The understanding of nonlinear light–matter interactions at the nanoscale has fueled worldwide interest in upconversion emission for imaging, lasing, and sensing. Upconversion lasers with anti-Stokes-type emission with various designs have been reported. However, reducing the volume and lasing threshold of such lasers to the nanoscale level is a fundamental photonics challenge. Here, we demonstrate that the upconversion efficiency can be improved by exploiting single-mode upconversion lasing from a single organo-lead halide perovskite nanocrystal in a resonance-adjustable plasmonic nanocavity. This upconversion plasmonic nanolaser has a very low lasing threshold (10 μJ cm⁻²) and a calculated ultrasmall mode volume (∼0.06 λ³) at 6 K. To provide the unique feature for lasing action, a temporal coherence signature of the upconversion plasmonic nanolasing was determined by measuring the second-order correlation function. The localized-electromagnetic-field confinement can be tailored in titanium nitride resonance-adjustable nanocavities, enhancing the pump-photon absorption and upconverted photon emission rate to achieve lasing. The proof-of-concept results significantly expand the performance of upconversion nanolasers, which are useful in applications such as on-chip, coherent, nonlinear optics, information processing, data storage, and sensing

Atwater, Harry A.

Chang, Shu-Wei

Cheng, Pi-Ju

Chu, Chih Wei

Guo, Tzung-Fang

Lu, Ming-Yen

Lu, Yu-Jung

Peng, Kang-Ning

Shen, Teng Lam

English

Caltech Authors - Main

 S1 
Supporting Information for 
Upconversion Plasmonic Lasing from an Organolead Trihalide 
Perovskite Nanocrystal with Low Threshold 
 
Yu-Jung Lu1,2,3*, Teng Lam Shen1,4, Kang-Ning Peng1, Pi-Ju Cheng1, Shu-Wei Chang1, Ming-Yen 
Lu5, Chih Wei Chu1, Tzung-Fang Guo4, and Harry A. Atwater2* 
 
1Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan 
2Thomas J. Watson Laboratories of Applied Physics, California Institute of Technology, Pasadena, California 91125, 
United States 
3Department of Physics, National Taiwan University, Taipei 10617, Taiwan 
4Department of Photonics, National Cheng Kung University, Tainan 701, Taiwan 
5Department of Materials Science and Engineering, National Tsing-Hua University, Hsinchu 30013, Taiwan 
 
 *To whom correspondence should be addressed.  
*E-mail: yujunglu@gate.sinica.edu.tw(Y.J.L.), haa@caltech.edu (H.A.A.) 
 
 
This PDF file includes: 
Note S1. Characterization of plasmonic TiN films…………………………………………………...S2 
Note S2. Optical properties of perovskite nanocrystal..……………………………………………....S4 
Note S3. Table of the reported two-photon-pumped perovskite lasers….…………………………….S7 
Note S4. Theoretical analysis of the lasing threshold………………………………………………....S8 
Note S5. Extraction of the spontaneous-emission coupling factor………...………………………....S10 
Note S6. Temporal coherence signature by second order correlation function measurements............S13 
 
 
 
 S2 
Note S1. Characterization of plasmonic TiN films 
Based on our previous work1, the properties of the TiN film can be varied with the argon/nitrogen flow 
rate, target, DC/RF power, and growth temperature. We sputtered TiN film on silicon substrate with DC/RF 
magnetron sputtering at a chamber pressure of < 6 × 10-8 torr and at 800 C. The detail growth parameters 
show in Table S1.  
 
Table S1. Material properties and growth parameters of TiN films. We deposit thin TiN films via DC/RF 
sputtering. The properties of the TiN films are controlled by changing the growth parameter. 
Epsilon near zero (ENZ) point (nm) 510 nm 670 nm 
Ellipsometry fitting model 1 Drude and  
2 Lorentz oscillators 
1 Drude and  
2 Lorentz oscillators 
Target TiN Ti 
Optical property Plasmonic Plasmonic 
Film thickness (nm) 80 88 
Substrate Si Si 
Applied Power (W) RF: 120 W DC: 200 W 
Ar/N2 flow rate 12/0 1.5/18 
Base Pressure (torr) 6 × 10-9 6 × 10-8 
Gas pressure (mtorr)  3 5  
Growth temperature (C) 800 800 
 
 S3 
We measure the complex dielectric permittivity of the fabricated TiN films by using spectroscopic 
ellipsometry (J.A.Woollam Co.). We fit the ellipsometrically measured data by using the Drude-Lorentz 
model2, which is a sum a Drude term and two Lorentz oscillators:  
                                          (S1) 
We identify the values of the free parameters incorporated in the model by fitting them to the 
ellipsometry data. There are three free parameters in the Drude terms of Eq. (S1): the damping factor ΓD, 
plasma frequency , and . The plasma frequency relates to the electron effective mass m* and the carrier 
density of the film N as follows: . Here, q is the electron charge,  is the dielectric permittivity 
of vacuum. Each Lorentz oscillator in Eq. (S1) contains three fitting parameters: the oscillator strength , the 
damping factor , and the oscillator position . Here, the index j numerates the Lorentz oscillators 
(j=1,2,3). Table S2 summarizes the values of the obtained fitting parameters that have been used to produce 
Figure 2. In addition, the electrical properties of TiN films can be derived from the fitting parameters of the 
ellipsometry spectra presented in Table S2.  
Resistivity:  (μΩ-cm)= 1/(0 p2 )                         (S2) 
Collision frequency:  (1/s)=/ћ                           (S3) 
The calculated electrical resistivity of TiN film is 21 μΩ-cm, which is ten times larger than the 
reported resistivity of gold film (2.44 μΩ-cm). Note that the conductivity σ is the reciprocal of the resistivity . 
The results indicate that the ohmic loss of TiN film is less than that of gold. 
 S4 
Table S2. The Drude-Lorentz fitting parameters for the complex dielectric permittivity of two different TiN 
fims.  
ENZ 
wavelength 
p 
(eV) 
ΓD 
(eV) 
f1  o, 1 
(eV) 
1 
(eV) 
f2 o, 2 
(eV) 
2 
 (eV) 
 
510 nm 6.9 0.5 4.8 5.5 3.1 0.4 2.5 2.1 1.4 
670 nm 4.4 1.1 3.8 5.0 3.4 0.5 2.7 1.2 2.1 
 
 
 
 
 
 
Note S2. Optical properties of perovskite nanocrystal 
 
 
Figure S1. Power-dependent PL spectra recorded under two-photon excitations from a single MAPbBr3 
nanocrystal on silicon substrate measured at 6 K. (a) Power-dependent PL spectra. (b) A quadratic dependence 
of PL emission on the pump fluence of two-photon excitation, representing the feature of spontaneous 
emission. The line widths of PNC on silicon at various pump levels remain at approximately 6-7 nm. 
 
 
 
 
 S5 
 
Figure S2. Optical characteristics of MAPbBr3 nanocrystals film at room temperature. Optical absorption 
spectrum (black line) and photoluminescence spectrum (green line) of MAPbBr3 Nanocrystals film. The 
perovskite nanocrystals with edge lengths in the range of 100 nm – 500 nm. 
 S6 
 
Figure S3. Temperature dependent photoluminescence (PL) of a single MAPbBr3 nanocrystal on silicon 
substrate (pump fluence= 156 Jcm–2). (a) The emission intensity as a function of temperature. (b) Position of 
the PL peaks as a function of temperature. (c) Linewidth of the PL peaks as a function of temperature. 
 
 
 
 
 
 
 
 S7 
Note S3. Table of the reported two-photon-pumped perovskite lasers. 
Gain Material Geometry Dimension Pump (pulsed 
width, 
repetition 
rate) 
Temperature Lasing 
Threshold 
CH3NH3PbBr33 Microwire; 
Photonic mode 
18.64 m 840 nm 
625 nm 
100 fs, 1kHz  not mentioned 674 μJ/cm2  
MAPbBr34 Microwire and 
Microplate; 
Photonic mode 
Microwire: 5.5 m  
300 nm 370 nm 
Microplate: 4 m 4 
m 620 nm 
150 fs, 1 kHz not mentioned Microwire: 
112 μJ/cm2  
Microplate: 
 62 μJ/cm2  
CsPbBr35 Nanocrystal;  
Photonic mode 
Microring: 
Inner diameter: 60 
m  
Thickness: 300 nm 
90 fs, 1 kHz Room 
temperature 
0.8 mJ/cm2 
CsPbBr36 Nanorod; 
Photonic mode 
Triangular 
cross-sections 
Leg: 250 nm,  
Base: 400 nm 
Length: 10 mm 
80 fs, 1 kHz Room 
temperature 
0.60 mJ/cm2 
CsPb2Br57  Microplate; 
Photonic mode 
4.5 m 4.5 m 
0.3–1.8 m 
100 fs, 1 kHz  Room 
temperature 
21.5 mJ/cm2 
CsPbBr2Cl8  Nanoplate; 
Photonic mode 
1 m 1 m 150 nm 100 fs, 79 
MHz 
77 K 4.84 μJ/cm2 
CsPbBr39 Microrod; 
Photonic mode 
33.96 m 5.622 
m 3.494 m  
100 fs, 1 kHz Room 
temperature 
34.5 mJ/cm2 
CsPbBr310 Microsphere;  
Photonic mode 
Diameter of 0.6–1.5 
m 
40 fs, 10 kHz Room 
temperature 
203.7 µJ/cm2 
CsPbI311  Nanosheet; 
Photonic mode 
10 m 10 m  
6 nm 
80 fs, 1 kHz Room 
temperature 
2.6 mJ/cm2  
CsPbBr312 Quantum Dots in 
silica sphere; 
Photonic mode 
Diameter of 1–2 m 35 fs, 1 kHz Room 
temperature 
430 μJ/cm2  
This Work 
MAPbBr3 
Nanocrystal; 
Plasmonic mode 
300 nm 300 nm 
100 nm 
100 fs, 80 
MHz 
6 K 10 μJ/cm2 
Table S3. Lasing threshold of the reported upconversion perovskite lasers. 
 S8 
Note S4. Theoretical analysis of the lasing threshold. 
 
Figure S4. Field profile of potential lasing mode at a wavelength of 551 nm on the middle plane of the oxide 
layer. 
 
We solved the eigenmodes and corresponding frequencies of the plasmonic nanocavity inside the gain 
window of perovskite with the three-dimensional finite-element method (COMSOL eigenfrequency solver). 
In the model, the perovskite nanocrystal is placed on the three-layer structure composed of Al2O3, TiN, and Si. 
In the calculation, the refractive indices are 2.413 for the perovskite, 1.68 for the oxide layer, and 4.09 for the 
silicon substrate. The index of TiN is extracted from the ellipsometry data. Only two modes with adequate 
quality factors and well-confined modal profiles were found. The one with the longer photon lifetime is the 
Fabry-Perot-like mode, whose modal profile |E| on the middle plane of Al2O3 is shown in Figure S4. This 
modal profile exhibits strong confinement at the wavelength of 551 nm. A very small modal volume of a 
confined mode (~0.06 3) is calculated by the three-dimensional finite-element method. The effective mode 
volume, Vm, is the ratio of a mode's total energy density per unit length to its peak energy density, where W(r) 
is the energy density. 
 S9 
                  (S5) 
                      (S6) 
To estimate the threshold gain of the mode, we solved the eigenmodes at an increasing imaginary part 
of permittivity (gain) of the perovskite. The threshold gain that compensates the absorption and radiation 
losses (real oscillation frequency) is approximately 3382 cm-1. The other mode has a larger threshold gain and 
a frequency that deviates farther from the gain window of perovskite; hence, it is less likely to be the lasing 
mode. 
 
 
 
 
 
 
 
 
 
 
 
 S10 
Note S5. Extraction of the spontaneous-emission coupling factor. 
We used the rate equations of carrier density  and photon density S to fit the light-in-versus-light-out 
curves of nanolasers: 
,                           (1a) 
,                          (1b) 
,                                (1c) 
where  is the volume of the active region;  is the order of the pump process;  is the -photon 
pump coefficient;  is the pump power;  is the photon energy of the pump;  is the spontaneous 
emission lifetime;  is the group velocity;  is the material gain and is modeled as a linear function of 
;  is the photon lifetime;  is the confinement factor;  is the spontaneous-emission coupling factor; 
 is the differential gain; and  is the transparency density. 
The pump can be a pulse train with period  and variable peak power, or a continuous-wave (CW) 
beam with infinite period but constant power. For a physical variable , let us define its time average within 
a period  as  and apply this average to Eqs. (1a) and (1b). 
With ,  (  is a factor depending on the pulse shape and repetition 
rate), and the approximation , we can eliminate  and express  as a function of the mean pump 
power . The time-averaged observed power  is then 
 S11 
,                                  (2) 
where  is the external quantum efficiency including the effects of out-coupling from the nanolaser to free 
space and detectability of the characterization system;  is the photon energy of the lasing mode; and 
 is the mode volume. 
In practice, we rescale  and  with some scaling powers  and , respectively, which are 
chosen at one’s convenience (they are not fitting parameters). After solving the time average of Eqs. (1a) and 
(1b), we express the scaled observed power  in terms of the scaled pump power /  as 
,    (3) 
where parameters  to  are defined as follows: 
,                              (4a) 
,                              (4b) 
,                       (4c) 
 .                                    (4d) 
At the high-pump limit, equation (3) can be approximated as 
,                            (5a) 
 S12 
and therefore parameter  is related to the time-average threshold pump power  at which the 
right-hand side of Eq. (5a) vanishes: 
.                               (5b) 
We adopt the method of least-square fitting and treat parameters  to  as fitting parameters to the 
relation between  and / . The reason for the logarithmic-scale fitting is to 
grasp the turn-on behavior of nanolasers which may appear insignificant in the linear scale. In addition, the 
order  of pump process is taken as a fitting parameter ( ) since it may deviate from the ideal number in 
some experimental conditions. The parameter  can be fixed if necessary. After these fitting parameters are 
obtained, we then estimate the spontaneous-emission coupling factor  as 
,                                   (6) 
where we have further assumed that the condition  holds so that the corresponding term in 
Eq. (4c) is dropped. 
 
 
 
 
 
 
 
 
 
 
 
 
 S13 
Note S6. Temporal coherence signature by second order correlation function measurements. 
 
 
 
Figure S5. Temporal coherence signature of the plasmonic upconverting nanolaser determined from 
second-order photon correlation function measurements obtained at 7 K. (a) Optical intensity versus 
pump fluences for the nanolasing mode at 551 nm with a lasing threshold of approximately 10 J cm2. The 
black and red dashed lines indicate the fixed pump fluence that we use below and well above the lasing 
threshold, respectively. (b) Below the lasing threshold (5 J cm2), g(2)(t = 0) is greater than one, representing 
spontaneous emission (thermal bunched state). (c) Above the lasing threshold (26 J cm2), g(2)(t = 0) 
approaches unity, which represents the temporal coherence signature of lasing. This result was obtained by 
using a Hanbury Brown–Twiss (HBT) setup equipped with quantum correlation analysis software (QuCou, 
PicoQuant). 
 
 
 S14 
 
Figure S6. Second-order photon correlation function of the pulsed laser at 800 nm with an ultrafast pulsed 
duration of 100 fs and repetition rate of 80 MHz. This plot can be used to identify the point of zero time delay 
in the Hanbury Brown–Twiss system. 
 
 
 
 
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Upconversion Plasmonic Lasing from an Organolead Trihalide Perovskite Nanocrystal with Low Threshold

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Upconversion Plasmonic Lasing from an Organolead Trihalide Perovskite Nanocrystal with Low Threshold

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