Saturable absorption and self-defocusing response of 2D monoelemental germanium nanosheets in broadband spectra

Li Zhou; Yingwei Wang; Yingwei Wang; Yiduo Wang; Si Xiao; Jun He; Jun He

doi:10.1364/OE.445958

Optics Express
Vol. 29,
Issue 24,
pp. 39115-39124
(2021)
•https://doi.org/10.1364/OE.445958

Saturable absorption and self-defocusing response of 2D monoelemental germanium nanosheets in broadband spectra

Li Zhou, Yingwei Wang, Yiduo Wang, Si Xiao, and Jun He

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Li Zhou, Yingwei Wang, Yiduo Wang, Si Xiao, and Jun He, "Saturable absorption and self-defocusing response of 2D monoelemental germanium nanosheets in broadband spectra," Opt. Express 29, 39115-39124 (2021)

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- Nonlinear Optics
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About this Article
History
- Original Manuscript: October 14, 2021
- Revised Manuscript: October 27, 2021
- Manuscript Accepted: October 29, 2021
- Published: November 8, 2021

Abstract

Germanium has caused a research boom in recent years due to its high carrier mobility and good stability. Although germanium has been proven to have application potential in photodetectors and other fields, its nonlinear optical properties are rarely reported. Herein, we prepared 2D germanium nanosheets by liquid phase-exfoliation (LPE) method and studied its third-order nonlinear optical response. It is found that the germanium nanosheets exhibit a broadband nonlinear optical response such as it has a large nonlinear absorption coefficient α_NL ≈ −0.87 cm GW⁻¹ and a negative nonlinear refractive index n₂ ≈ −6.30 × 10⁻¹³ cm² W⁻¹ at 1064 nm wavelength. The experimental results show the excellent nonlinear optical performance of germanium nanosheets and indicate that 2D germanium nanosheets have promising potential in a wide range of photonics device applications.

1. Introduction

The outstanding third-order nonlinear optical properties of two-dimensional (2D) materials, eg. nonlinear optical absorption and refractive, open up a wide range of potential applications in the emerging nanophotonic region, such as all optical switches, saturable absorbers, and harmonic generators [1–7]. Saturable absorption (SA) effect can occur in 2D materials in which the excited electrons will occupy possible states in the conduction band, following induced “optical bleaching” as the increasing of incident light intensity. Such effects and corresponding applications have been demonstrated in a series of 2D materials, such as graphene [8,9], topological insulators [10,11], black phosphorous (BP) [12,13], transition-metal dichalcogenides (TMDs) [14–16], transition-metal carbides/carbonitrides (MXene) [17,18] and other 2D heterostructure. Consequently, such 2D materials have been designed as saturable absorbers which can be constructed into fiber laser or solid laser cavity to generate ultrashort pulse [8,14,18]. Excellent SA response of 2D materials is needed when it used in saturable absorbers applications. Tremendous investigations have leveraged the giant nonlinear optical refractive response to achieve effective light manipulation including frequency regulation, phase regulation and amplitude regulation [19]. 2D materials also exhibit outstanding performance in those fields [20,21]. Spatial self-phase modulation (SSPM) effect of 2D materials, for instance, have been extensively investigated to realize phase modulation and optical switch practical application. In addition, 2D materials with strong nonlinear optical response can demonstrate wavefront engineering of light beams by building properly 2D material metastructure.

Those strong light-matter interaction induced by nonlinear optical properties of 2D materials endow the wide range of nonlinear nanophotonics applications. As above mentioned, the nonlinear optical properties of various 2D materials have been reported previously range from graphene to emerging MXene. However, insurmountable challenges still exist during the development of those 2D materials, for instance, the bad ambient stability of BP and high risk preparation of MXene. Therefore, the exploring of new materials with giant third nonlinear optical response is one of the most vital strategies to promote the development of nonlinear nanophotonics applications. Single-element materials have attracted widespread attention due to their simple composition and excellent photoelectric properties. As a single element material, germanium has the similar electron configurations to silicon and carbon, and it has the stable and buckled honeycomb structures by first-principles calculation [22], which is similar to BP. Moreover, germanium shows high carrier mobility, good stability at ambient and broadband absorption range from ultraviolet to near-infrared (NIR) region [23–25]. As far as we know, germanium has been proven to have application potential in the field of field-effect transistors [24], photothermal therapy [25] and photodetectors [26]. In the field of nonlinear optics, Mu et al. reported that the germanium nanosheets can be used as saturable absorber to construct an ultrafast mode-locked laser [27]. It is clear that the content of this work is focused on nonlinear absorption response of Ge nanosheets at optical communication band 1550 nm.

In present work, we not only studied its nonlinear absorption characteristics, but also reported the nonlinear refraction response of Ge nanosheets from visible light to near-infrared. The 2D germanium nanosheets exhibit a wide band nonlinear optical response in the visible to NIR range. The broadband nonlinear optical properties of germanium nanosheets especially a large nonlinear absorption coefficient α_NL ≈ −0.87 cm GW⁻¹ and a negative nonlinear refractive index n₂ ≈ −6.30 × 10⁻¹³ cm² W⁻¹ at 1064 nm wavelength have been obtained. The experimental results show the excellent third-order nonlinear optical properties of germanium nanosheets which indicated that germanium is a promising material that can be used in the field of optoelectronics and ultrafast photonics, such as saturable absorbers, optical switch, and optical diodes.

2. Preparation and characterizations of germanium nanosheets

2D germanium nanosheets were fabricated from its bulk format by a facile top-down method, including ultrasound probe and ice-bath sonication. The surface morphology of Ge powder was investigated using scanning electron microscopy (SEM) (Fig. 1(a)). The transmission electron microscopy (TEM) and atomic force microscopy (AFM) were employed to characterize the morphology of the obtained 2D germanium nanosheets. Figure 1(b) shows the TEM images of germanium nanosheets. From the TEM images, the lateral size of germanium nanosheets can be observed, which is about hundreds nanometers. The insertion high-resolution TEM (HRTEM) image exhibits a clear crystalline lattice of spacing 0.35 nm, which is ascribed to the (111) plane of Ge. Scanning transmission electron microscopy (STEM) with energy-dispersive X-ray spectroscopy (EDS) mapping results are shown in Fig. 1(c), where the Ge and O elements were indicated in Fig. 1(c). The morphology of germanium is characterized by atomic force microscope (AFM), as shown in Fig. 1(d). The height of germanium is approximately 4 nm. The Raman spectroscopy and X-ray diffractometry (XRD) were applied to confirm the crystalline structure of germanium nanosheets. The Raman spectroscopy of the Ge powder showed an obvious Raman peak at 296.6 cm⁻¹ (Fig. 1(e)), which corresponds to the in-plane vibration mode (E_2g). This result is consistent with previous reports [25] and proves the crystal structure of Ge. Compare to the Ge powder, there is a 4 cm⁻¹ shift toward a high wavenumber in the in-plane vibration mode (E_2g) of germanium nanosheets. The XRD patterns of 2D germanium nanosheets and Ge standard card (JCDS PDF#04-0545) were showed in Fig. 1(e) . Compared with Ge standard card, there is almost no change in all XRD peaks of germanium nanosheets [25]. In Fig. 1(f), the absorption spectra of germanium exhibits a broad absorption from the UV band to the infrared band, which is characterized by UV-visible spectrometry.

Fig. 1. Characterizations of germanium nanosheets. (a) SEM image of Ge powder. (b) TEM image of germanium nanosheets and its corresponding HRTEM image (inset). (c) STEM image and corresponding EDS mapping images of germanium nanosheets. (d) AFM image of germanium nanosheets and the corresponding film thickness (inset). (e) Raman spectra of germanium (top) and XRD pattern of germanium, JCDS PDF#04-0545 (bottom). (f) Absorbance of germanium solution.

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3. Third-order nonlinear optical characteristics of germanium nanosheets

The Z-scan technology was applied to measure the third-order nonlinear optical properties of germanium nanosheets at different wavelengths. In this test system, the femtosecond pulse laser (operating at 800 nm, repetition rate ∼2 kHz and pulse duration ∼ 35 fs) was used as light source in the experiment. The laser is produced by a mode-locked Ti: sapphire regenerative amplifier system (Spectra-Physics, Spitfire ACE-35F-2KXP, Maitai SP and Empower 30). The optical parametric amplifier (TOPAS, USF-UV2) is used to output femtosecond laser.

As shown in Fig. 2, in the Z-scan measurement system, the laser beam is divided into two beams by the beam splitter, one beam is used as the reference beam, while the other is used to excite the sample in a 1 mm quartz cuvette through a focusing lens with a focal length of 150 mm. Both beams are collected by optical power meter detectors which are controlled by computer. The reference light is collected by the detector 1 to eliminate the influence of laser light intensity variation on the test signal. The excitation light passes through a focusing lens and reach the sample which is placed on the Z-axis movement stage. The detector 2 is used to collect the transmitted light intensity of the sample at different positions. The optical power density near the focal point of the lens will change drastically to excite the nonlinear optical response of the sample. The nonlinear optical properties of the sample will change the luminous flux through the aperture. Therefore, the transmittance of the sample is related to its position on the Z-axis. The size of aperture will affect the experimental test results. When the aperture is completely opened, the nonlinear optical absorption signal was collected by the detector which is called open aperture (OA) Z-scan technology, and when the aperture is in low flux, the nonlinear optical refractive properties were characterized which is called closed aperture (CA) Z-scan technique. In order to ensure the reliability of the experimental data, we conducted Z-scan measurement from low light intensity to high light intensity. After that, the experiment was performed again under low light intensity for comparison.

Fig. 2. The experimental diagram of Z-scan.

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As shown in Fig. 3(a)-(d), the OA Z-scan results of germanium exhibit a typical peak at the beam focus, which indicates that germanium nanosheets have a saturable absorption (SA) response in a broad range (600, 800, 1064 and 1300 nm) . As the sample approached the focus point (Z=0), the normalized transmittances increased. And the normalized transmittance at the focal point is related to the light intensity. When the incident intensity increased, the normalized transmittance also increased. This indicated that when the light intensity increases to a certain value, the absorption of germanium will tend to be saturated.

Fig. 3. Open-aperture Z-scan results of germanium nanosheets with different excitation intensities at (a) 600 nm, (b) 800 nm, (c) 1064 nm, (d) 1300 nm. Wavelength dependence of (e) nonlinear absorption coefficient α_NL (color bar represents different excitation light intensities), (f) imaging part of the third-order nonlinear optical susceptibility Imχ⁽³⁾ and figure of merit (FOM).

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To describe the nonlinear optical properties of germanium quantitatively, the nonlinear propagation equation was applied to fit the Z-scan results. When the absorption coefficient of 2D materials changes with the applied light intensity, the absorption coefficient $\alpha $ can be expressed as $\alpha = {\alpha _0} + {\alpha _{NL}}I$, where ${\alpha _0}$ is the linear absorption coefficient, ${\alpha _{NL}}$ is the nonlinear absorption coefficient, and I is the incident light intensity. The corresponding light intensity loss equation is expressed as $\frac{{dI}}{{dZ}} ={-} ({{\alpha_0} + {\alpha_{NL}}I} )I$. Based on the incident light is Gaussian light, the transmittance can be obtained by the following equation: [28]

(1)$$T(z )= \frac{1}{{\sqrt {\pi {q_0}} }}\mathop \smallint \nolimits_{ - \infty }^\infty \ln [{1 + {q_0}\; exp({ - {x^2}} )} ]dx$$

where ${q_0} = {\alpha _{NL}}{I_0}{L_{eff}}$, ${I_0}$ is the peak intensity at the focus (Z=0), and ${L_{eff}} = ({1 - {e^{ - {\alpha_0}L}}} )/{\alpha _0}$ is the effective thickness of sample, where L is the thickness of the sample. By fitting the experimental date with Eq. (1), the nonlinear absorption coefficient of germanium at different wavelengths can be obtained. The Fig. 3(e) shows the nonlinear absorption coefficient at different wavelengths. The imaginary part of the third-order nonlinear optical susceptibility $Im{\chi ^{(3 )}}$ can obtained from the following formula [15] $Im{\chi ^{(3 )}} = \frac{{{{10}^{ - 7}}c\lambda n_0^2}}{{96{\pi ^2}}}{\alpha _{NL}}$, where c is the velocity of light, $\lambda $ is the excitation wavelength, and ${n_0}$ is the linear refractive index of germanium [29]. The figure of merit (FOM) for the third-order optical nonlinearity is related to $Im{\chi ^{(3 )}}$, which is defined as $FOM = {\mid }Im{\chi ^{(3 )}}/{\alpha _0}{\mid }$. The determined $Im{\chi ^{(3 )}}$ and FOM at different wavelengths are concluded in Fig. 3(f). There was a similar trend between the wavelength dependence of $Im{\chi ^{(3 )}}$ and ${\alpha _{NL}}$.

The linear and nonlinear optical parameters of germanium obtained by OA Z-scan technique are summarized in the Table 1. From the Table 1, we can clearly see that the broadband absorption characteristics of layered germanium and it has a large nonlinear absorption coefficient α_NL ≈ −0.87 cm/GW at 1064 nm wavelength, which is comparable with some NLO materials. These results also indicate that the germanium nanosheet is a superior nonlinear candidate layered material compared with other materials.

Table 1. Nonlinear absorption parameters of various 2D materials.

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The saturated absorption mechanism of 2D germanium is described in Fig. 4. When the excitation light photon energy is larger than the optical transition band gap of 2D germanium, under the action of low-intensity incident light (left picture), the ground state electron located in the valence band absorbs the photon energy and transitions to the conduction band. Then, these photo-generated heat carriers (electrons and holes) quickly cool down, and finally enter an equilibrium state through phonon scattering and the recombination of electron-hole pairs. The hot electrons then formed a thermal Fermi-Dirac distribution (center diagram). These stimulated electro-hole pairs can block the future interband transitions and suppress the absorption of photons. When the light intensity is strong enough, the density of photogenerated carriers increases rapidly and fills the energy state near the edge of the conduction and valence bands. According to the Pauli blocking principle, the transition between bands is blocked and photons pass without loss. At this time, the sample is in a state of absorption saturation (right diagram).

Fig. 4. Saturable absorption mechanism of 2D germanium nanosheets.

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The CA Z-scan technique was used to characterize the nonlinear refractive index (n₂) of germanium nanosheets. The results of CA Z-scan at different wavelengths (600, 800, 1064, and 1300 nm) were shown in Fig. 5(a)-(d). It can be seen from the Fig. 5(a)-(d) that at four different excitation wavelengths, the transmittance is trend of the valley after the peak, which indicates that germanium is a self-defocusing Kerr medium with negative refractive index. The sample can be regarded as a small defocusing lens whose focal length changes with laser intensity.

Fig. 5. Closed-aperture Z-scan results of germanium nanosheets with different excitation intensities at (a) 600 nm, (b) 800 nm, (c) 1064 nm, (d) 1300 nm. Wavelength dependence of (e) nonlinear refractive index (n₂) and linear refractive index (n₀), (f) real part of the third-order nonlinear optical susceptibility Reχ⁽³⁾ (color bar represents different excitation light intensities).

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In the CA Z-scan technique, the normalized transmittance can be fitted by the following formula [37]:

(2)$$T(x )= 1 - \frac{{4\Delta {\varphi _0}x}}{{({1 + {x^2}} )({9 + {x^2}} )}}$$

where $\Delta {\varphi _0} = 2\pi {n_2}{I_0}{L_{eff}}/\lambda $ is the phase change, $x = z/{z_0}$, ${z_0} = \pi \omega _0^2/\lambda $ is the Rayleigh length of the Gaussian beam, ${\omega _0}$ is the beam waist, and $\lambda $ is the excitation wavelength. The large refraction characteristics of germanium nanosheets were obtained by analyzing the CA curves. The nonlinear refractive index ${n_2}$ of germanium at 600, 800, 1064, and 1300 nm were calculated to be -(0.07, 0.18, 6.30, 0.90)×10⁻¹³ cm²/W, respectively. The real part of the third-order nonlinear susceptibility (Reχ⁽³⁾) is related to the ${n_2}$, which can be expressed as [36]:

(3)$$Re{\chi ^{(3 )}} = \frac{{4{\varepsilon _0}cn_0^2}}{3}{n_2}$$

where ${\varepsilon _o}$ is the permittivity of vacuum. The calculated Reχ⁽³⁾ at 600, 800, 1064, and 1300 nm are -(0.61, 1.30, 30.99, and 4.34)×10⁻¹¹ esu. The nonlinear refractive index and the real part of the third-order nonlinear susceptibility of germanium at different wavelengths are shown in Fig. 5(e)-(f). The nonlinear refractive index of 2D materials is a key parameter for studying various applications. We compare the nonlinear refractive index of germanium nanosheets with other 2D materials, such as MoS₂, WS₂, MXene, MOF, as shown in Table 2. It can be seen that the 2D germanium nanosheets have excellent nonlinear optical properties.

Table 2. Nonlinear refraction parameters of various 2D materials.

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4. Conclusion

In summary, we have synthesized 2D germanium nanosheets by liquid phase-exfoliation (LPE) method and studied its third-order nonlinear optical properties by Z-Scan methods. The germanium nanosheets exhibit strong SA and self-defocusing characteristics at wavelengths of 600 nm, 800 nm, 1064 nm and 1300 nm. The results show that the germanium nanosheets have excellent broadband nonlinear optical properties which indicated that germanium is a promising material that can be used in the field of optoelectronics and ultrafast photonics.

Funding

National Natural Science Foundation of China (11904239, 61874141, 61875232); Natural Science Foundation of Hunan Province (2021JJ40709); China Postdoctoral Science Foundation (2021M690169).

Disclosures

The authors declare no competing financial interest.

Data availability

Data underlying the results presented in this paper may be obtained from the authors upon reasonable request.

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34. J. Tang, F. Zhang, F. Zhou, X. Tang, X. Dai, and S. Lu, “Broadband nonlinear optical response in GeSe nanoplates and its applications in all-optical diode,” Nanophotonics 9(7), 2007–2015 (2020). [CrossRef]

35. X. Jiang, L. Zhang, S. Liu, Y. Zhang, Z. He, W. Li, F. Zhang, Y. Shi, W. Lue, Y. Li, Q. Wen, J. Li, J. Feng, S. Ruan, Y.-J. Zeng, X. Zhu, Y. Lu, and H. Zhang, “Ultrathin Metal-Organic Framework: An Emerging Broadband Nonlinear Optical Material for Ultrafast Photonics,” Adv. Opt. Mater. 6(16), 1800561 (2018). [CrossRef]

36. X. Jiang, S. Liu, W. Liang, S. Luo, Z. He, Y. Ge, H. Wang, R. Cao, F. Zhang, Q. Wen, J. Li, Q. Bao, D. Fan, and H. Zhang, “Broadband Nonlinear Photonics in Few-Layer MXene Ti₃C₂T_x(T = F, O, or OH),” Laser Photonics Rev. 12(2), 1700229 (2018). [CrossRef]

37. J. Guo, D. Huang, Y. Zhang, H. Yao, Y. Wang, F. Zhang, R. Wang, Y. Ge, Y. Song, Z. Guo, F. Yang, J. Liu, C. Xing, T. Zhai, D. Fan, and H. Zhang, “2D GeP as a Novel Broadband Nonlinear Optical Material for Ultrafast Photonics,” Laser Photonics Rev. 13(9), 1900123 (2019). [CrossRef]

38. X. Li, K. Hu, B. Lyu, J. Zhang, Y. Wang, P. Wang, S. Xiao, Y. Gao, and J. He, “Enhanced Nonlinear Optical Response of Rectangular MoS₂ and MoS₂/TiO₂ in Dispersion and Film,” J. Phys. Chem. C 120(32), 18243–18248 (2016). [CrossRef]

39. X. Zheng, Y. Zhang, R. Chen, X. A. Cheng, Z. Xu, and T. Jiang, “Z-scan measurement of the nonlinear refractive index of monolayer WS₂,” Opt. Express 23(12), 15616–15623 (2015). [CrossRef]

40. S. Lu, Y. Ge, Z. Sun, Z. Huang, R. Cao, C. Zhao, S. Wen, D. Fan, J. Li, and H. Zhang, “Ultrafast nonlinear absorption and nonlinear refraction in few-layer oxidized black phosphorus,” Photonics Res. 4(6), 286–292 (2016). [CrossRef]

41. S. Kumar, N. Kamaraju, K. S. Vasu, A. Nag, A. K. Sood, and C. N. R. Rao, “Graphene analogue BCN: Femtosecond nonlinear optical susceptibility and hot carrier dynamics,” Chem. Phys. Lett. 499(1-3), 152–157 (2010). [CrossRef]

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References

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Year
Author
Publication

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]
G. Wang, A. A. Baker-Murray, and W. J. Blau, “Saturable Absorption in 2D Nanomaterials and Related Photonic Devices,” Laser Photonics Rev. 13(7), 1800282 (2019).
[Crossref]
B. Guo, Q.-l. Xiao, S.-H. Wang, and H. Zhang, “2D Layered Materials: Synthesis, Nonlinear Optical Properties, and Device Applications,” Laser Photonics Rev. 13(12), 1800327 (2019).
[Crossref]
L. Wu, Y. Dong, J. Zhao, D. Ma, W. Huang, Y. Zhang, Y. Wang, X. Jiang, Y. Xiang, J. Li, Y. Feng, J. Xu, and H. Zhang, “Kerr Nonlinearity in 2D Graphdiyne for Passive Photonic Diodes,” Adv. Mater. 31(14), 1807981 (2019).
[Crossref]
L. Gao, W. Bao, A. Kuklin, V. kuklin, S. Mei, H. Zhang, and H. Agren, “Hetero-MXenes: Theory, Synthesis, and Emerging Applications,” Adv. Mater. 33(10), 2004129 (2021).
[Crossref]
W. Chen, F. Zhang, C. Wang, M. Jia, X. Zhao, Z. Liu, Y. Ge, Y. Zhang, and H. Zhang, “Nonlinear Photonics Using Low-Dimensional Metal-Halide Perovskites: Recent Advances and Future Challenges,” Adv. Mater. 33(11), 2004446 (2021).
[Crossref]
J. He, L. Tao, H. Zhang, B. Zhou, and J. Li, “Emerging 2D materials beyond graphene for ultrashort pulse generation in fiber lasers,” Nanoscale 11(6), 2577–2593 (2019).
[Crossref]
Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[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]
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]
Y. Wang, S. Liu, J. Yuan, P. Wang, J. Chen, J. Li, S. Xiao, Q. Bao, Y. Gao, and J. He, “Ultra-broadband Nonlinear Saturable Absorption for Two-dimensional Bi2TexSe3-x Nanosheets,” Sci. Rep. 6(1), 33070 (2016).
[Crossref]
K. Wang, B. M. Szydlowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast Nonlinear Excitation Dynamics of Black Phosphorus Nanosheets from Visible to Mid-Infrared,” ACS Nano 10(7), 6923–6932 (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]
H. Zhang, S. B. Lu, J. Zheng, J. Du, S. C. Wen, D. Y. Tang, and K. P. Loh, “Molybdenum disulfide (MoS2) as a broadband saturable absorber for ultra-fast photonics,” Opt. Express 22(6), 7249–7260 (2014).
[Crossref]
K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast Saturable Absorption of Two-Dimensional MoS2 Nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref]
Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang, X.-F. Yu, and P. K. Chu, “From Black Phosphorus to Phosphorene: Basic Solvent Exfoliation, Evolution of Raman Scattering, and Applications to Ultrafast Photonics,” Adv. Funct. Mater. 25(45), 6996–7002 (2015).
[Crossref]
Y. Dong, S. Chertopalov, K. Maleski, B. Anasori, L. Hu, S. Bhattacharya, A. M. Rao, Y. Gogotsi, V. N. Mochalin, and R. Podila, “Saturable Absorption in 2D Ti3C2 MXene Thin Films for Passive Photonic Diodes,” Adv. Mater. 30(10), 1705714 (2018).
[Crossref]
Y. Wang, Y. Wang, K. Chen, K. Qi, T. Xue, H. Zhang, J. He, and S. Xiao, “Niobium Carbide MXenes with Broad-Band Nonlinear Optical Response and Ultrafast Carrier Dynamics,” ACS Nano 14(8), 10492–10502 (2020).
[Crossref]
G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2(5), 17010 (2017).
[Crossref]
Z. Dai, G. Hu, Q. Ou, L. Zhang, F. Xia, F. J. Garcia-Vidal, C.-W. Qiu, and Q. Bao, “Artificial Metaphotonics Born Naturally in Two Dimensions,” Chem. Rev. 120(13), 6197–6246 (2020).
[Crossref]
Y. Wang, Z.-L. Deng, D. Hu, J. Yuan, Q. Ou, F. Qin, Y. Zhang, X. Ouyang, Y. Li, B. Peng, Y. Cao, B. Guan, Y. Zhang, J. He, C.-W. Qiu, Q. Bao, and X. Li, “Atomically Thin Noble Metal Dichalcogenides for Phase-Regulated Meta-optics,” Nano Lett. 20(11), 7811–7818 (2020).
[Crossref]
S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, and S. Ciraci, “Two- and One-Dimensional Honeycomb Structures of Silicon and Germanium,” Phys. Rev. Lett. 102(23), 236804 (2009).
[Crossref]
W. Sun, G. Zhong, C. Kuebel, A. A. Jelle, C. Qian, L. Wang, M. Ebrahimi, L. M. Reyes, A. S. Helmy, and G. A. Ozin, “Size-Tunable Photothermal Germanium Nanocrystals,” Angew. Chem. Int. Ed. 56(22), 6329–6334 (2017).
[Crossref]
B. N. Madhushankar, A. Kaverzin, T. Giousis, G. Potsi, D. Gournis, P. Rudolf, G. R. Blake, C. H. van der Wal, and B. J. van Wees, “Electronic properties of germanane field-effect transistors,” 2D Mater. 4(2), 021009 (2017).
[Crossref]
J. Ouyang, C. Feng, X. Ji, L. Li, H. K. Gutti, N. Y. Kim, D. Artzi, A. Xie, N. Kong, Y.-N. Liu, G. J. Tearney, X. Sui, W. Tao, and O. C. Farokhzad, “2D Monoelemental Germanene Quantum Dots:Synthesis as Robust Photothermal Agents for Photonic Cancer Nanomedicine,” Angew. Chem. Int. Ed. 58(38), 13405–13410 (2019).
[Crossref]
C. Li, J. Kang, J. Xie, Y. Wang, L. Zhou, H. Hu, X. Li, J. He, B. Wang, and H. Zhang, “Two-dimensional monoelemental germanene nanosheets: facile preparation and optoelectronic applications,” J. Mater. Chem. C 8(46), 16318–16325 (2020).
[Crossref]
H. Mu, Y. Liu, S. R. Bongu, X. Bao, L. Li, S. Xiao, J. Zhuang, C. Liu, Y. Huang, Y. Dong, K. Helmerson, J. Wang, G. Liu, Y. Du, and Q. Bao, “Germanium Nanosheets with Dirac Characteristics as a Saturable Absorber for Ultrafast Pulse Generation,” Adv. Mater. 33(32), 2101042 (2021).
[Crossref]
J. He, Y. Qu, H. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13(23), 9235–9247 (2005).
[Crossref]
D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983).
[Crossref]
J. Huang, N. Dong, S. Zhang, Z. Sun, W. Zhang, and J. Wang, “Nonlinear Absorption Induced Transparency and Optical Limiting of Black Phosphorus Nanosheets,” ACS Photonics 4(12), 3063–3070 (2017).
[Crossref]
Y. Feng, N. Dong, G. Wang, Y. Li, S. Zhang, K. Wang, L. Zhang, W. J. Blau, and J. Wang, “Saturable absorption behavior of free-standing graphene polymer composite films over broad wavelength and time ranges,” Opt. Express 23(1), 559–569 (2015).
[Crossref]
H. Elim, J. Yang, J. Lee, J. Mi, and W. Ji, “Observation of saturable and reverse-saturable absorption at longitudinal surface plasmon resonance in gold nanorods,” Appl. Phys. Lett. 88(8), 083107 (2006).
[Crossref]
K. Wang, X. Zhang, I. M. Kislyakov, N. Dong, S. Zhang, G. Wang, J. Fan, X. Zou, J. Du, Y. Leng, Q. Zhao, K. Wu, J. Chen, S. M. Baesman, K.-S. Liao, S. Maharjan, H. Zhang, L. Zhang, S. A. Curran, R. S. Oremland, W. J. Blau, and J. Wang, “Bacterially synthesized tellurium nanostructures for broadband ultrafast nonlinear optical applications,” Nat. Commun. 10(1), 3985 (2019).
[Crossref]
J. Tang, F. Zhang, F. Zhou, X. Tang, X. Dai, and S. Lu, “Broadband nonlinear optical response in GeSe nanoplates and its applications in all-optical diode,” Nanophotonics 9(7), 2007–2015 (2020).
[Crossref]
X. Jiang, L. Zhang, S. Liu, Y. Zhang, Z. He, W. Li, F. Zhang, Y. Shi, W. Lue, Y. Li, Q. Wen, J. Li, J. Feng, S. Ruan, Y.-J. Zeng, X. Zhu, Y. Lu, and H. Zhang, “Ultrathin Metal-Organic Framework: An Emerging Broadband Nonlinear Optical Material for Ultrafast Photonics,” Adv. Opt. Mater. 6(16), 1800561 (2018).
[Crossref]
X. Jiang, S. Liu, W. Liang, S. Luo, Z. He, Y. Ge, H. Wang, R. Cao, F. Zhang, Q. Wen, J. Li, Q. Bao, D. Fan, and H. Zhang, “Broadband Nonlinear Photonics in Few-Layer MXene Ti3C2Tx(T = F, O, or OH),” Laser Photonics Rev. 12(2), 1700229 (2018).
[Crossref]
J. Guo, D. Huang, Y. Zhang, H. Yao, Y. Wang, F. Zhang, R. Wang, Y. Ge, Y. Song, Z. Guo, F. Yang, J. Liu, C. Xing, T. Zhai, D. Fan, and H. Zhang, “2D GeP as a Novel Broadband Nonlinear Optical Material for Ultrafast Photonics,” Laser Photonics Rev. 13(9), 1900123 (2019).
[Crossref]
X. Li, K. Hu, B. Lyu, J. Zhang, Y. Wang, P. Wang, S. Xiao, Y. Gao, and J. He, “Enhanced Nonlinear Optical Response of Rectangular MoS2 and MoS2/TiO2 in Dispersion and Film,” J. Phys. Chem. C 120(32), 18243–18248 (2016).
[Crossref]
X. Zheng, Y. Zhang, R. Chen, X. A. Cheng, Z. Xu, and T. Jiang, “Z-scan measurement of the nonlinear refractive index of monolayer WS2,” Opt. Express 23(12), 15616–15623 (2015).
[Crossref]
S. Lu, Y. Ge, Z. Sun, Z. Huang, R. Cao, C. Zhao, S. Wen, D. Fan, J. Li, and H. Zhang, “Ultrafast nonlinear absorption and nonlinear refraction in few-layer oxidized black phosphorus,” Photonics Res. 4(6), 286–292 (2016).
[Crossref]
S. Kumar, N. Kamaraju, K. S. Vasu, A. Nag, A. K. Sood, and C. N. R. Rao, “Graphene analogue BCN: Femtosecond nonlinear optical susceptibility and hot carrier dynamics,” Chem. Phys. Lett. 499(1-3), 152–157 (2010).
[Crossref]

2021 (3)

L. Gao, W. Bao, A. Kuklin, V. kuklin, S. Mei, H. Zhang, and H. Agren, “Hetero-MXenes: Theory, Synthesis, and Emerging Applications,” Adv. Mater. 33(10), 2004129 (2021).
[Crossref]

W. Chen, F. Zhang, C. Wang, M. Jia, X. Zhao, Z. Liu, Y. Ge, Y. Zhang, and H. Zhang, “Nonlinear Photonics Using Low-Dimensional Metal-Halide Perovskites: Recent Advances and Future Challenges,” Adv. Mater. 33(11), 2004446 (2021).
[Crossref]

H. Mu, Y. Liu, S. R. Bongu, X. Bao, L. Li, S. Xiao, J. Zhuang, C. Liu, Y. Huang, Y. Dong, K. Helmerson, J. Wang, G. Liu, Y. Du, and Q. Bao, “Germanium Nanosheets with Dirac Characteristics as a Saturable Absorber for Ultrafast Pulse Generation,” Adv. Mater. 33(32), 2101042 (2021).
[Crossref]

2020 (5)

Z. Dai, G. Hu, Q. Ou, L. Zhang, F. Xia, F. J. Garcia-Vidal, C.-W. Qiu, and Q. Bao, “Artificial Metaphotonics Born Naturally in Two Dimensions,” Chem. Rev. 120(13), 6197–6246 (2020).
[Crossref]

Y. Wang, Z.-L. Deng, D. Hu, J. Yuan, Q. Ou, F. Qin, Y. Zhang, X. Ouyang, Y. Li, B. Peng, Y. Cao, B. Guan, Y. Zhang, J. He, C.-W. Qiu, Q. Bao, and X. Li, “Atomically Thin Noble Metal Dichalcogenides for Phase-Regulated Meta-optics,” Nano Lett. 20(11), 7811–7818 (2020).
[Crossref]

C. Li, J. Kang, J. Xie, Y. Wang, L. Zhou, H. Hu, X. Li, J. He, B. Wang, and H. Zhang, “Two-dimensional monoelemental germanene nanosheets: facile preparation and optoelectronic applications,” J. Mater. Chem. C 8(46), 16318–16325 (2020).
[Crossref]

J. Tang, F. Zhang, F. Zhou, X. Tang, X. Dai, and S. Lu, “Broadband nonlinear optical response in GeSe nanoplates and its applications in all-optical diode,” Nanophotonics 9(7), 2007–2015 (2020).
[Crossref]

Y. Wang, Y. Wang, K. Chen, K. Qi, T. Xue, H. Zhang, J. He, and S. Xiao, “Niobium Carbide MXenes with Broad-Band Nonlinear Optical Response and Ultrafast Carrier Dynamics,” ACS Nano 14(8), 10492–10502 (2020).
[Crossref]

2019 (7)

J. He, L. Tao, H. Zhang, B. Zhou, and J. Li, “Emerging 2D materials beyond graphene for ultrashort pulse generation in fiber lasers,” Nanoscale 11(6), 2577–2593 (2019).
[Crossref]

G. Wang, A. A. Baker-Murray, and W. J. Blau, “Saturable Absorption in 2D Nanomaterials and Related Photonic Devices,” Laser Photonics Rev. 13(7), 1800282 (2019).
[Crossref]

B. Guo, Q.-l. Xiao, S.-H. Wang, and H. Zhang, “2D Layered Materials: Synthesis, Nonlinear Optical Properties, and Device Applications,” Laser Photonics Rev. 13(12), 1800327 (2019).
[Crossref]

L. Wu, Y. Dong, J. Zhao, D. Ma, W. Huang, Y. Zhang, Y. Wang, X. Jiang, Y. Xiang, J. Li, Y. Feng, J. Xu, and H. Zhang, “Kerr Nonlinearity in 2D Graphdiyne for Passive Photonic Diodes,” Adv. Mater. 31(14), 1807981 (2019).
[Crossref]

J. Guo, D. Huang, Y. Zhang, H. Yao, Y. Wang, F. Zhang, R. Wang, Y. Ge, Y. Song, Z. Guo, F. Yang, J. Liu, C. Xing, T. Zhai, D. Fan, and H. Zhang, “2D GeP as a Novel Broadband Nonlinear Optical Material for Ultrafast Photonics,” Laser Photonics Rev. 13(9), 1900123 (2019).
[Crossref]

K. Wang, X. Zhang, I. M. Kislyakov, N. Dong, S. Zhang, G. Wang, J. Fan, X. Zou, J. Du, Y. Leng, Q. Zhao, K. Wu, J. Chen, S. M. Baesman, K.-S. Liao, S. Maharjan, H. Zhang, L. Zhang, S. A. Curran, R. S. Oremland, W. J. Blau, and J. Wang, “Bacterially synthesized tellurium nanostructures for broadband ultrafast nonlinear optical applications,” Nat. Commun. 10(1), 3985 (2019).
[Crossref]

J. Ouyang, C. Feng, X. Ji, L. Li, H. K. Gutti, N. Y. Kim, D. Artzi, A. Xie, N. Kong, Y.-N. Liu, G. J. Tearney, X. Sui, W. Tao, and O. C. Farokhzad, “2D Monoelemental Germanene Quantum Dots:Synthesis as Robust Photothermal Agents for Photonic Cancer Nanomedicine,” Angew. Chem. Int. Ed. 58(38), 13405–13410 (2019).
[Crossref]

2018 (3)

Y. Dong, S. Chertopalov, K. Maleski, B. Anasori, L. Hu, S. Bhattacharya, A. M. Rao, Y. Gogotsi, V. N. Mochalin, and R. Podila, “Saturable Absorption in 2D Ti3C2 MXene Thin Films for Passive Photonic Diodes,” Adv. Mater. 30(10), 1705714 (2018).
[Crossref]

X. Jiang, L. Zhang, S. Liu, Y. Zhang, Z. He, W. Li, F. Zhang, Y. Shi, W. Lue, Y. Li, Q. Wen, J. Li, J. Feng, S. Ruan, Y.-J. Zeng, X. Zhu, Y. Lu, and H. Zhang, “Ultrathin Metal-Organic Framework: An Emerging Broadband Nonlinear Optical Material for Ultrafast Photonics,” Adv. Opt. Mater. 6(16), 1800561 (2018).
[Crossref]

X. Jiang, S. Liu, W. Liang, S. Luo, Z. He, Y. Ge, H. Wang, R. Cao, F. Zhang, Q. Wen, J. Li, Q. Bao, D. Fan, and H. Zhang, “Broadband Nonlinear Photonics in Few-Layer MXene Ti3C2Tx(T = F, O, or OH),” Laser Photonics Rev. 12(2), 1700229 (2018).
[Crossref]

2017 (4)

J. Huang, N. Dong, S. Zhang, Z. Sun, W. Zhang, and J. Wang, “Nonlinear Absorption Induced Transparency and Optical Limiting of Black Phosphorus Nanosheets,” ACS Photonics 4(12), 3063–3070 (2017).
[Crossref]

W. Sun, G. Zhong, C. Kuebel, A. A. Jelle, C. Qian, L. Wang, M. Ebrahimi, L. M. Reyes, A. S. Helmy, and G. A. Ozin, “Size-Tunable Photothermal Germanium Nanocrystals,” Angew. Chem. Int. Ed. 56(22), 6329–6334 (2017).
[Crossref]

B. N. Madhushankar, A. Kaverzin, T. Giousis, G. Potsi, D. Gournis, P. Rudolf, G. R. Blake, C. H. van der Wal, and B. J. van Wees, “Electronic properties of germanane field-effect transistors,” 2D Mater. 4(2), 021009 (2017).
[Crossref]

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2(5), 17010 (2017).
[Crossref]

2016 (6)

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

Y. Wang, S. Liu, J. Yuan, P. Wang, J. Chen, J. Li, S. Xiao, Q. Bao, Y. Gao, and J. He, “Ultra-broadband Nonlinear Saturable Absorption for Two-dimensional Bi2TexSe3-x Nanosheets,” Sci. Rep. 6(1), 33070 (2016).
[Crossref]

K. Wang, B. M. Szydlowska, G. Wang, X. Zhang, J. J. Wang, J. J. Magan, L. Zhang, J. N. Coleman, J. Wang, and W. J. Blau, “Ultrafast Nonlinear Excitation Dynamics of Black Phosphorus Nanosheets from Visible to Mid-Infrared,” ACS Nano 10(7), 6923–6932 (2016).
[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]

X. Li, K. Hu, B. Lyu, J. Zhang, Y. Wang, P. Wang, S. Xiao, Y. Gao, and J. He, “Enhanced Nonlinear Optical Response of Rectangular MoS2 and MoS2/TiO2 in Dispersion and Film,” J. Phys. Chem. C 120(32), 18243–18248 (2016).
[Crossref]

S. Lu, Y. Ge, Z. Sun, Z. Huang, R. Cao, C. Zhao, S. Wen, D. Fan, J. Li, and H. Zhang, “Ultrafast nonlinear absorption and nonlinear refraction in few-layer oxidized black phosphorus,” Photonics Res. 4(6), 286–292 (2016).
[Crossref]

2015 (4)

X. Zheng, Y. Zhang, R. Chen, X. A. Cheng, Z. Xu, and T. Jiang, “Z-scan measurement of the nonlinear refractive index of monolayer WS2,” Opt. Express 23(12), 15616–15623 (2015).
[Crossref]

Y. Feng, N. Dong, G. Wang, Y. Li, S. Zhang, K. Wang, L. Zhang, W. J. Blau, and J. Wang, “Saturable absorption behavior of free-standing graphene polymer composite films over broad wavelength and time ranges,” Opt. Express 23(1), 559–569 (2015).
[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]

Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang, X.-F. Yu, and P. K. Chu, “From Black Phosphorus to Phosphorene: Basic Solvent Exfoliation, Evolution of Raman Scattering, and Applications to Ultrafast Photonics,” Adv. Funct. Mater. 25(45), 6996–7002 (2015).
[Crossref]

2014 (1)

H. Zhang, S. B. Lu, J. Zheng, J. Du, S. C. Wen, D. Y. Tang, and K. P. Loh, “Molybdenum disulfide (MoS2) as a broadband saturable absorber for ultra-fast photonics,” Opt. Express 22(6), 7249–7260 (2014).
[Crossref]

2013 (2)

K. Wang, J. Wang, J. Fan, M. Lotya, A. O’Neill, D. Fox, Y. Feng, X. Zhang, B. Jiang, Q. Zhao, H. Zhang, J. N. Coleman, L. Zhang, and W. J. Blau, “Ultrafast Saturable Absorption of Two-Dimensional MoS2 Nanosheets,” ACS Nano 7(10), 9260–9267 (2013).
[Crossref]

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]

2010 (1)

S. Kumar, N. Kamaraju, K. S. Vasu, A. Nag, A. K. Sood, and C. N. R. Rao, “Graphene analogue BCN: Femtosecond nonlinear optical susceptibility and hot carrier dynamics,” Chem. Phys. Lett. 499(1-3), 152–157 (2010).
[Crossref]

2009 (2)

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-Layer Graphene as a Saturable Absorber for Ultrafast Pulsed Lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[Crossref]

S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, and S. Ciraci, “Two- and One-Dimensional Honeycomb Structures of Silicon and Germanium,” Phys. Rev. Lett. 102(23), 236804 (2009).
[Crossref]

2006 (1)

H. Elim, J. Yang, J. Lee, J. Mi, and W. Ji, “Observation of saturable and reverse-saturable absorption at longitudinal surface plasmon resonance in gold nanorods,” Appl. Phys. Lett. 88(8), 083107 (2006).
[Crossref]

2005 (1)

J. He, Y. Qu, H. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13(23), 9235–9247 (2005).
[Crossref]

1983 (1)

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983).
[Crossref]

Agren, H.

L. Gao, W. Bao, A. Kuklin, V. kuklin, S. Mei, H. Zhang, and H. Agren, “Hetero-MXenes: Theory, Synthesis, and Emerging Applications,” Adv. Mater. 33(10), 2004129 (2021).
[Crossref]

Akturk, E.

S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, and S. Ciraci, “Two- and One-Dimensional Honeycomb Structures of Silicon and Germanium,” Phys. Rev. Lett. 102(23), 236804 (2009).
[Crossref]

Anasori, B.

Artzi, D.

Aspnes, D. E.

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983).
[Crossref]

Baesman, S. M.

Baker-Murray, A. A.

G. Wang, A. A. Baker-Murray, and W. J. Blau, “Saturable Absorption in 2D Nanomaterials and Related Photonic Devices,” Laser Photonics Rev. 13(7), 1800282 (2019).
[Crossref]

Bao, Q.

Z. Dai, G. Hu, Q. Ou, L. Zhang, F. Xia, F. J. Garcia-Vidal, C.-W. Qiu, and Q. Bao, “Artificial Metaphotonics Born Naturally in Two Dimensions,” Chem. Rev. 120(13), 6197–6246 (2020).
[Crossref]

Bao, W.

L. Gao, W. Bao, A. Kuklin, V. kuklin, S. Mei, H. Zhang, and H. Agren, “Hetero-MXenes: Theory, Synthesis, and Emerging Applications,” Adv. Mater. 33(10), 2004129 (2021).
[Crossref]

Bao, X.

Bhattacharya, S.

Blake, G. R.

Blau, W. J.

G. Wang, A. A. Baker-Murray, and W. J. Blau, “Saturable Absorption in 2D Nanomaterials and Related Photonic Devices,” Laser Photonics Rev. 13(7), 1800282 (2019).
[Crossref]

Bongu, S. R.

Cahangirov, S.

S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, and S. Ciraci, “Two- and One-Dimensional Honeycomb Structures of Silicon and Germanium,” Phys. Rev. Lett. 102(23), 236804 (2009).
[Crossref]

Cao, R.

Cao, Y.

Chen, J.

Chen, K.

Chen, R.

X. Zheng, Y. Zhang, R. Chen, X. A. Cheng, Z. Xu, and T. Jiang, “Z-scan measurement of the nonlinear refractive index of monolayer WS2,” Opt. Express 23(12), 15616–15623 (2015).
[Crossref]

Chen, S.

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]

Chen, W.

Chen, Y.

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]

Cheng, X. A.

X. Zheng, Y. Zhang, R. Chen, X. A. Cheng, Z. Xu, and T. Jiang, “Z-scan measurement of the nonlinear refractive index of monolayer WS2,” Opt. Express 23(12), 15616–15623 (2015).
[Crossref]

Chertopalov, S.

Chu, P. K.

Ciraci, S.

S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, and S. Ciraci, “Two- and One-Dimensional Honeycomb Structures of Silicon and Germanium,” Phys. Rev. Lett. 102(23), 236804 (2009).
[Crossref]

Coleman, J. N.

Curran, S. A.

Dai, X.

Dai, Z.

Z. Dai, G. Hu, Q. Ou, L. Zhang, F. Xia, F. J. Garcia-Vidal, C.-W. Qiu, and Q. Bao, “Artificial Metaphotonics Born Naturally in Two Dimensions,” Chem. Rev. 120(13), 6197–6246 (2020).
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Dong, Y.

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Feng, C.

Feng, J.

Feng, Y.

Fox, D.

Gao, L.

L. Gao, W. Bao, A. Kuklin, V. kuklin, S. Mei, H. Zhang, and H. Agren, “Hetero-MXenes: Theory, Synthesis, and Emerging Applications,” Adv. Mater. 33(10), 2004129 (2021).
[Crossref]

Gao, Y.

Garcia-Vidal, F. J.

Z. Dai, G. Hu, Q. Ou, L. Zhang, F. Xia, F. J. Garcia-Vidal, C.-W. Qiu, and Q. Bao, “Artificial Metaphotonics Born Naturally in Two Dimensions,” Chem. Rev. 120(13), 6197–6246 (2020).
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B. Guo, Q.-l. Xiao, S.-H. Wang, and H. Zhang, “2D Layered Materials: Synthesis, Nonlinear Optical Properties, and Device Applications,” Laser Photonics Rev. 13(12), 1800327 (2019).
[Crossref]

Guo, J.

Guo, Z.

Gutti, H. K.

He, J.

J. He, L. Tao, H. Zhang, B. Zhou, and J. Li, “Emerging 2D materials beyond graphene for ultrashort pulse generation in fiber lasers,” Nanoscale 11(6), 2577–2593 (2019).
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J. He, Y. Qu, H. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13(23), 9235–9247 (2005).
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He, Z.

Helmerson, K.

Helmy, A. S.

Hu, D.

Hu, G.

Z. Dai, G. Hu, Q. Ou, L. Zhang, F. Xia, F. J. Garcia-Vidal, C.-W. Qiu, and Q. Bao, “Artificial Metaphotonics Born Naturally in Two Dimensions,” Chem. Rev. 120(13), 6197–6246 (2020).
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Hu, K.

Hu, L.

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Huang, G.

Huang, J.

Huang, W.

Huang, Y.

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J. He, Y. Qu, H. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13(23), 9235–9247 (2005).
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Jia, M.

Jiang, B.

Jiang, T.

X. Zheng, Y. Zhang, R. Chen, X. A. Cheng, Z. Xu, and T. Jiang, “Z-scan measurement of the nonlinear refractive index of monolayer WS2,” Opt. Express 23(12), 15616–15623 (2015).
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Kang, J.

Kaverzin, A.

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Kuklin, A.

L. Gao, W. Bao, A. Kuklin, V. kuklin, S. Mei, H. Zhang, and H. Agren, “Hetero-MXenes: Theory, Synthesis, and Emerging Applications,” Adv. Mater. 33(10), 2004129 (2021).
[Crossref]

kuklin, V.

L. Gao, W. Bao, A. Kuklin, V. kuklin, S. Mei, H. Zhang, and H. Agren, “Hetero-MXenes: Theory, Synthesis, and Emerging Applications,” Adv. Mater. 33(10), 2004129 (2021).
[Crossref]

Kumar, S.

Lee, J.

Leng, Y.

Li, C.

Li, G.

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2(5), 17010 (2017).
[Crossref]

Li, H.

J. He, Y. Qu, H. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13(23), 9235–9247 (2005).
[Crossref]

Li, J.

J. He, L. Tao, H. Zhang, B. Zhou, and J. Li, “Emerging 2D materials beyond graphene for ultrashort pulse generation in fiber lasers,” Nanoscale 11(6), 2577–2593 (2019).
[Crossref]

Li, L.

Li, W.

Li, X.

Li, Y.

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]

Liang, W.

Liao, K.-S.

Lin, S.

Liu, C.

Liu, G.

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Loh, K. P.

Lotya, M.

Lu, S.

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]

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Lu, Y.

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Luo, S.

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Martinez, A.

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

Mei, S.

L. Gao, W. Bao, A. Kuklin, V. kuklin, S. Mei, H. Zhang, and H. Agren, “Hetero-MXenes: Theory, Synthesis, and Emerging Applications,” Adv. Mater. 33(10), 2004129 (2021).
[Crossref]

Mi, J.

J. He, Y. Qu, H. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13(23), 9235–9247 (2005).
[Crossref]

Mochalin, V. N.

Mu, H.

Nag, A.

Ni, Z.

O’Neill, A.

Oremland, R. S.

Ou, Q.

Z. Dai, G. Hu, Q. Ou, L. Zhang, F. Xia, F. J. Garcia-Vidal, C.-W. Qiu, and Q. Bao, “Artificial Metaphotonics Born Naturally in Two Dimensions,” Chem. Rev. 120(13), 6197–6246 (2020).
[Crossref]

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Ouyang, X.

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Peng, B.

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Qi, K.

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Qiu, C.-W.

Z. Dai, G. Hu, Q. Ou, L. Zhang, F. Xia, F. J. Garcia-Vidal, C.-W. Qiu, and Q. Bao, “Artificial Metaphotonics Born Naturally in Two Dimensions,” Chem. Rev. 120(13), 6197–6246 (2020).
[Crossref]

Qu, Y.

J. He, Y. Qu, H. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13(23), 9235–9247 (2005).
[Crossref]

Rao, A. M.

Rao, C. N. R.

Reyes, L. M.

Ruan, S.

Rudolf, P.

Sahin, H.

S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, and S. Ciraci, “Two- and One-Dimensional Honeycomb Structures of Silicon and Germanium,” Phys. Rev. Lett. 102(23), 236804 (2009).
[Crossref]

Shao, J.

Shen, Z. X.

Shi, Y.

Song, Y.

Sood, A. K.

Studna, A. A.

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983).
[Crossref]

Sui, X.

Sun, W.

Sun, Z.

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

Szydlowska, B. M.

Tang, D.

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]

Tang, D. Y.

Tang, J.

Tang, S.

Tang, X.

Tao, L.

J. He, L. Tao, H. Zhang, B. Zhou, and J. Li, “Emerging 2D materials beyond graphene for ultrashort pulse generation in fiber lasers,” Nanoscale 11(6), 2577–2593 (2019).
[Crossref]

Tao, W.

Tearney, G. J.

Topsakal, M.

S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, and S. Ciraci, “Two- and One-Dimensional Honeycomb Structures of Silicon and Germanium,” Phys. Rev. Lett. 102(23), 236804 (2009).
[Crossref]

van der Wal, C. H.

van Wees, B. J.

Vasu, K. S.

Wang, B.

Wang, C.

Wang, F.

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

Wang, G.

G. Wang, A. A. Baker-Murray, and W. J. Blau, “Saturable Absorption in 2D Nanomaterials and Related Photonic Devices,” Laser Photonics Rev. 13(7), 1800282 (2019).
[Crossref]

Wang, H.

Wang, J.

Wang, J. J.

Wang, K.

Wang, L.

Wang, P.

Wang, R.

Wang, S.-H.

B. Guo, Q.-l. Xiao, S.-H. Wang, and H. Zhang, “2D Layered Materials: Synthesis, Nonlinear Optical Properties, and Device Applications,” Laser Photonics Rev. 13(12), 1800327 (2019).
[Crossref]

Wang, Y.

Wang, Z.

Wen, Q.

Wen, S.

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]

Wen, S. C.

Wu, K.

Wu, L.

Xia, F.

Z. Dai, G. Hu, Q. Ou, L. Zhang, F. Xia, F. J. Garcia-Vidal, C.-W. Qiu, and Q. Bao, “Artificial Metaphotonics Born Naturally in Two Dimensions,” Chem. Rev. 120(13), 6197–6246 (2020).
[Crossref]

Xiang, Y.

Xiao, Q.-l.

B. Guo, Q.-l. Xiao, S.-H. Wang, and H. Zhang, “2D Layered Materials: Synthesis, Nonlinear Optical Properties, and Device Applications,” Laser Photonics Rev. 13(12), 1800327 (2019).
[Crossref]

Xiao, S.

Xie, A.

Xie, H.

Xie, J.

Xing, C.

Xu, J.

Xu, Z.

X. Zheng, Y. Zhang, R. Chen, X. A. Cheng, Z. Xu, and T. Jiang, “Z-scan measurement of the nonlinear refractive index of monolayer WS2,” Opt. Express 23(12), 15616–15623 (2015).
[Crossref]

Xue, T.

Yan, Y.

Yang, F.

Yang, J.

Yao, H.

Yu, X.-F.

Yuan, J.

Zeng, Y.-J.

Zentgraf, T.

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2(5), 17010 (2017).
[Crossref]

Zhai, T.

Zhang, F.

Zhang, H.

L. Gao, W. Bao, A. Kuklin, V. kuklin, S. Mei, H. Zhang, and H. Agren, “Hetero-MXenes: Theory, Synthesis, and Emerging Applications,” Adv. Mater. 33(10), 2004129 (2021).
[Crossref]

J. He, L. Tao, H. Zhang, B. Zhou, and J. Li, “Emerging 2D materials beyond graphene for ultrashort pulse generation in fiber lasers,” Nanoscale 11(6), 2577–2593 (2019).
[Crossref]

B. Guo, Q.-l. Xiao, S.-H. Wang, and H. Zhang, “2D Layered Materials: Synthesis, Nonlinear Optical Properties, and Device Applications,” Laser Photonics Rev. 13(12), 1800327 (2019).
[Crossref]

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]

Zhang, J.

Zhang, L.

Z. Dai, G. Hu, Q. Ou, L. Zhang, F. Xia, F. J. Garcia-Vidal, C.-W. Qiu, and Q. Bao, “Artificial Metaphotonics Born Naturally in Two Dimensions,” Chem. Rev. 120(13), 6197–6246 (2020).
[Crossref]

Zhang, S.

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2(5), 17010 (2017).
[Crossref]

Zhang, W.

Zhang, X.

Zhang, Y.

X. Zheng, Y. Zhang, R. Chen, X. A. Cheng, Z. Xu, and T. Jiang, “Z-scan measurement of the nonlinear refractive index of monolayer WS2,” Opt. Express 23(12), 15616–15623 (2015).
[Crossref]

Zhao, C.

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]

Zhao, J.

Zhao, Q.

Zhao, X.

Zheng, J.

Zheng, X.

X. Zheng, Y. Zhang, R. Chen, X. A. Cheng, Z. Xu, and T. Jiang, “Z-scan measurement of the nonlinear refractive index of monolayer WS2,” Opt. Express 23(12), 15616–15623 (2015).
[Crossref]

Zhong, G.

Zhou, B.

J. He, L. Tao, H. Zhang, B. Zhou, and J. Li, “Emerging 2D materials beyond graphene for ultrashort pulse generation in fiber lasers,” Nanoscale 11(6), 2577–2593 (2019).
[Crossref]

Zhou, F.

Zhou, L.

Zhu, X.

Zhuang, J.

Zou, X.

Zou, Y.

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]

2D Mater. (1)

ACS Nano (3)

ACS Photonics (1)

Adv. Funct. Mater. (2)

Adv. Mater. (5)

L. Gao, W. Bao, A. Kuklin, V. kuklin, S. Mei, H. Zhang, and H. Agren, “Hetero-MXenes: Theory, Synthesis, and Emerging Applications,” Adv. Mater. 33(10), 2004129 (2021).
[Crossref]

Adv. Opt. Mater. (1)

Angew. Chem. Int. Ed. (2)

Appl. Phys. Lett. (3)

Chem. Phys. Lett. (1)

Chem. Rev. (1)

Z. Dai, G. Hu, Q. Ou, L. Zhang, F. Xia, F. J. Garcia-Vidal, C.-W. Qiu, and Q. Bao, “Artificial Metaphotonics Born Naturally in Two Dimensions,” Chem. Rev. 120(13), 6197–6246 (2020).
[Crossref]

J. Mater. Chem. C (1)

J. Phys. Chem. C (1)

Laser Photonics Rev. (4)

G. Wang, A. A. Baker-Murray, and W. J. Blau, “Saturable Absorption in 2D Nanomaterials and Related Photonic Devices,” Laser Photonics Rev. 13(7), 1800282 (2019).
[Crossref]

B. Guo, Q.-l. Xiao, S.-H. Wang, and H. Zhang, “2D Layered Materials: Synthesis, Nonlinear Optical Properties, and Device Applications,” Laser Photonics Rev. 13(12), 1800327 (2019).
[Crossref]

Nano Lett. (1)

Nanophotonics (1)

Nanoscale (1)

J. He, L. Tao, H. Zhang, B. Zhou, and J. Li, “Emerging 2D materials beyond graphene for ultrashort pulse generation in fiber lasers,” Nanoscale 11(6), 2577–2593 (2019).
[Crossref]

Nat. Commun. (1)

Nat. Photonics (1)

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

Nat. Rev. Mater. (1)

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2(5), 17010 (2017).
[Crossref]

Opt. Express (5)

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]

J. He, Y. Qu, H. Li, J. Mi, and W. Ji, “Three-photon absorption in ZnO and ZnS crystals,” Opt. Express 13(23), 9235–9247 (2005).
[Crossref]

X. Zheng, Y. Zhang, R. Chen, X. A. Cheng, Z. Xu, and T. Jiang, “Z-scan measurement of the nonlinear refractive index of monolayer WS2,” Opt. Express 23(12), 15616–15623 (2015).
[Crossref]

Photonics Res. (1)

Phys. Rev. B (1)

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983).
[Crossref]

Phys. Rev. Lett. (1)

S. Cahangirov, M. Topsakal, E. Akturk, H. Sahin, and S. Ciraci, “Two- and One-Dimensional Honeycomb Structures of Silicon and Germanium,” Phys. Rev. Lett. 102(23), 236804 (2009).
[Crossref]

Sci. Rep. (1)

Data availability

Data underlying the results presented in this paper may be obtained from the authors upon reasonable request.

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Fig. 2. The experimental diagram of Z-scan.

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Fig. 4. Saturable absorption mechanism of 2D germanium nanosheets.

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Tables (2)

Table 1. Nonlinear absorption parameters of various 2D materials.

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Table 2. Nonlinear refraction parameters of various 2D materials.

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Equations (3)

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

T (z) = \frac{1}{\sqrt{π q_{0}}} \int_{- \infty}^{\infty} \ln [1 + q_{0} e x p (- x^{2})] d x

T (x) = 1 - \frac{4 Δ φ_{0} x}{(1 + x^{2}) (9 + x^{2})}

R e χ^{(3)} = \frac{4 ε_{0} c n_{0}^{2}}{3} n_{2}

Sample	Excitation laser	n₀	α₀ (cm⁻¹)	α_NL (cm/GW)	Imχ⁽³⁾ (esu)	FOM (esu cm)	Ref.
germanium	600 nm, 35 fs, 2 KHz	5.72	42.48	−0.19	−1.21×10⁻¹²	2.86×10⁻¹⁴	Present work
	800 nm, 35 fs, 2 KHz	4.69	32.62	−0.06	−3.13×10⁻¹³	9.60×10⁻¹⁵
	1064 nm, 35 fs, 2 KHz	4.41	28.31	−0.87	−5.68×10⁻¹²	2.02×10⁻¹³
	1300 nm, 35 fs, 2KHz	4.31	27.08	−0.70	−5.34×10⁻¹²	1.97×10⁻¹³
MoS₂	800 nm, 100 fs, 1 KHz			−4.6×10⁻³	−1.6×10⁻¹⁴	1.4×10⁻¹⁵	[15]
BP	1030 nm, 340 fs, 100 Hz			−8.62×10⁻³	−5.28×10⁻¹⁵	2.40×10⁻¹⁵	[30]
graphene	1030 nm, 340 fs, 100 Hz			−0.66	−5.0×10⁻¹³	9.3×10⁻¹⁵	[31]
Au	800 nm, 220 fs, 1KHz			−1.5	−1.2×10⁻¹²	4.0×10⁻¹³	[32]
Te	2500 nm, 35 fs, 1 KHz				−20.5×10⁻¹⁴	7.99×10⁻¹⁵	[33]
GeSe	800 nm, 56 fs, 1 KHz				−1.81×10⁻¹⁴	3.66×10⁻¹⁵	[34]
MOF	800 nm, 95 fs, 1 KHz			−3×10⁻²	−3×10⁻¹⁴		[35]
MXene	1550 nm			−0.358	×10⁻¹³		[36]
GeP	1550 nm, 100 fs, 1 KHZ			−0.12			[37]

Sample	Excitation laser	n₂ (cm²/W)	Reχ⁽³⁾ (esu)	Ref.
germanium	600 nm, 35 fs, 2 KHz	−0.07×10⁻¹³	−0.61×10⁻¹¹	Present work
	800 nm, 35 fs, 2 KHz	−0.18×10⁻¹³	−1.30×10⁻¹¹
	1064 nm, 35 fs, 2 KHz	−6.30×10⁻¹³	−30.99×10⁻¹¹
	1300 nm, 35 fs, 2 KHz	−0.90×10⁻¹³	−4.34×10⁻¹¹
MoS₂	700 nm, 2 KHz	−1.16×10⁻¹⁰		[38]
WS₂	800 nm, 100 fs, 1KHz	8.1×10⁻⁹		[39]
Bi₂Se₃	800 nm, 100 fs, 1KHz	2.26×10⁻¹⁰		[10]
Oxidized BP	800 nm, 100 fs, 1KHz	−3.61×10⁻¹⁶	−5.27×10⁻¹⁴	[40]
RGO	790 nm, 1KHz	7.5×10⁻¹²	1×10⁻¹⁰	[41]
MXene	1550 nm	−4.89×10⁻¹⁶	−4.96×10⁻¹⁴	[36]
MOF	800 nm, 95 fs, 1 KHz	−4.3×10⁻¹⁶	−4.4×10⁻¹⁴	[35]
GeP	1550 nm, 100 fs, 1 KHZ	0.33×10⁻¹⁴		[37]

Sample	Excitation laser	n₀	α₀ (cm⁻¹)	α_NL (cm/GW)	Imχ⁽³⁾ (esu)	FOM (esu cm)	Ref.
germanium	600 nm, 35 fs, 2 KHz	5.72	42.48	−0.19	−1.21×10⁻¹²	2.86×10⁻¹⁴	Present work
	800 nm, 35 fs, 2 KHz	4.69	32.62	−0.06	−3.13×10⁻¹³	9.60×10⁻¹⁵
	1064 nm, 35 fs, 2 KHz	4.41	28.31	−0.87	−5.68×10⁻¹²	2.02×10⁻¹³
	1300 nm, 35 fs, 2KHz	4.31	27.08	−0.70	−5.34×10⁻¹²	1.97×10⁻¹³
MoS₂	800 nm, 100 fs, 1 KHz			−4.6×10⁻³	−1.6×10⁻¹⁴	1.4×10⁻¹⁵	[15]
BP	1030 nm, 340 fs, 100 Hz			−8.62×10⁻³	−5.28×10⁻¹⁵	2.40×10⁻¹⁵	[30]
graphene	1030 nm, 340 fs, 100 Hz			−0.66	−5.0×10⁻¹³	9.3×10⁻¹⁵	[31]
Au	800 nm, 220 fs, 1KHz			−1.5	−1.2×10⁻¹²	4.0×10⁻¹³	[32]
Te	2500 nm, 35 fs, 1 KHz				−20.5×10⁻¹⁴	7.99×10⁻¹⁵	[33]
GeSe	800 nm, 56 fs, 1 KHz				−1.81×10⁻¹⁴	3.66×10⁻¹⁵	[34]
MOF	800 nm, 95 fs, 1 KHz			−3×10⁻²	−3×10⁻¹⁴		[35]
MXene	1550 nm			−0.358	×10⁻¹³		[36]
GeP	1550 nm, 100 fs, 1 KHZ			−0.12			[37]

Sample	Excitation laser	n₂ (cm²/W)	Reχ⁽³⁾ (esu)	Ref.
germanium	600 nm, 35 fs, 2 KHz	−0.07×10⁻¹³	−0.61×10⁻¹¹	Present work
	800 nm, 35 fs, 2 KHz	−0.18×10⁻¹³	−1.30×10⁻¹¹
	1064 nm, 35 fs, 2 KHz	−6.30×10⁻¹³	−30.99×10⁻¹¹
	1300 nm, 35 fs, 2 KHz	−0.90×10⁻¹³	−4.34×10⁻¹¹
MoS₂	700 nm, 2 KHz	−1.16×10⁻¹⁰		[38]
WS₂	800 nm, 100 fs, 1KHz	8.1×10⁻⁹		[39]
Bi₂Se₃	800 nm, 100 fs, 1KHz	2.26×10⁻¹⁰		[10]
Oxidized BP	800 nm, 100 fs, 1KHz	−3.61×10⁻¹⁶	−5.27×10⁻¹⁴	[40]
RGO	790 nm, 1KHz	7.5×10⁻¹²	1×10⁻¹⁰	[41]
MXene	1550 nm	−4.89×10⁻¹⁶	−4.96×10⁻¹⁴	[36]
MOF	800 nm, 95 fs, 1 KHz	−4.3×10⁻¹⁶	−4.4×10⁻¹⁴	[35]
GeP	1550 nm, 100 fs, 1 KHZ	0.33×10⁻¹⁴		[37]