The Origin of Threshold Reduction in Random Lasers Based on MoS2/Au NPs: Charge Transfer

Abstract

Random lasers have attracted much attention in recent years owing to their advantages of a simple fabrication process, low processing cost, and material flexibility for any lasing wavelengths. They provide a roadmap for the design of ultra-bright lighting, displays, etc. However, the threshold reduction in random nanolasers remains a challenge in practical applications. In this work, lower-threshold random laser action from monolayer molybdenum disulfide film-encapsulated Au nanoparticles (MoS₂/Au NPs) is demonstrated. The observed laser action of the MoS₂/Au NPs shows a lower threshold of about 0.564 µJ/mm², which is about 46.2% lower than the threshold of random lasers based on Au NPs. We proposed that the charge transfer between MoS₂ and the gain material is the main reason for the reduction in the random laser threshold. The finite-difference time-domain (FDTD) method was used to calculate the lasing action of these two nanostructures. When charge transfer is taken into account, the theoretically calculated threshold of the MoS₂/Au NPs is reduced by 46.8% compared to Au NP samples, which is consistent with the experimental results. This study provides a new mechanism to achieve low-threshold and high-quality random lasers, which has the potential to facilitate the application of random lasers and the development of high-performance optoelectronic devices.

1. Introduction

Random lasers have attracted great attention due to their unique physical mechanisms and applications in fields such as biosensing, optical information processing, and so on. They have the advantages of simple manufacturing processes [1], low processing costs [2], and low flexibility for materials of any laser wavelength [3]. In contrast to traditional lasers, the feedback amplification in a random laser is not provided by a cavity formed by reflecting elements but by the disorder-induced scattering of light in the random medium [4,5]. As the research on random lasers has improved, significant progress has been made in reducing their thresholds [6,7,8,9], regulating them [10], and finding new materials [11]. Reducing the random laser threshold can increase the efficiency and lifespan of a laser, as well as reduce energy consumption and costs, which will promote the miniaturization and integration of random lasers. However, threshold reduction remains a challenge in practical applications [12,13].

The enhanced localization of electromagnetic fields and scattering effects can reduce the threshold of random lasers. Zhao et al. demonstrated that the threshold of a random laser is reduced from ~2.0 mJ/cm² to ~1.6 mJ/cm² when a layer of polymethyl methacrylate (PMMA)-doped CdSe/ZnS colloidal quantum dots (CQDs) is coated onto Ag nano-island structures, which is caused by the strong surface plasmon resonance and plasmonic scattering of the Ag nano-islands [14]. Wan et al. found that a random laser containing TiN nanoparticles (NPs) had a lower threshold than a random laser containing TiO₂ NPs due to the stronger localized surface plasmon resonance of TiN NPs [15]. There are also some works that have effectively reduced the threshold of random lasers by designing structures that support strong surface plasmons [16,17]. Moreover, increasing the scattering cross-section can increase the probability of photon scattering in random media, which can lower the threshold of random lasers. Some works have proposed that adding two-dimensional materials to random laser structures can effectively lower the threshold. Wan et al. demonstrated that the lasing threshold of a random laser with graphene nanosheets is only about 31.8% of that of a random laser without graphene nanosheets [18]. Shen et al. confirmed that the introduction of graphene can reduce the threshold of a random laser by 34.8% [19]. Roy et al. also reduced the threshold of a random laser by utilizing vertically oriented graphene nanowalls [20].

Two-dimensional materials are a current research hotspot [21,22], among which molybdenum disulfide (MoS₂) is a promising candidate for two-dimensional (2D) transition-metal dichalcogenides. Monolayer MoS₂ has a direct bandgap of 1.9 eV, which makes it a very promising optoelectronic material for potential applications in solar cells [23,24], photodetectors [25], optoelectronic converters, and so on [26]. MoS₂ is also used in the field of surface-enhanced Raman spectroscopy (SERS) because it can undergo a charge transfer with dye molecules, resulting in a chemical enhancement that increases the SERS signal intensity and sensitivity, which has been demonstrated experimentally and theoretically [27,28,29]. With deep research into the unique structure and properties of MoS₂, nanolasers based on MoS₂ have been studied. However, it is primarily used to modulate nanolasers’ characteristics and as a gain material to realize nanolasers [30]. To the best of our knowledge, there are almost no studies reporting that the charge transfer between MoS₂ and dye molecules can reduce the threshold of nanolasers. However, charge transfer has been proposed as a possible reason for random lasing [31].

Herein, we demonstrate that the charge transfer between MoS₂ and the gain material can reduce the threshold of a random laser. We fabricated high-quality, large-area, and uniform Au NPs, and then MoS₂ was directly fabricated onto the Au NPs to form MoS₂-encapsulated Au NPs (MoS₂/Au NPs). A rhodamine 6G (R6G)-doped PMMA layer was spun onto the Au NPs and MoS₂/Au NPs to form random laser structures based on the waveguide effect. We studied the random laser’s properties based on Au NPs and MoS₂/Au NPs and found that after the Au NPs were encapsulated in MoS₂, the threshold of the random laser could be reduced by 46.2%. Then, the lasing threshold was calculated by using commercial simulation software (FDTD Solutions) based on the finite difference in the time domain method, and we found that the charge transfer between MoS₂ and R6G is the main reason for the reduction in the random laser threshold. This paper explores a new mechanism to achieve low-threshold random lasers and the potential of using 2D materials to improve their performance.

2. Preparation of Experimental Sample

A schematic diagram showing the preparation process of the Au NPs and MoS₂/Au NP samples is shown in Figure 1. It mainly consists of the following steps: 1. A thermal-evaporation system (1 Å/s rate, 10⁻³ Pa) was used to deposit about a 12 nm Au film on the SiO₂ plates. 2. The SiO₂ plates with gold films were placed in a quartz tube at a pressure of 10⁻³ Pa, and then the quartz tube was heated to 600 °C with a flow of Ar/H₂ of about 100/20 sccm for the annealing treatment. After this process, the gold film transformed into randomly distributed Au NPs. 3. A mixture of ethylene glycol (1 mL) and high-purity (NH₄)₂MoS₄ (0.01 g) was ultrasonically treated for 20 min until they entirely dissolved, then the (NH₄)₂MoS₄ solution was spin-coated onto the Au NP samples using a spinner with a rotation speed of 2000 rpm for 3 min. 4. In order to remove sulfide in the precursor solution and obtain MoS₂, we continued annealing the samples at 500 °C with the gas flow (Ar/H₂ about 80/20 sccm). After the samples cooled to an ambient temperature, a MoS₂ film formed on the surface of the Au NPs. 5. The samples were then treated with Ar plasma (13.56 MHz RF source) with power of 10 W and a pressure of 10 Pa, which thins down the MoS₂ film on the Au NPs to a monolayer. 6. The random laser studied here is based on the waveguide effect. We mixed 40 mg/mL polyvinyl alcohol aqueous (PVA) solution and 3 mg/mL R6G aqueous solution in a 1:1 volume ratio. Then, the mixed solution was ultrasonically treated for 20 min until they were completely mixed. The mixed solution was spun onto the surface of Au NPs and MoS₂/Au NPs samples to obtain the random laser samples. R6G serves as the gain material, Au NPs or MoS₂/Au NPs serve as multiple scattering, and PVA forms the waveguide layer. When the pump laser is irradiated on the structure, light is strongly scattered by the Au NPs or MoS₂/Au NPs. A large part of the scattered light was reflected totally back at the PVA/air interface to propagate within the active waveguide and scattered further by the Au NPs or MoS₂/Au NPs, which experiences strong amplification through stimulated emission, through which a random lasing can be generated [32].

3. Results and Discussion

The Au NPs were obtained by annealing the gold film, which is more uniform, as shown by the SEM in Figure 2a. The uniform and large-area MoS₂ films were synthesized by thermal decomposition. By growing directly on the surface of Au NPs, MoS₂ can be very tightly attached to the surface of the gold nanoparticles, which is shown in Figure 2b; the samples thus formed are more favorable for random laser generation than the MoS₂−Au−MoS₂ structure [33]. The MoS₂/Au NPs formed by this method not only effectively suppress lattice defects but also reduce the scattering enhancement caused by the introduction of MoS₂. After the MoS₂/Au NPs were dissolved in an ethanol solution, we captured the TEM images of the MoS₂/Au NPs, as shown in Figure 2c,d, where the MoS₂ is tightly wrapped around the surface of Au NPs. The thickness of the MoS₂ layer is about 0.65 nm, indicating that the MoS₂ is monolayer. In addition, a Raman spectrometer (Horiba HR Evolution 800) with laser excitation (2.4 mW laser power, 532 nm excitation, acquisition time of 4 s, etc.) was used to carry out the Raman analysis of the MoS₂/Au NPs. As shown in Figure 2e, there are two peaks at 384.2 and 403.9 cm⁻¹, which correspond to the in-plane E₁^2g and out-of-plane A_1g modes of 2H−MoS₂, respectively. These characteristic peaks once again indicate that the gold particles are coated with MoS₂.

The SEM images in Figure 2a,b show the morphological characteristics of Au NPs and MoS₂/Au NPs. These nanoparticles are distributed relatively uniformly, with an average size of about 80 nm. We measured the absorption spectra of the Au NPs and MoS₂/Au NPs using UV−vis spectroscopy (UV−vis), as shown in Figure 2f. Their absorption peaks are at 539.2 and 570.5 nm, respectively. The absorption of MoS₂/Au NPs undergoes a red shift compared with Au NPs. This is mainly attributed to the close relationship between the surface plasmon resonance absorption peaks of Au NPs and the ambient medium of the Au NPs and an increase in the refractive index of the dielectric ambient when the Au NPs are covered with MoS₂, resulting in the red-shifted surface plasmon resonance absorption peaks. The photoluminescence (PL) peak of R6G is at 575 nm, as shown by the blue line in Figure 2f. It can be seen that both the absorption spectra of Au NPs and MoS₂/Au NPs can overlap with the PL spectrum of R6G, which makes it easier to achieve random lasing. The absorption peak of the MoS₂/Au NPs is closer to the fluorescence peak of R6G, which will facilitate their interactions with the gain material [32]. In addition, the type and size of metal nanoparticles also affect the PL [34], potentially leading to an increase in the laser threshold if the luminescence peak of R6G does not overlap well with the absorption of the sample.

We measured the random lasing action of the random laser based on Au NPs and MoS₂/Au NPs. The schematic diagram of the experimental setup is shown in Figure 3a. In the experiment, an Nd:YAG mode-locked laser (532 nm, 25 ps, 10 Hz) was used as a pump source. The energy of the pump light is manipulated by adjusting the energy attenuator. The pump light is divided into two beams by the beam splitter. One beam is used to record the energy of the pump light, and the other one is used to excite the samples. The light emitted from the samples is collected by an optical fiber spectrometer for analysis. Figure 3b shows the emission spectra of the Au NPs sample as a function of the energy. The wavelength, shown by the dashed line, is the pump light. When the pump energy is small, the emission spectrum is very wide, which is the spontaneous emission spectrum of the R6G. As the pump light energy continues to increase, a narrow peak appears at 575 nm, which is the random laser peak. Figure 3c shows the variation in the emission peak intensity and FWHM of the emission spectrum with the pump energy. It can be seen that when the pump energy exceeds 1.048 µJ/mm², the peak intensity increases rapidly, and the FWHM of the spectrum drops sharply, from about 66 nm to 15 nm. This is a typical stimulated emission behavior in a laser system. This pump energy is called the lasing threshold of the random laser based on Au NPs. The emission spectra of the MoS₂/Au NPs samples with different pump energies are shown in Figure 3d. The variation trend of the spectra with respect to pump energy is essentially the same as that of the Au NPs. The lasing action can still occur as the pump energy increases. However, the lasing red peak shifts to 591 nm due to the addition of MoS₂. Figure 3e shows the peak intensity and FWHM of the emission spectrum of MoS₂/Au NPs as a function of the pump energy. The lasing threshold for the random laser based on MoS₂/Au NPs is approximately 0.564 µJ/mm², which is approximately 46.2% lower than the threshold of the random laser based on Au NPs. We also measured the ablation threshold of the sample as 135 µJ/mm²; the sample was not optically damaged during the experiment. In addition, we found that for the MoS₂/Au NPs random laser, the intensity of the emission peak was stronger, and the width of the lasing peak was wider than that of the Au NPs. These phenomena are all attributed to the charge transfer between MoS₂ and R6G, which we will discuss in detail below. It should be noted that the pump laser spectra overlap with the spontaneous emission spectra of R6G. We carried out peak fitting when measuring the FWHM.

We calculated the properties and laser actions of the Au NPs and MoS₂/Au NPs using FDTD Solutions software. In order to save computational memory and time, we calculated the scenario in which four nanoparticles are arranged along the polarization direction of the incident light. The structure mainly consists of a gain material layer, a substrate, the Au NPs, and a MoS₂ layer. The gain material layer is composed of PVA doped with R6G (n_PVA = 1.52), the substrate material is silica with n_s = 1.48, and the refractive index of Au is taken from experimental data [35]. The radius of the Au NPs was set to 40 nm, and the gap between them was 5 nm. The Au NPs were coated with a monolayer MoS₂, which had a thickness of 0.65 nm. When the 532 nm pump light was incident, the dielectric constant of MoS₂ was set as ε = 5.9 + i1.4. The gain material used a four-level, two-electron model to describe the outcome. The four energy levels involved in laser generation include ground-state level E₀, lower laser level E₁, upper laser level E₂ (metastable level), and excited-state level E₃. The pumped light excites electrons from the ground-state (E₀) level to the excited-state (E₃) level and then relaxes it to the E₂ level, and the transition between E₂ and E₁ is responsible for the coherent emission of laser light. N₀, N₁, N₂, and N₃ represent the population distribution of electrons in the respective energy levels, which satisfy the following equation [36,37]:

(1)$\begin{array}{c}\frac{d{N}_3}{dt}=\frac{N_3\left(1-N_2\right)}{{\tau }_{32}}-\frac{N_3(1-N_0)}{{\tau }_{30}}+\frac{1}{\hslash {\omega }_b}\mathit{E}·\frac{d{\mathit{P}}_b}{dt}\\ \frac{d{N}_2}{dt}=\frac{N_3\left(1-N_2\right)}{{\tau }_{32}}-\frac{N_2(1-N_1)}{{\tau }_{21}}+\frac{1}{\hslash {\omega }_a}\mathit{E}·\frac{d{\mathit{P}}_{\mathit{a}}}{dt}\\ \frac{d{N}_1}{dt}=\frac{N_2\left(1-N_1\right)}{{\tau }_{21}}-\frac{N_1\left(1-N_0\right)}{{\tau }_{10}}-\frac{1}{\hslash {\omega }_a}\mathit{E}·\frac{d{\mathit{P}}_{\mathit{a}}}{dt}\\ \frac{d{N}_0}{dt}=\frac{N_3\left(1-N_0\right)}{{\tau }_{30}}+\frac{N_1(1-N_0)}{{\tau }_{10}}-\frac{1}{\hslash {\omega }_b}\mathit{E}·\frac{d{\mathit{P}}_{\mathit{b}}}{dt}\end{array}$

where τ_ij is the decay time between level i and level j (i, j = 0, 1, 2, 3), ω_a is the transition frequency between level 2 and level 1, and ω_b is the transition frequency between level 3 and level 0. E represents the total electric field and can be calculated by solving the Maxwell equations. P_a and P_b correspond to the net macroscopic polarization associated with the emission and absorption transitions from level 2 to level 1 and level 3 to level 0, which are coupled with the electromagnetic fields by using the following equation [36]:

(2)$\begin{array}{c}\frac{d^2{\mathit{P}}_{\mathit{a}}}{{dt}^2}+{\gamma }_{21}\frac{d{\mathit{P}}_{\mathit{a}}}{dt}+{\omega }_{21}^2{\mathit{P}}_{\mathit{a}}={\xi }_{21}\left(N_2-N_1\right)\mathit{E}\\ \frac{d^2{\mathit{P}}_{\mathit{b}}}{{dt}^2}+{\gamma }_{30}\frac{d{\mathit{P}}_{\mathit{b}}}{dt}+{\omega }_{30}^2{\mathit{P}}_{\mathit{b}}={\xi }_{30}(N_3-N_0)\mathit{E}\end{array}$

where γ_ij is the full-widths at half-maximum for the transitions from level i to j. ${\xi }_{21}=6\pi {\epsilon }_0{c}^3/{\omega }_a^2{\tau }_{21}$, ${\xi }_{30}=6\pi {\epsilon }_0{c}^3/{\omega }_b^2{\tau }_{30}$. By coupling Equations (1) and (2), the amplification process of the nanolaser can be studied. The relevant parameters for R6G are as follows [38]: ω_a = 3.30 × 10¹⁵ rad/s and ω_b = 3.68 × 10¹⁵ rad/s, τ₃₀ = 1 ns, τ₂₁ = 3 ns, τ₁₀ = τ₃₂ = 50 fs, γ₂₁ = 1.54 × 10¹⁴ rad/s, and γ₃₀ = 3.26 × 10¹⁴ rad/s. According to the concentration of the solution prepared for the experiment, the total population density is N = 1.89 × 10²⁴ m⁻³. The x, y, and z directions of our simulation domain are set with perfectly matched layer (PML) boundary conditions. Both a total field and scatter field were set in the simulation domain.

Figure 4 presents our calculation results regarding the lasing behavior of Au NPs and MoS₂/Au NPs. Figure 4a,b depict the lasing emission spectra of Au NPs and MoS₂/Au NPs at different pump energies. It can be observed that when the pump energy is low, the emission spectrum is broad, indicating that there is no population inversion. When the pump energy reaches a certain value, the emission intensity suddenly increases, and the FWHM decreases sharply. At this point, population inversion takes place, and random lasing occurs. This pump energy is the threshold of the random laser. The normalized maximum emission intensity and the FWHM of the emission peak as a function of the pump energy are shown in Figure 4c,d. It can be distinctly seen that the threshold of the random laser based on the Au NPs and MoS₂/Au NPs are 0.734 µJ/mm² and 0.878 µJ/mm², respectively. The threshold of the random laser based on MoS₂/Au NPs is higher than that of Au NPs, which is inconsistent with the experimental result. In order to investigate the reasons for this phenomenon, we plotted the field distributions of the two structures without gain material, as shown in Figure 5a,b. The electric field localized the gap between the particles due to the coupling of the Au NP surface plasmons. The enhancement of the electric field of Au NPs relative to the background field can reach 44.5, while the field enhancement of MoS₂/Au NPs is only 37.2. This is due to the absorption loss of MoS₂. Thus, the threshold of the MoS₂/Au NPs increased in the theoretical calculations. It can be seen that if the charge transfer is not considered, the threshold will increase when Au NPs are coated with MoS₂.

The threshold of a random laser can also be affected by the scattering strength of the NPs [18]. Under the same concentration of scattered nanoparticles, the larger the scattering cross-section of the nanoparticle, the smaller the threshold of the random laser based on that nanoparticle. The scattering strength of four Au NPs and MoS₂/Au NPs was evaluated by their scattering cross-section, as shown in Figure 5c,d. We can see that when Au NPs were covered with MoS₂, the scattering cross-section was slightly reduced. Therefore, the scattering effect is not the reason for the decrease in the random laser threshold in MoS₂/Au NPs.

It has been reported that MoS₂ will transfer charge to R6G under the 532 nm excitation wavelength. And Dixit et al. reported that a charge transfer is also a random lasing reason [31]. We investigated the effect of the charge transfer on the random laser threshold. To confirm the charge transfer mechanism between MoS₂ and R6G, we measured the PL spectra of MoS₂/Au NPs with different concentrations of R6G, as shown in Figure 6a. The PL peaks of Au NPs and MoS₂ are at 578 and 647 nm, respectively (as indicated by the fitted dotted line). Clearly, this indicates that the PL intensity of Au NPs and MoS₂ with the R6G molecule is significantly reduced at higher concentrations, indicating that both Au NPs and MoS₂ transfer charge to R6G [39]. Here, we mainly studied the effect of MoS₂ on the threshold of a random laser. The PL intensity of MoS₂ decreases with increasing R6G concentration, as the inset in Figure 6a shows, indicating that there are fewer electrons jumping from the conduction band (CB) back to the valence band (VB) for MoS₂; that is, more electrons are transferred from MoS₂ to R6G. This phenomenon is consistent with that in reference [27]. The PL spectra of R6G on both the Au NP and MoS₂/Au NP substrates are also measured in Figure 6b. It can be seen that the intensity of R6G on the MoS₂/Au NPs substrate is much stronger than that on the Au NPs substrate, which further confirms the charge transfer mechanism between MoS₂ and R6G. The band (energy level) alignment between MoS₂ and R6G is illustrated in Figure 6c. The charge transfer between the conduction band minimum (CBM) of MoS₂ and the lowest unoccupied molecular orbital (LUMO) of an R6G molecule is achieved during the excitation process with a wavelength of 532 nm [27], which results in the lower threshold of the MoS₂/Au NPs random laser.

An et al. performed density functional theory calculations and revealed that the CBM of MoS₂ will transfer 0.2e to the LUMO of R6G molecules under the 532 nm excitation wavelength [27], which will increase the initial population of the E₂ or E₃ level of R6G. Therefore, we added a 20% population of particles to the higher level (E₂ or E₃) of the four-level system of R6G. The calculated results are the same whether we increase the 20% population of the particles in the E₂ level or the E₃ level. The lasing action of the random laser based on MoS₂/Au NPs is calculated when the charge transfer is considered, as shown in Figure 6d. The lasing action was similar to that in Figure 4c,d, but the threshold value was reduced to 0.39 µJ/mm². Compared with the Au NPs without MoS₂, the lasing threshold is reduced by about 46.8%, which is essentially consistent with the experimental result. Moreover, the increase in the population in the higher energy level can also enhance the intensity of the emission peak, so the emission peak of the MoS₂/Au NPs is stronger, as shown in Figure 2c. The emission peak width of the MoS₂/Au NPs sample is broader than that of the Au NPs in the experiment, which can also be explained by charge transfer. As can be seen from the charge transfer in Figure 6c, the valence band maximum (VBM) of MoS₂ is close to the highest occupied molecular orbital (HOMO) of R6G. When the electrons transfer from LUMO to HOMO of R6G, they can also transfer to the VBM of MoS₂ (as the yellow dotted line shown), which leads to an increase in the emission spectral width. It can be seen from the above that charge transfer is the reason for the lower threshold of the MoS₂/Au NPs random laser.

It is worth noting that the threshold of the random laser we calculated theoretically is lower than the experimental results because we set the gap between the Au NPs to 5 nm during the above-mentioned theoretical calculation, which results in a strong electric field enhancement between the Au NPs. As shown in Figure 7a, when the gap is increased to 10 nm, the enhancement of the electric field of Au NPs decreases to 19.2, and the threshold of the random laser increases to 1.369 µJ/mm². The random laser action of Au NPs coated with MoS₂ is shown in Figure 7b, and its threshold is 0.719 µJ/mm², which also reduces by 47.4%. We also calculated the lasing behavior of a single Au NP, as shown in Figure 7c,d. The enhancement of the electric field decreases to 4.4, and the threshold of the random laser increases to 1.561 µJ/mm². When Au NPs are coated with MoS₂, the threshold is reduced to 0.828 µJ/mm², which also reduces by 46.9%, which is still consistent with the experimental results. The enhancement of the electric field affects only the threshold of the nanolaser but does not affect the effect of charge transfer on the threshold.

4. Conclusions

In summary, we successfully synthesized the MoS₂/Au NPs composite structure through annealing (NH₄)₂MoS₄ on Au NPs and studied the lasing action of a random laser based on them. By comparing the lasing measurements of Au NPs and MoS₂/Au NPs, we studied the effect of MoS₂ on the threshold of the random laser. The results showed that the addition of MoS₂ reduced the random laser threshold. Compared to the Au NPs sample, the threshold was reduced by 46.2%. Through theoretical calculation, it was found that the electric field and scattering cross-section decreased after MoS₂ was added, which did not lead to a decrease in the random laser threshold. The combined experimental and computational study demonstrates that charge transfer is the dominant mechanism behind the reduction in threshold for the MoS2/Au NPs random laser. A 20% population of particles was added to the E₂ or E₃ energy level of the four-level two-electron model of R6G. The calculated threshold can be reduced by about 46.8% compared to Au NPs samples, which is consistent with the experimental results. This study provides a convenient and efficient method for the study of random lasers based on novel 2D materials and metallic nanostructures and provides a technological route to realize low-threshold, high-performance random lasers.

Author Contributions

Y.H., Z.L. and Y.R. proposed the project. K.S. conducted the equation derivation and simulation and wrote the manuscript. Y.W., L.Z. and T.N. helped to modify the manuscript. Y.Z., W.L. and J.W. helped to translate the paper and conduct a relevant literature search. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data supporting the findings of this study are available within the article.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures

Figure 1. Schematic illustration of the process of random laser based on MoS2/Au NPs.

Figure 2. SEM image of Au NPs (a) and MoS2/Au NPs (b) (inset is a particle size distribution statistical chart of MoS2/Au NPs); (c,d) TEM images of MoS2/Au NPs with different resolutions; (e) Raman spectra of MoS2/Au NPs; (f) the UV−vis absorption spectra of Au NPs (red), MoS2/Au NPs (black), and PL spectrum of R6G (blue).

Figure 3. (a) Schematic diagram of the experimental setup; (b,d) the emission spectra of the Au NPs (b) and MoS2/Au NPs (d) lasing samples at different pump energies; and (c,e) the lasing peak intensity and FWHM of the corresponding emission peak as a function of the pump energy.

Figure 4. (a,b) The emission spectra of Au NPs (a) and MoS2/Au NPs (b) at different pump energies. (c,d) The normalized maximum emission intensity and FWHM of the Au NPs (c) and MoS2/Au NPs (d) emission peak as a function of pump energy.

Figure 5. (a,b) Electric field distribution of Au NPs with a gap of 5 nm without (a) and with (b) MoS2; (c,d) scattering cross-section of Au NPs without (c) and with MoS2 (d).

Figure 6. (a) PL spectra of MoS2/Au NPs without and with R6G at different concentrations. Inset: the fitted PL spectra of MoS2 without and with R6G at different concentrations. (b) PL spectra of R6G on Au NP and MoS2/Au NP substrates. (c) The band alignment (energy level alignment) between R6G and MoS2, where charge transfer is highlighted in the red path. (d) The normalized maximum emission intensity and FWHM of the MoS2/Au NPs emission peak as a function of pump energy when charge transfer is considered.

Figure 7. The normalized maximum emission intensity and FWHM of the emission peak as a function of pump energy for four Au NPs (a,b) and a single Au NP (c,d) without (a,c) and with MoS2 (b,d). Inset: The electric field distribution of Au NPs with a gap of 10 nm and a single Au NP.

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