nm thick
Al2O3 films, respectively. The resistance is also inversely proportional to the area of
11
the top electrode. For an area similar to the CdSe nanobelt (8 μm  250 nm), the
corresponding resistance is in the order of 2  105 ohm across the Ag-Al2O3-Ag
junction. These results suggest that a much broadened conduction band edge in our
Al2O3 film is developed, which can extends a few eV below the band onset of bulk
sapphire and even to the Fermi level of the Ag electrodes,6 making the charge transfer
across the Al2O3 film possible. We attribute the broadening of the conduction band of
Al2O3 film to the specific atomic layer deposition procedure used in our experiments.
Figure S12: current as a function of applied voltage across the Ag-Al2O3-Ag junction
for different Al2O3 thickness.
13. Comparison of averaged transparency threshold for different samples:
The data in the following table were obtained 11 months after the original
measurements of the plasmonic and photonic waveguides. The CdSe NBs have
degraded slightly from the original condition. The quality of the NBs also varies more
from one to another than the original case. The thresholds changed a bit compared to
the numbers presented in the main paper. Nevertheless, the trend obtained from the
following table still show consistency with our expectation.
Sample
Al2O3 thickness of 5 nm
Al2O3 thickness of 15 nm
Photonic case
Averaged Itr (W/cm2)
10.4
19.6
76.6
Error (W/cm2)
8.5
15.3
33.6
Table S1. The comparison of the averaged transparency pump intensities and the
errors for different nanostructures.
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