Supporting Information for
Integration of Nanoscale Light Emitters and Hyperbolic Metamaterials: An Efficient Platform for the Enhancement of Random Laser Action Hung-I Lin1,2, Kun-Ching Shen3, Yu-Ming Liao1,4, Yao-Hsuan Li1, Packiyaraj Perumal2,4, Golam Haider2, Bo Han Cheng3, Wei-Cheng Liao2, Shih-Yao Lin2, Wei-Ju Lin2, Tai-Yuan Lin5, and Yang-Fang Chen1,2* 1
Graduate Institute of Applied Physics, National Taiwan University, Taipei 106, Taiwan 2
Department of Physics, National Taiwan University, Taipei 106, Taiwan Research Center for Applied Sciences, Academia Sinica, Taipei 115, Taiwan 4 Nano Science and Technology Program, Taiwan International Graduate Program, Academia Sinica and National Taiwan University, Taiwan 3
5
Institute of Optoelectronic Sciences, National Taiwan Ocean University, Keelung 202, Taiwan *corresponding author: Yang-Fang Chen:
[email protected]
S1
1. Schematic diagram of ZnO nanoparticles on SiO2/Si substrate.
Figure S1 presents the ZnO nanoparticles on SiO2/Si substrate as a reference sample with 266 nm laser irradiation. The emission intensity is much weaker and the random laser action is much less pronounced than that of the HMM sample due to the absence of high-k modes. The absorption of the emitted light by the SiO2/Si substrate is explicitly shown as dark color in the figure.
Figure S1 | Schematic diagram of ZnO nanoparticles on SiO2/Si substrate.
S2
2. Maxwell-Garnett theory calculation.
To determine the dispersion relation of the HMM and EMM samples, we used the Maxwell-Garnett theory for calculation as shown in Figure S2.1 Thus the dielectric tensor components can be determined by:
Ag (1 ) MoO ,
(S1)
3
and
||
2 (1 ) Ag MoO3 (1 ) MoO 3
(1 ) Ag (1 ) MoO3
,
(S2)
where ρ is the fill fraction of Ag in the multilayer stack.
a
b
HMM
Elliptical Hyperbolic ZnO dispersion random lasing dispersion
ZnO Elliptical random lasing dispersion
Hyperbolic dispersion
50
140 120 100 80 60 40 20 0 400
500
600
700
800
Effective Dielectric Tensor
Effective Dielectric Tensor
160
-20 300
EMM
Wavelength (nm)
40 30 20 10 0 -10 300
400
500
600
700
800
Wavelength (nm)
Figure S2 | (a) and (b) are the effective dielectric tensors calculation for the HMM and EMM samples, respectively. Light red regions are the wavelength range that show hyperbolic dispersion. Black dashed lines are the transition wavelength changing from elliptical dispersion to hyperbolic dispersion. Light green regions are the random lasing wavelength region of ZnO nanoparticles.
S3
3. Comparison of random lasing for the samples with the HMM, EMM, and SiO2/Si substrates. Figure S3 shows the random lasing spectra at high pumping energy (28.4, 29.6, and 32.4 mJ/cm2) for all the measured samples. Clearly separated lasing peaks can be observed demonstrating that the characteristics of random laser after the lasing threshold.
a
b 1200
600
300
0 380
385
390
395
Wavelength (nm)
400
29.6 m J /cm 2
HMM EMM Ref
1200 900 600 300 0 380
385
390
395
Wavelength (nm)
400
1600
Intensity (a.u.)
HMM EMM Ref
900
Intensity (a.u.)
28.4 m J /cm 2 Intensity (a.u.)
c 1500
32.4 m J /cm 2
HMM EMM Ref
1200 800 400 0 380
385
390
395
400
Wavelength (nm)
Figure S3 | Comparison of random lasing for the samples with the HMM, EMM, and SiO2/Si substrates. (a-c) are the emission intensity at pumping energy density of 28.4, 29.6, and 32.4 mJ/cm2, respectively, which is very useful to clearly observe the distinct lasing characteristics for different samples.
S4
4. Emission stability of random lasing action. Figure S4 presents the emission spectra of random lasing action detected with a tilted sample holder angle of 30° and 60°. We found that the emission intensity and the lasing threshold retains the similar behavior demonstrating that the unique characteristics of the broad angular emission. The average enhancement in emission intensity of the HMM is ~6 times and the ~20% reduction of lasing threshold.
a
b 2500
2500
Intensity (a.u.)
2000
Emission Pump laser θ=30°
1500 1000 500 0 16
20
24
HMM EMM Ref
2000
Intensity (a.u.)
HMM EMM Ref
Pumping energy density (mJ/cm2)
Pump laser θ=60°
1500 1000 500 0 16
28
Emission
20
24
28
Pumping energy density (mJ/cm2)
Figure S4 | Emission spectra of random lasing action detected in different angle. (a) 30° and (b) 60°.
S5
5. Additional red-shift laser action spectrum occurred on the HMM. Figure S5 presents the additional strong red-shift laser action spectrum, which only occurs for the HMM sample under the pumping energy density of 26.8 and 29.6 mJ/cm2. The additional central emission wavelengths are at 391.8 and 392.3 nm, respectively.
26.8 mJ/cm2 29.6 mJ/cm2
Intensity (a.u.)
1200 900 600 300 0 380
385
390
395
400
Wavelength (nm)
Figure S5 | Emission intensity at pumping energy density of 26.8 and 29.6 mJ/cm2 for the HMM sample.
S6
6. Emission stability of random lasing action. Figure S6 shows the emission stability for ZnO nanoparticles deposited on the HMM, EMM, and references samples under the pumping energy density of 26.8 mJ/cm2. The emission shows an excellent stability that can be repeated for more than 200 times without photodegradation.
Intensity (a.u.)
1200
900
600
26.8 mJ/cm2
HMM EMM Ref
300
0 0
50
100
150
200
Cycle index Figure S6 | The evolution of emission peak intensity as a function of repeating cycles.
S7
7. Additional Purcell factor calculations. Figure S7 depicts the Purcell factor for the dipole distances at 30 and 50 nm above the substrates at the emission wavelength of 395 nm, which shows the similar trends for both cases.
a
b 6
HMM EMM Ref
Purcell factor
Purcell factor
15
30 nm
10
5
0 380
385
390
395
HMM EMM Ref
2
0 380
400
Wavelength (nm)
50 nm
4
385
390
395
400
Wavelength (nm)
Figure S7 | Calculated Purcell factors for a dipole source located at (a) 30 and (b) 50 nm above the substrates (insets images).
S8
8. Discussion of scattering efficiency. The scattering cross-sectional area is a projected plane perpendicular to the incident
3 3 2 R , and for sphere size is R 2 , where 2
light,2 that is, for hexagonal column size is
R is the radius of ZnO nanoparticles. For a hexagonal column size with the incident field Ei Ex ex E y ey , the σscat is given by:2
scat ( hexagon )
4
| T |2 d , k 2 | Ei |2
(S3)
where k is the wave number, is the solid angle, T E x X E yY and Y is the scattering amplitude for incident light with y-polarization. On the other hand, for a ZnO nanoparticle with sphere size can be calculated based on the Mie theory. The scattering cross-section for the Mie theory is given by:2
scat ( sphere)
2 k2
(2n 1)(| a
n
n 1
|2 | bn |2 ) ,
(S4)
where the scattering coefficients an and bn are determined by:
m n mx n' x n x n' mx an , m n mx n' x n x n' mx
(S5)
n mx n' x m n x n' mx bn , n mx n' x mn x n' mx
(S6)
where n and n can be realized as the Riccati-Bessel functions, x is the size parameter and m is the relative refractive index are:
x kR
S9
2 NR
,
(S7)
m
k1 N1 , k N
(S8)
where N1 and N are the refractive indices of ZnO nanoparticles and medium, respectively. 9. Simulation for the cross-sectional distributions of |E|2 around the ZnO nanoparticles on different substrates. Figure S8 presents the simulation results for the cross-sectional distributions of |E|2 for all the samples. The central emission wavelength is set at 388 nm.
a
b
HMM
c
EMM
Re f
Figure S8 | (a-c) The cross-sectional distributions of |E|2 around the ZnO nanoparticles placed on the HMM, EMM, and reference substrate under a normally incident light at a wavelength of 388 nm, respectively.
S10
10. Complex refractive index of MoO3, Ag, and ZnO.
Complex Refractive Index
The complex refractive indices for MoO3,2 Ag,3 and ZnO4 used in this work are shown in Figure S9.
5 0 -5
n_MoO3 n_Ag n_ZnO
-10 -15
k_MoO3 k_Ag k_ZnO
-20 -25 300
400
500
600
700
800
Wavelength (nm) Figure S9 | Complex refractive indices of real (solid lines) and imaginary (dashed lines) parts used in our theoretical calculations and numerical simulations.
S11
References 1.
Cortes, C. L.; Newman, W.; Molesky, S.; Jacob, Z. Quantum Nanophotonics
2.
Using Hyperbolic Metamaterials. J. Opt. 2012, 14, 063001. Bohren, C. F. & Huffman, D. R. Absorption and Scattering of Light by Small
3.
Particles. 2008 (Wiley, New York). Shi, X. B.; Hu, Y.; Wang, B.; Zhang, L.; Wang, Z. K.; Liao, L. S. Conductive
4.
Inorganic-Organic Hybrid Distributed Bragg Reflectors. Adv. Mater. 2015, 27, 6696-6701. Rakić, A. D.; Djurišić, A. B.; Elazar, J. M.; Majewski, M. L. Optical Properties
5.
of Metallic Films for Vertical-Cavity Optoelectronic Devices. Appl. Opt. 1998, 37, 5271-5283. Zhang, D. Y.; Wang, P. P.; Murakami, R. I.; Song, X. P. First-Principles Simulation and Experimental Evidence for Improvement of Transmittance in ZnO Films. Prog. Nat. Sci.: Mater. Int. 2011, 21, 40-45.
S12
