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 MX2 (where M is a transition metal element and X is chalcogen) have potential for a wide variety of optoelectronic applications. In recent years, MX2 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, MX2 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 MX2 materials to work at a wider variety of light wavelengths than other 2D materials.

Recently, WTe2 has attracted considerable attention due to its large unsaturated positive magnetoresistance ^[23]. A great deal of work around WTe2 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 WTe2 very promising in photonic devices. The nonlinear optical properties of the MoTe2/WTe2 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 MoTe2/WTe2 nanosheets exhibit saturable absorption properties ^[33]. Bulk-like WTe2 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 WTe2 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 WTe2 in optical devices.

In this work, the third-order nonlinear optical processes of WTe2 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 WTe2 exhibits saturable absorption. The closed-aperture (CA) Z-scan signals reveal that the WTe2 films exhibit a self-defocusing optical effect. Combining these results with first-principles calculations, the third-order nonlinear susceptibility of WTe2 is estimated.

WTe2 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 WTe2 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 (1cm×1cm) was cleaned. The mica substrate and WTe2 target were positioned in the PLD reaction cavity (vacuum to ∼4×107mbar). The films were then fabricated with the help of a 248 nm KrF excimer laser beam at 1.5mJ/cm2 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.

X-ray photoelectron spectrum (XPS, VGESCA Lab220I-XL) was employed to study the surface chemical states of the WTe2 thin film. The Raman spectrum of the WTe2 thin film was characterized by Raman spectroscopy (Laboratory Ram HR800, excitation wavelength at 532 nm). The thickness and morphology of the WTe2 thin film are measured by atomic force microscopy (AFM, Dimension Icon Bruker AXS Inc.). The optical absorption properties of the WTe2 thin film are studied intensively by linear absorption spectrum (R1, IdeaOptics, China) in wavelength range from 400 to 1100 nm.

The Z-scan system setup was utilized to study the nonlinear response processes of the WTe2 sample, as shown in Fig. 1. The nonlinear absorption and refraction process of the WTe2 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.

The X-ray photoelectron spectrum (XPS) was measured to reveal the surface chemical states of the WTe2 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) (WO3), and W 4f (5/2) (WO3) ^[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) (TeO2), respectively ^[42,43]. The existence of the oxidation state is ascribed to the oxidization since WTe2 is inclined to be oxidized in the ambient environment ^[44].

Figure 2(b) shows Raman spectrum of WTe2 thin film. Six Raman spectral peaks located at 89.7, 111.0, 116.4, 134.1, 164.1, and 211.6cm−1 are attributed to the A25, A24, A19, A18, A15, and A12 phonon modes, respectively ^[26,45]. The existence of the A24 phonon mode indicates that the film is not a monolayer or few-layer WTe2, as confirmed by atomic force microscope image [see Fig. 2(c)] ^[26], where the thickness is determined to be ∼70nm, corresponding to about 100 monolayers of WTe2.

Optical absorption results of WTe2 are shown in Fig. 2(d), indicating that WTe2 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=I0e−αL, where I is the transmitted light intensity, I0 is the incident light intensity, and L is the film thickness. The value of transmittance (I/I0) and L are 0.5404 and 70 nm, respectively, at 1030 nm. Linear absorbtion coefficient is deduced to be 8.8×104cm−1.

For the sake of eliminating the influence of the mica substrate on the nonlinear absorption effect of WTe2, 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.

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 WTe2 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 WTe2 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)=∑m=0∞(−βI0Leff1+z2/z02)m(m+1)3/2,(1)where β is the nonlinear absorption coefficient, I0 is incident intensity at focus point, Leff=1−exp(−α0L)α0 is the effective film thickness, α0 is the linear absorption coefficient, L is the sample length along the z axis, and z0=πω02/λ is the Rayleigh diffraction length. The fitting results are shown in Fig. 3(b). The fitting results of nonlinear absorption coefficient β, for WTe2 at 2.08, 5.201, 10.402, and 15.603GW/cm2 were found to be −14.91×103, −7.89×103, −4.33×103 and −3.37×103cm/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 WTe2, which are not enough to overcome the ground state bleaching. In the measurement, we found that when the intensity was greater than 20.804GW/cm2, 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 WTe2 to be about 20.804GW/cm2 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−α0L),(2)where T is the transmission and L is thickness of sample. α0 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)=α01+I/IS+βI,(3)where I is incident light intensity, α0 is saturation loss (also called modulation depth), IS 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 20.29GW/cm2 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 WTe2. 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 4×4×1k-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‐WTe2 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 WTe2; 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, σgs is ground state absorption cross section, σes is excited state absorption cross section, and RP represents a relaxation process. The photon absorption by WTe2 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 WTe2, the subpicosecond time scale of the relaxation process is greater than the light pulse duration (∼340fs) in our experiment ^[49]. The result was fitted via the modified Frantz–Nodvik solution of a slow saturable absorber model: T(L)=T0+TFN(L)−T01−T0(Tmax−T0),(4)where T0=e−NσgsL is the transmission at low pulse power, Tmax=e−NσesL is the transmission achieved at high pulse power, N is the absorber density in WTe2 film, and σgs and σes are the ground state and excited state absorption cross sections, respectively. The TFN can be expressed as follows: TFN=ln{1+T0[eσgsE(0)−1]}/σgsE(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 σgs and σes of WTe2 film are determined to be 1.4938×10−16cm2 and 1.2536×10−16cm2. Up to now, this is the first time, to our knowledge, that the ground state and excited state absorption cross sections of WTe2 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 6.2390×1020cm−3.

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 WTe2 at the intensity of 15.603GW/cm2 at the beam waist is shown in Fig. 4(a). The transition from peak to valley indicates that the nonlinear refractive index of WTe2 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)=1−4ΔΦ0(z/z0)(z2/z02+1)(z2/z02+9),(6)where ΔΦ0=kn2I0Leff is the on-axis nonlinear phase shift at the focus, k=2π/λ is the wavelength number, I0 is incident intensity at the focus point, Leff is the effective film thickness, α0 is the linear absorption coefficient, L is the sample length along the z axis, and z0 is the Rayleigh diffraction length. The fitting result of nonlinear refractive index n2 at 15.603GW/cm2 was found to be −1.629×10−2cm2/GW for WTe2.

Generally, the high-order nonlinear phase shift can be expressed by the intensity-dependent refractive index: n=n0+n2I+n4I2+n6I3+⋯+n2nIn ^[51,52]. For the Z-scan theory, nonlinear phase shift ΔΦ=kn2I0Leff. An obvious linear relationship between nonlinear phase shift ΔΦ and effective nonlinear refractive index n2 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 Δn=n2*I=n2I+σrN(t), where n2 is the third-order nonlinear refractive index and σrN(t) is the higher-order nonlinearity. In particular, σr and N(t) are the free carrier refractive index and photoexcited carrier density, respectively. The valid nonlinear refractive coefficient n2*=n2+σrN(t)/I. Thus, the nonlinear refractive index change with incident light intensity increase can be understood in our experiment.

The real and imaginary parts of the third-order nonlinear susceptibility of the WTe2 sample can be deduced through the following formulas ^[56]: Imχ(3)(esu)=c2n02β(m/W)/240π2ω,(7)Reχ(3)(esu)=cn02n2(m2/W)/120π2,(8)where c is the velocity of light, n0 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 WTe2, 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)=12[ϵ1(ω)2+ϵ2(ω)2+ϵ1(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 n0 is seen to be about 3.7910 at 1030 nm in Fig. 5(b).

The values of Imχ(3) and Reχ(3) were calculated to be −1.01×10−8 and −5.93×10−9esu. Figure of merit (FOM) for third-order nonlinear absorption is defined as FOM=|Imχ(3)/α0| ^[19], where linear absorption coefficient α0∼8.8×104cm−1 can be gained from the linear absorption spectrum of the WTe2 sample. FOM for the WTe2 sample can be calculated as 1.143×10−13esu·cm. The comparison of third-order nonlinear properties between WTe2 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 WTe2 has a great potential applications in high-performance optical switching, mode-locking, Q-switching, and optoelectronic devices.

In conclusion, the third-order nonlinear optical response of WTe2 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 WTe2 film are investigated at diverse incident light intensities. The results of OA Z-scan measurements show that WTe2 has a saturable absorption under measurement conditions. The nonlinear absorption coefficient, saturation intensity, and modulation depth were calculated as −3.37×103cm/GW, 20.29GW/cm2, 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 1.4938×10−16cm2, 1.2536×10−16cm2, and 6.2396×1020cm−3, respectively. The nonlinear refractive index n2 was fitted to be −1.629×10−2cm2/GW. It is discovered that the measured value of the nonlinear refractive index n2 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 Reχ(3) and Imχ(3) of WTe2 film were calculated to be −5.93×10−9 and −1.01×10−8esu. The significant third-order nonlinearity manifest in WTe2 has great potential in applications such as high-performance optical switching, mode-locking, Q-switching, and optoelectronic devices.

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.