Integration of Nanoscale Light Emitters and Hyperbolic Metamaterials

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Letter

Integration of Nanoscale Light Emitters and Hyperbolic Metamaterials: An Efficient Platform for the Enhancement of Random Laser Action Hung-I Lin, Kun-Ching Shen, Yu-Ming Liao, Yao-Hsuan Li, Packiyaraj Perumal, Golam Haider, Bo Han Cheng, Wei-Cheng Liao, Shih-Yao Lin, Wei-Ju Lin, Tai-Yuan Lin, and Yang-Fang Chen ACS Photonics, Just Accepted Manuscript • Publication Date (Web): 20 Dec 2017 Downloaded from http://pubs.acs.org on December 20, 2017

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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

3

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

5

Institute of Optoelectronic Sciences, National Taiwan Ocean University, Keelung 202, Taiwan *corresponding author: Yang-Fang Chen: [email protected]

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Abstract Hyperbolic metamaterials have emerged as novel materials with exciting functionalities, especially for optoelectronic devices. Here, we provide the first attempt to integrate hyperbolic metamaterials with light emitting nanostructures, which enables to strongly enhance random laser action with reduced lasing threshold. Interestingly, the differential quantum efficiency can be enhanced by more than four times. The underlying mechanism can be interpreted well based on the fact that the high-k modes excited by hyperbolic metamaterials can greatly increase the possibility of forming close loops decreasing the energy consumption for the propagation of scattered photons in the matrix. In addition, out-coupled propagation of the high-k modes reaches to the far-field without being trapped inside the metamaterials due to the coupling with the random distribution of light emitting nanoparticles also plays an important role. Electromagnetic simulations derived from the finite-difference time-domain (FDTD) method are executed to support our interpretation. Realizing strong enhancement of laser action assisted by hyperbolic metamaterials provides an attractive, very simple and efficient scheme for the development of high performance optoelectronic devices, including phototransistors, and many other solid state lighting systems. Besides, because of increasing light absorption assisted by hyperbolic metamaterials structure, our approach shown is also useful for the application of highly efficient solar cells.

Keywords hyperbolic metamaterials, random lasers, zinc oxide, scattering, high-k modes

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Laser plays a significant role in our daily life nowadays since discovered in 1954.1 Among various kinds of lasers, random laser has attracted a great deal of attention recently, in which light can be amplified by multiple scatterings in a random system.2 While gain exceeds loss, together with population inversion and simulated emission, random laser action can be observed.2 Because of the inherent advantages including low cost, simple design, and angle-free emission, random lasers have an excellent potential for the applications in various fields such as display, biological probe, speckle-free images, and highly stretchable optoelectronics.3-7 Recently, plasmonic resonance is of great interest in random lasers since plasmonic-based systems can greatly enhance lasing intensity and reduce threshold.8 Owing to coherent oscillations of delocalized electrons near the nanoparticles surface, light intensity can be drastically amplified. However, in a broadband emission system, plasmonic-based systems are not feasible, because in such systems, they can only enhance a specific wavelength, due to the fact that their effects are strongly related to the geometry and type of nanoparticles.9 Consequently, the demand for developing a new methodology is highly desirable. On the other hand, recent studies related to metamaterials have achieved enormous breakthroughs, such as breaking diffraction limit,10-12 meta-lens,13,14 and invisible cloak,15,16 by controlling electromagnetic waves to pass through artificial metamaterials of sub-wavelength thickness. One class of metamaterials, defined as the hyperbolic metamaterials (HMMs), composed of precise design with alternate metal-dielectric multilayers or parallel metallic nano-rods in a dielectric matrix are distinguished

by

their

hyperbolic

dispersion

of

iso-frequency

curve

in

momentum-space.17,18 Interestingly, the sign of the effective permittivity (ε) (or permeability (µ)) of the HMMs exhibits the opposite direction in the optical tensor 3


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(i.e.,

ω2 c2

=

ε ⊥ ⋅ ε || is the matrix element of inner product perturbation Hamiltonian ( H' ) between the initial state and the final state. The density of state is determined by wavevector:

ρ (k ) ∝ k 3 ,

(2)

leading the HMM is larger than the isotropic medium because of the wavevector in isotropic medium is bounded by the volume of sphere. Notably, the HMM allows the unbounded value of wavevector with higher transition rate. Hence, the stimulated emission for the HMM sample is theoretically enhanced compared with the isotropic medium samples. Closed loop paths acting as laser resonators are essential for a laser action to 9


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occur.36 In addition, 3D disordered skeleton of ZnO nanoparticles as shown in Fig. 1b provides an excellent platform for the formation of suspended closed loop paths. This unique feature is beneficial for the light confinement and to achieve random laser action easily. To confirm the mechanism of random lasing from the closed loop paths, we have further examined the mode spacing ( ∆λ ), two nearest lasing peaks, which are about 1.5, 2.4, and 3.0 nm for the HMM, EMM, and reference samples, respectively (database from more than 100 sets statistics). This distinct behavior provides an addition evidence that the laser action is much easier to achieve for the HMM system because the lasing peak density is higher. Importantly, the shortened mode spacing for the HMM can be understood as follows. First, the out-coupled energy from the high-k modes can reemit into a wider free space covering a large area of ZnO nanoparticles, resulting in the higher probability for the formation of the closed loops. Second, in the HMM scheme, photons propagate with higher efficiency and lower cavity losses.

Photoluminescence spectra and the corresponding kinetics In order to provide additional evidence, we have performed the photoluminescence kinetics for the three samples. Figure 3a presents the photoluminescence spectra, measured by 375 nm pulsed diode laser with pumping energy density of 103 µJ/cm2. Note that the photoluminescence intensity for the HMM is 1.93 and 3.92 times stronger than that of the EMM and reference samples, respectively, which is about 1.6 times smaller than using 266 nm pulse laser as the pumping light source, this may be attributed to the smaller pumping energy density. Again, we can ascribe this enhancement to the high-k modes from the HMM sample. Besides, a slight red shift on the photoluminescence spectrum is also observed. The center wavelengths of the HMM, EMM, and reference samples are 396.0, 394.8, and 394.6 nm, respectively. 10


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This is due to the dispersion of the Purcell enhancement factor from the high PDOS with hyperbolic dispersion.37 Purcell factor is used to characterize the enhancement rate influenced by the surroundings with the dipole radiation based on the spontaneous emission dynamics.38 Figure 3b is the calculated Purcell factor composed of the dipole direction that perpendicular ( F⊥ ) and parallel ( F|| ) to the substrates by putting a dipole source above the surface for 10 nm of all the samples, while Purcell factor is determined by:39 Fiso =

1 2 F⊥ + F|| . 3 3

(3)

Note that, the Purcell factor for the HMM at the wavelength of 395 nm, which corresponds to the spontaneous emission of ZnO nanoparticles, is larger than that of the EMM leading to the red shift of the spectrum shown in Fig. 3a. Similar trends can also be seen in Figs. S7a and S7b for the dipole distances at 30 and 50 nm above the substrates. Figure 3c shows that the Purcell factor decreases exponentially with increasing dipole distance away from the substrates. Next, to understand the charrier dynamics for ZnO nanoparticles on all three samples, time-resolved photoluminescence (TRPL) has been conducted as shown in Fig. 3d. All the fitting curves were well fitted by two exponentials arising from the random distribution of ZnO nanoparticles. The shorter (longer) lifetime for the HMM, EMM, and reference samples are 2.82 (3.21), 3.64 (4.80), and 4.73 (6.24) ns, respectively. The averaged lifetime of the HMM is about 44% shorter than that of the reference sample. The shorter lifetime can be attributed to the ZnO nanoparticles close to the substrate, which possess a strong out-coupled effect from the substrate, while the longer lifetime is determined by those ZnO nanoparticles away from the substrate. For the HMM sample, the shortened lifetime can be attributed to the effect of the 11


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excited high-k modes, which can increase the recombination rate of photogenerated carriers inside ZnO nanoparticles, and therefore the lifetime is reduced. To understand the lifetime reduction dynamics, we consider the decay rate of high-k modes from the HMM. The emission of ZnO nanoparticles can be assumed as a dipole emitter on the surface of the HMM, thus the enhancement of the decay rate is given by: 18

Γ high − k =

µ ⊥2 2 | ε || | ε ⊥ , 8hd 3 1+ | ε || | ε ⊥

(4)

where µ⊥ is the perpendicularly oriented dipole and d is the distance from the dipole of ZnO nanoparticles to the HMM. This additional decay rate factor should be considered when the dispersion changes from elliptical to hyperbolic relationship for the EMM to the HMM compared with the reference samples. As a consequence, the reduction of lifetime for ZnO nanoparticles on the HMM becomes much more pronounced. Besides, optical gain of random laser action can be determined by the measured lifetime:40 ∑(ω ) = −

σ0

1 1 [ ], + 2 1 + i (ω − ω0 )τ 1 + i (ω + ω0 )τ

(5)

where σ 0 is the peak value of optical gain set that is determined by the pumping level, and τ is the dipole relation time, which corresponds to the measured lifetime. Note that the lifetime is inversely proportional to the optical gain enabling to explain the fact that the measured emission intensity for the HMM is stronger than that of the EMM and reference samples.

Numerical simulation Light being scattered by passing through the randomly distributed ZnO nanoparticles may excite more high-k modes in the reciprocal space for the HMM sample, which 12


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only exist along the specific directions close to the asymptotic cone of the hyperboloid. In addition to excite high-k modes, out-coupled power reaching to the far-field rather than being trapped or annihilated inside the multilayers due to ohmic loss owing to its metal composition is also a critical issue for random lasing action.41 To circumvent this challenge, previous studies have implemented nanopatterned grating structures fabricated by electron beam lithography to achieve the propagation of out-coupling power.42,43 However, this method is too costive, which is a major drawback for future industrial application. Notably, by our proposed design using random distribution of ZnO nanoparticles with proper geometries deposited on the HMM, we can overcome this issue easily. To prove our proposed method, we have performed the distributions of time-resolved electric field intensity (|E|2) using 3D FDTD method for a ZnO nanoparticle with hexagonal column size (radius=40 nm, height=100 nm) placed on the HMM, EMM, and SiO2/Si substrates, respectively, as shown in the supporting movie. The incident light is the plane wave with central wavelength of 388 nm. Note that, only the scattered |E|2 can be shown in the scattering monitor (outside the square box). For the HMM sample, we can clearly observe that the majority of the scattered |E|2 from the ZnO nanoparticle will be out-coupled to the far-field owing to the higher transition rate from the high-k modes instead of being confined in the multilayers. The strong out-coupled effect can be realized as VPP, which is the result of the coupling effect from SPP between the metal-dielectric interfaces. Note that, these strong scattered |E|2 gives a strong feedback to the high-k modes inside the HMM, resulting in the gain that can overcome its loss with higher possibility. On the other hand, for the EMM sample, about half of the scattered |E|2 will be trapped inside the multilayers and then propagate to the forward direction or even being annihilated inside the multilayers due to ohmic loss, which is known for the SPP effect. As for the reference sample, without 13


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the assist from VPP and SPP, the majority of the |E|2 is scattered in the forward direction. Thus, this supporting movie for the distributions of time-resolved |E|2 provides an additional evidence for our proposed mechanism. The interaction of light with ZnO nanoparticles is mainly determined by the size and geometry of the nanoparticles and its surroundings. Figures 4a and 4b present the efficiencies44 (scattering cross-section (σscat) divided by its scattering cross-sectional area) for ZnO nanoparticles with a hexagonal column size (radius=40 nm, height=100 nm) and a sphere size (radius=40 nm) influenced by the substrates, respectively, where the detailed calculation method is shown in the Supplementary Information. We can clearly observe that the efficiency for the ZnO nanoparticles with hexagonal column size is an order of magnitude higher than the sphere size due to the additional |E|2 excited from the different geometries. For example, at 388.6 nm, which corresponds to the random lasing emission of ZnO nanoparticles, the HMM reaches efficiency of 2.26 (0.19) for a hexagonal column (sphere) size. Note that for the HMM sample, the highest efficiency is located at 389 nm while for the EMM sample is at 387 nm, which is in excellent agreement with the experimental results shown in Figs. 2 and 3, and gives a strong evidence for the red shift observed in the random lasing action. This result arises from the existence of high-k modes owing to the lower propagation dissipation in the HMM sample rather than being decayed as an evanescent field. Besides, we further examine the out-coupling configurations for the HMM sample as shown in Fig. 4c. The formula of iso-frequency curve is given by: 2

2

 k HMM , ⊥  1  k HMM , z  1 + = 1,     k 0  ε zz  k0  ε ⊥

where k0 = ω c , while k HMM , ⊥ and k HMM,z

(6)

are the corresponding effective

14


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wave-vectors perpendicular and parallel to the optical axis of the HMM sample, respectively. Importantly, the out-coupling effect of high-k modes occurs when

| k HMM | > | kair | . Since random lasing action is induced by multiple scattering in between ZnO nanoparticles, light can be easily scattered and then spread out to all the directions into the HMM sample, making the proposed design to have a higher chance to excite the additional high-k modes. As expected, the additional excitation of high-k modes results in the increased PDOS, consequently the transition rate for occurring the random lasing action of the ZnO nanoparticles on top of the HMM substrate is enhanced, which can suppress the optical loss due to the involvement of metal. Figures 4d-4f (Figs. S8a-S8c) depict the top-view (cross-sectional) distributions of |E|2 using a normally incident light at 388 nm wavelength around the ZnO nanoparticle with a hexagonal column size placed on the HMM, EMM, and reference substrate, respectively. As expected, most of the |E|2 out-coupled to the free-space for the HMM sample instead of being trapped inside the multilayers. To further understand the scattered field intensity from the ZnO nanoparticles on different substrates, here we perform the far-field angular |E|2 distributions as shown in Figs. 5a-5c for the HMM, EMM, and references samples, respectively. The incident light with central wavelength of 388 nm is set at the normal direction. Moreover, since the random lasing action is a process of random scattering from the ZnO nanoparticles nearby, we also perform the simulation from the multiple incident angles as shown in Figs. 5d-5f for all the samples from normal to 85° with XY, XZ, and YZ planes, respectively. To get a clear understanding of the scattered intensity to the side of ZnO nanoparticles, here we only show the scattered angles from 0° to 180°. For the XY plane (Fig. 5d), the variation of far-field angular |E|2 distributions for all the samples are not clear. Remarkably, by considering the XZ and YZ planes (while Z 15


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is the scattering direction normal to the substrate which is beneficial for the formation of the close-loop path thus to generate random lasing with higher possibility), a significant increment of intensity for the HMM sample can be observed. Finally, we stress here that our current study is to provide a proof of concept for the physics behind using HMM with high-k modes to interact with semiconductor nanoparticles to achieve a broadband enhancement of emission spectra. To illustrate the underlying working principle, we have demonstrated that these high-k modes can induce a higher PDOS and then the transition rate is subsequently higher, resulting in the enhancement of the random laser action in ZnO nanoparticles. Notably, the enhancement factor can be further increased by an extra fabrication work with more dedicated experimental systems. For example, a suitable design of two-dimensional photonic crystal with resonant cavity, periodical monolayer semiconductor nanoparticles array, or even patterned two dimensional materials are very useful to observe a more pronounced effect. Nevertheless, our work shown here can serve as an important guideline for the future development.

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Conclusion We have made the first attempt to successfully demonstrate the integration of the HMM with random laser systems for enhancing stimulated emission and reducing lasing threshold. With proper design of metal-dielectric structures, elliptical or hyperbolic dispersion can be obtained, leading to the different emission enhancement for a laser action. Compared with the reference sample based on SiO2/Si substrate, the HMM sample achieves ~6 times lasing intensity, lowers ~20% of lasing threshold, shortens 44% lifetime, and enhances the differential quantum efficiency by 4.5 times. Moreover, rough interface between ZnO nanoparticles and the HMM can assist the propagation of the out-coupling power of the high-k modes to the far-field easily rather than let the emitted light get trapped inside the multilayer structure. Red shift occurs on the HMM sample showing the reduction of optical loss of photon propagation, which enables to enhance random lasing action and reduce threshold. The results from FDTD simulations confirm the existence of high-k modes in the HMM, which can be used to interpret the enhanced performance of laser action well. We believe that our study can not only broaden the application of metamaterials, but also provide a novel module for high efficiency optoelectronic devices, including many other solid state lighting systems, solar cells, and phototransistors.

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Methods Fabrication of layered structures and ZnO nanoparticles The Si wafer with a 150 nm thick SiO2 dielectric layer is used as the substrate in this work. Before depositing the multilayers, the SiO2/Si substrate was previously ultrasonically cleaned for 10 min in acetone, ethanol and deionized (DI) water in sequence to remove any unwanted contaminant. Then, the substrate was heated on a hotplate at 80 °C for 10 min to remove the absorbed moisture in order to reach a high quality for the following multilayers deposition. Both the HMM and EMM samples with 6 pairs of Ag-MoO3 multilayer structures were alternately deposited on the pre-cleaned SiO2/Si substrate using thermal evaporation under high vacuum condition (< 5 x 10-7 Torr). Based on the recent report of using 4 pairs of multilayers to compose HMM structure for increasing the charge transfer dynamics,45 here we used 6 pairs of multilayers which are enough to enhance the emission property. The source of Ag (99.99% trace metals basis (Sigma Aldrich)) is used for the evaporation slug and MoO3 (99.97% trace metals basis (Sigma Aldrich)) is in a powder form. Both the deposition rates were fixed at 0.3 Å/s. Since MoO3 is in a powder form, so after depositing each layer of MoO3, it is necessary to vacuum another 30 min to keep the chamber clean enough then to deposit another Ag film to get the high quality multilayers. Finally, another 8 nm MoO3 was deposited on the multilayers serving as a capping layer to prevent quenching from the emission of ZnO nanoparticles for both the HMM and EMM samples. Next, to prepare the ZnO nanoparticles, high purity of 18


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ZnO nanoparticles (99.99%) and ethanol (99.98%) were ultrasonically mixed for 30 min with a concentration of 20 mg/mL and then dropped cast of 0.03 mL on the surface of the three different substrates (HMM, EMM, and SiO2/Si as a reference sample). To remove the ethanol from ZnO nanoparticles, all three samples were placed on a hotplate at 50 °C for 10 min.

Characterization of layered structures To analysis the internal nanostructures from the bulk multilayer structures (for the HMM and EMM samples), we used the focused ion beam (FIB) system (Helios Nanolab™ 660 DualBeam™). This FIB system used the Gallium ion source under the operating voltage of 30 kV and the current at 50 pA to cut the multilayers. Importantly, these high energy Gallium ion source may damage the multilayer components making the unwanted intermixing each other. Thus operating at the low milling current to reduce this effect is required. Finally, we used field emission scanning electron microscopy (FE-SEM) to image the multilayer distributions for cross-section with a 52° tilt angle. On the other hand, we used another FE-SEM (JSM-6500F) to take the morphology of ZnO nanoparticles.

Random lasing action measurement The random lasing emission spectra were optically excited by frequency-quadrupled 266 nm pulsed Nd:YAG laser (NewWave, Tempest 300) with 4 ns pulse width and 10 Hz repetition. The energy of single pulse shot is up to 200 mJ. The pumping beam was focused into a spot of 200 µm diameter by a cylindrical lens (f=100 mm). A bandpass filter of a 20 nm width was used to block the pump laser illumination. The emission properties were spectrally analyzed by means of a high resolution spectrometer Jobin Yvon iHR550 with gratings of 300, 1200, and 2400 grooves/mm 19


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(spectral resolution 0.1 nm, 0.025 nm, and 0.0125 nm, respectively). A Synapse Thermoelectric Cooled charge-coupled device (CCD) guaranteed to -75 °C was connected to the spectroscopy software SynerJY™. All the measurement results were performed at room temperature.

Photoluminescence spectra and lifetime measurement The excitation source to measure photoluminescence spectra was a pulsed diode laser (Picoquant, PDL 800-B, center wavelength of 375 nm, 70 ps, 2.5 MHz) with pumping energy density of 103 µJ/cm2 and recorded using a Horiba Jobin Yvon TRIAX 320 spectrometer. Then, we used a time corrected single photon counting (Pico Harp 300) system with a time resolution of about 36 ps from the function of instrument response to determine TRPL spectra.

Numerical simulation All results of simulation shown in this work were conducted by the commercial electromagnetic software Lumerical. Incident wave polarized in the x-direction is launched from the top of the simulation region. The relative permittivities of MoO3, Ag, and ZnO used in this study are shown in Fig. S9 of supplementary information. Perfectly matched layer is used in all simulation direction, therefore an infinite spatial space can be achieved and those unwanted artificial numerical results from the boundary of computational region can be avoided. To get a higher accuracy from the calculated results, we set 2 nm as the mesh setup.

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Figure 1

Figure 1 | Schematic diagram of random lasing assisted by the HMM. (a) The proposed ZnO nanoparticles on the HMM for random laser action. The structure contains 6 pairs of Ag/MoO3 multilayer with thickness ratio of 2.2:1 and MoO3 capping layer with ZnO nanoparticles on the top. The propagating wave of high-k modes inside the HMM is known as the volume plasmon polariton (VPP). Inset image is the formation of closed loop paths for random laser action assisted by the HMM. (b) FE-SEM image of ZnO nanoparticles. (c) and (d) are the cross-sectional FE-SEM images for the HMM and EMM samples fabricated by FIB system, respectively.

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Figure 2 a

c

b 1000

EMM 1000

600 400 200 0 380

385

390

395

16.2 18.4 22.4 24.8 26.8 unit: mJ/cm2

800

Intensity (a.u.)

16.2 18.4 22.4 24.8 26.8 unit: mJ/cm2

800

600 400 200 0 380

400

385

Wavelength (nm)

395

16.2 18.4 22.4 24.8 26.8 2 unit: mJ/cm

800 600 400 200 0 380

400

385

390

395

400

Wavelength (nm)

e

2500

Emission

HMM EMM Ref

2000

Intensity (a.u.)

390

1000

Wavelength (nm)

20

θ=45°

1500 1000 500 0 16

20

HMM EMM Ref

Pump laser

FWHM (nm)

d

Ref

Intensity (a.u.)

HMM

Intensity (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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24

15

10

5

0 16

28 2

20

24

28 2

Pumping energy density (mJ/cm )

Pumping energy density (mJ/cm )

Figure 2 | Random laser action characteristics. (a-c) Emission spectra of the HMM, EMM, and reference samples, respectively. Light blue regions are the spontaneous emission. Then, light green regions are the amplified spontaneous emission known as ASE. Finally, the random lasing action occurred are marked as the light red regions. (d) Combined emission intensity as a function of pumping energy density. All points and error bars represent within one standard deviation of the mean for random lasing intensity, respectively. The solid black lines are the fitted data of the mean value to determine the lasing threshold. Inset image is the schematic diagram of measuring the random lasing action with a tilt of sample angle of 45°. (e) The FWHM versus pumping energy density.

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Figure 3

Figure 3 | Photoluminescence spectra and the corresponding kinetics. (a) Photoluminescence spectra were measured by 375 nm pulsed diode laser. (b) Calculated Purcell factors for a dipole source located at 10 nm above the substrates (inset image). The Purcell factors as an isotropic dipole (solid line) are derived from the dipole direction that perpendicular (dash line) and parallel (dot line) to the substrates. (c) Purcell factors with increasing dipole distance to 50 nm from the substrates. Inset is a magnified image for the dipole distance from 30 to 50 nm. (d) TRPL measurement to determine the decay lifetime. The shorter (longer) lifetime for

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the HMM, EMM, and reference samples are 2.82 (3.21), 3.64 (4.80), and 4.73 (6.24) ns, respectively.

Figure 4

Figure 4 | Theoretical analysis for scattering efficiency and |E|2 distributions. (a) and (b) are the calculated scattering efficiencies for the ZnO hexagonal column with radius of 40 nm and height of 100 nm, and the ZnO sphere with radius of 40 nm. (c) are the iso-frequency curves of the HMM and air. Green region represents the out-coupled modes from the HMM to air. (d-f) are the top-view distributions of |E|2 around the ZnO nanoparticles placed on the HMM, EMM, and reference substrate, respectively, under a normally incident light with a wavelength of 388 nm.

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Figure 5 a

b

HMM

120

60

150

210

240

240

d

330

240

300

e

XY

0

210

330

300 270

30

180

0

210

330

60

150

30

180

0

XY XZ YZ

Ref 90 120

60

150

30

180

c

EMM 90

90

120

300

f

270

XZ

270

YZ 12

10

10

6 4

8 6 4

(θ)

ide nt

Inc

15 0

0

gle

0 5

0

(θ)

ide nt

Inc

15 0

gle

0

0 0

(θ) gle

5

1

20

le

Inc

ide nt

0

40

g an

le

le

15 0

an

0 5

0 1

60

ed er

g an

g an

20

0

80

00

tt

40

ca S

60

ed er

ed er

20

0

tt

tt

40

2 80

00

ca S

60

an

80

0.00

an

2

0

0.5

8

1

1.0

2 Re(E )*10

1.5

-16

12

2 Re(E )*10

-16

2.0

2 Re(E )*10

-16

2.5

ca S

(Ω

(Ω

(Ω

)

)

)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

Figure 5 | Far-field angular distributions. (a-c) are the scattered |E|2 intensity from the ZnO nanoparticles on the HMM, EMM, and reference samples, respectively. The incident light is set at the normal direction with central wavelength of 388 nm. (d-f) are the incident angles from normal to 85° for all the samples with XY, XZ, and YZ planes, respectively. We show the scattered angles from 0° to 180°. Red, green, and blue color represent the HMM, EMM, and reference sample, respectively.

25


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ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. (PDF) Author information 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

3

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 5

Institute of Optoelectronic Sciences, National Taiwan Ocean University, Keelung

202, Taiwan *corresponding author: Yang-Fang Chen: [email protected] Acknowledgments This work was supported by the Ministry of Science and Technology and the Ministry of Education of the Republic of China. Author contributions H-I L., Y-M. L., and Y-F.C. conceived the idea of random lasing assisted by 26


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hyperbolic metamaterials and designed the experiments. H-I L., Y-M.L., and W-J.L. fabricated and measured the samples. P.P. took the SEM image. H-I L. and S-Y.L. designed simulation. H-I L., K-C.S., Y-H. Li, and B-H. C. discussed the mechanism of hyperbolic metamaterials. H-I L., Y-M. L., W-C.L., and T.-Y.L. discussed random lasing mechanism. Y.-F.C. supervised the project. H-I L., Y.-M. L., G.H., and Y.-F.C. wrote the paper. All the authors were involved in analyzing the data. Funding Sources This work was supported by the Ministry of Science and Technology and Ministry of Education of the Republic of China. References 1.

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The table of contents

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Integration of Nanoscale Light Emitters and Hyperbolic Metamaterials

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