Integration of Nanoscale Light Emitters and ... - ACS Publications

Letter Cite This: ACS Photonics XXXX, XXX, XXX−XXX

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*,†,‡ †

Graduate Institute of Applied Physics, National Taiwan University, Taipei 106, Taiwan Department of Physics, National Taiwan University, Taipei 106, Taiwan § Research Center for Applied Sciences, Academia Sinica, Taipei 115, Taiwan ∥ Nano Science and Technology Program, Taiwan International Graduate Program, Academia Sinica and National Taiwan University, Taipei, Taiwan ⊥ Institute of Optoelectronic Sciences, National Taiwan Ocean University, Keelung 202, Taiwan ‡

S Supporting Information *

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 finitedifference 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

L

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 limit10−12 meta-lens,13,14 and invisible cloak,15,16 by controlling electromagnetic waves to pass through artificial metamaterials of subwavelength thickness. One class of metamaterials, defined as the hyperbolic metamaterials (HMMs), composed of precise design with alternate metal-

aser 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 © XXXX American Chemical Society

Received: October 25, 2017 Published: December 20, 2017 A

DOI: 10.1021/acsphotonics.7b01266 ACS Photonics XXXX, XXX, XXX−XXX

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ACS Photonics

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 six 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, d) Cross-sectional FE-SEM images for the HMM and EMM samples fabricated by FIB system, respectively.

the dye will degrade under high power pumping. Therefore, the superior high-k modes should be explored further for achieving laser action with low threshold. In this study, we report the attempt to strongly enhance random lasing emission intensity with the implementation of semiconductor quantum dots to achieve a reduced lasing threshold based on the assistance of high-k modes derived from the HMMs. In order to stand out the effect of the HMMs, we deposited Ag/MoO3 as the multilayers with two different structures for comparison, in which one multilayer shows hyperbolic dispersion (marked as the HMM), and the other one shows elliptic dispersion (marked as the EMM). The random laser action was realized with zinc oxide (ZnO) nanoparticles of proper arrangement and geometry. We have deposited ZnO nanoparticles on SiO2/Si substrate as a reference sample to consolidate our observation. Furthermore, the underlying mechanism of our design and the existence of excited high-k modes inside the HMM have been confirmed theoretically using three-dimensional (3D) finite-difference time-domain (FDTD) simulation. Design and Materials Characteristics. Figure 1a presents the schematic diagram of our proposed random laser action arising from ZnO nanoparticles assisted by the HMM, while the schematic diagram of ZnO nanoparticles on the SiO2/Si substrate is shown in Figure S1. ZnO with a wide band gap (3.37 eV) and a high exciton binding energy (60 meV) has been widely used for light-emitting diodes and laser devices.27 For the HMM sample, based on the FDTD simulation, the optimized thicknesses of Ag and MoO3 are 22 and 10 nm, respectively, with the corresponding fill-fraction of 68.75% for Ag film; while for the EMM sample, the thicknesses of Ag and MoO3 are 12 and 20 nm, respectively, with the corresponding fill-fraction of 37.5% for Ag film. To prevent unwanted oxidation on the top layer of Ag surface, another 8 nm MoO3 is deposited as a capping layer.19 Furthermore, this capping layer can prevent the quenching of the emission from ZnO nanoparticles.28 Based on the composition of multilayer and the relative permittivity, the effective dielectric tensor of the HMM and the EMM samples can be determined by Maxwell-Garnett theory,28,29 which are

dielectric multilayers or parallel metallic nanorods 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 (i.e., ε⊥·ε∥ < 0 or μ⊥·μ∥ < 0), which provides the hyperbolic dispersion

ω2 c2

=

kx2 + k y2 ε⊥

+

kz2 17,18 . ε

This

hyperbolic dispersion allows the high-wave vector states inside the HMMs.16 Here, the subscripts of ⊥ and ∥ refer to the perpendicular and parallel direction along the anisotropy axis, respectively. These high-wave vector states are known as high-k modes, resulting from the increment of photonic density of states (PDOS), which make the enhancement of spontaneous emission for dipole-like emitters on the near-field surface of the HMMs.19 Importantly, these propagating waves of high-k modes can be understood as the volume plasmon polariton (VPP).20,21 VPP arises from the coupling of surface plasmon polariton (SPP) between the metal-dielectric interface that can propagate inside the whole structure of the HMMs. To describe the propagating waves of dipole-like emitters, the decay rate is defined as ΓHMM = Γvacuum + Γspp + Γhigh‑k, where Γvacuum and Γspp are the decay rates in vacuum and the SPP modes of metamaterials, respectively.18,19 Moreover, Γhigh‑k is the decay rate only existing in the HMMs due to the unique feature of high-k modes.18,19 Taking these superior features into account, several intriguing phenomena have been demonstrated during past few years, such as strong enhancement of spontaneous emission,22 extremely sensitive biosensors,23,24 and perfect broadband absorber applications.25 The existence of these high-k modes is also foreseeable to increase optical gain and reduce stimulated emission threshold for lasers, which is of the outmost importance to circumvent the power consumption of a laser system. For instance, using rhodamine dye deposited on top of the HMMs for enhancing emission twice compared with the samples with elliptic dispersion has been demonstrated.26 Even though the line width of the emission spectra has been observed to reduce after a threshold, the line width still has a value as large as 6 nm, which is not convincing to claim as laser action. Besides, B


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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 vs pumping energy density.

spontaneous emission below the pumping energy density of 22.4 mJ/cm2, the ASE at 24.8 mJ/cm2 and then sharp peaks at 26.8 mJ/cm2. The formation of random lasing peaks can be understood as follows. The light propagates inside random arrays of ZnO nanoparticles will experience multiple scatterings, which enables to form closed loop paths, enlarge the optical gain, amplify light intensity, induce stimulated emission, and then achieve laser action. Once the random lasing action is achieved, the lasing intensity and lasing wavelength are determined by the resonance of the cavity, making the formation of many narrow spikes. Because there exist many possible path ways for the formation of closed loops, a large amount of random lasing peaks can thus be observed. Compared with several previous reports on the studies of ZnO nanoparticles, the appearance of sharp peaks with line width less than 1 nm can be attributed to the occurrence of random laser action.5 To confirm random lasing phenomena and determine lasing threshold, we set the pumping energy density covering from 16.2 to 29.6 mJ/cm2 with a tilted sample holder angle of 45°, as shown in Figure 2d. We averaged the maximum emission peak intensity based on database for more than 100 sets statistics marked with an error bar within one standard deviation of the mean. Then, we fitted the line from the averaged database to obtain the threshold and the pump-emission curve (Figure 2d). After determining the fitted line, we further examined the transition slope of the spontaneous emission (with a flat slope) and stimulated emission (with a sharp slope). The intersection of these two lines was defined as the threshold.36 Before lasing, the line width was around 10 nm, which can be considered as the

shown in Figure S2a,b of Supporting Information, with the corresponding random lasing regions of ZnO nanoparticles covering from 385 to 395 nm. Field emission scanning electron microscope (FE-SEM) image of ZnO nanoparticles (30−350 nm) is shown in Figure 1b. To examine the quality of multilayer deposition, the focused ion beam (FIB) system is used to prepare the uniform cross-sectional FE-SEM images for the HMM and EMM samples (shown in Figure 1c,d). The clear boundaries in the superlattice structure provides an excellent platform for the existence of the high-k modes inside the HMM instead of localized resonance from Ag clusters.30 Random Laser Action Characteristics. The random lasing action from ZnO nanoparticles was studied using a 266 nm Q-switched Nd: YAG pulse laser. The spectral evolution with increasing pumping energy density and the emission peak intensity as a function of the pumping energy density are shown in Figure 2. Figure 2a−c depict the emission spectra of the HMM, EMM, and reference samples, respectively. As the pumping energy density (16.2 mJ/cm2) well below the threshold for all three samples, only the weak spontaneous emission can be detected. Then, by increasing the pumping energy density to 18.4 mJ/cm2, the HMM sample shows a pronounced peak with a line width of about 3 nm, which is a typical behavior of amplified spontaneous emission (ASE). With increasing pumping energy density to 22.4 mJ/cm2, several sharp peaks with line widths less than 1 nm can be detected for the HMM sample. While for the EMM sample, the ASE action occurs at 22.4 mJ/cm2, and the sharps peaks can be seen after the pumping energy density above 24.8 mJ/ cm2. As for the reference sample, the spectra show the C


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Figure 3. Photoluminescence spectra and the corresponding kinetics. (a) Photoluminescence spectra were measured by a 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 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 the HMM, EMM, and reference samples are 2.82 (3.21), 3.64 (4.80), and 4.73 (6.24) ns, respectively.

amplified spontaneous emission.36 Then, with increasing the pumping energy density, the line width shrank to ∼0.3 nm. Under low pumping energy density, the increment of emission intensity for the HMM, EMM, and reference samples are linear, while the significant increment of the slopes were observed after lasing thresholds. The wavelength and the intensity of separated lasing peaks fluctuate at different measuring time providing another firm signature of random laser action.5 Figure S3a−c presents all three samples with higher pumping energy densities (28.4, 29.6, and 32.4 mJ/ cm2) well above the lasing threshold. Figure 2e shows the full width at half-maximum (fwhm) versus pumping energy density, which provides a strong evidence of random lasing action. Concurrently, the fwhm of emission spectra reaches about 0.3 nm for all the samples. Thus, the calculated coherent length for the random lasing action is about 0.14 cm.31 To further confirm that the observed sharp peaks do arise from random laser action, we have detected the emission at different angles (Figure S4a at 30° and Figure S4b at 60°). And the result shows that the lasing behavior can be observed at different angles, which is quite different from conventional laser system. It is worth mentioning that the HMM shows ∼20% reduction of lasing threshold and ∼6 times higher emission intensity. Interestingly, the differential quantum efficiency32 of the curve relating to the slope of the output power to the input pumping power also increases by 4.5 times. Furthermore, for the HMM sample, a slight red shift can be observed. For example, at pumping energy density of 29.6 mJ/cm2, the

central emission wavelength of the HMM, EMM, and reference samples are 389.5, 387.9, and 387.5 nm, respectively, which shows a red shift. This behavior is well-known in dye lasers, in which an increase of cavity losses will cause stimulated emission closer to the maximum of the emission cross section and lead to a blue shift in the emission spectra.33,34 By the same token, the lower propagating dissipation induced the red shift in the HMM sample can be well understood, which also provides an additional evidence to support the existence of high-k modes from the HMM. We even found that strong red shift modes occur only for the HMM sample, such as the central emission wavelengths at 391.8 and 392.3 nm for the pumping energy density of 26.8 and 29.6 mJ/cm2, respectively, as shown in Figure S5. Besides, these evolution of emission intensity shows stable intensities for more than 200 repeating cycles without any photodegradation of the random lasing measurements, as shown in Figure S6. In addition, the cavity loss of forming close loops for ZnO nanoparticles on the HMM is lower than that of the EMM and reference samples due to additional effect from the high-k modes, since the incident light can propagate through the HMM to reduce the optical loss and increase the possibility to form closed loops. It is worth mentioning that random laser action is a process of multiple scatterings occurred in between the ZnO nanoparticles, which is strongly related to the transition rate and will be influenced by the environment. According to Fermi’s golden rule, the transition rate from the initial state Ψi to the final state Ψf is35 D


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2π 2 |⟨Ψ|i H′|Ψ⟩| i ρ (k ) ℏ

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 Figure 3a. Similar trends can also be seen in Figure S7a,b 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 carrier dynamics for ZnO nanoparticles on all three samples, time-resolved photoluminescence (TRPL) has been conducted as shown in Figure 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 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 by18

(1)

where ℏ is Dirac’s constant, ρ(k) is the density of state and ⟨Ψi|H′|Ψi⟩ 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 occur.36 In addition, 3D disordered skeleton of ZnO nanoparticles as shown in Figure 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 (Δλ), 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× stronger than that of the EMM and reference samples, respectively, which is about 1.6× 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. 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 by39 Fiso =

1 2 F⊥ + F 3 3

Γhigh‐k =

μ⊥2

2 |ε |ε⊥ 3

8ℏd 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 ÄÅ ÉÑ ÑÑ σ0 ÅÅÅ 1 1 ÑÑ Å + ∑ (ω) = − ÅÅÅ Ñ 2 ÅÇ 1 + i(ω − ω0)τ 1 + i(ω + ω0)τ ÑÑÑÖ (5)

where σ0 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 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

(3) E


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Figure 4. Theoretical analysis for scattering efficiency and |E|2 distributions. (a, b) 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) Iso-frequency curves of the HMM and air. Green region represents the out-coupled modes from the HMM to air. (d−f) 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.

The interaction of light with ZnO nanoparticles is mainly determined by the size and geometry of the nanoparticles and its surroundings. Figure 4a,b presents 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 Supporting 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 Figures 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 Figure 4c. The formula of iso-frequency curve is given by

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 Information, 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 outcoupled 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 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 additional evidence for our proposed mechanism.

ij kHMM, ⊥ yz 1 ij kHMM, z yz 1 jj zz j z jj k zz ε + jjj k zzz ε = 1 0 0 k { zz k { ⊥ 2

2

(6)

where k 0 = ω/c, while k HMM,⊥ and k HMM,z are the corresponding effective wave-vectors perpendicular and parallel to the optical axis of the HMM sample, respectively. F


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Figure 5. Far-field angular distributions. (a−c) 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) 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.

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 (Figure 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 is the scattering direction normal to the substrate, which is beneficial for the formation of the closeloop 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 highk 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 twodimensional 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.

Importantly, the out-coupling effect of high-k modes occurs when |kHMM| > |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. Figure 4d−f (Figure S8a−c) 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 outcoupled 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 Figure 5a−c 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 Figure 5d−f for all the samples from normal to 85° with XY, XZ, and YZ planes, respectively. G


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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 600 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 (JSM6500F) to take the morphology of ZnO nanoparticles. Random Lasing Action Measurement. The random lasing emission spectra were optically excited by frequencyquadrupled 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 (spectral resolution 0.1, 0.025, 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 Figure S9 of Supporting 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.

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× lasing intensity, lowers ∼20% of lasing threshold, shortens 44% lifetime, and enhances the differential quantum efficiency by 4.5×. 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 hot plate 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 six pairs of Ag-MoO3 multilayer structures were alternately deposited on the precleaned SiO2/ Si substrate using thermal evaporation under high vacuum condition (