Third-order nonlinear optical properties of WTe2 films synthesized by pulsed laser deposition

Mi He; Yequan Chen; Lipeng Zhu; Huan Wang; Xuefeng Wang; Xinlong Xu; Zhanyu Ren

doi:10.1364/PRJ.7.001493

Abstract

The prominent third-order nonlinear optical properties of

{WTe}_{2}

films are studied through the Z-scan technique using a femtosecond pulsed laser at 1030 nm. Open-aperture (OA) and closed-aperture (CA) Z-scan measurements are performed at different intensities to investigate the nonlinear absorption and refraction properties of

{WTe}_{2}

films. OA Z-scan results show that

{WTe}_{2}

films always hold a saturable absorption characteristic without transition to reverse saturable absorption. Further, a large nonlinear absorption coefficient

β

is determined to be

3.37 \times 10^{3} cm / GW

by fitting the OA Z-scan curve at the peak intensity of

15.603 GW / {cm}^{2}

. In addition, through the slow saturation absorption model, the ground state absorption cross section, excited state absorption cross section, and absorber’s density were found to be

1.4938 \times 10^{16} {cm}^{2}

1.2536 \times 10^{16} {cm}^{2}

, and

6.2396 \times 10^{20} {cm}^{3}

, respectively. CA Z-scan results exhibit a classic peak–valley shape of the CA Z-scan signal, which reveals a self-defocusing optical effect of

{WTe}_{2}

films under the measured environment. Furthermore, a considerable nonlinear refractive index value

n_{2}

can be obtained at

1.629 \times 10^{2} {cm}^{2} / GW

. Ultimately, the values of the real and imaginary parts of the third-order nonlinear s

1. INTRODUCTION

Optical materials that possess large third-order nonlinear optical coefficients $χ^{(3)}$ have great potential in nonlinear optical devices such as saturable absorbers ^[1], optical switches ^[2], optical limiters ^[3], and wavelength converters ^[4]. The widely studied optical materials include organic materials ^[5], inorganic semiconductor materials ^[6], chalcogenide glasses ^[7], and other inorganic materials ^[8]. With the increasing demand for optical information processing, more novel materials are in great demand to achieve higher performance and easier integration. Recently, two-dimensional (2D) materials with atomic thickness have attracted widespread attention thanks to their large optical nonlinearity and fast broadband response ^[9,10]. Furthermore, these 2D materials are easily integrated and have excellent mechanical ^[11], chemical ^[12], and optical properties ^[13,14], which make them superb photoelectric materials.

Among the most promising 2D materials, the family of layered transition metal dichalcogenides with the general formula ${MX}_{2}$ (where M is a transition metal element and X is chalcogen) have potential for a wide variety of optoelectronic applications. In recent years, ${MX}_{2}$ materials have been intensely studied; it has been found that they possess significant ultrafast nonlinear optical properties, which suggest great potential for the development of nanophotonic devices such as mode-lockers, optical switches, ultrashort pulse generation, optical limiting, and all-optical logic gates ^[15–18]. In addition to their large third-order nonlinearity, ${MX}_{2}$ materials have unique energy gaps ^[19,20] which can be tunable depending on the component, structure, and number of layers ^[21,22]. Therefore, it is possible for ${MX}_{2}$ materials to work at a wider variety of light wavelengths than other 2D materials.

Recently, ${WTe}_{2}$ has attracted considerable attention due to its large unsaturated positive magnetoresistance ^[23]. A great deal of work around ${WTe}_{2}$ has been done to understand its band structure and magnetic properties ^[24,25]. Detailed Raman spectra have revealed a relationship between vibrational mode and crystal structures ^[26–29]. Photoconductivity ^[30], strong spin-orbit coupling ^[31], and tunable bandgap ^[32] make ${WTe}_{2}$ very promising in photonic devices. The nonlinear optical properties of the ${MoTe}_{2} / {WTe}_{2}$ nanosheets created by a liquid exfoliation method was investigated by a balanced twin-detector measurement scheme. To our knowledge, this is the first demonstration that ${MoTe}_{2} / {WTe}_{2}$ nanosheets exhibit saturable absorption properties ^[33]. Bulk-like ${WTe}_{2}$ microflakes served as the base material for an alternative near-infrared saturable absorber to generate femtosecond mode-locked pulses from a 1.55 μm fiber laser ^[34]. A mode-locked thulium fiber laser using a ${WTe}_{2}$ absorber was demonstrated ^[35]. However, third-order nonlinear processes, especially third-order refractive index, have remained largely unexplored, which may significantly limit the applications of ${WTe}_{2}$ in optical devices.

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In this work, the third-order nonlinear optical processes of ${WTe}_{2}$ films fabricated by pulsed laser deposition (PLD) are obtained by the Z-scan technique with a femtosecond pulse laser at 1030 nm. The open-aperture (OA) Z-scan measurement results show that ${WTe}_{2}$ exhibits saturable absorption. The closed-aperture (CA) Z-scan signals reveal that the ${WTe}_{2}$ films exhibit a self-defocusing optical effect. Combining these results with first-principles calculations, the third-order nonlinear susceptibility of ${WTe}_{2}$ is estimated.

2. EXPERIMENT

A. Fabrication of ${WTe}_{2}$ Thin Films

${WTe}_{2}$ films were fabricated by PLD technique and post-annealing. The detailed process is reported elsewhere ^[36]. Briefly, tungsten and tellurium are mixed at a stoichiometric ratio of 1:2 to compound precursor ${WTe}_{2}$ powder by heating to 700°C for a week; this was carried out in a vacuum quartz tube drained by a turbo molecular pump. The fully reactive precursor is pressed and sintered at 700°C in a sealed pipe. The mica substrate ( $1 cm \times 1 cm$ ) was cleaned. The mica substrate and ${WTe}_{2}$ target were positioned in the PLD reaction cavity (vacuum to $\sim 4 \times 10^{7} mbar$ ). The films were then fabricated with the help of a 248 nm KrF excimer laser beam at $1.5 mJ / {cm}^{2}$ average fluence and 1 Hz repetition rate. Finally, the films and tellurium powder were placed in a quartz tube at 700°C for 48 h to obtain good crystalline films.

B. Characterization of ${WTe}_{2}$ Thin Film

X-ray photoelectron spectrum (XPS, VGESCA Lab220I-XL) was employed to study the surface chemical states of the ${WTe}_{2}$ thin film. The Raman spectrum of the ${WTe}_{2}$ thin film was characterized by Raman spectroscopy (Laboratory Ram HR800, excitation wavelength at 532 nm). The thickness and morphology of the ${WTe}_{2}$ thin film are measured by atomic force microscopy (AFM, Dimension Icon Bruker AXS Inc.). The optical absorption properties of the ${WTe}_{2}$ thin film are studied intensively by linear absorption spectrum (R1, IdeaOptics, China) in wavelength range from 400 to 1100 nm.

C. Z-Scan Experimental Setup

The Z-scan system setup was utilized to study the nonlinear response processes of the ${WTe}_{2}$ sample, as shown in Fig. 1. The nonlinear absorption and refraction process of the ${WTe}_{2}$ thin films were explored through OA and CA Z-scan systems, respectively. The OA Z-scan measurements acquired the relationship between transmittance and sample location $z$ , while the sample slowly passed through the focal point of the focusing lens along the direction of laser propagation. The closed aperture relationship can be gained by putting an aperture after the sample. The configuration of the Z-scan optical path parameters was the same as in the previous report ^[37]. All measurements were carried out with a mode-locked fiber laser at 1030 nm; its pulse width and repetition rate were 340 fs and 100 Hz, respectively. The focal length of the focusing lens was 15 cm. The beam waist radius was about 30 μm at the focal point. The reference signals (for eliminating the influence of pulse laser energy fluctuation) and open and closed aperture signals were detected by three Si amplified detectors.

Optical path diagram of the Z-scan experiment.

Figure 1.Optical path diagram of the Z-scan experiment.

3. RESULTS AND DISCUSSION

A. Characterization of ${WTe}_{2}$ Thin Film

The X-ray photoelectron spectrum (XPS) was measured to reveal the surface chemical states of the ${WTe}_{2}$ thin film, as shown in Fig. 2(a). Four typical peaks at 31.4, 33.5, 35.4, and 37.5 eV are from the W element originating from W 4f (7/2) (metal), W 4f (5/2) (metal), W 4f (7/2) ( ${WO}_{3}$ ), and W 4f (5/2) ( ${WO}_{3}$ ) ^[38–41], while the pronounced peaks at 572.6 and 576.4 eV are attributed to Te 3d (5/2) (metal) and Te 3d(5/2) ( ${TeO}_{2}$ ), respectively ^[42,43]. The existence of the oxidation state is ascribed to the oxidization since ${WTe}_{2}$ is inclined to be oxidized in the ambient environment ^[44].

Figure 2.Characterization of thin ${WTe}_{2}$ film. (a) XPS. (b) Raman spectrum. (c) Atomic force microscopy (AFM) image. The step at the edge shows that the thickness of the film is typically $\sim 70 nm$ . (d) Absorption curve along with the reference mica substrate.

Figure 2(b) shows Raman spectrum of ${WTe}_{2}$ thin film. Six Raman spectral peaks located at 89.7, 111.0, 116.4, 134.1, 164.1, and $211.6 {cm}^{- 1}$ are attributed to the $A_{2}^{5}$ , $A_{2}^{4}$ , $A_{1}^{9}$ , $A_{1}^{8}$ , $A_{1}^{5}$ , and $A_{1}^{2}$ phonon modes, respectively ^[26,45]. The existence of the $A_{2}^{4}$ phonon mode indicates that the film is not a monolayer or few-layer ${WTe}_{2}$ , as confirmed by atomic force microscope image [see Fig. 2(c)] ^[26], where the thickness is determined to be $\sim 70 nm$ , corresponding to about 100 monolayers of ${WTe}_{2}$ .

Optical absorption results of ${WTe}_{2}$ are shown in Fig. 2(d), indicating that ${WTe}_{2}$ absorbs light from a range of 400 to 1100 nm. Optical absorption reduced gradually with the increase of wavelength. Meanwhile, an obviously weaker constant absorption can be observed in the pure mica substrate in the entire test wavelength region, which rules out its contribution. The linear absorption coefficient is calculated by Lambert’s law, $I = I_{0} e^{- α L}$ , where $I$ is the transmitted light intensity, $I_{0}$ is the incident light intensity, and $L$ is the film thickness. The value of transmittance ( $I / I_{0}$ ) and $L$ are 0.5404 and 70 nm, respectively, at 1030 nm. Linear absorbtion coefficient is deduced to be $8.8 \times 10^{4} {cm}^{- 1}$ .

B. Nonlinear Absorption Properties of ${WTe}_{2}$ Film

For the sake of eliminating the influence of the mica substrate on the nonlinear absorption effect of ${WTe}_{2}$ , OA Z-scan measurement of the mica substrate is performed. As shown in Fig. 3(a), there is no obvious nonlinear absorption behavior in the mica substrate.

Figure 3.OA Z-scan results of the ${WTe}_{2}$ sample deposited on the mica substrate. (a) OA Z-scan result of the ${WTe}_{2} / mica$ and the mica substrate. (b) Normalized transmission as a function of the ${WTe}_{2}$ sample position under different intensities at the focal point. (c) Saturation absorption fitting. (d) Electronic band structures of ${WTe}_{2}$ . (e) Simplified electronic band model of ${WTe}_{2}$ . (f) Slow saturation absorption fitting.

In order to study the nonlinear absorption effect of different incident intensity, OA Z-scan measurements were performed at different light intensities. Figure 3(b) shows the typical OA Z-scan measuring curves for ${WTe}_{2}$ thin films grown on mica substrates obtained at various light intensities. The normalized transmittance gradually increased as the sample got closer to the focal point, indicating that the absorption of ${WTe}_{2}$ is gradually saturated with the increase of the incident light intensity. This is widely known as a saturable absorption behavior. Nonlinear absorption coefficient can be obtained by fitting the experiment data. For OA Z-scan, the normalized transmittance as a function of sample position $z$ may be expressed as ^[46] $T (z) = \sum_{m = 0}^{\infty} \frac{{(\frac{- β I_{0} L_{eff}}{1 + z^{2} / z_{0}^{2}})}^{m}}{{(m + 1)}^{3 / 2}},$ (1)where $β$ is the nonlinear absorption coefficient, $I_{0}$ is incident intensity at focus point, $L_{eff} = \frac{1 - \exp (- α_{0} L)}{α_{0}}$ is the effective film thickness, $α_{0}$ is the linear absorption coefficient, $L$ is the sample length along the $z$ axis, and $z_{0} = π ω_{0}^{2} / λ$ is the Rayleigh diffraction length. The fitting results are shown in Fig. 3(b). The fitting results of nonlinear absorption coefficient $β$ , for ${WTe}_{2}$ at 2.08, 5.201, 10.402, and $15.603 GW / {cm}^{2}$ were found to be $- 14.91 \times 10^{3}$ , $- 7.89 \times 10^{3}$ , $- 4.33 \times 10^{3}$ and $- 3.37 \times 10^{3} cm / GW$ , respectively.

As shown in Fig. 3(b), the peaks of the OA Z-scan curves increase with the increasing input power intensity. From low power to high power or even damage threshold, the reverse saturable absorption effect was not observed. These results can be ascribed to smaller two-photon absorption coefficients of ${WTe}_{2}$ , which are not enough to overcome the ground state bleaching. In the measurement, we found that when the intensity was greater than $20.804 GW / {cm}^{2}$ , the sample’s peak transmittance suddenly increased with increasing of light intensity, and the original saturation absorption curve could not reappear when the intensity decreased to the initial intensity. We guess the damage threshold of ${WTe}_{2}$ to be about $20.804 GW / {cm}^{2}$ at 1030 nm.

Based on the relationship between the laser beam spot size and Z position of the sample, the normalized transmittance under variable incident intensity can be derived. A nonlinear saturable absorption curve is calculated as shown in Fig. 3(c). OA Z-scan measurement result shows the power-dependent normalized transmittance. We fitted this curve with a normalized equation: $T = [1 - α (I) L] / (1 - α_{0} L),$ (2)where $T$ is the transmission and $L$ is thickness of sample. $α_{0}$ is saturation loss (also called modulation depth) and $α (I)$ is the total absorption coefficient. For a process that combines saturable absorption and two-photon absorption, the total absorption coefficient can be written as $α (I) = \frac{α_{0}}{1 + I / I_{S}} + β I,$ (3)where $I$ is incident light intensity, $α_{0}$ is saturation loss (also called modulation depth), $I_{S}$ is saturation light intensity, and $β$ is two-photon absorption coefficient. $β$ is determined to be 0 in this experiment via fitting the curve. The fitting results indicate that saturation intensity was around $20.29 GW / {cm}^{2}$ and the modulation depth was 14.87% at 1030 nm.

It is necessary to analyze the electronic band structure in order to have a deeper understanding of the nonlinear absorption process of ${WTe}_{2}$ . The first-principles calculations were carried out using the VASP code ^[47] with the standard frozen-core projector augmented-wave (PAW) method. The cut-off energy for basis functions was 400 eV. The generalized gradient approximation of Perdew–Burke–Ernzerhof ^[48] was used for the exchange-correlation functional. A $4 \times 4 \times 1 k$ -point grid was used for computing the next electronic structures and linear index of refraction mentioned later. The calculation result is shown in Fig. 3(d). A small overlap between the conduction and valence bands can be clearly observed at the Fermi energy, and $Td ‐ {WTe}_{2}$ exhibits a classic semimetal behavior. According to the electronic structure, a simplified electronic band model can be found in Fig. 3(e). In this figure, the three-state energy diagram can be used for explaining the nonlinear absorption process of ${WTe}_{2}$ ; here, A is ground state, T is the final state of the ground state absorption, E1 is first excited state, E2 is second excited state, $σ_{g s}$ is ground state absorption cross section, $σ_{e s}$ is excited state absorption cross section, and RP represents a relaxation process. The photon absorption by ${WTe}_{2}$ causes electrons to transform from A to T. After a relaxation process, the electrons in T easily jump to E1 because of the small overlap between the conduction and valence bands. Then, electrons in the E1 absorb photons and convert to the more active state E2. Based on this, the solutions of basic rate equations ^[49] can be employed for further analysis of the saturated absorption process. By comparing the relative values of the first excited state decay time $τ$ and laser pulse duration, the solutions can be divided into two limiting cases. When the lifetime of first excited state is shorter than light pulse duration, a fast saturable absorber model is suited. A slow saturable absorber model is adaptive when the lifetime of the first excited state is longer compared to the light pulse duration. As for ${WTe}_{2}$ , the subpicosecond time scale of the relaxation process is greater than the light pulse duration ( $\sim 340 fs$ ) in our experiment ^[49]. The result was fitted via the modified Frantz–Nodvik solution of a slow saturable absorber model: $T (L) = T_{0} + \frac{T_{FN} (L) - T_{0}}{1 - T_{0}} (T_{\max} - T_{0}),$ (4)where $T_{0} = e^{- N σ_{g s} L}$ is the transmission at low pulse power, $T_{\max} = e^{- N σ_{e s} L}$ is the transmission achieved at high pulse power, $N$ is the absorber density in ${WTe}_{2}$ film, and $σ_{g s}$ and $σ_{e s}$ are the ground state and excited state absorption cross sections, respectively. The $T_{FN}$ can be expressed as follows: $T_{FN} = \ln {1 + T_{0} [e^{σ_{g s} E (0)} - 1]} / σ_{g s} E (0),$ (5)where $E (0)$ is the incident light fluence in units of photons per unit area. By fitting the experimental data through a slow saturation absorption model, it can be observed that the fitting red line matches the data points well, as presented in Fig. 3(f). The values of $σ_{g s}$ and $σ_{e s}$ of ${WTe}_{2}$ film are determined to be $1.4938 \times 10^{- 16} {cm}^{2}$ and $1.2536 \times 10^{- 16} {cm}^{2}$ . Up to now, this is the first time, to our knowledge, that the ground state and excited state absorption cross sections of ${WTe}_{2}$ have been estimated. The ratio of the excited state to the ground state absorption cross section is obtained to be 0.84 at 1030 nm, which is consistent with the saturation absorption process in our experiments. The ratio of the ground state and excited state absorption cross section is less than 1 for the saturable absorber. The absorber’s density is deduced to be $6.2390 \times 10^{20} {cm}^{- 3}$ .

C. Nonlinear Refractive Index of ${WTe}_{2}$ Film

The nonlinear refractive index can be extracted from the division of the CA measurement by the OA measurement. The typical CA Z-scan trace of ${WTe}_{2}$ at the intensity of $15.603 GW / {cm}^{2}$ at the beam waist is shown in Fig. 4(a). The transition from peak to valley indicates that the nonlinear refractive index of ${WTe}_{2}$ is negative. As for the CA Z-scan measurements, the relationship between normalized transmittance and sample location in the $z$ axis can be described as follows ^[46,50]: $T (z) = 1 - \frac{4 Δ Φ_{0} (z / z_{0})}{(z^{2} / z_{0}^{2} + 1) (z^{2} / z_{0}^{2} + 9)},$ (6)where $Δ Φ_{0} = k n_{2} I_{0} L_{eff}$ is the on-axis nonlinear phase shift at the focus, $k = 2 π / λ$ is the wavelength number, $I_{0}$ is incident intensity at the focus point, $L_{eff}$ is the effective film thickness, $α_{0}$ is the linear absorption coefficient, $L$ is the sample length along the $z$ axis, and $z_{0}$ is the Rayleigh diffraction length. The fitting result of nonlinear refractive index $n_{2}$ at $15.603 GW / {cm}^{2}$ was found to be $- 1.629 \times 10^{- 2} {cm}^{2} / GW$ for ${WTe}_{2}$ .

$CA Z-scan results of the WTe2 sample deposited on mica substrate. (a) CA Z-scan result under 15.603 GW/cm2 incident peak power intensity. (b) Nonlinear refractive index and nonlinear phase shift as a function of excitation peak power intensity.$

Figure 4.CA Z-scan results of the ${WTe}_{2}$ sample deposited on mica substrate. (a) CA Z-scan result under $15.603 GW / {cm}^{2}$ incident peak power intensity. (b) Nonlinear refractive index and nonlinear phase shift as a function of excitation peak power intensity.

Generally, the high-order nonlinear phase shift can be expressed by the intensity-dependent refractive index: $n = n_{0} + n_{2} I + n_{4} I^{2} + n_{6} I^{3} + \dots + n_{2 n} I^{n}$ ^[51,52]. For the Z-scan theory, nonlinear phase shift $Δ Φ = k n_{2} I_{0} L_{eff}$ . An obvious linear relationship between nonlinear phase shift $Δ Φ$ and effective nonlinear refractive index $n_{2}$ usually suggests a pure third-order nonlinear effect. However, in our experiment, the change of nonlinear phase shift is not completely linear with the increase of incident light intensity, as shown in Fig. 4(b). This implies that high-order nonlinear processes take place in our experiments.

That the nonlinear refractive index change depends on the light intensity can be attributed to the free-carrier nonlinearities and bound-electronic nonlinearities ^[53–55]. We assume that both mechanisms are present in the measurement. When it comes a process that has a higher order nonlinear effect, the dependence of the change of refractive index on the intensity takes the form $Δ n = n_{2}^{*} I = n_{2} I + σ_{r} N (t)$ , where $n_{2}$ is the third-order nonlinear refractive index and $σ_{r} N (t)$ is the higher-order nonlinearity. In particular, $σ_{r}$ and $N (t)$ are the free carrier refractive index and photoexcited carrier density, respectively. The valid nonlinear refractive coefficient $n_{2}^{*} = n_{2} + σ_{r} N (t) / I$ . Thus, the nonlinear refractive index change with incident light intensity increase can be understood in our experiment.

D. Third-Order Nonlinear Susceptibility Estimation of ${WTe}_{2}$ Film

The real and imaginary parts of the third-order nonlinear susceptibility of the ${WTe}_{2}$ sample can be deduced through the following formulas ^[56]: $Im χ^{(3)} (esu) = c^{2} n_{0}^{2} β (m / W) / 240 π^{2} ω,$ (7) $Re χ^{(3)} (esu) = c n_{0}^{2} n_{2} (m^{2} / W) / 120 π^{2},$ (8)where $c$ is the velocity of light, $n_{0}$ is linear refractive index, and $ω$ is the angular frequency of the excited light. Parameters other than linear refractive index have been acquired from experimental results. In order to have a basic knowledge of the magnitude of the third-order nonlinear optical susceptibility of ${WTe}_{2}$ , a theoretical calculation of linear refractive index is carried out via density functional theory. The details of the first-principles calculation are the same as the configuration of the band structure calculation mentioned earlier in this work. First, the theoretical dielectric function is computed through first-principles calculation. Then, the following equation is utilized to gain linear refractive index ^[57]: $n (ω) = \frac{1}{\sqrt{2}} {[\sqrt{ϵ_{1} {(ω)}^{2} + ϵ_{2} {(ω)}^{2}} + ϵ_{1} (ω)]}^{1 / 2}$ . The complete result is represented in Fig. 5(a). In order to show the results more clearly, the local theoretical results of the linear refractive index are exhibited in Fig. 5(b). Linear refractive index $n_{0}$ is seen to be about 3.7910 at 1030 nm in Fig. 5(b).

$First-principles calculation of linear refractive index of WTe2. (a) Linear refractive index. (b) Local image of refractive index.$

Figure 5.First-principles calculation of linear refractive index of ${WTe}_{2}$ . (a) Linear refractive index. (b) Local image of refractive index.

The values of $Im χ^{(3)}$ and $Re χ^{(3)}$ were calculated to be $- 1.01 \times 10^{- 8}$ and $- 5.93 \times 10^{- 9} esu$ . Figure of merit (FOM) for third-order nonlinear absorption is defined as $FOM = | Im χ^{(3)} / α_{0} |$ ^[19], where linear absorption coefficient $α_{0} \sim 8.8 \times 10^{4} {cm}^{- 1}$ can be gained from the linear absorption spectrum of the ${WTe}_{2}$ sample. FOM for the ${WTe}_{2}$ sample can be calculated as $1.143 \times 10^{- 13} esu \cdot cm$ . The comparison of third-order nonlinear properties between ${WTe}_{2}$ and the other two-dimensional materials is summarized in Table 1, which includes the nonlinear absorption coefficient, the imaginary part of third-order nonlinear susceptibility, nonlinear refractive coefficient, the real part of third-order nonlinear susceptibility, and FOM. Compared to other materials, WTe₂ exhibits the real part of third-order nonlinear susceptibility two orders of magnitude greater than MoTe₂ and graphene. Meanwhile, the imaginary part of third-order nonlinear susceptibility is three orders of magnitude larger than that of MoS₂ and WS₂. These calculation results imply that ${WTe}_{2}$ has a great potential applications in high-performance optical switching, mode-locking, $Q$ -switching, and optoelectronic devices.

Sample	β(cm/GW)	n2(cm2/GW)	Reχ(3)(esu)	Imχ(3)(esu)	FOM(esu·cm)	Refs.
WTe2	−3.37×103	−1.629×10−2	−5.93×10−9	−1.01×10−8	1.143×10−13	This work
MoS2	−3.8	1.88×10−3	8.71×10−10	−1.5×10−11	—	[56]
WS2	−5.1	5.83×10−2	2.31×10−8	−1.75×10−11	—	[56]
MoTe2	−7.50×10−3	−0.160×10−3	−0.92×10−11	−5.50×10−15	6.38×10−15	[58]
Graphene	−9.4×10−2	−13.7×10−3	−78.2×10−11	−6.9×10−14	4.03×10−15	[58]

Table 1. Comparison of Third-Order Nonlinear Coefficients between ${WTe}_{2}$ and Other Two-Dimensional Materials

View all Tables

4. CONCLUSION

In conclusion, the third-order nonlinear optical response of ${WTe}_{2}$ film synthesized by PLD has been researched via the OA and CA Z-scan technique with a 1030 nm femtosecond pulse laser. The nonlinear absorption properties of ${WTe}_{2}$ film are investigated at diverse incident light intensities. The results of OA Z-scan measurements show that ${WTe}_{2}$ has a saturable absorption under measurement conditions. The nonlinear absorption coefficient, saturation intensity, and modulation depth were calculated as $- 3.37 \times 10^{3} cm / GW$ , $20.29 GW / {cm}^{2}$ , and 14.87%, respectively. By further analyzing the nonlinear absorption processes, the ground and excited state absorption cross sections and the absorber’s density were found to be $1.4938 \times 10^{- 16} {cm}^{2}$ , $1.2536 \times 10^{- 16} {cm}^{2}$ , and $6.2396 \times 10^{20} {cm}^{- 3}$ , respectively. The nonlinear refractive index $n_{2}$ was fitted to be $- 1.629 \times 10^{- 2} {cm}^{2} / GW$ . It is discovered that the measured value of the nonlinear refractive index $n_{2}$ decreases with increasing input power in the experiments, which is caused by higher-order nonlinear effect due to free carrier and bound-electronic nonlinearities. By means of first-principles calculation, the real and imaginary parts of third-order nonlinear coefficients $Re χ^{(3)}$ and $Im χ^{(3)}$ of ${WTe}_{2}$ film were calculated to be $- 5.93 \times 10^{- 9}$ and $- 1.01 \times 10^{- 8} esu$ . The significant third-order nonlinearity manifest in ${WTe}_{2}$ has great potential in applications such as high-performance optical switching, mode-locking, $Q$ -switching, and optoelectronic devices.

Acknowledgment

Acknowledgment. X.W. is supported by the National Natural Science Foundation of China. The authors thank Ningning Dong and Jun Wang for providing the Z-scan measurements.

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