Third-order nonlinear properties and reverse absorption behavior in layered Ti<sub>3</sub>C<sub>2</sub> MXene in the near infrared region

Tong Zhang; Hongwei Chu; Hongwei Chu; Ying Li; Shengzhi Zhao; Dechun Li; Dechun Li

doi:10.1364/OME.445753

Optical Materials Express
Vol. 11,
Issue 12,
pp. 4051-4057
(2021)
•https://doi.org/10.1364/OME.445753

Third-order nonlinear properties and reverse absorption behavior in layered Ti₃C₂ MXene in the near infrared region

Tong Zhang, Hongwei Chu, Ying Li, Shengzhi Zhao, and Dechun Li

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Tong Zhang, Hongwei Chu, Ying Li, Shengzhi Zhao, and Dechun Li, "Third-order nonlinear properties and reverse absorption behavior in layered Ti₃C₂ MXene in the near infrared region," Opt. Mater. Express 11, 4051-4057 (2021)

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- Two-dimensional Materials
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: October 11, 2021
- Revised Manuscript: November 9, 2021
- Manuscript Accepted: November 15, 2021
- Published: November 23, 2021

Abstract

Two-dimensional transition metal carbides/nitrides (MXenes) have attracted a lot of attention as optical materials owing to their unique electronic and optical features. In this paper, we demonstrated the nonlinear optical response of Ti₃C₂ MXene in the near infrared (NIR) regime at 1 and 1.3 µm. The nonlinear optical absorption behavior was systematically studied by the open/closed aperture (OA/CA) Z-scan techniques. Under a low excitation intensity, the saturable absorption dominated the optical nonlinear process, and the maximum effective nonlinear absorption coefficients β_eff were −0.59 cm/MW and −0.68 cm/MW at 1 and 1.3 µm, respectively. The nonlinear refractive index n₂ and the third-order susceptibility of Ti₃C₂ Mxene at 1 µm were −2.18 ×10⁻² cm²/GW and 3.65×10⁻³ esu, respectively. While with the excitation laser at 1.3 µm, the nonlinear refractive index n₂ was −1.64×10⁻² cm²/GW and the third-order susceptibility was 2.75×10⁻³ esu. With the increase of incident optical intensity, the two-photon absorption (TPA) process was observed, leading to the reverse absorption phenomenon. Our results confirmed that Ti₃C₂ MXene possessed intensity-depended nonlinear optical properties, which could be applied in various nonlinear optical devices.

1. Introduction

Nowadays, optical materials are of great importance for the applications in optical communications [1], data processing and storage [2], photoelectrochemistry [3], and photoharvesting, etc. Thus an agent with large nonlinear optical (NLO) response could be of interest for the optical pulse modulation and manipulation. In these NLO media, saturable absorption, reverse saturable absorption (RSA) and multi-photon absorption (MPA) are usually performed with the different-intensity light interaction [4,5].

Up to date, a plenty of two-dimensional materials have emerged in the nonlinear optical material family, such as graphene [6–9], black phosphorus [10–13], topological materials [14], and transition metal compounds [15,16]. Recently, transition metal compound MXenes have drawn an intense of attention owing to the special optical and electronic properties. As a branch of MXenes, Ti₃C₂ MXene has been widely used in the fields of chemical batteries [17–19], photocatalysis [20–23] and microwave absorption [24–26] due to the unique layered structure and superior electrochemical properties. Besides, Ti₃C₂ MXene exhibits excellent nonlinear optical performance. So far, Ti₃C₂ MXene has been employed as a saturable absorber to realize wide-band Q-switching and mode-locking operations [27–33]. Moreover, monolayer Ti₃C₂ MXene has the strong two-photon absorption (TPA) effect at 780 and 1100 nm, which is of great importance for the possible photonics applications [34]. However, the systematic study on the NLO properties of Ti₃C₂ MXene is still a blank, and more details need to be done in order to assist with the practical applications.

In this paper, the NLO properties of Ti₃C₂ MXene were investigated at 1 and 1.3 µm for the first time using open and closed aperture (OA/CA) Z-scan techniques. The NLO response was revealed to change with the variation of excitation pump energy. Through fitting experimental data, we obtained the effective nonlinear absorption coefficient β_eff, nonlinear refractive index n₂ and third-order susceptibility χ⁽³⁾ of the synthesized sample. The results confirmed the large NLO response of Ti₃C₂ MXene, which can be applied as a potential saturable absorber.

2. Characterization

We used the same preparation method reported in the previous study [35] to obtain Ti₃C₂ MXene sample. Before analyzing the NLO properties of Ti₃C₂ MXene, we made a series of characterization to show its surface morphology and structure. Figure 1(a) shows the scanning electron microscopy (SEM) results of Ti₃C₂ MXene. We can clearly see the layered structure of MXene, which is consistent with previous report [36]. The material was further observed by the transmission electron microscopy (TEM). According to Fig. 1(b), the monolayer thickness of Ti₃C₂ MXene is 0.89 nm. Then we determined the microstructure of the sample by HRTEM images. A very regular and well-defined hexagonal lattice can be observed in Fig. 1(c), showing the excellent crystallinity of Ti₃C₂ MXene. The inset of Fig. 1(c) demonstrates the selected area electron diffraction (SAED) map of the corresponding region with obvious diffraction points, which is consistent with the observed results in Fig. 1(c). We also measured the atomic composition and corresponding proportion of the prepared Ti₃C₂ MXene. As shown in Fig. 1(d), we can get that the weight ratios of Ti, C, O and F in the sample are 48.8%, 20.5%, 17.7% and 12.9%, respectively. Figure 1(e) shows the detailed element distribution of Ti₃C₂ MXene, demonstrating the homogeneity of our prepared material. To understand the internal structure of Ti₃C₂ MXene in more detail, we measured the XRD and Raman spectra. By analyzing the XRD pattern of Ti₃C₂ MXene in Fig. 1(f), we can see that the peak at 2θ = 39° is weakened compared with the standard peak of Ti₃AlC₂ (JCPDS No.52-0875), indicating that the Al layer is selectively etched by HF acid solution. Figure 1(g) shows the Raman spectrum of Ti₃C₂ MXene, whose characteristic peaks are located at 390 cm⁻¹ and 619 cm⁻¹, respectively. All characterization data confirmed that the Ti₃C₂ MXene was successfully prepared. The MXene was transferred on a quartz substrate via the spin-coating method. Figure 1(h) clearly displays the linear absorption spectra of transferred Ti₃C₂ MXene from 900 to 1500 nm, which also indicates the possible optical application in the near infrared region. The inset of Fig. 1(h) gives the morphology and thickness of the MXene on the quartz with a maximum thickness of ∼ 118 nm. After the laser beam excitation, we observed no light-induced degradation, showing the quite stability of the as-prepared MXene.

Fig. 1. Ti₃C₂ MXene characterization: (a) SEM; (b) TEM; (c) HRTEM and SAED pattern (inset); (d) Elemental content ratio; (e) Detailed element distribution; (f) XRD pattern and (g) Raman spectrum; (h) UV-vis-NIR absorption spectrum and morphology and thickness diagram of experimental sample (inset).

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3. Nonlinear optical properties

3.1 Nonlinear saturable absorption

The detailed NLO response of Ti₃C₂ MXene was studied by a conventional open/closed aperture (OA/CA) Z-scan system with different excitation intensity at 1 and 1.3 µm in the nanosecond level. Therefore, in our case, we mainly investigated the nanosecond nonlinearities of the as-prepared Ti₃C₂ MXene. In order to comprehensively study the NLO characteristics of Ti₃C₂ MXene, different excitation intensities were implemented to excite Ti₃C₂ MXene at both wavelengths. The nonlinear transmissivities with the excitation intensities are given in Fig. 2. It can be seen that Ti₃C₂ Mxene exhibits strong intensity-dependent nonlinear saturable absorption properties. The nonlinear transmission can be fitted with the following formulas:

(1)$$\textrm{T} = \mathop \sum \nolimits_{m = 0}^\infty \frac{{{{[{ - {q_0}({z,0} )} ]}^m}}}{{{{({m + 1} )}^{\frac{3}{2}}}}} \qquad m \in N, \qquad {q_0}({z,0} )= \frac{{{\beta _{eff}}{L_{eff}}{I_0}}}{{1 + {\raise0.7ex\hbox{${{z^2}}$} \!\mathord{/ {\vphantom {{{z^2}} {z_0^2}}} }\!\lower0.7ex\hbox{${z_0^2}$}}}}, $$

where, ${L_{eff}} = ({1 - {e^{ - L{\alpha_0}}}} )/{\alpha _0}$ is the effective length of the sample, α₀ represents the linear absorption coefficient, I₀ represents the peak intensity on the axis, L represents the sample length, β_eff represents the effective nonlinear absorption coefficient.

Fig. 2. The OA Z-scan results of Ti₃C₂ Mxene at (a) 1.06 µm and (b) 1.34 µm. Solid lines: fittings, dots: experimental data. Modulation depth (c) at 1.06 µm and 1.34 µm versus incident intensity. Effective nonlinear absorption coefficient β_eff versus incident intensity (d) at 1.06 µm and 1.34 µm.

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As can be seen from the normalized transmittance curves given in Fig. 2(a) and (b), the transmittance at different incidence intensities change symmetrically with the position of the Z-axis, which belongs to typically saturated absorption. This proved that the prepared Ti₃C₂ MXene material had good nonlinear absorption characteristics. Meanwhile, as shown in Fig. 2(c), the modulation depths at both wavelengths increase with the incident intensity. The maximum modulation depths were 10.9% and 9.3% at 1.06 and 1.34 µm, respectively. Figure 2(d) shows the variation of effective nonlinear absorption coefficient β_eff with incident intensity. Obviously, |β_eff| decreased with the increase of incident intensities. At a lower excitation intensity, the single-photon saturable absorption played a dominant role in the nonlinear absorption. With the increase of incident intensity, the two-photon absorption (TPA) and reverse saturable absorption (RSA) would occur, resulting in the decrease of |β_eff|. The maximum β_eff at 1 and 1.3 µm were −0.59 and −0.68 cm/MW, respectively.

3.2 Third-order NLO susceptibility

In order to obtain nonlinear refractive index n₂ and third-order nonlinear susceptibility, the CA Z-scan technology was implemented. Figure 3 shows the transmission differences of CA/OA Z-scan experiments at 1 and 1.3 µm, respectively, and the transmission can be fitted with the following expression [37]:

(2)$${T_{CA/OA}} = 1 + \frac{{4({{\raise0.7ex\hbox{$z$} \!\mathord{/ {\vphantom {z {{z_0}}}} }\!\lower0.7ex\hbox{${{z_0}}$}}} )\Delta \phi }}{{({{{({{\raise0.7ex\hbox{$z$} \!\mathord{/ {\vphantom {z {{z_0}}}} }\!\lower0.7ex\hbox{${{z_0}}$}}} )}^2} + 9} )({{{({{\raise0.7ex\hbox{$z$} \!\mathord{/ {\vphantom {z {{z_0}}}} }\!\lower0.7ex\hbox{${{z_0}}$}}} )}^2} + 1} )}}, $$

where $\Delta \phi \cong {n_2}{I_0}kd$ is the nonlinear phase shift, and I₀ is peak intensity, k and d are the wave vector and sample thickness, respectively. The nonlinear refractive index of Ti₃C₂ MXene at 1 and 1.3 µm were −2.18×10⁻² and −1.64×10⁻² cm²/GW, respectively.

Fig. 3. The normalized transmission curve at (a) 1 µm and (b) 1.3 µm.

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In addition, the third-order susceptibility is an essential parameter of the NLO materials. We can obtain the third-order NLO susceptibility χ⁽³⁾ of the sample from the nonlinear absorption coefficient β_eff and nonlinear refractive index n₂, and the real part $\mathrm{\Re }$χ⁽³⁾ and imaginary part $\mathrm{\Im }$χ⁽³⁾ can be calculated by the following formula [37]:

(3)$$\mathrm{\Re }{\chi ^{(3 )}} = \frac{{{{10}^{ - 4}}{\varepsilon _0}{c^2}n_0^2{n_2}}}{\pi },\,\,\,\mathrm{\Im }{\chi ^{(3 )}} = \frac{{{{10}^{ - 2}}{\varepsilon _0}{c^2}n_0^2\lambda {\beta _{eff}}}}{{4{\pi ^2}}}$$

where, ε₀ and c are the dielectric constant and the speed of light in the vacuum, respectively. And the absolute value of the magnetic susceptibility of third-order NLO can be obtained by:

(4)$$|{{\chi^{(3 )}}} |= \sqrt {{{|{\mathrm{\Re }{\chi^{(3 )}}} |}^2} + {{|{\mathrm{\Im }{\chi^{(3 )}}} |}^2}} $$

The typical NLO parameters are listed in Table 1.

Table 1. NLO parameters summary of Ti₃C₂ MXene in the NIR spectral band.

View Table

3.3 Two-photon absorption

To confirm the TPA effect in the saturable absorption progress, we further increased the excitation intensity. As shown in Fig. 4, with the increase of the pump intensities, the transmission curve of Ti₃C₂ MXene exhibits the valley at each wavelength. When the incidence range was strong enough, the evident desaturation absorption phenomenon appeared, which can be attributed to the TPA effect. The TPA coefficient can be fitted by the following formula [37]:

(5)$$\textrm{T} = {\raise0.7ex\hbox{$ {\left[ {1 - \frac{{{\alpha_0}L{I_s}}}{{{I_s} + \frac{{{I_0}}}{{1 + {\raise0.7ex\hbox{$ {{z^2}}$} \!\mathord{/ {\vphantom {{{z^2}} {z_0^2}}} }\!\lower0.7ex\hbox{$ {z_0^2}$ }}}}}} - \frac{{\beta L{I_0}}}{{1 + {\raise0.7ex\hbox{$ {{z^2}}$ } \!\mathord{/ {\vphantom {{{z^2}} {z_0^2}}} }\!\lower0.7ex\hbox{$ {z_0^2}$ }}}}} \right]}$} \!\mathord{\left/ {\vphantom {{\left[ {1 - \frac{{{\alpha_0}L{I_s}}}{{{I_s} + \frac{{{I_0}}}{{1 + {\raise0.7ex\hbox{$ {{z^2}}$ } \!\mathord{/ {\vphantom {{{z^2}} {z_0^2}}} }\!\lower0.7ex\hbox{$ {z_0^2}$ }}}}}} - \frac{{\beta L{I_0}}}{{1 + {\raise0.7ex\hbox{$ {{z^2}}$ } \!\mathord{/ {\vphantom {{{z^2}} {z_0^2}}} }\!\lower0.7ex\hbox{$ {z_0^2}$ }}}}} \right]} {({1 - {\alpha_0}L} )}}}\right.}\!\lower0.7ex\hbox{$ {({1 - {\alpha_0}L} )}$ }}$$

Where, I_s represents the saturable absorption intensity, z₀ is the diffraction length of the incident laser beam and β is the TPA coefficient. β at 1 and 1.3µm were 1.99 and 1.21 cm/MW, respectively, which were also summarized in Table 1.

Fig. 4. TPA phenomena of Ti₃C₂ Mxene at (a) 1.06 µm and (b) 1.34 µm.

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4. Conclusion

In summary, we synthesized Ti₃C₂ MXene and carried out a series of characterization. The nonlinear optical responses at 1 and 1.3 µm were studied by the open/closed aperture Z-scan technique for the first time. The open-aperture Z-scan technique was used to measure the saturation absorption of Ti₃C₂ MXene at different incidence intensities. It was found that at low incidence intensities, the saturable absorption played a dominant role in the nonlinear absorption. With the increase of incidence intensities, the proportion of two-photon absorption and reverse saturable absorption gradually increased. The third-order optical susceptibility of the sample was measured by the closed-aperture Z-scan technique. χ⁽³⁾ of the Ti₃C₂ MXene sample were 3.65×10⁻³ and 2.75×10⁻³ esu at 1 and 1.3 µm, respectively. Our work confirmed Ti₃C₂ Mxene can be used as an alternate material for nonlinear optical devices with large NLO response in the near-infrared region.

Funding

National Natural Science Foundation of China (12004213, 12174223, 21872084).

Acknowledgments

H. C. would like to thank the financial support from the Young Scholar Program of Shandong University.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Year
Author
Publication

M. Sorokina, S. Sygletos, and S. Turitsyn, “Sparse identification for nonlinear optical communication systems: SINO method,” Opt. Express 24(26), 30433–30443 (2016).
[Crossref]
D. Psaltis and N. Farhat, “Optical information processing based on an associative-memory model of neural nets with thresholding and feedback,” Opt. Lett. 10(2), 98–100 (1985).
[Crossref]
A. Szukalski, A. Ayadi, K. Haupa, A. El-Ghayoury, B. Sahraoui, and J. Mysliwiec, “All-optical switching and two-states light-controlled coherent-incoherent random lasing in a thiophene-based donor-acceptor system,” ChemPhysChem 19(13), 1605–1616 (2018).
[Crossref]
J. Perry, D. Alvarez, I. Choong, K. Mansour, S. Marder, and K. Perry, “Enhanced reverse saturable absorption and optical limiting in heavy-atom-substituted phthalocyanines,” Opt. Lett. 19(9), 625–627 (1994).
[Crossref]
L. Tutt and S. McCahon, “Reverse saturable absorption in metal cluster compounds,” Opt. Lett. 15(12), 700–702 (1990).
[Crossref]
L. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
[Crossref]
E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref]
M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]
J. Wang, Y. Hernandez, M. Lotya, J. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[Crossref]
S. Lu, L. Miao, Z. Guo, X. Qi, C. Zhao, H. Zhang, S. Wen, D. Tang, and D. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (2015).
[Crossref]
K. Wang, B. Szydłowska, G. Wang, X. Zhang, J. Wang, J. Magan, L. Zhang, J. Coleman, J. Wang, and W. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref]
Y. Xu, X. Jiang, Y. Ge, Z. Guo, Z. Zeng, Q. Xu, H. Zhang, X. Yu, and D. Fan, “Size-dependent nonlinear optical properties of black phosphorus nanosheets and their applications in ultrafast photonics,” J. Mater. Chem. C 5(12), 3007–3013 (2017).
[Crossref]
R. Chen, X. Zheng, and T. Jiang, “Broadband ultrafast nonlinear absorption and ultra-long exciton relaxation time of black phosphorus quantum dots,” Opt. Express 25(7), 7507–7519 (2017).
[Crossref]
T. Morimoto and N. Nagaosa, “Topological nature of nonlinear optical effects in solids,” Sci. Adv. 2(5), e1501524 (2016).
[Crossref]
A. Delin, O. Eriksson, R. Ahuja, B. Johansson, and M. Brooks, “Optical properties of the group-IVB refractory metal compounds,” Phys. Rev. B 54(3), 1673–1681 (1996).
[Crossref]
J. Wilson and A. Yoffe, “The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties,” Adv. Phys. 18(73), 193–335 (1969).
[Crossref]
W. Liu, Z. Wang, Y. Su, Q. Li, Z. Zhao, and F. Geng, “Molecularly stacking manganese dioxide/titanium carbide sheets to produce highly flexible and conductive film electrodes with improved pseudocapacitive performances,” Adv. Energy Mater. 7(22), 1602834 (2017).
[Crossref]
Q. Tang, Z. Zhou, and P. Shen, “Are MXenes promising anode materials for Li ion batteries? Computational studies on electronic properties and Li storage capability of Ti3C2 and Ti3C2X2 (X = F, OH) monolayer,” J. Am. Chem. Soc. 134(40), 16909–16916 (2012).
[Crossref]
Y. Wang, Y. Li, Z. Qiu, X. Wu, P. Zhou, T. Zhou, J. Zhao, Z. Miao, J. Zhou, and S. Zhuo, “Fe3O4@Ti3C2 MXene hybrids with ultrahigh volumetric capacity as an anode material for lithium-ion batteries,” J. Mater. Chem. A 6(24), 11189–11197 (2018).
[Crossref]
A. Shahzad, K. Rasool, M. Nawaz, W. Miran, J. Jang, M. Moztahida, K. Mahmoud, and D. Lee, “Heterostructural TiO2/Ti3C2Tx (MXene) for photocatalytic degradation of antiepileptic drug carbamazepine,” Chem. Eng. J. 349, 748–755 (2018).
[Crossref]
J. Low, L. Zhang, T. Tong, B. Shen, and J. Yu, “TiO2/MXene Ti3C2 composite with excellent photocatalytic CO2 reduction activity,” J. Catal. 361, 255–266 (2018).
[Crossref]
Z. Guo, J. Zhou, L. Zhu, and Z. Sun, “MXene: a promising photocatalyst for water splitting,” J. Mater. Chem. A 4(29), 11446–11452 (2016).
[Crossref]
L. Cheng, X. Li, H. Zhang, and Q. Xiang, “Two-dimensional transition metal MXene-based photocatalysts for solar fuel generation,” J. Phys. Chem. Lett. 10(12), 3488–3494 (2019).
[Crossref]
W. Feng, H. Luo, Y. Wang, S. Zeng, L. Deng, X. Zhou, H. Zhang, and S. Peng, “Ti3C2 MXene: a promising microwave absorbing material,” RSC Adv. 8(5), 2398–2403 (2018).
[Crossref]
Y. Qing, W. Zhou, F. Luo, and D. Zhu, “Titanium carbide (MXene) nanosheets as promising microwave absorbers,” Ceram. Int. 42(14), 16412–16416 (2016).
[Crossref]
M. S. Cao, Y. Z. Cai, P. He, J. C. Shu, W. Q. Cao, and J. Yuan, “2D MXenes: electromagnetic property for microwave absorption and electromagnetic interference shielding,” Chem. Eng. J. 359, 1265–1302 (2019).
[Crossref]
X. Feng, B. Ding, W. Liang, and F. Zhang, “MXene Ti3C2Tx absorber for a 1.06 µ m passively Q-switched ceramic laser,” Laser Phys. Lett. 15(8), 085805 (2018).
[Crossref]
J. Li, Z. Zhang, L. Du, L. Miao, J. Yi, B. Huang, Y. Zou, C. Zhao, and S. Wen, “Highly stable femtosecond pulse generation from a MXene Ti3C2Tx (T = F, O, or OH) mode-locked fiber laser,” Photonics Res. 7(3), 260–264 (2019).
[Crossref]
Y. Jhon, J. Koo, B. Anasori, M. Seo, J. Lee, Y. Gogotsi, and Y. Jhon, “Metallic MXene saturable absorber for femtosecond mode-locked lasers,” Adv. Mater. 29(40), 1702496 (2017).
[Crossref]
C. Wang, Q. Q. Peng, X. W. Fan, W. Y. Liang, F. Zhang, J. Liu, and H. Zhang, “MXene Ti3C2Tx saturable absorber for pulsed laser at 1.3 µm,” Chin. Phys. B 27(9), 094214 (2018).
[Crossref]
L. Wang, X. Li, C. Wang, W. Luo, T. Feng, Y. Zhang, and H. Zhang, “Few-layer Mxene Ti3C2Tx (T = F, O, Or OH) for robust pulse generation in a compact er-doped fiber laser,” ChemNanoMat 5(9), 1233–1238 (2019).
[Crossref]
Q. Wu, X. Jin, S. Chen, X. Jiang, Y. Hu, Q. Jiang, L. Wu, J. Li, Z. Zheng, M. Zhang, and H. Zhang, “MXene-based saturable absorber for femtosecond mode-locked fiber lasers,” Opt. Express 27(7), 10159–10170 (2019).
[Crossref]
Q. Hao, J. Liu, Z. Zhang, B. Zhang, F. Zhang, J. Yang, J. Liu, L. Su, and H. Zhang, “Mid-infrared Er:CaF2–SrF2 bulk laser Q-switched by MXene Ti3C2Tx absorber,” Appl. Phys. Express 12(8), 085506 (2019).
[Crossref]
G. Wang, D. Bennett, C. Zhang, C. Ó Coileáin, M. Liang, N. McEvoy, J. J. Wang, J. Wang, K. Wang, V. Nicolosi, and W. J. Blau, “Two-photon absorption in monolayer MXenes,” Adv. Opt. Mater. 8(9), 1902021 (2020).
[Crossref]
T. Zhang, H. Chu, L. Dong, Y. Li, S. Zhao, Y. Wang, J. Zhou, and D. Li, “Synthesis and optical nonlinearity investigation of novel Fe3O4@Ti3C2 MXene hybrid nanomaterials from 1 to 2 µm,” J. Mater. Chem. C 9(5), 1772–1777 (2021).
[Crossref]
M. Naguib, M. Kurtoglu, V. Presser, J. Lu, J. Niu, M. Heon, L. Hultman, Y. Gogotsi, and M. W. Barsoum, “Two-dimensional nanocrystals produced by exfoliation of Ti3AlC2,” Adv. Mater. 23(37), 4248–4253 (2011).
[Crossref]
L. Dong, H. Chu, Y. Li, S. Zhao, G. Li, and D. Li, “Nonlinear optical responses of α-Fe2O3 nanosheets and application as a saturable absorber in the wide near-infrared region,” Opt. Laser Technol. 136, 106812 (2021).
[Crossref]

2021 (2)

T. Zhang, H. Chu, L. Dong, Y. Li, S. Zhao, Y. Wang, J. Zhou, and D. Li, “Synthesis and optical nonlinearity investigation of novel Fe3O4@Ti3C2 MXene hybrid nanomaterials from 1 to 2 µm,” J. Mater. Chem. C 9(5), 1772–1777 (2021).
[Crossref]

L. Dong, H. Chu, Y. Li, S. Zhao, G. Li, and D. Li, “Nonlinear optical responses of α-Fe2O3 nanosheets and application as a saturable absorber in the wide near-infrared region,” Opt. Laser Technol. 136, 106812 (2021).
[Crossref]

2020 (1)

G. Wang, D. Bennett, C. Zhang, C. Ó Coileáin, M. Liang, N. McEvoy, J. J. Wang, J. Wang, K. Wang, V. Nicolosi, and W. J. Blau, “Two-photon absorption in monolayer MXenes,” Adv. Opt. Mater. 8(9), 1902021 (2020).
[Crossref]

2019 (6)

J. Li, Z. Zhang, L. Du, L. Miao, J. Yi, B. Huang, Y. Zou, C. Zhao, and S. Wen, “Highly stable femtosecond pulse generation from a MXene Ti3C2Tx (T = F, O, or OH) mode-locked fiber laser,” Photonics Res. 7(3), 260–264 (2019).
[Crossref]

L. Wang, X. Li, C. Wang, W. Luo, T. Feng, Y. Zhang, and H. Zhang, “Few-layer Mxene Ti3C2Tx (T = F, O, Or OH) for robust pulse generation in a compact er-doped fiber laser,” ChemNanoMat 5(9), 1233–1238 (2019).
[Crossref]

Q. Wu, X. Jin, S. Chen, X. Jiang, Y. Hu, Q. Jiang, L. Wu, J. Li, Z. Zheng, M. Zhang, and H. Zhang, “MXene-based saturable absorber for femtosecond mode-locked fiber lasers,” Opt. Express 27(7), 10159–10170 (2019).
[Crossref]

Q. Hao, J. Liu, Z. Zhang, B. Zhang, F. Zhang, J. Yang, J. Liu, L. Su, and H. Zhang, “Mid-infrared Er:CaF2–SrF2 bulk laser Q-switched by MXene Ti3C2Tx absorber,” Appl. Phys. Express 12(8), 085506 (2019).
[Crossref]

L. Cheng, X. Li, H. Zhang, and Q. Xiang, “Two-dimensional transition metal MXene-based photocatalysts for solar fuel generation,” J. Phys. Chem. Lett. 10(12), 3488–3494 (2019).
[Crossref]

M. S. Cao, Y. Z. Cai, P. He, J. C. Shu, W. Q. Cao, and J. Yuan, “2D MXenes: electromagnetic property for microwave absorption and electromagnetic interference shielding,” Chem. Eng. J. 359, 1265–1302 (2019).
[Crossref]

2018 (7)

X. Feng, B. Ding, W. Liang, and F. Zhang, “MXene Ti3C2Tx absorber for a 1.06 µ m passively Q-switched ceramic laser,” Laser Phys. Lett. 15(8), 085805 (2018).
[Crossref]

W. Feng, H. Luo, Y. Wang, S. Zeng, L. Deng, X. Zhou, H. Zhang, and S. Peng, “Ti3C2 MXene: a promising microwave absorbing material,” RSC Adv. 8(5), 2398–2403 (2018).
[Crossref]

Y. Wang, Y. Li, Z. Qiu, X. Wu, P. Zhou, T. Zhou, J. Zhao, Z. Miao, J. Zhou, and S. Zhuo, “Fe3O4@Ti3C2 MXene hybrids with ultrahigh volumetric capacity as an anode material for lithium-ion batteries,” J. Mater. Chem. A 6(24), 11189–11197 (2018).
[Crossref]

A. Shahzad, K. Rasool, M. Nawaz, W. Miran, J. Jang, M. Moztahida, K. Mahmoud, and D. Lee, “Heterostructural TiO2/Ti3C2Tx (MXene) for photocatalytic degradation of antiepileptic drug carbamazepine,” Chem. Eng. J. 349, 748–755 (2018).
[Crossref]

J. Low, L. Zhang, T. Tong, B. Shen, and J. Yu, “TiO2/MXene Ti3C2 composite with excellent photocatalytic CO2 reduction activity,” J. Catal. 361, 255–266 (2018).
[Crossref]

C. Wang, Q. Q. Peng, X. W. Fan, W. Y. Liang, F. Zhang, J. Liu, and H. Zhang, “MXene Ti3C2Tx saturable absorber for pulsed laser at 1.3 µm,” Chin. Phys. B 27(9), 094214 (2018).
[Crossref]

A. Szukalski, A. Ayadi, K. Haupa, A. El-Ghayoury, B. Sahraoui, and J. Mysliwiec, “All-optical switching and two-states light-controlled coherent-incoherent random lasing in a thiophene-based donor-acceptor system,” ChemPhysChem 19(13), 1605–1616 (2018).
[Crossref]

2017 (4)

Y. Xu, X. Jiang, Y. Ge, Z. Guo, Z. Zeng, Q. Xu, H. Zhang, X. Yu, and D. Fan, “Size-dependent nonlinear optical properties of black phosphorus nanosheets and their applications in ultrafast photonics,” J. Mater. Chem. C 5(12), 3007–3013 (2017).
[Crossref]

R. Chen, X. Zheng, and T. Jiang, “Broadband ultrafast nonlinear absorption and ultra-long exciton relaxation time of black phosphorus quantum dots,” Opt. Express 25(7), 7507–7519 (2017).
[Crossref]

W. Liu, Z. Wang, Y. Su, Q. Li, Z. Zhao, and F. Geng, “Molecularly stacking manganese dioxide/titanium carbide sheets to produce highly flexible and conductive film electrodes with improved pseudocapacitive performances,” Adv. Energy Mater. 7(22), 1602834 (2017).
[Crossref]

Y. Jhon, J. Koo, B. Anasori, M. Seo, J. Lee, Y. Gogotsi, and Y. Jhon, “Metallic MXene saturable absorber for femtosecond mode-locked lasers,” Adv. Mater. 29(40), 1702496 (2017).
[Crossref]

2016 (5)

Z. Guo, J. Zhou, L. Zhu, and Z. Sun, “MXene: a promising photocatalyst for water splitting,” J. Mater. Chem. A 4(29), 11446–11452 (2016).
[Crossref]

Y. Qing, W. Zhou, F. Luo, and D. Zhu, “Titanium carbide (MXene) nanosheets as promising microwave absorbers,” Ceram. Int. 42(14), 16412–16416 (2016).
[Crossref]

K. Wang, B. Szydłowska, G. Wang, X. Zhang, J. Wang, J. Magan, L. Zhang, J. Coleman, J. Wang, and W. Blau, “Ultrafast nonlinear excitation dynamics of black phosphorus nanosheets from visible to mid-infrared,” ACS Nano 10(7), 6923–6932 (2016).
[Crossref]

T. Morimoto and N. Nagaosa, “Topological nature of nonlinear optical effects in solids,” Sci. Adv. 2(5), e1501524 (2016).
[Crossref]

M. Sorokina, S. Sygletos, and S. Turitsyn, “Sparse identification for nonlinear optical communication systems: SINO method,” Opt. Express 24(26), 30433–30443 (2016).
[Crossref]

2015 (1)

S. Lu, L. Miao, Z. Guo, X. Qi, C. Zhao, H. Zhang, S. Wen, D. Tang, and D. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (2015).
[Crossref]

2012 (1)

Q. Tang, Z. Zhou, and P. Shen, “Are MXenes promising anode materials for Li ion batteries? Computational studies on electronic properties and Li storage capability of Ti3C2 and Ti3C2X2 (X = F, OH) monolayer,” J. Am. Chem. Soc. 134(40), 16909–16916 (2012).
[Crossref]

2011 (2)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

M. Naguib, M. Kurtoglu, V. Presser, J. Lu, J. Niu, M. Heon, L. Hultman, Y. Gogotsi, and M. W. Barsoum, “Two-dimensional nanocrystals produced by exfoliation of Ti3AlC2,” Adv. Mater. 23(37), 4248–4253 (2011).
[Crossref]

2010 (1)

E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref]

2009 (1)

J. Wang, Y. Hernandez, M. Lotya, J. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[Crossref]

2008 (1)

L. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
[Crossref]

1996 (1)

A. Delin, O. Eriksson, R. Ahuja, B. Johansson, and M. Brooks, “Optical properties of the group-IVB refractory metal compounds,” Phys. Rev. B 54(3), 1673–1681 (1996).
[Crossref]

1969 (1)

J. Wilson and A. Yoffe, “The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties,” Adv. Phys. 18(73), 193–335 (1969).
[Crossref]

Ahuja, R.

A. Delin, O. Eriksson, R. Ahuja, B. Johansson, and M. Brooks, “Optical properties of the group-IVB refractory metal compounds,” Phys. Rev. B 54(3), 1673–1681 (1996).
[Crossref]

Alvarez, D.

Anasori, B.

Y. Jhon, J. Koo, B. Anasori, M. Seo, J. Lee, Y. Gogotsi, and Y. Jhon, “Metallic MXene saturable absorber for femtosecond mode-locked lasers,” Adv. Mater. 29(40), 1702496 (2017).
[Crossref]

Ayadi, A.

Barsoum, M. W.

Bennett, D.

Blau, W.

Blau, W. J.

J. Wang, Y. Hernandez, M. Lotya, J. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[Crossref]

Brooks, M.

A. Delin, O. Eriksson, R. Ahuja, B. Johansson, and M. Brooks, “Optical properties of the group-IVB refractory metal compounds,” Phys. Rev. B 54(3), 1673–1681 (1996).
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Cai, Y. Z.

Cao, M. S.

Cao, W. Q.

Chen, R.

Chen, S.

Cheng, L.

L. Cheng, X. Li, H. Zhang, and Q. Xiang, “Two-dimensional transition metal MXene-based photocatalysts for solar fuel generation,” J. Phys. Chem. Lett. 10(12), 3488–3494 (2019).
[Crossref]

Choong, I.

Chu, H.

Coileáin, C. Ó

Coleman, J.

J. Wang, Y. Hernandez, M. Lotya, J. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[Crossref]

Delin, A.

A. Delin, O. Eriksson, R. Ahuja, B. Johansson, and M. Brooks, “Optical properties of the group-IVB refractory metal compounds,” Phys. Rev. B 54(3), 1673–1681 (1996).
[Crossref]

Deng, L.

W. Feng, H. Luo, Y. Wang, S. Zeng, L. Deng, X. Zhou, H. Zhang, and S. Peng, “Ti3C2 MXene: a promising microwave absorbing material,” RSC Adv. 8(5), 2398–2403 (2018).
[Crossref]

Ding, B.

X. Feng, B. Ding, W. Liang, and F. Zhang, “MXene Ti3C2Tx absorber for a 1.06 µ m passively Q-switched ceramic laser,” Laser Phys. Lett. 15(8), 085805 (2018).
[Crossref]

Dong, L.

Du, L.

El-Ghayoury, A.

Eriksson, O.

A. Delin, O. Eriksson, R. Ahuja, B. Johansson, and M. Brooks, “Optical properties of the group-IVB refractory metal compounds,” Phys. Rev. B 54(3), 1673–1681 (1996).
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L. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
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Fan, X. W.

C. Wang, Q. Q. Peng, X. W. Fan, W. Y. Liang, F. Zhang, J. Liu, and H. Zhang, “MXene Ti3C2Tx saturable absorber for pulsed laser at 1.3 µm,” Chin. Phys. B 27(9), 094214 (2018).
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W. Feng, H. Luo, Y. Wang, S. Zeng, L. Deng, X. Zhou, H. Zhang, and S. Peng, “Ti3C2 MXene: a promising microwave absorbing material,” RSC Adv. 8(5), 2398–2403 (2018).
[Crossref]

Feng, X.

X. Feng, B. Ding, W. Liang, and F. Zhang, “MXene Ti3C2Tx absorber for a 1.06 µ m passively Q-switched ceramic laser,” Laser Phys. Lett. 15(8), 085805 (2018).
[Crossref]

Ge, Y.

Geng, B.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Geng, F.

Gogotsi, Y.

Y. Jhon, J. Koo, B. Anasori, M. Seo, J. Lee, Y. Gogotsi, and Y. Jhon, “Metallic MXene saturable absorber for femtosecond mode-locked lasers,” Adv. Mater. 29(40), 1702496 (2017).
[Crossref]

Guo, Z.

Z. Guo, J. Zhou, L. Zhu, and Z. Sun, “MXene: a promising photocatalyst for water splitting,” J. Mater. Chem. A 4(29), 11446–11452 (2016).
[Crossref]

Hale, P.

E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref]

Hao, Q.

Haupa, K.

He, P.

Hendry, E.

E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
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Heon, M.

Hernandez, Y.

J. Wang, Y. Hernandez, M. Lotya, J. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[Crossref]

Hu, Y.

Huang, B.

Hultman, L.

Jang, J.

Jhon, Y.

Y. Jhon, J. Koo, B. Anasori, M. Seo, J. Lee, Y. Gogotsi, and Y. Jhon, “Metallic MXene saturable absorber for femtosecond mode-locked lasers,” Adv. Mater. 29(40), 1702496 (2017).
[Crossref]

Jiang, Q.

Jiang, T.

Jiang, X.

Jin, X.

Johansson, B.

A. Delin, O. Eriksson, R. Ahuja, B. Johansson, and M. Brooks, “Optical properties of the group-IVB refractory metal compounds,” Phys. Rev. B 54(3), 1673–1681 (1996).
[Crossref]

Ju, L.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Koo, J.

Y. Jhon, J. Koo, B. Anasori, M. Seo, J. Lee, Y. Gogotsi, and Y. Jhon, “Metallic MXene saturable absorber for femtosecond mode-locked lasers,” Adv. Mater. 29(40), 1702496 (2017).
[Crossref]

Kurtoglu, M.

Lee, D.

Lee, J.

Y. Jhon, J. Koo, B. Anasori, M. Seo, J. Lee, Y. Gogotsi, and Y. Jhon, “Metallic MXene saturable absorber for femtosecond mode-locked lasers,” Adv. Mater. 29(40), 1702496 (2017).
[Crossref]

Li, D.

Li, G.

Li, J.

Li, Q.

Li, X.

L. Cheng, X. Li, H. Zhang, and Q. Xiang, “Two-dimensional transition metal MXene-based photocatalysts for solar fuel generation,” J. Phys. Chem. Lett. 10(12), 3488–3494 (2019).
[Crossref]

Li, Y.

Liang, M.

Liang, W.

X. Feng, B. Ding, W. Liang, and F. Zhang, “MXene Ti3C2Tx absorber for a 1.06 µ m passively Q-switched ceramic laser,” Laser Phys. Lett. 15(8), 085805 (2018).
[Crossref]

Liang, W. Y.

C. Wang, Q. Q. Peng, X. W. Fan, W. Y. Liang, F. Zhang, J. Liu, and H. Zhang, “MXene Ti3C2Tx saturable absorber for pulsed laser at 1.3 µm,” Chin. Phys. B 27(9), 094214 (2018).
[Crossref]

Liu, J.

C. Wang, Q. Q. Peng, X. W. Fan, W. Y. Liang, F. Zhang, J. Liu, and H. Zhang, “MXene Ti3C2Tx saturable absorber for pulsed laser at 1.3 µm,” Chin. Phys. B 27(9), 094214 (2018).
[Crossref]

Liu, M.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Liu, W.

Lotya, M.

J. Wang, Y. Hernandez, M. Lotya, J. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[Crossref]

Low, J.

J. Low, L. Zhang, T. Tong, B. Shen, and J. Yu, “TiO2/MXene Ti3C2 composite with excellent photocatalytic CO2 reduction activity,” J. Catal. 361, 255–266 (2018).
[Crossref]

Lu, J.

Lu, S.

Luo, F.

Y. Qing, W. Zhou, F. Luo, and D. Zhu, “Titanium carbide (MXene) nanosheets as promising microwave absorbers,” Ceram. Int. 42(14), 16412–16416 (2016).
[Crossref]

Luo, H.

W. Feng, H. Luo, Y. Wang, S. Zeng, L. Deng, X. Zhou, H. Zhang, and S. Peng, “Ti3C2 MXene: a promising microwave absorbing material,” RSC Adv. 8(5), 2398–2403 (2018).
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E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref]

Miran, W.

Moger, J.

E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
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T. Morimoto and N. Nagaosa, “Topological nature of nonlinear optical effects in solids,” Sci. Adv. 2(5), e1501524 (2016).
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Moztahida, M.

Mysliwiec, J.

Nagaosa, N.

T. Morimoto and N. Nagaosa, “Topological nature of nonlinear optical effects in solids,” Sci. Adv. 2(5), e1501524 (2016).
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Naguib, M.

Nawaz, M.

Nicolosi, V.

Niu, J.

Peng, Q. Q.

C. Wang, Q. Q. Peng, X. W. Fan, W. Y. Liang, F. Zhang, J. Liu, and H. Zhang, “MXene Ti3C2Tx saturable absorber for pulsed laser at 1.3 µm,” Chin. Phys. B 27(9), 094214 (2018).
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ACS Nano (1)

Adv. Energy Mater. (1)

Adv. Mater. (3)

J. Wang, Y. Hernandez, M. Lotya, J. Coleman, and W. J. Blau, “Broadband nonlinear optical response of graphene dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
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Adv. Opt. Mater. (1)

Adv. Phys. (1)

Appl. Phys. Express (1)

Ceram. Int. (1)

Y. Qing, W. Zhou, F. Luo, and D. Zhu, “Titanium carbide (MXene) nanosheets as promising microwave absorbers,” Ceram. Int. 42(14), 16412–16416 (2016).
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Chem. Eng. J. (2)

ChemNanoMat (1)

ChemPhysChem (1)

Chin. Phys. B (1)

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J. Am. Chem. Soc. (1)

J. Catal. (1)

J. Low, L. Zhang, T. Tong, B. Shen, and J. Yu, “TiO2/MXene Ti3C2 composite with excellent photocatalytic CO2 reduction activity,” J. Catal. 361, 255–266 (2018).
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J. Mater. Chem. A (2)

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J. Mater. Chem. C (2)

J. Phys. Chem. Lett. (1)

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L. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
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X. Feng, B. Ding, W. Liang, and F. Zhang, “MXene Ti3C2Tx absorber for a 1.06 µ m passively Q-switched ceramic laser,” Laser Phys. Lett. 15(8), 085805 (2018).
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Nature (1)

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Opt. Express (4)

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Opt. Laser Technol. (1)

Opt. Lett. (3)

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Photonics Res. (1)

Phys. Rev. B (1)

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Phys. Rev. Lett. (1)

E. Hendry, P. Hale, J. Moger, A. Savchenko, and S. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
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RSC Adv. (1)

W. Feng, H. Luo, Y. Wang, S. Zeng, L. Deng, X. Zhou, H. Zhang, and S. Peng, “Ti3C2 MXene: a promising microwave absorbing material,” RSC Adv. 8(5), 2398–2403 (2018).
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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Fig. 3. The normalized transmission curve at (a) 1 µm and (b) 1.3 µm.

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Fig. 4. TPA phenomena of Ti₃C₂ Mxene at (a) 1.06 µm and (b) 1.34 µm.

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Tables (1)

Table 1. NLO parameters summary of Ti₃C₂ MXene in the NIR spectral band.

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Equations (5)

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

T = \sum_{m = 0}^{\infty} \frac{{[- q_{0} (z, 0)]}^{m}}{{(m + 1)}^{\frac{3}{2}}} m \in N, q_{0} (z, 0) = \frac{β_{e f f} L_{e f f} I_{0}}{1 + z^{2} / z_{0}^{2}},

T_{C A / O A} = 1 + \frac{4 (z / z_{0}) Δ ϕ}{({(z / z_{0})}^{2} + 9) ({(z / z_{0})}^{2} + 1)},

ℜ χ^{(3)} = \frac{10^{- 4} ε_{0} c^{2} n_{0}^{2} n_{2}}{π}, ℑ χ^{(3)} = \frac{10^{- 2} ε_{0} c^{2} n_{0}^{2} λ β_{e f f}}{4 π^{2}}

| χ^{(3)} | = \sqrt{{| ℜ χ^{(3)} |}^{2} + {| ℑ χ^{(3)} |}^{2}}

T = [1 - \frac{α_{0} L I_{s}}{I_{s} + \frac{I_{0}}{1 + z^{2} / z_{0}^{2}}} - \frac{β L I_{0}}{1 + z^{2} / z_{0}^{2}}] / (1 - α_{0} L)

λ (nm)	β_eff(cm/MW)	n₂ (cm²/GW)	β_TPA(cm/MW)	$ℜ χ^{(3)}$ ⁾ (esu)	$ℑ χ^{(3)}$ (esu)	χ⁽³⁾ (esu)
1064	−0.59	−2.18 ×10⁻²	1.99	−3.65×10⁻³	−1.57×10⁻⁴	3.65×10⁻³
1342	−0.68	−1.64 ×10⁻²	1.21	−2.74×10⁻³	−2.87×10⁻⁴	2.75×10⁻³

Abstract

1. Introduction

2. Characterization

3. Nonlinear optical properties

3.1 Nonlinear saturable absorption

3.2 Third-order NLO susceptibility

3.3 Two-photon absorption

4. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

References

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1969 (1)

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