Abstract

This paper describes the tri-phase all-optical switching and broadband nonlinear optical response in Bi2Se3 nanosheets. Using Bi2Se3 nanosheets dispersion solution as the sample, the spatial phase of controlled light can be modulated as three phases (unchanging, focusing, diffraction) by changing the incident intensity of controlling light. The mechanism is conjectured that the controlling light changes the phase distribution of overlapping region and then modulates the phase distribution of the controlled light. Based on Gerchberg-Saxton algorithm, the phase distribution of the controlling light and controlled light is retrieved from the transmitted patterns. In dynamic spatial self-phase modulation (SSPM) experiment, the three processes including self-focusing, self-diffraction ring formation, and self-diffraction ring deformation can also be observed. In addition, the SSPM of controlling light is measured at the typical wavelengths from 350 nm to 1160 nm, which demonstrates that this all-optical switching is available in broadband. These results provide the great potential of Bi2Se3 as an all-optical switching for various optoelectronic applications.

© 2017 Optical Society of America

1. Introduction

Self-diffraction, a kind of spatial self-phase modulation (SSPM), has been regarded as an important method to measure the nonlinear optical properties of layered materials. For example, Li et al. observed the gravitation-dependent thermally-induced self-diffraction in carbon nanotubes [1]. The effective third-order nonlinear susceptibility χ(3) for graphene nanosheets has been reported [2, 3]. The nonlinear optical characters of transition metal dichalcogenides (TMDs) [4–7] and black phosphorous [8–10] were also measured. Wu et al. discovered the two-color all-optical switching in MoS2 dispersion solution based on self-diffraction. They utilized the intensity of controlling light beam to modulate the diffraction pattern of the controlled light, and conjectured that the mechanism was the electron coherence [11].

Topological insulators are a new class of quantum matter and also possess self-focusing and self-diffraction effects resulted from the spatial self-phase modulation. Recently, the self-diffraction phenomenon of Bi2Te3 nanosheets was observed from ultraviolet (UV) to near-infrared (NIR) regions and the corresponding χ(3) was obtained [12]. Among various layered materials, Bi2Se3 nanosheet has aroused special research interest because it has a large energy gap of 0.3 eV (equivalent to 3600 K). Such topology behavior can even be observed at room temperature. Therefore, it enables the applications of corresponding spintronic devices at room temperature with low energy consumption condition. Very recently, the self-focusing character of Bi2Se3 was studied by using a closed aperture Z-scan measurement [13].

In this paper, we investigate the tri-phase all-optical switching and broadband nonlinear optical response of Bi2Se3 dispersed in solution. It is uncovered that the spatial phase of controlled light can be modulated as three phases (unchanging, focusing, diffraction) by changing the incident intensity of controlling light, and the corresponding mechanism is discussed. The dynamic spatial self-phase modulation (SSPM) experiment was performed by using the intense controlling laser beam, which irradiates on the left edge, middle area, and right edge of the cuvette. The SSPM induces three processes including self-focusing, self-diffraction ring formation, and self-diffraction ring deformation. In addition, the SSPM of the controlling light can be measured from 350 nm to 1160 nm, exemplifying that this all-optical switching is available in broadband. The third-order optical susceptibility χ(3) in the corresponding wavelengths of the Bi2Se3 dispersion solution can also be obtained.

2. Experiment and discussion

2.1 Characterization of the sample

The Bi2Se3 nanosheets were prepared by a simple solution-based method reported previously [14]. Their size and morphology were characterized by atomic force microscope (AFM) and scanning electron microscope (SEM), as shown in Fig. 1. It can be observed that the Bi2Se3 nanosheets have a uniform disc-like morphology with height of about 8 nm and diameter of about 250 nm. Figure 1(c) shows the absorption spectrum of the Bi2Se3 nanosheets dispersed in ethanediol solution, which exhibits a broad absorption band ranging from 250 nm to 1000 nm, similar with that reported previously [15, 16]. Figure 1(d) shows the X-ray diffraction (XRD) pattern of the Bi2Se3 nanosheets. All the peaks in the pattern are in accordance with the peaks of bulk Bi2Se3 (JCPDS Card No. 33-0214) with lattice constants a = b = 0.414 nm, and c = 2.864 nm.

 

Fig. 1 Characterizations of Bi2Se3 nanosheets: (a) AFM image with inset height profile. (b) SEM image. (c) UV-vis-NIR absorption spectrum. (d) XRD pattern.

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2.2 Tri-phase all-optical switching in Bi2Se3 dispersion solution

All-optical switching of the Bi2Se3 nanosheets dispersion solution was performed by using a femto-second pulse laser, which was produced by an optical parametric amplifier (TOPAS, USF-UV2). The laser beam was pumped by a Ti with the pulse repetition rate of 2 kHz. Sapphire regenerative amplifier system contained Spectra-Physics, Spitfire ACE-35F-2KXP, Maitai SP and Empower 30. The horizontal laser beam was used to investigate the all-optical switching of the sample. The Bi2Se3 nanosheets dispersion solution was contained in a 10 mm thick quartz cuvette. The excitation wavelength was 700 nm. The controlling light and controlled light were kept at the same level. The laser beams irradiated the dispersion through a focusing lens (f = 250 mm). The intensities of controlling light and controlled light were changed by attenuation slices. Two beams were focused on the center of cuvette. The angle of both beams was 2.6°, as shown in Fig. 2(a). The distance between the lens and the center of the cuvette was 165 mm. The transmitted laser was collected by a fixed CCD camera. The attenuation slices were used in front of CCD to avoid saturation and damage.

 

Fig. 2 (a) Schematic diagram of tri-phase all-optical switching. (b, c) Transmitted signals of (b) controlling light and (c) controlled light when the controlling light intensity is 0.9 mW, 4 mW, and 10 mW and the controlled light intensity is kept as 0.9 mW. (d-i) The phase distribution patterns of (d, g) unchanging, (e, h) focusing, and (f, i) diffraction for the controlling light and controlled light.

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The corresponding results were shown in Figs. 2(b) and 2(c). When the intensities of the controlling light and controlled light were fixed at only 0.9 mW, the collected pattern of the sample was just Gauss laser spot, demonstrating no nonlinear optical effect at this incident intensity. When the controlling light was increased to 4 mW and the controlled light was kept at 0.9 mW, the sizes of transmitted spots of the controlled light gradually decreased. This phenomenon is similar to the transmitted spot of the controlling light. It can be attributed to the self-focusing property of the Bi2Se3 nanosheets [13]. Gauss beam induced that the refractive index change of the sheet central part was larger than the edge part. Propagation velocity of the center is slower than that of the edge, hence the laser beam is focusing [17, 18]. Such distortion of wave-front is similar with the phenomenon of a laser beam passing through a plus lens. When the controlling light increased to 10 mW and the controlled light was still kept at 0.9 mW, the diffraction rings can be observed in the transmitted spots of both the controlling light and controlled light. We also done a similar experiment with ethanediol only in quartz cuvetter under the same measurement conditions. However, SSPM was not be observed. These results demonstrate that the controlled light can be modulated to realize the three phases (unchanging, focusing, and diffraction) by changing only the controlling light incident intensity.

In addition, according to the pattern of the transmitted light, the phase distribution of irradiated region can be obtained based on the Gerchberg-Saxton algorithm [19]. Figures 2(d) - 2(f) show the rough phase distribution of the irradiated region of the controlling light with intensity of 0.9 mW, 4 mW, and 10 mW. The unchanged phase distribution shown in Fig. 2(d) exhibits the gradually enhanced signals from the top to bottom, which probably originates from the Boltzmann distribution of the Bi2Se3 nanosheets in the vertical direction. The phase distribution of self-focusing is shown in Fig. 2(e), in which the phase distribution of the center region is relatively weaker. The phase distribution of self-diffraction is shown in Fig. 2(f), in which the phase distribution of the center region is relatively greater. Such phase changes of Figs. 2(e) and 2(f) maybe originate from the laser Gaussian distribution. The powerful intensity causes the change of nonlinear refractive index of the Bi2Se3 nanosheets, resulting in self-focusing and self-diffraction.

Figures 2(g)-2(i) show the rough phase distribution of the irradiated region of controlled light with the intensity kept at 0.9 mW. Since the controlled light is oblique incidence and the overlapping region is in front of focus, the optical path of left is longer than right, thus the left phase distribution in all the images is greater than the right one. Similar phase changes can be observed in Figs. 2(h) and 2(i). The phase distribution of the center region becomes weaker in Fig. 2(h), while becomes stronger in Fig. 2(i). It is supported that the controlling light changed the spatial nonlinear refractive index of the center overlapping region, resulting in the phase change of the controlled light. These results confirm the realization of the tri-phase optical switching including unchanging, focusing, and diffraction.

The dynamic SSPM of intense controlling laser beam was further measured to prove that self-focusing is an essential step to realize the self-diffraction. The schematic diagram of the SSPM setup is shown in Fig. 3(a). In this experiment, the horizontal laser beam was same as aforementioned. The laser beam irradiated the dispersion by a focusing lens (f = 200 mm) in normal incidence with the distance between the focusing lens and center of the cuvette was 100 mm. The SSPM pattern of the controlling light was received by a CCD which was fixed at 130 mm. The excitation wavelength was 700 nm with average power of 110 mW. The irradiated positions included the left edge, middle area, and right edge of the cuvette, as shown in Fig. 3(b). The blue arrowhead is the direction of laser propagation.

 

Fig. 3 (a) Schematic diagram of the SSPM setup. (b) Three kinds of irradiated paths including left edge, middle area, and right edge of the cuvette. (c-e) The corresponding SSPM processes of (b).

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The corresponding SSPM processes are shown in Figs. 3(c)-3(e). According to the patterns, the SSPM contains three processes: self-focusing process, self-diffraction ring formation process, and self-diffraction ring deformation process. The self-focusing process is extremely fast with time of less than 0.07 s. Then, the self-diffraction process turns up. The number of the rings increases with the diameter becomes bigger and bigger within 3.64 s. After that, the SSPM pattern distorts due to thermal convection, and the stable time is less than 10 s.

In the SSPM experiment, the SSPM contains three processes including self-focusing, self-diffraction ring formation, and self-diffraction ring deformation. The self-diffraction ring deformation process maybe originates from thermal convection [20, 21] rather than gravity [1]. As shown in Figs. 3(c)-3(e), the left-edge irradiation induces the unbalanced SSPM pattern with right higher than the left, while right-edge irradiation induces the unbalanced SSPM pattern with left higher than the right. In contrast, the middle-area irradiation results in a left-right balanced SSPM pattern. This phenomenon can be ascribed to the following points: when the laser irradiates on the left-edge of the cuvette, the laser-induced thermal convection of the left and right sides is asymmetry because of viscous forces between the dispersion and cuvette wall. The left concentration of the upper part is higher than the right, resulting in the unbalanced SSPM pattern with right higher than the left. In contrast, the viscous force between the dispersion and the cuvette wall is perfectly symmetric with the middle-area irradiation, thus balanced SSPM pattern can be obtained. Therefore, thermal convection is perhaps the main reason for the distortion, which originates from the phase distribution.

The phenomenon of self-focusing is observed for the first time in SSPM processes of layered materials. The reasons are as follow: On the one hand, as the Fig. 3 (dynamic SSPM) shown, the emergence of self-focusing is instantaneous in high excited power. Then, this phenomenon is replaced by self-diffraction immediately. It is easy to be neglected. Self-focusing phenomenon is an ultrafast nonlinear optical property. The carrier dynamic relaxation process of Bi2Se3 nanosheets was observed in pump-probe system. The time range is about femtosecond level, as Fig. 4 shown. On the other hand, as Fig. 2 (steady SSPM) shown, self-focusing only exists steadily in low excited power (but high instantaneous intensity).The laser source in our experiments is a femtosecond pulsed laser, which has a low repetition rate (2 kHz). The higher instantaneous intensity of fs laser could arouse the self-focusing, while the smaller thermal effect restrains the self-diffraction. In previous works [1, 20], the thermal effect is very big in chosen CW laser, so the self-diffraction based on thermal effect [20] conceals the self-focusing immediately.

 

Fig. 4 The ultrafast nonlinear process for Bi2Se3 film with a pump wavelength of 700 nm.

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The ultrafast nonlinear process of Bi2Se3 can be observed in Fig. 4 by pump-probe system. The dynamic relaxation process exhibits an exponential decay, and it can be fitted by exponential decay function ofy=A1e(xx0)/τs+y0, where τs is the fast relaxation time and is acquired as τs=98fs. It means, such as self-focusing, the timescale of these ultrafast nonlinear processes is femtosecond level.

For the more easily and earlier emergence, the self-focusing is an important state and process in SSPM of layered material. Furthermore, it is a meaningful attempt to use self-focusing and self-diffraction to realize tri-phase modulation.

2.3 Broadband SSPM of Bi2Se3 dispersion solution

Figure 5 shows the SSPM experiment by using the laser with four typical excitation wavelengths (350 nm, 600 nm, 700 nm, and 1160 nm) spanning from the UV to NIR region. The stable SSPM patterns (self-focusing and self-diffraction) can be observed in all these wavelengths, demonstrating that this all-optical switching is available in broadband. The relationships between the number of rings (N) and the incident intensity (I) are also obtained. The slopes (N/I) are 1.23 ± 0.23 cm2/W (λ = 350 nm), 0.98 ± 0.05 cm2/W (λ = 600 nm), 0.81 ± 0.03 cm2/W (λ = 700 nm), and 0.50 ± 0.02 cm2/W (λ = 1160 nm). It is obvious that the slope gradually decreases with the increase of the excitation wavelength. Furthermore, the slope value is larger than other layered materials such as graphene [2], TMDs (MoS2, WS2, MoSe2) [5], Bi2Te3 [12], and black phosphorous [8], demonstrating the excellently photosensitive properties of Bi2Se3.

 

Fig. 5 Number of rings (N) vs incident intensity (W/cm2) with the inset maximal SSPM pattern with the excitation wavelength of 350 nm, 600 nm, 700 nm, and 1160 nm.

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The refractive index of the sample is proportional to the intensity, n(r) = n0 + n2I(r), where n0 and n2 are the linear and nonlinear refractive index, respectively. When the beam irradiates through the Bi2Se3, the phase shifts and refractive index can be expressed as [2, 20], where r is the radial position, and λ is excitation wavelength.

Δψ(r)=(2πn0λ)0Leffn2I(r,z)dz
The effective optical thickness of the laser beam passing the dispersion Leff can be obtained by [2]
Leff=L1L2(1+z2z02)1dz=z0arctan(zz0)|L1L2
L1 and L2 are the distance between the focus and front wall or later wall. For a Gaussian beam, the intensity I(0,z) at the center is twice of the average intensity I measured in the experiments. The diffraction rings are determined by [22]
Δψ(0)Δψ()=2Nπ
Then, the nonlinear refractive index can be obtained as
n2=(λ2n0Leff)NI
Where n0 is similar to the line refractive index of ethylene glycol [20], N/I is the slope value.

The third-order nonlinear susceptibility χ(3) is an important parameter of optical nonlinear material. The effective nonlinear refractive index can be expressed as [2]

n2=(12π2/n02c)103χ(3)
The third-order nonlinear susceptibility of the Bi2Se3 dispersionχtotal(3)and the third-order nonlinear susceptibility of the Bi2Se3 nanosheetχsingle(3) can be expressed as [5]
χtotal(3)K2χsingle(3)
Where K is the effective layers corresponding to Leff. In this experiment, the concentration of Bi2Se3 suspension solution is ρ = 4.6 × 10−4 mol/L. The volume is V = 4 × 10−3 L. The total molecules in solution is M = ρ × V × NA = 1.1 × 1018. According to the XRD pattern, all the peaks in the pattern are in accordance with the peaks of bulk Bi2Se3 with the crystal structure (JCPDS Card No. 33-0214). Thus, a single effective layer contains m = S / unit cell area in ab section = 1 × 4 cm2 / (sin 90°) × (4.14)2 Å2 = 2.3 × 1015 molecules. Then the layer number is K = M /m = 478. Because of the instability of the dispersion solution, the order of magnitude ofχsingle(3) can be estimated.

The third-order optical susceptibility χ(3) of the Bi2Se3 dispersion solution with the corresponding wavelengths is obtained, as shown in Table 1. The third-order optical susceptibility increases with the incident photon energy [11], however, we partly ignore the thermal effect of low repetition frequency fs laser pulses [23]. The results accord with those in previous works [12, 13].

Tables Icon

Table 1. Third-order optical susceptibility χ(3) of Bi2Se3 dispersion solution at 350 nm - 1160 nm.

3. Conclusion

In summary, the tri-phase all-optical switching has successfully been realized in the Bi2Se3 dispersion solution. The controlled light can be modulated as three phases (unchanging, focusing, and diffraction) by changing the controlling light incident intensity. The dynamic SSPM experiment of intense controlling laser beam further proves that self-focusing is the essential step to realize the self-diffraction. In addition, the stable SSPM of controlling light can be achieved at different wavelengths from 350 nm to 1160 nm, demonstrating that this all-optical switching is available in broadband. These results provide the great potential of Bi2Se3 as an all-optical switching for various optoelectronic applications.

Funding

National Natural Science Foundation of China (NSFC) (11334014); Hunan Provincial Natural Science Foundation (2016JJ3140); Fundamental Research Funds for the Central Universities of Central South University (2016zzts225, 2017zzts327); Undergraduate Training Program for Innovation and Entrepreneurship of Central South University (ZY2016616, 201610533392).

References and links

1. W. Ji, W. Chen, S. Lim, J. Lin, and Z. Guo, “Gravitation-dependent, thermally-induced self-diffraction in carbon nanotube solutions,” Opt. Express 14(20), 8958–8966 (2006). [CrossRef]   [PubMed]  

2. R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011). [CrossRef]   [PubMed]  

3. Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016). [CrossRef]  

4. S. Xiao, B. Lv, L. Wu, M. Zhu, J. He, and S. Tao, “Dynamic self-diffraction in MoS2 nanoflake solutions,” Opt. Express 23(5), 5875–5887 (2015). [CrossRef]   [PubMed]  

5. 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 [Invited],” Photon. Res. 3(2), A51–A55 (2015). [CrossRef]  

6. W. Wang, Y. Wu, Q. Wu, J. Hua, and J. Zhao, “Coherent nonlinear optical response spatial self-phase modulation in MoSe2 nano-sheets,” Sci. Rep. 6(1), 22072 (2016). [CrossRef]   [PubMed]  

7. Y. Wang, J. He, S. Xiao, N. Yang, and H. Chen, “Wavelength selective optical limiting effect on MoS2 solution,” Wuli Xuebao 14(63), 144204 (2014).

8. 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(8), 1704–1707 (2016). [CrossRef]   [PubMed]  

9. Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015). [CrossRef]  

10. Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017). [CrossRef]   [PubMed]  

11. 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. U.S.A. 112(38), 11800–11805 (2015). [CrossRef]   [PubMed]  

12. 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(15), 151101 (2015). [CrossRef]  

13. S. Lu, C. Zhao, Y. Zou, S. Chen, Y. Chen, Y. Li, H. Zhang, S. Wen, and D. Tang, “Third order nonlinear optical property of Bi2Se3,” Opt. Express 21(2), 2072–2082 (2013). [CrossRef]   [PubMed]  

14. Y. Min, G. D. Moon, B. S. Kim, B. Lim, J.-S. Kim, C. Y. Kang, and U. Jeong, “Quick, controlled synthesis of ultrathin Bi2Se3 nanodiscs and nanosheets,” J. Am. Chem. Soc. 134(6), 2872–2875 (2012). [CrossRef]   [PubMed]  

15. M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016). [CrossRef]   [PubMed]  

16. H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016). [CrossRef]   [PubMed]  

17. P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965). [CrossRef]  

18. S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968). [CrossRef]  

19. L. Wu, S. Tao, and S. Xiao, “Phase retrieval-based distribution detecting method for transparent objects,” Opt. Eng. 54(11), 113103 (2015). [CrossRef]  

20. 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(14), 141909 (2014). [CrossRef]  

21. R. Karimzadeh, “Spatial self-phase modulation of a laser beam propagating through liquids with self-induced natural convection flow,” J. Opt. 14(9), 095701 (2012). [CrossRef]  

22. S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Laser-induced diffraction rings from a nematic-liquid-crystal film,” Opt. Lett. 6(9), 411–413 (1981). [CrossRef]   [PubMed]  

23. L. Miao, J. Yi, Q. Wang, D. Feng, H. He, S. Lu, C. Zhao, H. Zhang, and S. Wen, “Broadband third order nonlinear optical responses of bismuth telluride nanosheets,” Opt. Mater. Express 6(7), 2244–2251 (2016). [CrossRef]  

References

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  1. W. Ji, W. Chen, S. Lim, J. Lin, and Z. Guo, “Gravitation-dependent, thermally-induced self-diffraction in carbon nanotube solutions,” Opt. Express 14(20), 8958–8966 (2006).
    [Crossref] [PubMed]
  2. R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
    [Crossref] [PubMed]
  3. Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016).
    [Crossref]
  4. S. Xiao, B. Lv, L. Wu, M. Zhu, J. He, and S. Tao, “Dynamic self-diffraction in MoS2 nanoflake solutions,” Opt. Express 23(5), 5875–5887 (2015).
    [Crossref] [PubMed]
  5. 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 [Invited],” Photon. Res. 3(2), A51–A55 (2015).
    [Crossref]
  6. W. Wang, Y. Wu, Q. Wu, J. Hua, and J. Zhao, “Coherent nonlinear optical response spatial self-phase modulation in MoSe2 nano-sheets,” Sci. Rep. 6(1), 22072 (2016).
    [Crossref] [PubMed]
  7. Y. Wang, J. He, S. Xiao, N. Yang, and H. Chen, “Wavelength selective optical limiting effect on MoS2 solution,” Wuli Xuebao 14(63), 144204 (2014).
  8. 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(8), 1704–1707 (2016).
    [Crossref] [PubMed]
  9. Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
    [Crossref]
  10. Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
    [Crossref] [PubMed]
  11. 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. U.S.A. 112(38), 11800–11805 (2015).
    [Crossref] [PubMed]
  12. 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(15), 151101 (2015).
    [Crossref]
  13. S. Lu, C. Zhao, Y. Zou, S. Chen, Y. Chen, Y. Li, H. Zhang, S. Wen, and D. Tang, “Third order nonlinear optical property of Bi2Se3,” Opt. Express 21(2), 2072–2082 (2013).
    [Crossref] [PubMed]
  14. Y. Min, G. D. Moon, B. S. Kim, B. Lim, J.-S. Kim, C. Y. Kang, and U. Jeong, “Quick, controlled synthesis of ultrathin Bi2Se3 nanodiscs and nanosheets,” J. Am. Chem. Soc. 134(6), 2872–2875 (2012).
    [Crossref] [PubMed]
  15. M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
    [Crossref] [PubMed]
  16. H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
    [Crossref] [PubMed]
  17. P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).
    [Crossref]
  18. S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968).
    [Crossref]
  19. L. Wu, S. Tao, and S. Xiao, “Phase retrieval-based distribution detecting method for transparent objects,” Opt. Eng. 54(11), 113103 (2015).
    [Crossref]
  20. 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(14), 141909 (2014).
    [Crossref]
  21. R. Karimzadeh, “Spatial self-phase modulation of a laser beam propagating through liquids with self-induced natural convection flow,” J. Opt. 14(9), 095701 (2012).
    [Crossref]
  22. S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Laser-induced diffraction rings from a nematic-liquid-crystal film,” Opt. Lett. 6(9), 411–413 (1981).
    [Crossref] [PubMed]
  23. L. Miao, J. Yi, Q. Wang, D. Feng, H. He, S. Lu, C. Zhao, H. Zhang, and S. Wen, “Broadband third order nonlinear optical responses of bismuth telluride nanosheets,” Opt. Mater. Express 6(7), 2244–2251 (2016).
    [Crossref]

2017 (1)

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

2016 (6)

Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016).
[Crossref]

W. Wang, Y. Wu, Q. Wu, J. Hua, and J. Zhao, “Coherent nonlinear optical response spatial self-phase modulation in MoSe2 nano-sheets,” Sci. Rep. 6(1), 22072 (2016).
[Crossref] [PubMed]

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(8), 1704–1707 (2016).
[Crossref] [PubMed]

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

L. Miao, J. Yi, Q. Wang, D. Feng, H. He, S. Lu, C. Zhao, H. Zhang, and S. Wen, “Broadband third order nonlinear optical responses of bismuth telluride nanosheets,” Opt. Mater. Express 6(7), 2244–2251 (2016).
[Crossref]

2015 (6)

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

S. Xiao, B. Lv, L. Wu, M. Zhu, J. He, and S. Tao, “Dynamic self-diffraction in MoS2 nanoflake solutions,” Opt. Express 23(5), 5875–5887 (2015).
[Crossref] [PubMed]

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 [Invited],” Photon. Res. 3(2), A51–A55 (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. U.S.A. 112(38), 11800–11805 (2015).
[Crossref] [PubMed]

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(15), 151101 (2015).
[Crossref]

L. Wu, S. Tao, and S. Xiao, “Phase retrieval-based distribution detecting method for transparent objects,” Opt. Eng. 54(11), 113103 (2015).
[Crossref]

2014 (2)

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(14), 141909 (2014).
[Crossref]

Y. Wang, J. He, S. Xiao, N. Yang, and H. Chen, “Wavelength selective optical limiting effect on MoS2 solution,” Wuli Xuebao 14(63), 144204 (2014).

2013 (1)

2012 (2)

Y. Min, G. D. Moon, B. S. Kim, B. Lim, J.-S. Kim, C. Y. Kang, and U. Jeong, “Quick, controlled synthesis of ultrathin Bi2Se3 nanodiscs and nanosheets,” J. Am. Chem. Soc. 134(6), 2872–2875 (2012).
[Crossref] [PubMed]

R. Karimzadeh, “Spatial self-phase modulation of a laser beam propagating through liquids with self-induced natural convection flow,” J. Opt. 14(9), 095701 (2012).
[Crossref]

2011 (1)

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

2006 (1)

1981 (1)

1968 (1)

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968).
[Crossref]

1965 (1)

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).
[Crossref]

Akhmanov, S. A.

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968).
[Crossref]

Arakelian, S. M.

Bai, X.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Bao, Q.

Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016).
[Crossref]

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Bian, F.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Blau, W. J.

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 [Invited],” Photon. Res. 3(2), A51–A55 (2015).
[Crossref]

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(14), 141909 (2014).
[Crossref]

Bosman, M.

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

Chen, H.

Y. Wang, J. He, S. Xiao, N. Yang, and H. Chen, “Wavelength selective optical limiting effect on MoS2 solution,” Wuli Xuebao 14(63), 144204 (2014).

Chen, J.

Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016).
[Crossref]

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Chen, S.

Chen, W.

Chen, Y.

Cheng, C.

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. U.S.A. 112(38), 11800–11805 (2015).
[Crossref] [PubMed]

Cheng, X.

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(14), 141909 (2014).
[Crossref]

Cheng, Y.

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 [Invited],” Photon. Res. 3(2), A51–A55 (2015).
[Crossref]

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(14), 141909 (2014).
[Crossref]

Chu, P. K.

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

Coghlan, D.

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(14), 141909 (2014).
[Crossref]

Coleman, J. N.

Dong, N.

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(14), 141909 (2014).
[Crossref]

Du, J.

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(15), 151101 (2015).
[Crossref]

Durbin, S. D.

Feng, D.

Fox, D.

Gao, N.

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

Gao, Y.

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(8), 1704–1707 (2016).
[Crossref] [PubMed]

Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016).
[Crossref]

Gao, Y. L.

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

Guo, Z.

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

W. Ji, W. Chen, S. Lim, J. Lin, and Z. Guo, “Gravitation-dependent, thermally-induced self-diffraction in carbon nanotube solutions,” Opt. Express 14(20), 8958–8966 (2006).
[Crossref] [PubMed]

Han, W.

He, H.

He, J.

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

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(8), 1704–1707 (2016).
[Crossref] [PubMed]

Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016).
[Crossref]

S. Xiao, B. Lv, L. Wu, M. Zhu, J. He, and S. Tao, “Dynamic self-diffraction in MoS2 nanoflake solutions,” Opt. Express 23(5), 5875–5887 (2015).
[Crossref] [PubMed]

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Y. Wang, J. He, S. Xiao, N. Yang, and H. Chen, “Wavelength selective optical limiting effect on MoS2 solution,” Wuli Xuebao 14(63), 144204 (2014).

Hua, J.

W. Wang, Y. Wu, Q. Wu, J. Hua, and J. Zhao, “Coherent nonlinear optical response spatial self-phase modulation in MoSe2 nano-sheets,” Sci. Rep. 6(1), 22072 (2016).
[Crossref] [PubMed]

Huang, G.

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Huang, H.

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

Jeong, U.

Y. Min, G. D. Moon, B. S. Kim, B. Lim, J.-S. Kim, C. Y. Kang, and U. Jeong, “Quick, controlled synthesis of ultrathin Bi2Se3 nanodiscs and nanosheets,” J. Am. Chem. Soc. 134(6), 2872–2875 (2012).
[Crossref] [PubMed]

Ji, W.

Kang, C. Y.

Y. Min, G. D. Moon, B. S. Kim, B. Lim, J.-S. Kim, C. Y. Kang, and U. Jeong, “Quick, controlled synthesis of ultrathin Bi2Se3 nanodiscs and nanosheets,” J. Am. Chem. Soc. 134(6), 2872–2875 (2012).
[Crossref] [PubMed]

Karimzadeh, R.

R. Karimzadeh, “Spatial self-phase modulation of a laser beam propagating through liquids with self-induced natural convection flow,” J. Opt. 14(9), 095701 (2012).
[Crossref]

Kelley, P. L.

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).
[Crossref]

Khokhlov, R. V.

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968).
[Crossref]

Kim, B. S.

Y. Min, G. D. Moon, B. S. Kim, B. Lim, J.-S. Kim, C. Y. Kang, and U. Jeong, “Quick, controlled synthesis of ultrathin Bi2Se3 nanodiscs and nanosheets,” J. Am. Chem. Soc. 134(6), 2872–2875 (2012).
[Crossref] [PubMed]

Kim, J.-S.

Y. Min, G. D. Moon, B. S. Kim, B. Lim, J.-S. Kim, C. Y. Kang, and U. Jeong, “Quick, controlled synthesis of ultrathin Bi2Se3 nanodiscs and nanosheets,” J. Am. Chem. Soc. 134(6), 2872–2875 (2012).
[Crossref] [PubMed]

Li, J. B.

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

Li, X.

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(8), 1704–1707 (2016).
[Crossref] [PubMed]

Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016).
[Crossref]

Li, Y.

Li, Z.

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

Lim, B.

Y. Min, G. D. Moon, B. S. Kim, B. Lim, J.-S. Kim, C. Y. Kang, and U. Jeong, “Quick, controlled synthesis of ultrathin Bi2Se3 nanodiscs and nanosheets,” J. Am. Chem. Soc. 134(6), 2872–2875 (2012).
[Crossref] [PubMed]

Lim, S.

Lin, J.

Lin, S.

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Liu, J.

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(15), 151101 (2015).
[Crossref]

Liu, S.

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

Loh, K. P.

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

Long, M. Q.

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

Lu, S.

Lu, X.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Lv, B.

Meng, S.

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. U.S.A. 112(38), 11800–11805 (2015).
[Crossref] [PubMed]

Miao, L.

L. Miao, J. Yi, Q. Wang, D. Feng, H. He, S. Lu, C. Zhao, H. Zhang, and S. Wen, “Broadband third order nonlinear optical responses of bismuth telluride nanosheets,” Opt. Mater. Express 6(7), 2244–2251 (2016).
[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(15), 151101 (2015).
[Crossref]

Min, Y.

Y. Min, G. D. Moon, B. S. Kim, B. Lim, J.-S. Kim, C. Y. Kang, and U. Jeong, “Quick, controlled synthesis of ultrathin Bi2Se3 nanodiscs and nanosheets,” J. Am. Chem. Soc. 134(6), 2872–2875 (2012).
[Crossref] [PubMed]

Moon, G. D.

Y. Min, G. D. Moon, B. S. Kim, B. Lim, J.-S. Kim, C. Y. Kang, and U. Jeong, “Quick, controlled synthesis of ultrathin Bi2Se3 nanodiscs and nanosheets,” J. Am. Chem. Soc. 134(6), 2872–2875 (2012).
[Crossref] [PubMed]

Mu, H.

Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016).
[Crossref]

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Peng, B.

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

Qiu, C. W.

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

Shao, J.

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

Shen, Y. R.

Shi, B.

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(15), 151101 (2015).
[Crossref]

Song, P.

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

Sukhorukov, A. P.

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968).
[Crossref]

Sun, B.

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

Sun, F.

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. U.S.A. 112(38), 11800–11805 (2015).
[Crossref] [PubMed]

Sun, Z.

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

Tang, D.

Tang, P.

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(15), 151101 (2015).
[Crossref]

Tao, S.

L. Wu, S. Tao, and S. Xiao, “Phase retrieval-based distribution detecting method for transparent objects,” Opt. Eng. 54(11), 113103 (2015).
[Crossref]

S. Xiao, B. Lv, L. Wu, M. Zhu, J. He, and S. Tao, “Dynamic self-diffraction in MoS2 nanoflake solutions,” Opt. Express 23(5), 5875–5887 (2015).
[Crossref] [PubMed]

Umran, F. A.

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(14), 141909 (2014).
[Crossref]

Wang, E.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Wang, G.

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 [Invited],” Photon. Res. 3(2), A51–A55 (2015).
[Crossref]

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(14), 141909 (2014).
[Crossref]

Wang, H.

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

Wang, J.

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

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 [Invited],” Photon. Res. 3(2), A51–A55 (2015).
[Crossref]

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(14), 141909 (2014).
[Crossref]

Wang, Q.

L. Miao, J. Yi, Q. Wang, D. Feng, H. He, S. Lu, C. Zhao, H. Zhang, and S. Wen, “Broadband third order nonlinear optical responses of bismuth telluride nanosheets,” Opt. Mater. Express 6(7), 2244–2251 (2016).
[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(15), 151101 (2015).
[Crossref]

Wang, Q. Q.

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

Wang, W.

W. Wang, Y. Wu, Q. Wu, J. Hua, and J. Zhao, “Coherent nonlinear optical response spatial self-phase modulation in MoSe2 nano-sheets,” Sci. Rep. 6(1), 22072 (2016).
[Crossref] [PubMed]

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Wang, Y.

Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016).
[Crossref]

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

Y. Wang, J. He, S. Xiao, N. Yang, and H. Chen, “Wavelength selective optical limiting effect on MoS2 solution,” Wuli Xuebao 14(63), 144204 (2014).

Wang, Y. W.

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

Wen, S.

Wu, L.

L. Wu, S. Tao, and S. Xiao, “Phase retrieval-based distribution detecting method for transparent objects,” Opt. Eng. 54(11), 113103 (2015).
[Crossref]

S. Xiao, B. Lv, L. Wu, M. Zhu, J. He, and S. Tao, “Dynamic self-diffraction in MoS2 nanoflake solutions,” Opt. Express 23(5), 5875–5887 (2015).
[Crossref] [PubMed]

Wu, Q.

W. Wang, Y. Wu, Q. Wu, J. Hua, and J. Zhao, “Coherent nonlinear optical response spatial self-phase modulation in MoSe2 nano-sheets,” Sci. Rep. 6(1), 22072 (2016).
[Crossref] [PubMed]

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. U.S.A. 112(38), 11800–11805 (2015).
[Crossref] [PubMed]

Wu, R.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Wu, Y.

W. Wang, Y. Wu, Q. Wu, J. Hua, and J. Zhao, “Coherent nonlinear optical response spatial self-phase modulation in MoSe2 nano-sheets,” Sci. Rep. 6(1), 22072 (2016).
[Crossref] [PubMed]

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. U.S.A. 112(38), 11800–11805 (2015).
[Crossref] [PubMed]

Xiao, J.

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

Xiao, Q.

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

Xiao, S.

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

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(8), 1704–1707 (2016).
[Crossref] [PubMed]

Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016).
[Crossref]

S. Xiao, B. Lv, L. Wu, M. Zhu, J. He, and S. Tao, “Dynamic self-diffraction in MoS2 nanoflake solutions,” Opt. Express 23(5), 5875–5887 (2015).
[Crossref] [PubMed]

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

L. Wu, S. Tao, and S. Xiao, “Phase retrieval-based distribution detecting method for transparent objects,” Opt. Eng. 54(11), 113103 (2015).
[Crossref]

Y. Wang, J. He, S. Xiao, N. Yang, and H. Chen, “Wavelength selective optical limiting effect on MoS2 solution,” Wuli Xuebao 14(63), 144204 (2014).

Xie, H.

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

Xu, Q. H.

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

Yan, S.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Yang, N.

Y. Wang, J. He, S. Xiao, N. Yang, and H. Chen, “Wavelength selective optical limiting effect on MoS2 solution,” Wuli Xuebao 14(63), 144204 (2014).

Yi, J.

Yu, X.

Yu, X. F.

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

Yuan, J.

Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016).
[Crossref]

Zeng, B. W.

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

Zhang, H.

Zhang, J.

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

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(8), 1704–1707 (2016).
[Crossref] [PubMed]

Zhang, L.

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 [Invited],” Photon. Res. 3(2), A51–A55 (2015).
[Crossref]

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(14), 141909 (2014).
[Crossref]

Zhang, S.

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 [Invited],” Photon. Res. 3(2), A51–A55 (2015).
[Crossref]

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(14), 141909 (2014).
[Crossref]

Zhang, X.

Zhang, Y.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Zhao, C.

Zhao, J.

W. Wang, Y. Wu, Q. Wu, J. Hua, and J. Zhao, “Coherent nonlinear optical response spatial self-phase modulation in MoSe2 nano-sheets,” Sci. Rep. 6(1), 22072 (2016).
[Crossref] [PubMed]

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. U.S.A. 112(38), 11800–11805 (2015).
[Crossref] [PubMed]

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Zhao, M.

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

Zhu, M.

Zou, Y.

Adv. Mater. (1)

M. Zhao, J. Zhang, N. Gao, P. Song, M. Bosman, B. Peng, B. Sun, C. W. Qiu, Q. H. Xu, Q. Bao, and K. P. Loh, “Actively tunable visible surface plasmons in Bi2Te3 and their energy-harvesting applications,” Adv. Mater. 28(16), 3138–3144 (2016).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

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(15), 151101 (2015).
[Crossref]

Y. Wang, H. Mu, X. Li, J. Yuan, J. Chen, S. Xiao, Q. Bao, Y. Gao, and J. He, “Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength,” Appl. Phys. Lett. 108(22), 221901 (2016).
[Crossref]

Y. Wang, G. Huang, H. Mu, S. Lin, J. Chen, S. Xiao, Q. Bao, and J. He, “Ultrafast recovery time and broadband saturable absorption properties of black phosphorus suspension,” Appl. Phys. Lett. 107(9), 091905 (2015).
[Crossref]

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(14), 141909 (2014).
[Crossref]

J. Am. Chem. Soc. (1)

Y. Min, G. D. Moon, B. S. Kim, B. Lim, J.-S. Kim, C. Y. Kang, and U. Jeong, “Quick, controlled synthesis of ultrathin Bi2Se3 nanodiscs and nanosheets,” J. Am. Chem. Soc. 134(6), 2872–2875 (2012).
[Crossref] [PubMed]

J. Opt. (1)

R. Karimzadeh, “Spatial self-phase modulation of a laser beam propagating through liquids with self-induced natural convection flow,” J. Opt. 14(9), 095701 (2012).
[Crossref]

Nano Lett. (1)

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Nanoscale (1)

Y. W. Wang, S. Liu, B. W. Zeng, H. Huang, J. Xiao, J. B. Li, M. Q. Long, S. Xiao, X. F. Yu, Y. L. Gao, and J. He, “Ultraviolet saturable absorption and ultrafast carrier dynamics in ultrasmall black phosphorus quantum dots,” Nanoscale 9(14), 4683–4690 (2017).
[Crossref] [PubMed]

Opt. Eng. (1)

L. Wu, S. Tao, and S. Xiao, “Phase retrieval-based distribution detecting method for transparent objects,” Opt. Eng. 54(11), 113103 (2015).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Opt. Mater. Express (1)

Photon. Res. (1)

Phys. Rev. Lett. (1)

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (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. U.S.A. 112(38), 11800–11805 (2015).
[Crossref] [PubMed]

Sci. Rep. (1)

W. Wang, Y. Wu, Q. Wu, J. Hua, and J. Zhao, “Coherent nonlinear optical response spatial self-phase modulation in MoSe2 nano-sheets,” Sci. Rep. 6(1), 22072 (2016).
[Crossref] [PubMed]

Small (1)

H. Xie, Z. Li, Z. Sun, J. Shao, X. F. Yu, Z. Guo, J. Wang, Q. Xiao, H. Wang, Q. Q. Wang, H. Zhang, and P. K. Chu, “Metabolizable ultrathin Bi2Se3 nanosheets in imaging-guided photothermal therapy,” Small 12(30), 4136–4145 (2016).
[Crossref] [PubMed]

Sov. Phys. Usp. (1)

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968).
[Crossref]

Wuli Xuebao (1)

Y. Wang, J. He, S. Xiao, N. Yang, and H. Chen, “Wavelength selective optical limiting effect on MoS2 solution,” Wuli Xuebao 14(63), 144204 (2014).

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Figures (5)

Fig. 1
Fig. 1 Characterizations of Bi2Se3 nanosheets: (a) AFM image with inset height profile. (b) SEM image. (c) UV-vis-NIR absorption spectrum. (d) XRD pattern.
Fig. 2
Fig. 2 (a) Schematic diagram of tri-phase all-optical switching. (b, c) Transmitted signals of (b) controlling light and (c) controlled light when the controlling light intensity is 0.9 mW, 4 mW, and 10 mW and the controlled light intensity is kept as 0.9 mW. (d-i) The phase distribution patterns of (d, g) unchanging, (e, h) focusing, and (f, i) diffraction for the controlling light and controlled light.
Fig. 3
Fig. 3 (a) Schematic diagram of the SSPM setup. (b) Three kinds of irradiated paths including left edge, middle area, and right edge of the cuvette. (c-e) The corresponding SSPM processes of (b).
Fig. 4
Fig. 4 The ultrafast nonlinear process for Bi2Se3 film with a pump wavelength of 700 nm.
Fig. 5
Fig. 5 Number of rings (N) vs incident intensity (W/cm2) with the inset maximal SSPM pattern with the excitation wavelength of 350 nm, 600 nm, 700 nm, and 1160 nm.

Tables (1)

Tables Icon

Table 1 Third-order optical susceptibility χ(3) of Bi2Se3 dispersion solution at 350 nm - 1160 nm.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Δ ψ ( r ) = ( 2 π n 0 λ ) 0 L e f f n 2 I ( r , z ) d z
L e f f = L 1 L 2 ( 1 + z 2 z 0 2 ) 1 d z = z 0 arc tan ( z z 0 ) | L 1 L 2
Δ ψ ( 0 ) Δ ψ ( ) = 2 N π
n 2 = ( λ 2 n 0 L e f f ) N I
n 2 = ( 12 π 2 / n 0 2 c ) 10 3 χ ( 3 )
χ t o t a l ( 3 ) K 2 χ sin g l e ( 3 )

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