Atomically thin semiconducting transition metal dichalcogenides (TMDs) exhibit remarkable nonlinear optical (NLO) properties including layer-dependent second/third harmonic generation^[1], two/multi-photon absorption^{[24" target="_self" style="display: inline;">–4]}, ultrafast saturable absorption^{[5–9" target="_self" style="display: inline;">–9]}, etc., which have been widely applied in two-dimensional (2D) photonics and optoelectronic devices^{[1012" target="_self" style="display: inline;">–12]}. Especially for 2D MoS2, researchers have made great effort to prepare large area monolayer and few-layer films with distinct NLO properties using chemical vapor deposition (CVD), mechanical exfoliation (ME), and liquid phase exfoliation (LPE) methods. However, samples prepared by different methods show distinct optical performance. Taking second harmonic generation (SHG) as an example, the ME monolayer MoS2 (χ(2)≈10−7m/V) exhibits a much stronger second-order NLO response than the CVD one (χ(2)≈10−9m/V)^[13,14]. In terms of nonlinear absorption, the ME MoS2 is greatly different from the CVD and LPE ones, which is reflected in practical mode-locking and Q-switching devices^{[1517" target="_self" style="display: inline;">–17]}. As a result, it is crucial for optical device applications to reveal the intrinsic optical properties of 2D TMDs prepared by different methods. As is well known, in the TMDs MX2 (M=Mo and W; X=S, Se, and Te), various types of defects, e.g., X vacancy, X interstitial, M vacancy, M interstitial, and MX and XX double vacancies, have been considered^{[1820" target="_self" style="display: inline;">–20]}. However, it still remains obscure how the defects affect the NLO properties of as-prepared MoS2 nanosheets.

Here, we choose CVD and ME MoS2 monolayers, typical TMDs with superior NLO properties, and make a comparative study of two-photon absorption (TPA) using a modified micro-intensity scan system. We found that the TPA coefficients of the two samples differed by nearly two times, which is ascribed to the large difference of the defect concentration between them^{[18–21" target="_self" style="display: inline;">–21]}. In view of the huge advantages of MoS2 in applications of pulse shaping and optical limiting due to its giant TPA coefficient, we simulated and compared the TPA-induced pulse modulation between CVD and ME monolayer cascaded structures.

Monolayer MoS2 nanosheets were prepared onto transparent quartz using ME from natural crystal^[22] and the CVD method^[23], respectively. All of these samples were preliminarily identified by the optical microscope. As shown in Figs. 1(a) and 1(c), the side length of the samples was determined to be ∼50μm. The thickness and surface morphology were measured using atomic force microscopy (AFM), as shown in Figs. 1(b) and 1(d). The thickness of the ME monolayer is ∼1.1nm and is slightly larger than that in general, which should be caused by the air gap between the sample and the substrate, while the thickness of the CVD monolayer is ∼0.7nm.

Fig. 1. (a)–(d) Optical microscope and AFM characterization of both CVD and ME MoS2 monolayers. (e) Raman spectra imply that there are more defects in the CVD MoS2 monolayer than in the ME one. (f) Steady PL spectra were measured, and strong PL quenching was observed in the CVD monolayer. (g), (h) The PL lifetime of an exciton in CVD and ME monolayers was measured using a streak camera.

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Raman spectroscopy has been identified as a convincing tool to determine the crystal structure of 2D MoS2 nanosheets^[24,25]. In this work, Raman spectroscopy measurements were conducted by using a confocal microscopy system combining a diode laser at 532 nm. The Raman peak interval between two active vibration modes, E2g1 and A1g, is ∼17.99cm−1 and ∼19.87cm−1 for CVD and ME monolayers, respectively. Figure 1(e) shows the broadening of two Raman peaks in the CVD monolayer, indicating that defects have made an impact on the crystal structure^[26,27]. In addition, the two Raman vibration modes give a strong proof that all the samples used in our work are 2H-MoS2^[28].

Under the same excitation, we acquired the steady photoluminescence (PL) spectra of ME and CVD monolayer MoS2. It is obvious that the ME monolayer exhibited much stronger PL intensity than the CVD one, as shown in Fig. 1(f). The PL quenching in the CVD monolayer indicates that the defect-assisted non-radiative transition plays an important role in it^[29]. In addition, the PL lifetime was measured using a streak camera (Optronis). The samples were excited by the ultrafast laser with the pulse width of 120 fs at the wavelength of 600 nm and repetition rate of 80 MHz. As Figs. 1(g) and 1(h) show, the CVD monolayer exhibited much faster and weaker excitonic emission than the ME one, which is exponentially fitted (Supplementary Information Fig. S1). It can be ascribed to stronger defect-assisted Auger scattering, leading to fast exciton annihilation and non-radiative electron-hole recombination^[30].

In this work, TPA processes in monolayer MoS2 were investigated at room temperature (∼300K) with a modified micro-intensity scan system, as illustrated in Fig. 2^[3,31]. The 350 fs laser pulses at 1030 nm (∼1.2eV) were generated from a mode-locked fiber laser (1 kHz) and attenuated with an electrically tunable neutral density filter. The laser beam was finally focused with a waist radius ω0 of ∼5μm on the surface of MoS2 using an f/35 mm lens. Herein, the excitation source with photon energy of 1.2 eV was chosen to generate good resonant interaction with monolayer MoS2 through a distinct two-photon process due to the existence of dark excitonic states^{[3133" target="_self" style="display: inline;">–33]}.

Fig. 2. Schematic diagram of the setup of the micro-intensity scan.

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Fig. 3. (a) Schematic structures of monolayer MoS2 and vacancies in it. SV, sulfur vacancy; MoV, molybdenum vacancy. (b) Energy levels in CVD and ME MoS2, optical transition, and defect-induced fast carrier capture processes (TPA, two-photon absorption; OPA, one-photon absorption). (c) Nonlinear transmittance versus incident pulse peak irradiance for MoS2 monolayers. The solid lines are the fitting results obtained by numerically solving Eq. (1). Inset: the values of the TPA coefficient and corresponding saturation intensity.

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Here, the absorption process can be analyzed using the propagation equation^[34,35]: dI(z)dz=−αI−β(I)I2(z),(1)where z is the propagation distance in the sample. α is the coefficient of one-photon absorption, which is negligible owing to the smaller value of the photon energy of 1.2 eV than the optical bandgap. β(I), the TPA coefficient, is dependent on the incident laser intensity. In our experiment, the excitation source was a series of Gaussian pulses in time and space, that is I(r,t)=I0·exp(−2r2/wp2)·exp(−t2/τ02).(2)

Here, wp and τ0 represent the radius of the pump beam waist and the half-pulse width, respectively.

The effective TPA coefficient can be obtained quantitatively using a homogeneously broadened two-band theory^{[3638" target="_self" style="display: inline;">–38]}: βeff(I)=β01+(I/Isat)2,(3)where β0=σTPAg2g1N0, N0 is the concentration of the absorber (i.e., MoS2 molecular density, in cm−3). In an ideal monolayer MoS2 crystal, N0 is estimated to be ∼1.8×1022cm−3. σTPA is the TPA cross section, g2 (g1) is the electronic degeneracy of the upper (lower) state. The TPA-active excitons are sixfold degenerate, which corresponds to the three degenerate 2p states in a 2D hydrogen model, multiplied by the two valleys of K and K′ points in the Brillouin zone, so that g2g1 equals six in Eq. (4)^[39]. Based on the above theories, the TPA coefficients are acquired and shown in Fig. 3(c). The ME monolayer exhibits a much larger TPA coefficient of (1.88±0.21)×103cm/GW than the CVD one of (1.04±0.15)×103cm/GW. The TPA process in MoS2 during the pulse duration time (τp=350fs) is illustrated in Fig. 3(b), where an electron transits from the energy level E0 to E2 via absorbing two degenerate photons instantaneously. According to the selection rule, E2 represents the 2p dark excitonic state here. Then, the excited excitons relax to E1 through an electron–electron scattering process in less than 60 fs^[40,41]. The detailed carrier dynamics of the TPA process are simulated in the Supplementary Information and schematically shown in Fig. S2. The mid-gap defect states will decrease the TPA coefficients, as defect-induced one-photon absorption in the CVD monolayer may play a role^[21].

The saturation intensity Isat obtained in the micro-intensity scan experiment based on Eqs. (1) and (3), as shown in the inset of Fig. 3(c), can be deduced theoretically. In the homogeneously broadened model, the saturation intensity can be expressed as^[36,37]Isat=2ℏωτpσTPA(1+g2g1),(4)where τp is the full width at half-maximum of the femtosecond laser pulse (τp=350fs). Therefore, with the TPA cross section σTPA obtained from σTPA=β0N0g1g2, the saturation intensity of ME monolayer MoS2 can be calculated as ∼128GW/cm2, while the value of our experimental fitting result is ∼146GW/cm2 according to Eqs. (1) and (3). Likewise, the calculated value for Isat of the CVD-grown monolayer is ∼172GW/cm2, which is comparable with the fitting value of ∼217GW/cm2. The estimation of the saturation intensity is in the same order of magnitude with the experimental fitting results for both CVD and ME monolayers, implying that our fitting is reasonable. The saturation intensity of TPA is larger than that of monolayer WS2 (∼26GW/cm2)^[2]. Our results indicate that it is more difficult for CVD monolayer MoS2 to be saturated in the TPA process than the ME one.

The TPA coefficient of monolayer MoS2 is 3–4 orders of magnitude larger than those of many common semiconductors like ZnO and GaAs^[42,43]. In view of this giant advantage, it possesses great potential in optical pulse modulation and optical limiting applications. Therefore, it is necessary and interesting to examine the difference between CVD and ME MoS2. In this part, we simulated how the TPA saturation effect modulates the optical pulse in CVD and ME monolayers and made a comparison with a cascaded multilayer structure.

The spatial intensity distribution of the femtosecond pulses we used is of a Gaussian profile with a waist radius of ω0≈5μm, the same as the experiment. Considering that the value of β changes with pulse intensity according to the homogeneously broadened model, the TPA coefficient will not be a constant in the radial direction of a laser spot. This means that the differential transmission intensity ΔI/I0 at different radial positions in the spot will change. The differential intensity reflects the spatial modulation ability of the MoS2 nanofilms. However, the ultrashort interaction length in the monolayer is detrimental to the modulator design. As a result, a simple solution to this problem is having a series of cascading MoS2 monolayers^[44], and the simulated results are demonstrated in Fig. 4. Figure 4(a) depicts the resulting ΔI/I0 distribution when a pulse passes through the 1L, 50L, and 100L CVD and ME MoS2, respectively, under the same excitation of 300GW/cm2. We can see that in the CVD 1L case, the TPA saturation effect is not large enough, and the central area shows an intensive absorption. But, in the ME 1L case, the TPA is remarkably saturated, and the absorption decreases, which results in the darker spot in Fig. 4(a). In a cascaded structure, the transmitted intensity decreases layer by layer, making the TPA saturation insignificant. Therefore, a more uniform absorption can be seen in the multilayer systems, and the largest pulse intensity differential will move from the margin of the spot to the center. From Fig. 4(b), it can be seen that the stronger TPA effect in the ME cascaded structure results in greater pulse modulation amplitude with the increasing of layers. Furthermore, Fig. 4(c) shows the optical limiting performance of both CVD and ME cascaded structures, which directly reveals the difference of these two systems. In conclusion, according to the simulation results, due to larger TPA coefficient, the ME MoS2 monolayer and the cascaded structure exhibit better optical pulse modulation and optical limiting performance compared to CVD ones.

Fig. 4. (a), (b) Differential intensity (ΔI/I0) distribution of the output pulse under the same excitation intensity of 300GW/cm2 in 1L, 50L, and 100L CVD and ME MoS2, respectively. (c) Optical limiting performance.

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In summary, monolayer MoS2 nanosheets have been prepared by ME and CVD methods. We studied the difference of the degenerate TPA effect between them. The TPA coefficient of the CVD monolayer is only about one half of that of the ME one, mainly due to the one-photon absorption induced by mid-gap defect states. Furthermore, we simulated and compared the pulse modulation performance between CVD and ME cascaded monolayer structures. It can provide meaningful guides for the design of optical devices like a beam shaper and optical limiters.