## Abstract

Transition metal dichalcogenides (TMDCs), such as tungsten disulfide (WS_{2}), are layered materials with strong in-plane bonding and weak out-of-plane interactions enabling exfoliation into two-dimensional layers of single unit cell thickness. Recent advances in nanoscale materials characterization and few layer TMDCs’ unique optical properties make them a research hot-spot in nonlinear optics. In this work, the nonlinear refractive index of monolayer WS_{2} has been characterized with Z-scan measurement under 800nm femtosecond pulsed laser excitation, and a value of *n _{2}* ≃ (8.1 ± 0.41) × 10

^{−13}m

^{2}/W is obtained. A shift from saturable absorption to reverse saturable absorption was observed at higher input pump intensities in the experiments. The transition process was analyzed using a phenomenological model based on two photon absorption, and the two photon absorption coeﬃcient was estimated about $(3.7\pm 0.28)\times {10}^{-6}m/W$.

© 2015 Optical Society of America

## 1. Introduction

Many two-dimensional (2D) materials exist in bulk form as stacks of strongly bonded layers with weak interlayer attraction, allowing exfoliation into individual, atomically thin layers. Many other 2D materials are known, such as the TMDCs [1, 2], transition metal oxides including titania- and perovskite-based oxides [3, 4], and graphene analogues such as boron nitride (BN) [5, 6]. In particular, TMDCs show a wide range of electronic, optical, mechanical, chemical and thermal properties that have been studied by researchers for decades [7–9]. There is at present a resurgence of scientific and engineering interest in TMDCs in their atomically thin 2D forms because of recent advances in sample preparation, optical detection, transfer and manipulation of 2D materials, and physical understanding of 2D materials learned from graphene.

The layer-dependent properties of TMDCs have recently attracted a great deal of attention. For example, in several semiconducting TMDCs there is a transition from an indirect bandgap in the bulk to a direct gap in the monolayer: for WS_{2} the bulk indirect bandgap of 1.3eV increases to a direct bandgap of 2.1 eV in single-layer form [10]. Besides, high carrier mobility and strong spin-orbit coupling due to their broken inversion symmetry [11, 12] make atomically thin WS_{2} nanosheets widely potential applications in viable photonic and optoelectronic devices [13, 14].

Nonlinear absorption materials with different nonlinear absorption processes (such as saturable absorption, two-photon absorption and multi-photon absorption) are promising in the different applications of nonlinear optics [15–18]. Therefore, it is necessary to identify their nonlinear absorption properties, and to determine their nonlinear absorption parameters. In this paper, we present results of study on the nonlinear refractive index of a monolayer WS_{2}. Under femtosecond pulsed laser excited at the near-infrared wavelength region (800 nm), we measured the real and imaginary part of the complex nonlinear refractive index (absorption coefficient and optical Kerr nonlinearity) with the Z-scan technique. Experiment results show that monolayer WS_{2} exhibits more than one nonlinear absorption process simultaneously under the excitation of intense laser pulses, which make the change of open-aperture Z-scan curves dependent on the intensity and have a transformation from saturable absorption (SA) to reverse saturable absorption (RSA). The saturable intensity and the nonlinear absorption coefficient are estimated by fitting the experimental curves with a phenomenological model of the combination of saturable absorption and two-photon absorption.

## 2. Experimental

#### 2.1 Characterization of monolayer WS_{2} sample

Large-area WS_{2} monolayer was grown on sapphire substrates by CVD. A multi-temperature-zone tube furnace (Lindberg/Blue M) equipped with a 1-inch-diameter quartz tube was used for growth. Sulphur powder was mildly sublimated at~100 °C and placed outside the hot zone. WO_{3} powder (Alfa Aesar, purity 99.9%and sapphire substrates (<0001> oriented single crystals) were successively placed in the hot centre. We used argon (flow rate 80 s.c.c.m.) or mixed argon and hydrogen gas (flow rates of 80 and 10 s.c.c.m., respectively) to carry WO_{3}– vapour species to the downstream substrates. The growth pressure was set at 30 Pa. Growth temperature was set at ~900 °C and growth time at ~60 min.

Although some bilayer and few-layer domains (hexagon) can also be found within the sample, the monolayer WS_{2} domains (triangle) is predominant can be seen in the scanning electron microscopy (SEM) image [Fig. 1(a)]. Monolayer is further confirmed by the atomic force microscopy (AFM) mapping of a triangle together with its height profile [Fig. 2(b)]. The height of ~0.7 nm is indicative of monolayer, in agreement with the previous studies [19–21]. The characteristic bands of Raman spectroscopy of the sample [Fig. 2(c)] at 352.3 and 418.9 cm^{−1} are assigned as the in-plane (${E}_{2g}^{1}$) and out-of -plane (${A}_{1g}^{}$) vibrational modes.

#### 2.2 Experimental setup

The Z-scan technique was applied to study the nonlinear optics coefficients of the monolayer WS_{2}. The experimental setup is shown in Fig. 2. The sample is excited by an 800 nm, 1 kHz repetition rate and 100 *fs* femtosecond pulsed laser, whose maximum single pulse energy is 0.8mJ. The laser beam is then focused by an objective lens (focal length: 500 mm), generating a beam waist of 40 μm at the focal point.

Open-aperture (OA) and closed-aperture (CA) Z-scans were employed simultaneously to study the nonlinear absorption and nonlinear refraction of monolayer WS_{2}, respectively. By properly monitoring the transmittance change through a small aperture (monitored by Detector 3) at the far field position (CA), it is able to determine the amplitude of the phase shift. While, by moving the sample through the focus without placing an aperture at the detector (OA) one can measure the intensity dependent absorption of the sample (monitored by Detector 2). The nonlinear refraction can be extracted from the division of the CA measurement by the OA measurement.

## 3. Results and discussion

#### 3.1 The nonlinear absorption of monolayer WS_{2} at 800nm

To determine the irradiance dependence of nonlinear absorption, our measurements were performed at diﬀerent laser energies. Some of the obtained OA experimental curves are present in Fig. 3. When the excitation energy was below 1.38μJ/pulse, corresponding to an estimated on-focus intensity of 275GW/cm^{2}, the monolayer WS_{2} sample exhibit obvious SA response; that is, the total transmission increases monotonically as the intensity of the incident beam increased (z→0). With higher excitation energy, nonlinear absorption of the sample transforms from SA to RSA, where the transmittances reduce with the increase of intensity (z→0). However, no obvious nonlinear absorption eﬀect was found in the OA measurements of pure sapphire substrate at these irradiances, which indicates that the nonlinear absorption and the transition arise mainly from monolayer WS_{2} sample. In fact, the nonlinear refractive of sapphire at 800nm is just ~3 × 10^{−20} m^{2}/W [22], which has little impact on our measurements of the nonlinear absorption properties of monolayer WS_{2}. To make sure that the WS_{2} is not damaged in our measurement, we have taken multiple measurements and got the similar results. For example, we firstly excited the sample from the lower intensity to higher and recorded the nonlinear responses. After the measurement under the highest peak light intensity, we put the sample under lower intensity again and got the similar results. It can be deduced that the WS_{2} is not damaged even under the highest peak light intensity in our measurements.

From the above-mentioned results, it can be seen that there are two nonlinear absorptions with opposite signs within the monolayer WS_{2} at 800 nm, namely SA and RSA. However, the monolayer WS_{2} is a direct semiconductor with a band gap of ~2.0 eV [10].That’s to say, for the photons with the energy of 1.55 eV(λ = 800 nm), it seems that the monolayer WS_{2} cannot be excited by only one photon and WS_{2} monolayer is beyond the application as a SA device. However, experimental results have revealed that WS_{2} exhibits saturable absorption property even for the photons with the energy of 0.8 eV [23]. Unfortunately, until now the nonlinear saturable absorption mechanism of WS_{2} nanosheets has not been clearly raveled at such waveband. One could infer that saturable absorption mechanism of WS_{2} may be defect induced bandgap decreasing [23] or exciton effect [10].

At high on-focus intensity (such as 850, 1250 and 2011GW/cm^{2}_{)}, the monolayer WS_{2} can be excited by two photons absorption (TPA). It should be pointed out that TPA of the WS_{2} monolayer will result in a decrease of the transmission, as opposed to the increase of the transmission around the focal point in the Z-scan experiment. However, WS_{2} monolayer lacks inversion symmetry and has non-vanishing second order nonlinear susceptibility (~4.5nm/V) [24]. When pumped by a strong pulse laser, the pump photons will be depleted through the second harmonic generation (SHG) as well, which could also result in the decrease of the pump transmission. We calculated the efficiency η for conversion of power from the fundamental wave (800nm) to the second harmonic wave (400nm) based on the nonlinear theory [25] and got the theoretical value of η is of the order of 0.5‰ for monolayer WS_{2}. And the experiment has just got an efficiency at 0.002‰ [24]. As a result, the influence of the SHG on the decrease of the pump transmission could be neglected.

Then, we could assume that the total absorption $\alpha (I)$consists of a linear absorption coeﬃcient ${\alpha}_{0}$ and a nonlinear absorption coeﬃcient ${\alpha}_{NL}$,

As for open aperture Z-scan, the normalized transmittance may be expressed as [25–28]:*L*the sample length, which is assumed equal to 0.7 nm, ${I}_{0}$ the on-axis peak intensity at the focus,

*z*the longitudinal displacement of the sample from the focus(z = 0), and ${z}_{0}$ the Rayleigh diﬀraction length. We measured and calculated the linear absorption coeﬃcient of the monolayer WS

_{2}sample with a spectrophotometer, and the result shows that${\alpha}_{0}$is ~8.88nm

^{−1}. In another word, for the photons with an energy of 1.55 eV (λ = 800 nm), the absorbance of the monolayer WS

_{2}sample (~0.7 nm) is only 0.002, which agrees with the previous studies [27–29]. By fitting the experimental data with Eq. (1) and Eq. (2), we obtained an average value of ${\alpha}_{NL}=-(3.7\pm 0.28)\times {10}^{-6}m/W$.

Overall, for the photons with the energy of 1.55 eV(λ = 800 nm), which is smaller than the band gap of monolayer WS_{2}, the monolayer WS_{2} sample absorbers a little when the excitation energy is relatively low(below 1.38μJ/pulse). Then, the total transmission increases monotonically as the intensity of the incident beam increased (z→0), which is similar to a SA process. However, once the excitation energy is high enough (above 1.38μJ/pulse), the effect of TPA is growing prominence with a decrease of the transmission with the increase of intensity (z→0), which is similar to a RSA process.

#### 3.2 The nonlinear refractive index of monolayer WS_{2}

As mentioned above, the nonlinear refraction can be extracted from the division of the CA measurement by the OA measurement. Typical results are showed in Fig. 4. A sharp and narrow peak located at the beam focus of the CA data clearly shows the characteristic of nonlinear absorption. The curves of CA/OA have the typical shapes of Z-scan measurements.

The experimental data can be fitted by the well-established formula [29]:

*T(x)*the normalized transmittance, $x=-z/{z}_{0}$,

*z*the longitudinal displacement of the sample from the focus(z = 0), ${z}_{0}=\pi {\omega}_{\text{0}}^{\text{2}}\text{/}\lambda $ the Rayleigh diﬀraction length, and $\Delta \Phi =k{n}_{2}{I}_{0}{L}_{eff}$ the on-axis nonlinear phase shift at the focus, where

*k*is the wavelength number,

*I*is the irradiance at the focus, and

_{0}*L*is the sample’s effective length. Then the refractive index

_{eff}*n*can be deduced from the slope of this curve at low intensities, based on${n}_{2}=\Delta \Phi /k{I}_{0}{L}_{eff}$. The nonlinear phase ΔΦ under different excited intensities is showed in Fig. 5 and a value of

_{2}*n*≃ 1.2 × 10

_{2}^{−12}m

^{2}/W is obtained.

The nonlinear refraction *n _{2}* changes under higher laser intensity in the experiments can be explained with the free-carrier nonlinearities and band-to-band nonlinearities [30–32]. The effective nonlinear index ${n}_{2}^{*}={n}_{2}+{\sigma}_{\gamma}N(t)/I$ becomes an intensity dependent parameter, with ${\sigma}_{\gamma}$the change in refractive index per unit conduction band electron density and $N(t)$the photo-excited carrier density. At lower power regime (below ~300GW/cm

^{2}), the TPA is very weak as seen in Fig. 3. Then the carrier density $N(t)$almost keeps constant. As a result, ${n}_{2}^{*}$decreases with the increase of the excitation power. At power regime between ~300GW/cm

^{2}and ~600GW/cm

^{2}, the TPA is growing and the carrier density $N(t)$ increase. That’s why there is fluctuate of ${n}_{2}^{*}$ as the increase of the excitation power. At higher power regime (~600GW/cm

^{2}to ~1200GW/cm

^{2}), the increase speed of $N(t)$grows slowly contrasted with that of excitation power. So, ${n}_{2}^{*}$decreases with the increase of the excitation power over again, but with a slower speed compared with the low power regime (below ~300GW/cm

^{2}). At even high regime (above ~1200GW/cm

^{2}), the free-carrier nonlinearities become weak and the nonlinear refraction ${n}_{2}^{*}$keeps almost a constant. Then one can argue that effective nonlinear Kerr index from the free carrier nonlinearity is about to 0.8 × 10

^{−12}m

^{2}/W.

As shown in Fig. 5, the average of measured nonlinear refractive index is about (8.4 ± 0.41) × 10^{−13}m^{2}/W. However, the measured value is a total nonlinear refractive which contains that of the sapphire substrate. To get a more accurate value of the nonlinear refraction of the monolayer WS_{2}, the influence of the sapphire substrate should be considered. According to calculation above, the n_{2} we obtained in the experiments is deduced from the ralation $\Delta \Phi =k{n}_{2}{I}_{0}{L}_{eff}$, which can be obtained from the experimental data. Considering the nonlinear refraction of the sapphire substrate, the phase shift should be rewritten as $\Delta \Phi =k{I}_{0}({n}_{2W{S}_{2}}{L}_{eff}+{n}_{2sapphire}{L}_{sapphire})$. As a result, the nonlinear refraction of pure monolayer WS_{2} is

*L*is~0.7nm, while

_{eff}*L*is ~1mm.

_{sapphire}*n*is the the average of measured nonlinear refractive index, which is about (8.4 ± 0.41) × 10

_{2}^{−13}m

^{2}/W and

*n*is the nonlinear refractive index of sapphire, which is about 3 × 10

_{2sapphire}^{−20}m

^{2}/W. Through use of Eq. (4) and the value given above, a more accurate value of the nonlinear refraction of monolayer WS

_{2}is obtained to be (8.1 ± 0.41) × 10

^{−13}m

^{2}/W.

## 4. Conclusion

In conclusion, the nonlinear refractive index of a monolayer WS_{2} sample is measured by the open and closed aperture Z-scan technique. It is found that the nonlinear refraction *n _{2}* changes with the incident laser intensity in the experiments, which is analyzed by the theory of free-carrier nonlinearities. The nonlinear absorption properties of monolayer WS

_{2}is investigated contemporary and a changeover from saturable absorption to reverse saturable absorption was found in the experiments. The sample shows reverse saturable absorption at higher intensities due to the two photon absorption.

## Acknowledgment

We thank Dr. Shunbin Lu and Dr. Chao Meng for their help with the absorption measurements. This work is partially supported by the National Natural Science Foundation of China (Grant No.61340017).

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