Abstract

As a kind of two-dimensional transition metal dichalcogenide material, tungsten diselenide (WSe2) has attracted increasing attention, owing to its gapped electronic structure, relatively high carrier mobility, and valley pseudospin, all of which show its valuable nonlinear optical properties. There are few studies on the nonlinear optical properties of WSe2 and correlation with its electronic structure. In this paper, the effects of spatial self-phase modulation (SSPM) and distortion influence of WSe2 ethanol suspensions are systematically studied, namely, the nonlinear refractive index and third-order nonlinear optical effect. We obtained the WSe2 dispersions SSPM distortion formation mechanism, and through it, we calculated the nonlinear refractive index n2, nonlinear susceptibility χ(3), and their wavelength dependence under the excitation of 457 nm, 532 nm, and 671 nm lasers. Moreover, by use of its strong and broadband nonlinear optical response, all-optical switching of two different laser beams due to spatial cross-phase modulation has been realized experimentally. Our results are useful for future optical devices, such as all-optical switching and all-optical information conversion.

© 2018 Chinese Laser Press

1. INTRODUCTION

From the early discovery of two-dimensional (2D) material graphene, many endeavors have concentrated on developing 2D materials that exceed graphene, such as transition metal dichalcogenides (TMDCs) [13]. TMDCs consist of two layers of sulfide atoms and a sandwiched layer of metal atoms [4], forming an atomic tri-layer chemical formula shaped like MX2. The tri-layer films are superposed by weak van der Waals interactions to form a 3D entity [5]. According to the combination of the sulfur family (S, Te, Se) and transition metals (Mo, Nb, Re, W, Ni, V) [6], TMDCs produce over 40 different kinds. TMDCs are likely to be integral parts of future electric optical devices, such as all-electric optical switches that act as metals, semi-metals, or semiconductors according to the selection of transition metals [7].

Tungsten diselenide (WSe2) is drawing more and more interest because of its comparatively high carrier mobility, interstitial electronic structure, and valley pseudospin, which all denote diverting nonlinear optical properties of this TMDC material [8,9]. In 1970, WSe2 ultrathin film comprising only two layers was favorably prepared by mechanical stripping, and the thickness effect of exciton transition was revealed [10]. WSe2 is a layered semiconductor with a hexagonal crystalline structure and an indirect bandgap of 1.35 eV. The optical properties of WSe2 transfer mainly from two direct excitons at 1.71 eV and 2.30 eV, called A and B excitons, severally [11,12]. WSe2 has been broadly used in photo-electron chemical solar cells as an electrode [13] and hydrogen evolution [14], according to its high absorption coefficients and photo-corrosion resistance in the visible range. In addition, depending on its flexible layered structure and low surface trap density, it is an attractive flexible electronic candidate. Formerly, we have proved that WSe2 field effect transistors have been obtained at room temperature, and the carrier mobility is equivalent to that of silicon [15]. Recently, WSe2 has been prepared in many ways, such as solution phase synthesis [16], mechanical exfoliation [17], rapid selenization process [18], and modulated elemental reaction [19].

To comprehend these 2D materials, the nonlinear refractive index n2 and third-order nonlinear susceptibility χ(3) have been studied by using four-wave mixing, Z-scan, and spatial self-phase modulation (SSPM) [2023]. The Z-scan mechanism is based upon self-focusing or self-defocusing whose spot is a Gaussian beam, and different from the mechanism of SSPM self-diffraction whose spot is a concentric circle. The SSPM technique has become a useful means for measuring the nonlinear coefficient of 2D materials. In order to estimate the nonlinear refractive index n2 of WSe2 [24,25], nonlinear characteristic parameters are analyzed by using SSPM in this paper.

Optical switching devices based on 2D materials can be designed using the nonlinear optical effect [26]. Wu et al. [27] exhibited an all-optical switch that relies on dual-color (473 nm and 532 nm) SSPM using MoS2 in 2015. They created a model at 473 nm (controlled light) by raising the beam intensity to 532 nm (controlling light). The ring numbers and diameters increase at the same time, and the fixed intensity of 473 nm is lower than the threshold. The physical mechanism can be traced back to cross-phase modulation (XPM) [28,29], which refers to a nonlinear phase change of the light field caused by other co-propagating fields [30]. In two or more laser fields, self-phase modulation (SPM) is always accompanied by XPM, which has always been covered in optical fibers [31].

In this paper, the SSPM effect of WSe2 ethanol suspension is studied. First, the conventional preparation method of WSe2 and the preparation steps of WSe2 dispersion in this experiment are briefly described. Then, the characterization method of WSe2 and the characterization results of this sample are summarized. Then, the apparatus diagram of this experiment is introduced. The images of the SSPM effect taken in multiple bands are also given, and n2 and χmonolayer(3) values of WSe2 are analyzed and calculated by taking the experiment at wavelengths of 457 nm, 532 nm, and 671 nm lasers. Taking advantage of the advanced optical properties of WSe2, we can design a novel nonlinear all-optical switching device combined with the information transmission system based on spatial cross-phase modulation (SXPM).

2. PREPARATION AND CHARACTERIZATION OF WSe2 NANOPARTICLES

A. Preparation of WSe2 Nanoparticles

2D material WSe2 ethanol suspensions were produced by the liquid phase stripping method for further experimental investigations. With the mixture of organic solvents, using ultrasound, the WSe2 interlayer van der Waals force was overcome, and then WSe2 dispersions were obtained through a centrifugal method removing the WSe2 block from a single layer, and multilayer WSe2 and fewer WSe2 block mixed suspensions. Bulk WSe2 (99.99%) and ethanol (CH3CH2OH, 99.9%) were purchased from Sigma-Aldrich. First, 20 mg WSe2 was added to 20 mL ethanol, and then the whole solution was treated with bath sonication whose power was set at 300 W for 10 h, and the working temperature of the bath sonication was at controlled around 10°C. After this process, the obtained WSe2 suspension was centrifuged for 60 min with a rotation rate of 5000 r/min, followed by 12 h natural settling. The upper layer liquid from the last step was centrifuged for 40 min with a rotation rate of 12,000 r/min. The resulting supernatant was composed of a few-layer WSe2 dispersion used in the following experiments.

B. Characterization of Few-Layer WSe2 Nanoparticles

The WSe2 dispersion solution was dropped onto an ultra-thin copper mesh, and then dried in an arid cabinet, imaged by transmission electron microscopy (TEM), which shows the bedded structure of WSe2 nanoparticles, as in Fig. 1(a). The WSe2 image edges are clearly visible, and the folds on the WSe2 surface are also obvious.

 figure: Fig. 1.

Fig. 1. Characterization of WSe2 nanoparticles after stable storing for two weeks. (a) TEM image, (b) HRTEM image, (c) AFM image, (d) transmittance spectrum, (e) Raman spectrum, and (f) XRD pattern.

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The high-resolution TEM (HRTEM) image in Fig. 1(b) shows the 2D honeycomb structure of WSe2 with a tight arrangement of atoms. The observed spacings of the lattice fringes are 0.329 nm and 0.247 nm, respectively. Atomic force microscopy (AFM) was used to characterize WSe2 thin film morphology and atom structure; the WSe2 thin film was made by deposition of WSe2 dispersion on a silicon wafer, as shown in Fig. 1(c). From WSe2 thin-film height of 4.1 nm, we also can identify the layer number as about six.

In the transmittance spectrum wavelength from 500 nm to 1100 nm, shown in Fig. 1(d), we can clearly find that the transmissivity of WSe2 nanoparticles is in the range of 4.87%–17.98% and has two peaks at 907 nm (12.82%) and 1016 nm (15.23%). In Fig. 1(e), Raman spectroscopy is one of the important means to distinguish the 1–10 layers of 2D ultra-thin layered materials. It analyzes the molecular structure of the sample by the principle of changing the frequency of the scattering light when the light is irradiated to the sample. The Raman spectrum of the WSe2 nanoparticle suspension displays a broad band with peak maximum at 220  cm1 [32]. Figure 1(f) gives the X-ray diffraction (XRD) curve of WSe2 nanoparticles, showing peaks at 13.6°, 27.5°, 37.8°, 41.8°, and 56.7°.

3. RESULTS AND DISCUSSION

A. Scheme of SSPM Experiment

Figure 2 displays a diagrammatic sketch of the SSPM experiment. A wavelength of λ=532  nm continuous-wave (CW) laser (while in the following experiment, wavelengths of λ=671  nm and λ=457  nm were also included) was used as a light source. This laser beam passed the polaroid, focalized after the lens (f=200  mm), and then passed through WSe2 dispersion, which was filled in a 10 mm thickness quartz cuvette. Distances between the focus point and sample L1 were set as 3.7 cm, 4.8 cm, and 9.2 cm. L2 values were quartz cuvette thickness plus L1. The CW laser engendered phase-shift passing the WSe2 dispersion, motivated the SSPM effect, and diverged into diffraction rings. The diffraction ring patterns can be obtained from a black screen suspended behind the sample quartz cuvette, and also can be obtained from a charge-coupled device (CCD, LaserCam HR II 2/3 inch), which was produced by Coherent.

 figure: Fig. 2.

Fig. 2. Diagrammatic sketch of the measuring experimental setup.

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The WSe2 nanoparticle dispersion was prepared by the liquid stripping technique. The results show that the diffraction ring pattern experienced rapid deformation when the incident CW laser passed through the dispersion horizontally. Figures 3(a)3(c) show the corresponding pictures taken by CCD and record all of the SSPM conversion process. From 0 to 0.42 s, after the CW laser passed through the few-layer WSe2 dispersion, the diffraction pattern started from a small round circle and quickly became a series of complete symmetric concentric rings. From 0.42 s the diffraction rings began to distort rapidly, until at 1.23 s reaching a stable collapsed pattern. The top half of the diffraction ring collapsed toward the center of the pattern, and the bottom half of the ring remained almost an original full round circle and formed a sub-elliptical diffraction ring. The collapse is very obvious in the vertical direction, and in the upper part of the ring, the closer to the outer collapse, the more obvious collapse effect we got.

 figure: Fig. 3.

Fig. 3. (a)–(c) Diffraction rings received by a CCD of SSPM transformation; (d) schematic of the distortion for WSe2 nanoparticle dispersions.

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The above phenomenon is called the collapse effect of diffraction rings in SSPM. The collapse effect is very important for studying the variation of the nonlinear refractive index of 2D materials. The change in refractive index for nonlinear materials caused by lasers can be measured by the collapse effect.

B. Collapse Dependent on Light Intensity

In addition to temperature response, collapse distortion also shows obvious regularity with the intensity of light, all of which shows linear variations. The patterns of classical SSPM effect are shown in Figs. 3(a)3(c); the collapse amplitude of the upper part can be described by angles formed from the sample to pattern. When diffraction rings appear, a series of coaxial cones are formed by a diffractive light path in space. The angle from the axis of the largest cone to the side of the cone is a half-conical angle, i.e., collapse distance RD, the maximum half diffraction angle is θH, and maximum diffraction radius is RH. D is the distance from the sample to the pattern; the values are 8.1 cm, 8.9 cm, and 9.8 cm at the wavelengths of λ=532  nm, λ=671  nm, and λ=457  nm, shown in Fig. 3(d). On the basis of DRH, the relationship can be explained as

θH=RHD.
When the diffraction ring collapses and stabilizes, the maximum half-angle of the diffraction pattern of the first half part is θH, and the maximum diffraction radius is changed to RH. If DRH, the relationship can be conveyed as the following equation:
θH=RHD.
The distortion angle and diffraction radius are defined as θD and RD; on the basis of RD=RHRH, the relationship between them can be displayed as
θD=θHθH=RDD.
The distortion angle can be displayed as the next expression [22]:
θD=θHθH=(n2n2)IC=Δn2IC.
Finally, the relation between the relative variable of the nonlinear refractive index and collapse angle and the maximum half-diffractive angle is obtained by eliminating the maximum half-diffraction angle constant [33]:
Δn2/n2=θD/θH.
From diffraction patterns caught by CCD, we obtained the distance from the pattern and got the variation of the distortion angle (θD) and half-cone angle (θH) with the incident intensity change at λ=532  nm, λ=671  nm, and λ=457  nm, as shown in Figs. 4(a) and 4(b).

 figure: Fig. 4.

Fig. 4. (a) Variation of the half-cone angle (θH) with incident intensity; (b) variation of the distortion angle (θD) with incident intensity; (c) change in the nonlinear refractive index of WSe2 after distortion.

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Through calculation, we can obtain the change rate of the nonlinear refractive index, as shown in Fig. 4(c). For λ=532  nm, intensity from 13.10  W/cm2 increases to 69.86  W/cm2, accomplishing the half-cone angle (θH) from 0.024 mrad to 0.121 mrad, in a nearly linear manner; distortion angle (θD) from 0.020 mrad to 0.037 mrad is also a linear change. λ=671  nm and λ=457  nm also have the same regular results. This means that the distortion results in a significant change of nonlinear refractive index in the dispersion of several layers WSe2 nanoparticles.

Therefore, in the measurement, through the ratio of collapse angle to maximum half-diffraction, θD/θH can obtain the relative change of the nonlinear refractive index of the WSe2 dispersion. The results show that the relative change in nonlinear refractive index varies with light intensity. When light intensity increased from 13.10  W/cm2 to 69.86  W/cm2, the change was monotone, from 30.57% to 83.33% at 532 nm. In other words, the larger the incident intensity, the greater the change in nonlinear refractive index and the more obvious the collapse, which is consistent with the observed collapse effect. Light sources at λ=671  nm and λ=457  nm have got the same regular results.

C. Wavelength Dependence of Third-Order Nonlinear Susceptibility

A light field through WSe2 nanoparticles can cause a change in refractive index, producing some well-known optical phenomena, for instance, self-phase modulation and self-focusing. According to the nonlinear optical Kerr’s law, when a laser beam passes through a nonlinear optical medium, in this case, WSe2 nanoparticles, the light intensity will cause the refractive index to change, and the change in refractive index causes the phase movement of the light; the change in refractive index can be explained as follows:

n=n0+n2I,
where n2 and n0 are the nonlinear and linear refractive indices, and I represents the incident intensity. It can be clearly seen from the above equation that the refractive index of the medium is related to the light intensity, and the refractive index of the medium changes with the intensity of light, which is also a significant feature of the optical Kerr effect.

When the laser beam passes through WSe2 dispersion, the SSPM phenomenon is generated, and the phase shift (Δψ) is shown as follows:

Δψ=2πn0λ0Leffn2I(r,z)dz,
where λ is the wavelength, Leff is an effective optical propagation length, r is the radial position, and I(r,z) is the intensity distribution. The effective thickness of the quartz cuvette can be calculated by [22]
Leff=L1L2(1+z2z02)1dz=z0arctan(zz0)|L2L1,
where z0 is the Rayleigh length, z is the propagation length, and L is the thickness of the cuvette. For a Gaussian beam, the phase shift Δψ=Δψ0exp(2r2/a2) can be satisfied, and a is equal to 1/e2 beam radius. The bright and dark rings [22] alternately occur when the phase shift is related to the ring number Δψ(0)Δψ()=2Nπ [34]. After derivation, the nonlinear refractive index of WSe2 can be written as [35]
n2=λ2n0Leff·NI.
The third-order nonlinear susceptibility of 2D nonlinear material WSe2 is defined as χtotal(3). From the slope of the ring number and incident intensity, χtotal(3) of WSe2 nanoparticles can be expressed by
χtotal(3)=cλn02.4×104π2Leff·dNdI.
The third-order nonlinear susceptibility for monolayer WSe2 nanoparticles can be obtained by
χtotal(3)=χmonolayer(3)Neff2,
where Neff is the effective amount of the monolayer.

Figure 5 shows the relationship between the diffraction ring number received by CCD and the intensity of different wavelengths at λ=532  nm, λ=671  nm, and λ=457  nm.

 figure: Fig. 5.

Fig. 5. Variation of diffraction ring numbers with incident intensity at λ=532  nm, λ=671  nm, and λ=457  nm, respectively.

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In Fig. 5, we clearly see the linear relationship between the number of rings and the intensity with a slope of dN/dI=0.15  cm2·W1 for λ=532  nm. After fitting, we yielded the nonlinear refractive index n2=2.940×106  cm2·W1 and the third-order nonlinear susceptibility χtotal(3)=1.371×106  (e.s.u.). The distance from the lens to the cuvette is 15.3 cm. The transmission of monolayer WSe2, which was got from Refs. [36,37], is 92.93% at the 532 nm wavelength, and for the WSe2 dispersion sample in this paper the transmission is 4.94%, and then we got the Neff as 41, and χmonolayer(3) as 8.14×1010  (e.s.u.).

Figure 5 shows the variation of diffraction rings for λ=671  nm with incident intensity, and the fitting result is n2=8.661×106  cm2·W1 and χtotal(3)=4.040×106  (e.s.u.). The length between the lens and cuvette is 14.2 cm for 671 nm. The transmissions of monolayer WSe2 and WSe2 dispersion in our research at 671 nm wavelength are 98.81% and 7.38%, respectively. We finally got the Neff as 218, and χmonolayer(3) as 8.44×1011  (e.s.u.).

In addition, Fig. 5 proves the change in diffraction rings with intensity at λ=457  nm, and n2=6.402×106  cm2·W1 and χtotal(3)=2.986×106  (e.s.u.) are acquired by fitting. The distance from the lens to the cuvette is 9.8 cm for the 457 nm laser beams. Neff is 28, and χmonolayer(3) is 3.69×109  (e.s.u.), which is calculated from the transmissions of monolayer WSe2 at 89.50% and our sample at 4.28%.

Table 1 give the summary of the relations between optical parameters and wavelengths of different 2D materials [3840].

Tables Icon

Table 1. n2 and χmonolayer(3) for a Variety of 2D Materials

D. Formation Mechanism of the Diffraction Rings

It is known that diffraction rings are a result of SSPM related to the local refractive index change caused by a laser. However, there are several competing theories about the origin of refractive index variations. For instance, the thermal lens theory is proposed to describe the change in the refractive index of the medium with the change in temperature resulted from absorbing the laser light [41]. In order to understand the origin of diffraction rings, we investigate the SSPM by a Nd:YAG nanosecond (ns) laser (Beamtech model DAWA-200, 532 nm, 8 ns) with low repetition rate (20 Hz) as a comparison to the results with the CW laser. The results are shown in Fig. 6(b). It is found that the number of rings in the ns laser is nearly half that of the CW laser at the same power. We tuned the repetition rate of the ns laser to 10 Hz; it is found that the number of rings is almost unchanged, indicating the possible electronic origin of SSPM. Moreover, the whole transformation processes of SSPM caught by a white screen are shown in Fig. 6(a). Under the CW laser, the formation of the whole diffraction rings needs 0.42 s, and going to distortion needs 1.23 s. But if we use the ns laser, the formation progress takes only 0.20 s, and distortion progress takes 0.65 s. It is obvious that the intrinsic nonlinear effect from the material plays an important role in the formation of diffraction rings in the low-repetition-rate pulsed laser. However, the thermal lens effects have a significant impact on the formation of diffraction rings using the CW laser. These indicate that both intrinsic nonlinear optics and thermal lens effect may have contributions to the phase modulation under intense CW laser excitation.

 figure: Fig. 6.

Fig. 6. (a) Transformation of SSPM. (1)–(3): continuous wave; (4)–(6): ultrafast wave. (b) Variation of diffraction ring numbers with continuous wave and ultrafast wave.

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E. All-Optical Switch Exhibition

In the experiment, the optical control of light technology based on the SXPM effect with WSe2 was discussed. This optical switching of WSe2 nanoparticle dispersion liquid was disposed by using CW 671 nm controlling light (HNL210L) to modulate/manipulate the propagation of the 532 nm controlled light (SPROUT-H-5W). The controlling light and controlled light were placed at equal height passing through the WSe2 nanoparticle dispersion liquid, which was put in a 2 mm thick quartz cuvette. The intensities of these two lights were changed by attenuation slices, passed a focusing f=200  mm lens, and focused on the center of the quartz cuvette. By increasing the incident intensity of the controlling light, the nonlinear phase in the WSe2 dispersion liquid could be controlled. Figure 6 shows the schematic diagram of the experimental configuration. After combining the laser beam through the lens and the sample, we can see the diffraction ring behind the white screen. Figure 7 shows the experimental configuration for the all-optical switching, and Figs. 8(b) and 8(c) show the images of the SXPM effect in WSe2.

 figure: Fig. 7.

Fig. 7. Schematic of the experimental configuration for all-optical switching.

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 figure: Fig. 8.

Fig. 8. (a) Results obtained by using a relatively strong λ=532  nm laser beam to control the other laser beam with relatively weak power at λ=671  nm; (b), (c) images obtained from white screen.

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In the beginning, laser intensity of controlled light at 671 nm is adjusted below the diffraction ring excitation threshold whose intensity is set at I=2.18  W/cm2 shown as a Gauss laser spot, which indicates that there is no nonlinear optical effect at this incident intensity. Later, the controlling light at 532 nm is used to excite the diffraction ring of controlled light at 671 nm. Slowly increasing the incident intensity of the controlling light to 2.45  W/cm2 while the controlled light was kept at an intensity of 2.18  W/cm2, the diffraction rings of both the controlling light and controlled light in the transmitted spots can be surveyed. In addition, the diffraction ring numbers of the 532 nm and 671 nm beams rise with the increasing of the incident intensity of the 532 nm controlled light.

Figure 8(a) shows the diffraction relationship between the controlling light and the controlled light. The results show that the diffraction ring number increases linearly with the increase of incident intensity of 532 nm, indicating that the phase of the controlling light (red 671 nm) changes with the increase of SXPM. These results show that the controlled light can be modulated only by changing the incident intensity of the controlling light so that three phases (constant, focused, and diffracted) can be achieved. The results show that we can use a strong beam to modulate the weaker beam, which indicates its application prospect in nonlinear phase modulation. Therefore, we can make use of this nonlinear optical effect to design all-optical switch devices with two different laser lights.

4. CONCLUSION

The SSPM effect was obtained from WSe2 ethanol suspension, which was synthesized using a liquid phase exfoliation method. The nonlinear refractive index and third-order nonlinear susceptibility of WSe2 were well characterized for the first time at wavelengths of λ=532  nm, λ=671  nm, and λ=457  nm, and its power-dependent nonlinear refractive index was experimentally verified. The brightness, diameter, and numbers of diffraction rings increase with the augmentation of incident light intensity and show the distribution characteristics of outer thick inner thin, external strong interior weak concentric circles. The diffraction ring will collapse over time, and after a period of time will achieve the stability of the pattern. TMDC WSe2 displays a large nonlinear optical response and high stability; by using these properties, an all-optical switch based on WSe2 was proved. Compared with other 2D materials, WSe2 has the advantages of high nonlinear response, high stability, narrow bandgap and rich properties. It is expected to be used in optical devices such as all-optical switches and all-optical information conversion in the near future.

Funding

National Natural Science Foundation of China (NSFC) (11604216, 61505111); China Postdoctoral Science Foundation (2017M622746, 2018M633129); Natural Science Foundation of Guangdong Province (2018A030313198).

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23. H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37, 1856–1858 (2012). [CrossRef]  

24. G. Wang, S. Zhang, X. Zhang, L. Zhang, Y. Cheng, D. Fox, H. Zhang, J. N. Coleman, W. J. Blau, and J. Wang, “Tunable nonlinear refractive index of two-dimensional MoS2, WS2 and MoSe2 nanosheet dispersions,” Photon. Res. 3, A51–A55 (2015). [CrossRef]  

25. G. Wang, S. Higgins, K. Wang, D. Bennett, N. Milosavljevic, J. J. Magan, S. Zhang, X. Zhang, J. Wang, and W. J. Blau, “Intensity-dependent nonlinear refraction of antimonene dispersions in the visible and near-infrared region,” Appl. Opt. 57, E147–E153 (2018). [CrossRef]  

26. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010). [CrossRef]  

27. Y. Wu, Q. Wu, F. Sun, C. Cheng, S. Meng, and J. Zhao, “Emergence of electron coherence and two-color all-optical switching in MoS2 based on spatial self-phase modulation,” Proc. Natl. Acad. Sci. 112, 11800–11805 (2015). [CrossRef]  

28. D. J. Jones, S. A. Diddams, M. S. Taubman, S. T. Cundiff, L. S. Ma, and J. L. Hall, “Frequency comb generation using femtosecond pulses and cross-phase modulation in optical fiber at arbitrary center frequencies,” Opt. Lett. 25, 308–310 (2000). [CrossRef]  

29. S. Matsuoka, N. Miyanaga, S. Amano, and M. Nakatsuka, “Frequency modulation controlled by cross-phase modulation in optical fiber,” Opt. Lett. 22, 25–27 (1997). [CrossRef]  

30. G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987). [CrossRef]  

31. Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu, “Low-light-level cross-phase-modulation based on stored light pulses,” Phys. Rev. Lett. 96, 043603 (2006). [CrossRef]  

32. P. Tonndorf, R. Schmidt, P. Bottger, X. Zhang, J. Borner, A. Liebig, M. Albrecht, C. Kloc, O. Gordan, and D. R. T. Zahn, “Photoluminescence emission and Raman response of MoS2, MoSe2, and WSe2 nanolayers,” Opt. Express 21, 4908–4916 (2013). [CrossRef]  

33. G. Wang, S. Zhang, F. A. Umran, X. Cheng, N. Dong, D. Coghlan, Y. Cheng, L. Zhang, W. J. Blau, and J. Wang, “Tunable effective nonlinear refractive index of graphene dispersions during the distortion of spatial self-phase modulation,” Appl. Phys. Lett. 104, 141909 (2014). [CrossRef]  

34. B. Shi, L. Miao, Q. Wang, J. Du, P. Tang, J. Liu, C. Zhao, and S. Wen, “Broadband ultrafast spatial self-phase modulation for topological insulator Bi2Te3 dispersions,” Appl. Phys. Lett. 107, 151101 (2015). [CrossRef]  

35. U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003). [CrossRef]  

36. J. K. Huang, J. Pu, C. L. Hsu, M. H. Chiu, Z. Y. Juang, Y. H. Chang, W. H. Chang, Y. Iwasa, T. Takenobu, and L. J. Li, “Large-area synthesis of highly crystalline WSe2 monolayers and device applications,” ACS Nano 8, 923–930 (2013). [CrossRef]  

37. Q. Cui, F. Ceballos, N. Kumar, and H. Zhao, “Transient absorption microscopy of monolayer and bulk WSe2,” ACS Nano 8, 2970–2976 (2014). [CrossRef]  

38. Y. L. Wu, L. L. Zhu, Q. Wu, F. Sun, J. K. Wei, Y. C. Tian, W. L. Wang, X. D. Bai, X. Zuo, and J. Zhao, “Electronic origin of spatial self-phase modulation: evidenced by comparing graphite with C60 and graphene,” Appl. Phys. Lett. 108, 241110 (2016). [CrossRef]  

39. X. Li, R. Liu, H. Xie, Y. Zhang, B. Lyu, P. Wang, J. Wang, Q. Fan, Y. Ma, S. Tao, S. Xiao, X. Yu, Y. Gao, and J. He, “Tri-phase all-optical switching and broadband nonlinear optical response in Bi2Se3 nanosheets,” Opt. Express. 25, 18346–18354 (2017). [CrossRef]  

40. J. Zhang, X. Yu, W. Han, B. Lv, X. Li, S. Xiao, Y. Gao, and J. He, “Broadband spatial self-phase modulation of black phosphorous,” Opt. Lett. 41, 1704–1707 (2016). [CrossRef]  

41. Y. Wang, Y. Tang, P. Cheng, X. Zhou, Z. Zhu, Z. Liu, D. Liu, Z. Wang, and J. Bao, “Distinguishing thermal lens effect from electronic third-order nonlinear self-phase modulation in liquid suspensions of 2D nanomaterials,” Nanoscale 9, 3547–3554 (2017). [CrossRef]  

References

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  1. A. H. C. Neto and K. Novoselov, “New directions in science and technology: two-dimensional crystals,” Rep. Prog. Phys. 74, 82501–82509 (2011).
    [Crossref]
  2. Q. H. Wang, K. Kalantarzadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
    [Crossref]
  3. S. Z. Butler, S. M. Hollen, L. Cao, Y. Cui, J. A. Gupta, H. R. Gutiérrez, T. F. Heinz, S. S. Hong, J. Huang, and A. F. Ismach, “Progress, challenges, and opportunities in two-dimensional materials beyond graphene,” ACS Nano 7, 2898–2926 (2013).
    [Crossref]
  4. R. H. Friend and A. D. Yoffe, Electronic Properties of Intercalation Complexes of the Transition Metal Dichalcogenides (Springer, 1984), pp. 1–94.
  5. S. Chuang, R. Kapadia, H. Fang, T. C. Chang, W. C. Yen, Y. L. Chueh, and A. Javey, “Near-ideal electrical properties of InAs/WSe2 van der Waals heterojunction diodes,” Appl. Phys. Lett. 102, 242101 (2013).
    [Crossref]
  6. A. Allain and A. Kis, “Electron and hole mobilities in single-layer WSe2,” ACS Nano 8, 7180–7185 (2014).
    [Crossref]
  7. M. Chhowalla, H. S. Shin, G. Eda, L. J. Li, K. P. Loh, and H. Zhang, “The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets,” Nat. Chem. 5, 263–275 (2013).
    [Crossref]
  8. S. Yoshida, Y. Terada, M. Yokota, O. Takeuchi, Y. Mera, and H. Shigekawa, “Direct probing of transient photocurrent dynamics in p-WSe2 by time-resolved scanning tunneling microscopy,” Appl. Phys. Express 6, 016601 (2013).
    [Crossref]
  9. W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P. H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
    [Crossref]
  10. F. Consadori and R. F. Frindt, “Crystal size effects on the exciton absorption spectrum of WSe2,” Phys. Rev. B 2, 4893–4896 (1970).
    [Crossref]
  11. A. R. Beal, W. Y. Liang, and H. P. Hughes, “Kramers–Kronig analysis of the reflectivity spectra of 3R-WS2 and 2H-WSe2,” J. Phys. C 9, 2449–2457 (1976).
    [Crossref]
  12. R. Coehoorn, C. Haas, and R. A. de Groot, “Electronic structure of MoSe2, MoS2, and WSe2. II. The nature of the optical band gaps,” Phys. Rev. B 35, 6203–6206 (1987).
    [Crossref]
  13. H. J. Lewerenz, A. Heller, and F. J. Disalvo, “Relationship between surface morphology and solar conversion efficiency of tungsten diselenide photoanodes,” J. Am. Chem. Soc. 102, 1877–1880 (1980).
    [Crossref]
  14. J. R. Mckone, A. P. Pieterick, H. B. Gray, and N. S. Lewis, “Hydrogen evolution from Pt/Ru-coated p-type WSe2 photocathodes,” J. Am. Chem. Soc. 135, 223–231 (2012).
    [Crossref]
  15. V. Podzorov, “High-mobility field-effect transistors based on transition metal dichalcogenides,” Appl. Phys. Lett. 84, 3301–3303 (2004).
    [Crossref]
  16. P. D. Antunez, D. H. Webber, and R. L. Brutchey, “Solution-phase synthesis of highly conductive tungsten diselenide nanosheets,” Chem. Mater. 25, 2385–2387 (2013).
    [Crossref]
  17. H. Li, G. Lu, Y. Wang, Z. Yin, C. Cong, Q. He, L. Wang, F. Ding, T. Yu, and H. Zhang, “Mechanical exfoliation and characterization of single- and few-layer nanosheets of WSe2, TaS2, and TaSe2,” Small 9, 1974–1981 (2013).
    [Crossref]
  18. H. Wang, D. Kong, P. Johanes, J. J. Cha, G. Zheng, K. Yan, N. Liu, and Y. Cui, “MoSe2 and WSe2 nanofilms with vertically aligned molecular layers on curved and rough surfaces,” Nano Lett. 13, 3426–3433 (2013).
    [Crossref]
  19. N. T. Nguyen, P. A. Berseth, Q. Lin, C. Chiritescu, D. G. Cahill, A. Mavrokefalos, L. Shi, P. Zschack, M. D. Anderson, and I. M. Anderson, “Synthesis and properties of turbostratically disordered, ultrathin WSe2 films,” Chem. Mater. 22, 2750–2756 (2010).
    [Crossref]
  20. C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321, 385–388 (2008).
    [Crossref]
  21. L. Wu, Z. Xie, L. Lu, J. Zhao, Y. Wang, X. Jiang, Y. Ge, F. Zhang, S. Lu, Z. Guo, J. Liu, Y. Xiang, S. Xu, J. Li, D. Fan, and H. Zhang, “Few-layer tin sulfide: a promising black-phosphorus-analogue 2D material with exceptionally large nonlinear optical response, high stability, and applications in all-optical switching and wavelength conversion,” Adv. Opt. Mater. 6, 1700985 (2018).
    [Crossref]
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    [Crossref]
  23. H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37, 1856–1858 (2012).
    [Crossref]
  24. G. Wang, S. Zhang, X. Zhang, L. Zhang, Y. Cheng, D. Fox, H. Zhang, J. N. Coleman, W. J. Blau, and J. Wang, “Tunable nonlinear refractive index of two-dimensional MoS2, WS2 and MoSe2 nanosheet dispersions,” Photon. Res. 3, A51–A55 (2015).
    [Crossref]
  25. G. Wang, S. Higgins, K. Wang, D. Bennett, N. Milosavljevic, J. J. Magan, S. Zhang, X. Zhang, J. Wang, and W. J. Blau, “Intensity-dependent nonlinear refraction of antimonene dispersions in the visible and near-infrared region,” Appl. Opt. 57, E147–E153 (2018).
    [Crossref]
  26. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
    [Crossref]
  27. Y. Wu, Q. Wu, F. Sun, C. Cheng, S. Meng, and J. Zhao, “Emergence of electron coherence and two-color all-optical switching in MoS2 based on spatial self-phase modulation,” Proc. Natl. Acad. Sci. 112, 11800–11805 (2015).
    [Crossref]
  28. D. J. Jones, S. A. Diddams, M. S. Taubman, S. T. Cundiff, L. S. Ma, and J. L. Hall, “Frequency comb generation using femtosecond pulses and cross-phase modulation in optical fiber at arbitrary center frequencies,” Opt. Lett. 25, 308–310 (2000).
    [Crossref]
  29. S. Matsuoka, N. Miyanaga, S. Amano, and M. Nakatsuka, “Frequency modulation controlled by cross-phase modulation in optical fiber,” Opt. Lett. 22, 25–27 (1997).
    [Crossref]
  30. G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
    [Crossref]
  31. Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu, “Low-light-level cross-phase-modulation based on stored light pulses,” Phys. Rev. Lett. 96, 043603 (2006).
    [Crossref]
  32. P. Tonndorf, R. Schmidt, P. Bottger, X. Zhang, J. Borner, A. Liebig, M. Albrecht, C. Kloc, O. Gordan, and D. R. T. Zahn, “Photoluminescence emission and Raman response of MoS2, MoSe2, and WSe2 nanolayers,” Opt. Express 21, 4908–4916 (2013).
    [Crossref]
  33. G. Wang, S. Zhang, F. A. Umran, X. Cheng, N. Dong, D. Coghlan, Y. Cheng, L. Zhang, W. J. Blau, and J. Wang, “Tunable effective nonlinear refractive index of graphene dispersions during the distortion of spatial self-phase modulation,” Appl. Phys. Lett. 104, 141909 (2014).
    [Crossref]
  34. B. Shi, L. Miao, Q. Wang, J. Du, P. Tang, J. Liu, C. Zhao, and S. Wen, “Broadband ultrafast spatial self-phase modulation for topological insulator Bi2Te3 dispersions,” Appl. Phys. Lett. 107, 151101 (2015).
    [Crossref]
  35. U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003).
    [Crossref]
  36. J. K. Huang, J. Pu, C. L. Hsu, M. H. Chiu, Z. Y. Juang, Y. H. Chang, W. H. Chang, Y. Iwasa, T. Takenobu, and L. J. Li, “Large-area synthesis of highly crystalline WSe2 monolayers and device applications,” ACS Nano 8, 923–930 (2013).
    [Crossref]
  37. Q. Cui, F. Ceballos, N. Kumar, and H. Zhao, “Transient absorption microscopy of monolayer and bulk WSe2,” ACS Nano 8, 2970–2976 (2014).
    [Crossref]
  38. Y. L. Wu, L. L. Zhu, Q. Wu, F. Sun, J. K. Wei, Y. C. Tian, W. L. Wang, X. D. Bai, X. Zuo, and J. Zhao, “Electronic origin of spatial self-phase modulation: evidenced by comparing graphite with C60 and graphene,” Appl. Phys. Lett. 108, 241110 (2016).
    [Crossref]
  39. X. Li, R. Liu, H. Xie, Y. Zhang, B. Lyu, P. Wang, J. Wang, Q. Fan, Y. Ma, S. Tao, S. Xiao, X. Yu, Y. Gao, and J. He, “Tri-phase all-optical switching and broadband nonlinear optical response in Bi2Se3 nanosheets,” Opt. Express. 25, 18346–18354 (2017).
    [Crossref]
  40. J. Zhang, X. Yu, W. Han, B. Lv, X. Li, S. Xiao, Y. Gao, and J. He, “Broadband spatial self-phase modulation of black phosphorous,” Opt. Lett. 41, 1704–1707 (2016).
    [Crossref]
  41. Y. Wang, Y. Tang, P. Cheng, X. Zhou, Z. Zhu, Z. Liu, D. Liu, Z. Wang, and J. Bao, “Distinguishing thermal lens effect from electronic third-order nonlinear self-phase modulation in liquid suspensions of 2D nanomaterials,” Nanoscale 9, 3547–3554 (2017).
    [Crossref]

2018 (2)

L. Wu, Z. Xie, L. Lu, J. Zhao, Y. Wang, X. Jiang, Y. Ge, F. Zhang, S. Lu, Z. Guo, J. Liu, Y. Xiang, S. Xu, J. Li, D. Fan, and H. Zhang, “Few-layer tin sulfide: a promising black-phosphorus-analogue 2D material with exceptionally large nonlinear optical response, high stability, and applications in all-optical switching and wavelength conversion,” Adv. Opt. Mater. 6, 1700985 (2018).
[Crossref]

G. Wang, S. Higgins, K. Wang, D. Bennett, N. Milosavljevic, J. J. Magan, S. Zhang, X. Zhang, J. Wang, and W. J. Blau, “Intensity-dependent nonlinear refraction of antimonene dispersions in the visible and near-infrared region,” Appl. Opt. 57, E147–E153 (2018).
[Crossref]

2017 (2)

X. Li, R. Liu, H. Xie, Y. Zhang, B. Lyu, P. Wang, J. Wang, Q. Fan, Y. Ma, S. Tao, S. Xiao, X. Yu, Y. Gao, and J. He, “Tri-phase all-optical switching and broadband nonlinear optical response in Bi2Se3 nanosheets,” Opt. Express. 25, 18346–18354 (2017).
[Crossref]

Y. Wang, Y. Tang, P. Cheng, X. Zhou, Z. Zhu, Z. Liu, D. Liu, Z. Wang, and J. Bao, “Distinguishing thermal lens effect from electronic third-order nonlinear self-phase modulation in liquid suspensions of 2D nanomaterials,” Nanoscale 9, 3547–3554 (2017).
[Crossref]

2016 (2)

Y. L. Wu, L. L. Zhu, Q. Wu, F. Sun, J. K. Wei, Y. C. Tian, W. L. Wang, X. D. Bai, X. Zuo, and J. Zhao, “Electronic origin of spatial self-phase modulation: evidenced by comparing graphite with C60 and graphene,” Appl. Phys. Lett. 108, 241110 (2016).
[Crossref]

J. Zhang, X. Yu, W. Han, B. Lv, X. Li, S. Xiao, Y. Gao, and J. He, “Broadband spatial self-phase modulation of black phosphorous,” Opt. Lett. 41, 1704–1707 (2016).
[Crossref]

2015 (3)

G. Wang, S. Zhang, X. Zhang, L. Zhang, Y. Cheng, D. Fox, H. Zhang, J. N. Coleman, W. J. Blau, and J. Wang, “Tunable nonlinear refractive index of two-dimensional MoS2, WS2 and MoSe2 nanosheet dispersions,” Photon. Res. 3, A51–A55 (2015).
[Crossref]

B. Shi, L. Miao, Q. Wang, J. Du, P. Tang, J. Liu, C. Zhao, and S. Wen, “Broadband ultrafast spatial self-phase modulation for topological insulator Bi2Te3 dispersions,” Appl. Phys. Lett. 107, 151101 (2015).
[Crossref]

Y. Wu, Q. Wu, F. Sun, C. Cheng, S. Meng, and J. Zhao, “Emergence of electron coherence and two-color all-optical switching in MoS2 based on spatial self-phase modulation,” Proc. Natl. Acad. Sci. 112, 11800–11805 (2015).
[Crossref]

2014 (3)

G. Wang, S. Zhang, F. A. Umran, X. Cheng, N. Dong, D. Coghlan, Y. Cheng, L. Zhang, W. J. Blau, and J. Wang, “Tunable effective nonlinear refractive index of graphene dispersions during the distortion of spatial self-phase modulation,” Appl. Phys. Lett. 104, 141909 (2014).
[Crossref]

A. Allain and A. Kis, “Electron and hole mobilities in single-layer WSe2,” ACS Nano 8, 7180–7185 (2014).
[Crossref]

Q. Cui, F. Ceballos, N. Kumar, and H. Zhao, “Transient absorption microscopy of monolayer and bulk WSe2,” ACS Nano 8, 2970–2976 (2014).
[Crossref]

2013 (10)

J. K. Huang, J. Pu, C. L. Hsu, M. H. Chiu, Z. Y. Juang, Y. H. Chang, W. H. Chang, Y. Iwasa, T. Takenobu, and L. J. Li, “Large-area synthesis of highly crystalline WSe2 monolayers and device applications,” ACS Nano 8, 923–930 (2013).
[Crossref]

M. Chhowalla, H. S. Shin, G. Eda, L. J. Li, K. P. Loh, and H. Zhang, “The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets,” Nat. Chem. 5, 263–275 (2013).
[Crossref]

S. Yoshida, Y. Terada, M. Yokota, O. Takeuchi, Y. Mera, and H. Shigekawa, “Direct probing of transient photocurrent dynamics in p-WSe2 by time-resolved scanning tunneling microscopy,” Appl. Phys. Express 6, 016601 (2013).
[Crossref]

W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P. H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
[Crossref]

S. Z. Butler, S. M. Hollen, L. Cao, Y. Cui, J. A. Gupta, H. R. Gutiérrez, T. F. Heinz, S. S. Hong, J. Huang, and A. F. Ismach, “Progress, challenges, and opportunities in two-dimensional materials beyond graphene,” ACS Nano 7, 2898–2926 (2013).
[Crossref]

S. Chuang, R. Kapadia, H. Fang, T. C. Chang, W. C. Yen, Y. L. Chueh, and A. Javey, “Near-ideal electrical properties of InAs/WSe2 van der Waals heterojunction diodes,” Appl. Phys. Lett. 102, 242101 (2013).
[Crossref]

P. D. Antunez, D. H. Webber, and R. L. Brutchey, “Solution-phase synthesis of highly conductive tungsten diselenide nanosheets,” Chem. Mater. 25, 2385–2387 (2013).
[Crossref]

H. Li, G. Lu, Y. Wang, Z. Yin, C. Cong, Q. He, L. Wang, F. Ding, T. Yu, and H. Zhang, “Mechanical exfoliation and characterization of single- and few-layer nanosheets of WSe2, TaS2, and TaSe2,” Small 9, 1974–1981 (2013).
[Crossref]

H. Wang, D. Kong, P. Johanes, J. J. Cha, G. Zheng, K. Yan, N. Liu, and Y. Cui, “MoSe2 and WSe2 nanofilms with vertically aligned molecular layers on curved and rough surfaces,” Nano Lett. 13, 3426–3433 (2013).
[Crossref]

P. Tonndorf, R. Schmidt, P. Bottger, X. Zhang, J. Borner, A. Liebig, M. Albrecht, C. Kloc, O. Gordan, and D. R. T. Zahn, “Photoluminescence emission and Raman response of MoS2, MoSe2, and WSe2 nanolayers,” Opt. Express 21, 4908–4916 (2013).
[Crossref]

2012 (3)

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37, 1856–1858 (2012).
[Crossref]

J. R. Mckone, A. P. Pieterick, H. B. Gray, and N. S. Lewis, “Hydrogen evolution from Pt/Ru-coated p-type WSe2 photocathodes,” J. Am. Chem. Soc. 135, 223–231 (2012).
[Crossref]

Q. H. Wang, K. Kalantarzadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
[Crossref]

2011 (1)

A. H. C. Neto and K. Novoselov, “New directions in science and technology: two-dimensional crystals,” Rep. Prog. Phys. 74, 82501–82509 (2011).
[Crossref]

2010 (2)

N. T. Nguyen, P. A. Berseth, Q. Lin, C. Chiritescu, D. G. Cahill, A. Mavrokefalos, L. Shi, P. Zschack, M. D. Anderson, and I. M. Anderson, “Synthesis and properties of turbostratically disordered, ultrathin WSe2 films,” Chem. Mater. 22, 2750–2756 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

2008 (1)

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321, 385–388 (2008).
[Crossref]

2006 (1)

Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu, “Low-light-level cross-phase-modulation based on stored light pulses,” Phys. Rev. Lett. 96, 043603 (2006).
[Crossref]

2004 (1)

V. Podzorov, “High-mobility field-effect transistors based on transition metal dichalcogenides,” Appl. Phys. Lett. 84, 3301–3303 (2004).
[Crossref]

2003 (1)

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003).
[Crossref]

2000 (1)

1997 (1)

1987 (2)

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[Crossref]

R. Coehoorn, C. Haas, and R. A. de Groot, “Electronic structure of MoSe2, MoS2, and WSe2. II. The nature of the optical band gaps,” Phys. Rev. B 35, 6203–6206 (1987).
[Crossref]

1981 (1)

1980 (1)

H. J. Lewerenz, A. Heller, and F. J. Disalvo, “Relationship between surface morphology and solar conversion efficiency of tungsten diselenide photoanodes,” J. Am. Chem. Soc. 102, 1877–1880 (1980).
[Crossref]

1976 (1)

A. R. Beal, W. Y. Liang, and H. P. Hughes, “Kramers–Kronig analysis of the reflectivity spectra of 3R-WS2 and 2H-WSe2,” J. Phys. C 9, 2449–2457 (1976).
[Crossref]

1970 (1)

F. Consadori and R. F. Frindt, “Crystal size effects on the exciton absorption spectrum of WSe2,” Phys. Rev. B 2, 4893–4896 (1970).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[Crossref]

Albrecht, M.

Allain, A.

A. Allain and A. Kis, “Electron and hole mobilities in single-layer WSe2,” ACS Nano 8, 7180–7185 (2014).
[Crossref]

Amano, S.

Anderson, I. M.

N. T. Nguyen, P. A. Berseth, Q. Lin, C. Chiritescu, D. G. Cahill, A. Mavrokefalos, L. Shi, P. Zschack, M. D. Anderson, and I. M. Anderson, “Synthesis and properties of turbostratically disordered, ultrathin WSe2 films,” Chem. Mater. 22, 2750–2756 (2010).
[Crossref]

Anderson, M. D.

N. T. Nguyen, P. A. Berseth, Q. Lin, C. Chiritescu, D. G. Cahill, A. Mavrokefalos, L. Shi, P. Zschack, M. D. Anderson, and I. M. Anderson, “Synthesis and properties of turbostratically disordered, ultrathin WSe2 films,” Chem. Mater. 22, 2750–2756 (2010).
[Crossref]

Antunez, P. D.

P. D. Antunez, D. H. Webber, and R. L. Brutchey, “Solution-phase synthesis of highly conductive tungsten diselenide nanosheets,” Chem. Mater. 25, 2385–2387 (2013).
[Crossref]

Arakelian, S. M.

Bai, X. D.

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[Crossref]

Yoffe, A. D.

R. H. Friend and A. D. Yoffe, Electronic Properties of Intercalation Complexes of the Transition Metal Dichalcogenides (Springer, 1984), pp. 1–94.

Yokota, M.

S. Yoshida, Y. Terada, M. Yokota, O. Takeuchi, Y. Mera, and H. Shigekawa, “Direct probing of transient photocurrent dynamics in p-WSe2 by time-resolved scanning tunneling microscopy,” Appl. Phys. Express 6, 016601 (2013).
[Crossref]

Yoshida, S.

S. Yoshida, Y. Terada, M. Yokota, O. Takeuchi, Y. Mera, and H. Shigekawa, “Direct probing of transient photocurrent dynamics in p-WSe2 by time-resolved scanning tunneling microscopy,” Appl. Phys. Express 6, 016601 (2013).
[Crossref]

Yu, I. A.

Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu, “Low-light-level cross-phase-modulation based on stored light pulses,” Phys. Rev. Lett. 96, 043603 (2006).
[Crossref]

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H. Li, G. Lu, Y. Wang, Z. Yin, C. Cong, Q. He, L. Wang, F. Ding, T. Yu, and H. Zhang, “Mechanical exfoliation and characterization of single- and few-layer nanosheets of WSe2, TaS2, and TaSe2,” Small 9, 1974–1981 (2013).
[Crossref]

Yu, X.

X. Li, R. Liu, H. Xie, Y. Zhang, B. Lyu, P. Wang, J. Wang, Q. Fan, Y. Ma, S. Tao, S. Xiao, X. Yu, Y. Gao, and J. He, “Tri-phase all-optical switching and broadband nonlinear optical response in Bi2Se3 nanosheets,” Opt. Express. 25, 18346–18354 (2017).
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L. Wu, Z. Xie, L. Lu, J. Zhao, Y. Wang, X. Jiang, Y. Ge, F. Zhang, S. Lu, Z. Guo, J. Liu, Y. Xiang, S. Xu, J. Li, D. Fan, and H. Zhang, “Few-layer tin sulfide: a promising black-phosphorus-analogue 2D material with exceptionally large nonlinear optical response, high stability, and applications in all-optical switching and wavelength conversion,” Adv. Opt. Mater. 6, 1700985 (2018).
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G. Wang, S. Zhang, F. A. Umran, X. Cheng, N. Dong, D. Coghlan, Y. Cheng, L. Zhang, W. J. Blau, and J. Wang, “Tunable effective nonlinear refractive index of graphene dispersions during the distortion of spatial self-phase modulation,” Appl. Phys. Lett. 104, 141909 (2014).
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Zhang, S.

Zhang, X.

Zhang, Y.

X. Li, R. Liu, H. Xie, Y. Zhang, B. Lyu, P. Wang, J. Wang, Q. Fan, Y. Ma, S. Tao, S. Xiao, X. Yu, Y. Gao, and J. He, “Tri-phase all-optical switching and broadband nonlinear optical response in Bi2Se3 nanosheets,” Opt. Express. 25, 18346–18354 (2017).
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Zhao, C.

B. Shi, L. Miao, Q. Wang, J. Du, P. Tang, J. Liu, C. Zhao, and S. Wen, “Broadband ultrafast spatial self-phase modulation for topological insulator Bi2Te3 dispersions,” Appl. Phys. Lett. 107, 151101 (2015).
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Zhao, H.

Q. Cui, F. Ceballos, N. Kumar, and H. Zhao, “Transient absorption microscopy of monolayer and bulk WSe2,” ACS Nano 8, 2970–2976 (2014).
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Zhao, J.

L. Wu, Z. Xie, L. Lu, J. Zhao, Y. Wang, X. Jiang, Y. Ge, F. Zhang, S. Lu, Z. Guo, J. Liu, Y. Xiang, S. Xu, J. Li, D. Fan, and H. Zhang, “Few-layer tin sulfide: a promising black-phosphorus-analogue 2D material with exceptionally large nonlinear optical response, high stability, and applications in all-optical switching and wavelength conversion,” Adv. Opt. Mater. 6, 1700985 (2018).
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Y. L. Wu, L. L. Zhu, Q. Wu, F. Sun, J. K. Wei, Y. C. Tian, W. L. Wang, X. D. Bai, X. Zuo, and J. Zhao, “Electronic origin of spatial self-phase modulation: evidenced by comparing graphite with C60 and graphene,” Appl. Phys. Lett. 108, 241110 (2016).
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Zhao, W.

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Zheng, G.

H. Wang, D. Kong, P. Johanes, J. J. Cha, G. Zheng, K. Yan, N. Liu, and Y. Cui, “MoSe2 and WSe2 nanofilms with vertically aligned molecular layers on curved and rough surfaces,” Nano Lett. 13, 3426–3433 (2013).
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Zhou, X.

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Zhu, L. L.

Y. L. Wu, L. L. Zhu, Q. Wu, F. Sun, J. K. Wei, Y. C. Tian, W. L. Wang, X. D. Bai, X. Zuo, and J. Zhao, “Electronic origin of spatial self-phase modulation: evidenced by comparing graphite with C60 and graphene,” Appl. Phys. Lett. 108, 241110 (2016).
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Y. Wang, Y. Tang, P. Cheng, X. Zhou, Z. Zhu, Z. Liu, D. Liu, Z. Wang, and J. Bao, “Distinguishing thermal lens effect from electronic third-order nonlinear self-phase modulation in liquid suspensions of 2D nanomaterials,” Nanoscale 9, 3547–3554 (2017).
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N. T. Nguyen, P. A. Berseth, Q. Lin, C. Chiritescu, D. G. Cahill, A. Mavrokefalos, L. Shi, P. Zschack, M. D. Anderson, and I. M. Anderson, “Synthesis and properties of turbostratically disordered, ultrathin WSe2 films,” Chem. Mater. 22, 2750–2756 (2010).
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Y. L. Wu, L. L. Zhu, Q. Wu, F. Sun, J. K. Wei, Y. C. Tian, W. L. Wang, X. D. Bai, X. Zuo, and J. Zhao, “Electronic origin of spatial self-phase modulation: evidenced by comparing graphite with C60 and graphene,” Appl. Phys. Lett. 108, 241110 (2016).
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ACS Nano (5)

S. Z. Butler, S. M. Hollen, L. Cao, Y. Cui, J. A. Gupta, H. R. Gutiérrez, T. F. Heinz, S. S. Hong, J. Huang, and A. F. Ismach, “Progress, challenges, and opportunities in two-dimensional materials beyond graphene,” ACS Nano 7, 2898–2926 (2013).
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A. Allain and A. Kis, “Electron and hole mobilities in single-layer WSe2,” ACS Nano 8, 7180–7185 (2014).
[Crossref]

W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P. H. Tan, and G. Eda, “Evolution of electronic structure in atomically thin sheets of WS2 and WSe2,” ACS Nano 7, 791–797 (2013).
[Crossref]

J. K. Huang, J. Pu, C. L. Hsu, M. H. Chiu, Z. Y. Juang, Y. H. Chang, W. H. Chang, Y. Iwasa, T. Takenobu, and L. J. Li, “Large-area synthesis of highly crystalline WSe2 monolayers and device applications,” ACS Nano 8, 923–930 (2013).
[Crossref]

Q. Cui, F. Ceballos, N. Kumar, and H. Zhao, “Transient absorption microscopy of monolayer and bulk WSe2,” ACS Nano 8, 2970–2976 (2014).
[Crossref]

Adv. Opt. Mater. (1)

L. Wu, Z. Xie, L. Lu, J. Zhao, Y. Wang, X. Jiang, Y. Ge, F. Zhang, S. Lu, Z. Guo, J. Liu, Y. Xiang, S. Xu, J. Li, D. Fan, and H. Zhang, “Few-layer tin sulfide: a promising black-phosphorus-analogue 2D material with exceptionally large nonlinear optical response, high stability, and applications in all-optical switching and wavelength conversion,” Adv. Opt. Mater. 6, 1700985 (2018).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Express (1)

S. Yoshida, Y. Terada, M. Yokota, O. Takeuchi, Y. Mera, and H. Shigekawa, “Direct probing of transient photocurrent dynamics in p-WSe2 by time-resolved scanning tunneling microscopy,” Appl. Phys. Express 6, 016601 (2013).
[Crossref]

Appl. Phys. Lett. (5)

S. Chuang, R. Kapadia, H. Fang, T. C. Chang, W. C. Yen, Y. L. Chueh, and A. Javey, “Near-ideal electrical properties of InAs/WSe2 van der Waals heterojunction diodes,” Appl. Phys. Lett. 102, 242101 (2013).
[Crossref]

V. Podzorov, “High-mobility field-effect transistors based on transition metal dichalcogenides,” Appl. Phys. Lett. 84, 3301–3303 (2004).
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G. Wang, S. Zhang, F. A. Umran, X. Cheng, N. Dong, D. Coghlan, Y. Cheng, L. Zhang, W. J. Blau, and J. Wang, “Tunable effective nonlinear refractive index of graphene dispersions during the distortion of spatial self-phase modulation,” Appl. Phys. Lett. 104, 141909 (2014).
[Crossref]

B. Shi, L. Miao, Q. Wang, J. Du, P. Tang, J. Liu, C. Zhao, and S. Wen, “Broadband ultrafast spatial self-phase modulation for topological insulator Bi2Te3 dispersions,” Appl. Phys. Lett. 107, 151101 (2015).
[Crossref]

Y. L. Wu, L. L. Zhu, Q. Wu, F. Sun, J. K. Wei, Y. C. Tian, W. L. Wang, X. D. Bai, X. Zuo, and J. Zhao, “Electronic origin of spatial self-phase modulation: evidenced by comparing graphite with C60 and graphene,” Appl. Phys. Lett. 108, 241110 (2016).
[Crossref]

Chem. Mater. (2)

N. T. Nguyen, P. A. Berseth, Q. Lin, C. Chiritescu, D. G. Cahill, A. Mavrokefalos, L. Shi, P. Zschack, M. D. Anderson, and I. M. Anderson, “Synthesis and properties of turbostratically disordered, ultrathin WSe2 films,” Chem. Mater. 22, 2750–2756 (2010).
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P. D. Antunez, D. H. Webber, and R. L. Brutchey, “Solution-phase synthesis of highly conductive tungsten diselenide nanosheets,” Chem. Mater. 25, 2385–2387 (2013).
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J. Phys. C (1)

A. R. Beal, W. Y. Liang, and H. P. Hughes, “Kramers–Kronig analysis of the reflectivity spectra of 3R-WS2 and 2H-WSe2,” J. Phys. C 9, 2449–2457 (1976).
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Nano Lett. (1)

H. Wang, D. Kong, P. Johanes, J. J. Cha, G. Zheng, K. Yan, N. Liu, and Y. Cui, “MoSe2 and WSe2 nanofilms with vertically aligned molecular layers on curved and rough surfaces,” Nano Lett. 13, 3426–3433 (2013).
[Crossref]

Nanoscale (1)

Y. Wang, Y. Tang, P. Cheng, X. Zhou, Z. Zhu, Z. Liu, D. Liu, Z. Wang, and J. Bao, “Distinguishing thermal lens effect from electronic third-order nonlinear self-phase modulation in liquid suspensions of 2D nanomaterials,” Nanoscale 9, 3547–3554 (2017).
[Crossref]

Nat. Chem. (1)

M. Chhowalla, H. S. Shin, G. Eda, L. J. Li, K. P. Loh, and H. Zhang, “The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets,” Nat. Chem. 5, 263–275 (2013).
[Crossref]

Nat. Nanotechnol. (1)

Q. H. Wang, K. Kalantarzadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
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F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
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Nature (1)

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Opt. Express (1)

Opt. Express. (1)

X. Li, R. Liu, H. Xie, Y. Zhang, B. Lyu, P. Wang, J. Wang, Q. Fan, Y. Ma, S. Tao, S. Xiao, X. Yu, Y. Gao, and J. He, “Tri-phase all-optical switching and broadband nonlinear optical response in Bi2Se3 nanosheets,” Opt. Express. 25, 18346–18354 (2017).
[Crossref]

Opt. Lett. (5)

Photon. Res. (1)

Phys. Rev. B (2)

R. Coehoorn, C. Haas, and R. A. de Groot, “Electronic structure of MoSe2, MoS2, and WSe2. II. The nature of the optical band gaps,” Phys. Rev. B 35, 6203–6206 (1987).
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Phys. Rev. Lett. (2)

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[Crossref]

Y. F. Chen, C. Y. Wang, S. H. Wang, and I. A. Yu, “Low-light-level cross-phase-modulation based on stored light pulses,” Phys. Rev. Lett. 96, 043603 (2006).
[Crossref]

Proc. Natl. Acad. Sci. (1)

Y. Wu, Q. Wu, F. Sun, C. Cheng, S. Meng, and J. Zhao, “Emergence of electron coherence and two-color all-optical switching in MoS2 based on spatial self-phase modulation,” Proc. Natl. Acad. Sci. 112, 11800–11805 (2015).
[Crossref]

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A. H. C. Neto and K. Novoselov, “New directions in science and technology: two-dimensional crystals,” Rep. Prog. Phys. 74, 82501–82509 (2011).
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Science (1)

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321, 385–388 (2008).
[Crossref]

Small (1)

H. Li, G. Lu, Y. Wang, Z. Yin, C. Cong, Q. He, L. Wang, F. Ding, T. Yu, and H. Zhang, “Mechanical exfoliation and characterization of single- and few-layer nanosheets of WSe2, TaS2, and TaSe2,” Small 9, 1974–1981 (2013).
[Crossref]

Other (1)

R. H. Friend and A. D. Yoffe, Electronic Properties of Intercalation Complexes of the Transition Metal Dichalcogenides (Springer, 1984), pp. 1–94.

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Figures (8)

Fig. 1.
Fig. 1. Characterization of WSe2 nanoparticles after stable storing for two weeks. (a) TEM image, (b) HRTEM image, (c) AFM image, (d) transmittance spectrum, (e) Raman spectrum, and (f) XRD pattern.
Fig. 2.
Fig. 2. Diagrammatic sketch of the measuring experimental setup.
Fig. 3.
Fig. 3. (a)–(c) Diffraction rings received by a CCD of SSPM transformation; (d) schematic of the distortion for WSe2 nanoparticle dispersions.
Fig. 4.
Fig. 4. (a) Variation of the half-cone angle (θH) with incident intensity; (b) variation of the distortion angle (θD) with incident intensity; (c) change in the nonlinear refractive index of WSe2 after distortion.
Fig. 5.
Fig. 5. Variation of diffraction ring numbers with incident intensity at λ=532  nm, λ=671  nm, and λ=457  nm, respectively.
Fig. 6.
Fig. 6. (a) Transformation of SSPM. (1)–(3): continuous wave; (4)–(6): ultrafast wave. (b) Variation of diffraction ring numbers with continuous wave and ultrafast wave.
Fig. 7.
Fig. 7. Schematic of the experimental configuration for all-optical switching.
Fig. 8.
Fig. 8. (a) Results obtained by using a relatively strong λ=532  nm laser beam to control the other laser beam with relatively weak power at λ=671  nm; (b), (c) images obtained from white screen.

Tables (1)

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Table 1. n2 and χmonolayer(3) for a Variety of 2D Materials

Equations (11)

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θH=RHD.
θH=RHD.
θD=θHθH=RDD.
θD=θHθH=(n2n2)IC=Δn2IC.
Δn2/n2=θD/θH.
n=n0+n2I,
Δψ=2πn0λ0Leffn2I(r,z)dz,
Leff=L1L2(1+z2z02)1dz=z0arctan(zz0)|L2L1,
n2=λ2n0Leff·NI.
χtotal(3)=cλn02.4×104π2Leff·dNdI.
χtotal(3)=χmonolayer(3)Neff2,

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