Open Access
Add to BibSonomyAbstract
We experimentally observed that a representative two-dimensional layered material, bismuth telluride (Bi2Te3) nanosheets, exhibit obvious broadband nonlinear absorption and large nonlinear refraction investigated by Z-scan technique. Our study may not only verify the giant nonlinear refractive index of Bi2Te3 (~10−8 cm2/W), but also provide some new insights for topological insulator-based photonics, potentially leading to the emergence of several new conceptual optoelectronics devices.
© 2016 Optical Society of America
1. Introduction
The discovery of two-dimensional (2D) layered materials, especially the Dirac materials graphene and topological insulator (TI), has stimulated great research interests in different fields [1–5]. TI, a new quantum state of matter, is totally different from the conventional metal and insulator. Namely, the bulk of such material is insulating and it also possesses conducting surface state (SS) at the surfaces or the boundaries which is protected by time-reversal symmetry [1,2]. Therefore, the electron in TIs can go through the boundaries freely without scattering and consuming energy. As a result, TI has exotic physical properties and potential technological applications in both spintronics and quantum computers. In particular, the Dirac-cone structure gives TI massless fermions, leading to half-integer fractional/fractal quantum Hall effects (QHE), ultrahigh carrier mobility, and many other novel phenomena and properties [1,2].
In parallel, the optical and optoelectronic properties of TI have received broad attentions, especially the 2D TIs which can be integrated into the functional devices easily for manipulation and manufacturing [5]. With the unique energy band, TIs have been demonstrated to have wideband nonlinear saturable absorption from visible to mid-infrared, even to the microwave band [6–14]. Besides, bismuth selenide, one of the TIs, has been demonstrated to exhibit large nonlinear refractive index at 800 nm wavelength, which is on the order of 10−14 m2/W, almost six orders of magnitude larger than that of bulk dielectrics [15]. Driven by the broadband and large nonlinear responses of the TIs, various nonlinear devices, such as optical Q-switcher [7–10], mode-locker [11–13], wavelength converter [16], have been demonstrated. In addition, various nonlinear optical phenomena have been observed for the large nonlinearity of TIs and the flexible dispersion tailoring ability in the fiber laser platform [16–20]. However, with the emergence of TI-based optical Kerr devices, the nonlinear refractive index of the TIs and their broadband operating potential have not been explored in detail yet.
Here, we explored the broadband third-order nonlinear responses of the Bi2Te3 nanosheets from 800 nm to 1930 nm wavelength range with the Z-scan technique. With the ultrafast laser illumination, the real and imaginary parts of the complex nonlinear refractive index (nonlinear absorption and optical Kerr nonlinearity) of TIs have been investigated experimentally. The results may provide new insights for TI-based nonlinear photonic devices, potentially leading to the emergence of several new conceptual optoelectronics devices for all optical signal processing.
2. Preparation and characterization of Bi2Te3 nanosheets
The demand for various photonic devices with reliable performance, unique functions, as well as inexpensive production process opens the door to novel processing technologies capable of high-yield, low-cost manufacturing [21]. Materials with nonlinear optical and optoelectronic properties, that can be prepared in large quantities in liquid environments and then coated on optical elements or embedded in polymers, are the ideal choice for integrating in optical platform. Solution processing has been demonstrated as an effective and flexible method to fabricate various 2D crystals for ultrafast laser applications, e.g., graphene and other 2D crystals, their deposition on optical elements, and their incorporation in polymer composites for economic and broadband ultrafast lasers [22–27].
TIs, such as Bi2Te3, Bi2Se3 and Sb2Te3, can be produced via chemical synthesis. The synthesis of Bi2Te3 via chemical synthesis method is carried out by mixing two reactants (e.g., Bismuth (III) nitrate pentahydrate and sodium tellurite), the precursors, with teflon and ethylene glycol lining up to 80% of the capacity into a stainless steel autoclave. The as-prepared dispersion is kept in an electric oven at high temperature (~200 ◦C under stirring for 2 hours) and then cooled down to room temperature naturally. The purification of the gray powders was then carried out via filtering, washing and drying processes. The as-prepared and washed powders was then dispersed in an alcohol solution and then purified via centrifugation processes [28,29]. The as-prepared dispersion is then mixed with the host polymer, and then is drop-cast or spin-coated to obtain free standing or substrate bound composites with homogeneous, sub-micrometer distribution of flakes [5].
The linear absorption of Bi2Te3 nanosheets has been characterized by the spectrometer (Perkins Elmer Lambda750) in Fig. 1(a). The linear absorption spectrum of the TI nanosheets film on SiO2 was measured, which was calibrated by the bare substrate of SiO2 and the ordinate mode was selected as A (Absorption). It is necessary to emphasize that a.u. here means absorbance unit, which is different from arbitrary unit (a.u.). It can be seen that the nanosheets have a relatively flat transmission curve at the wavelength from 400 nm to 2000 nm, indicating that the TI may be a promising wideband optical material. For comparison, absorption spectrum from a pure PMMA film is also presented. The XRD pattern of TI is shown in Fig. 1(b). All the diffraction peaks of the XRD pattern can be indexed to rhombohedra Bi2Te3 (space group: R-3m) with lattice constants a = b = 0.438 nm, c = 3.05 nm, which is consistent with the literature values (JCPDS No.15-0863). This result indicates that Bi2Te3 product obtained via our synthetic method consists of a pure phase.
Fig. 1 (a) The liner absorption spectrum of Bi2Te3 nanosheets and PMMA and (b) the XRD pattern of Bi2Te3 nanosheets.
The morphology and size of the as-prepared Bi2Te3 nanosheet were characterized by field emission scanning electron microscopy (FESEM, JSM-6700F) and transmission electron microscopy (TEM, JEOL 3010). Figure 2(a) is a typical TEM image of a single nanosheet, showing photographs of the microstructure details of Bi2Te3 nanostructures, which clearly demonstrates the as-prepared TI nanosheet has perfect hexagonal morphology. The corresponding single nanosheet high-magnification lattice uniform fringes are shown in Fig. 2(b). To determine size as well as thickness of as-prepared Bi2Te3 nanosheets, the AFM topography images (Multimode 8 system) have been investigated. As shown in Fig. 2(c) and (d), the surface of Bi2Te3 nanosheets is very clean and flat with a uniform thickness about 20 nm across the lateral dimensions. Figure 2(c) is the typical 3D AFM image, and Fig. 2(d) shows the height profiles corresponding to the line-cut in inset. The lower magnification FESEM image reveals that sheet-like structures randomly dispersed on the substrate and possessed hexagonal-based well-defined shape. A higher magnification of single nanosheet FESEM image shows that the edge length is in the range of 400–600 nm, as shown in Fig. 2(e) and Fig. 2(f).
Fig. 2 (a) Single hexagonal nanosheet TEM image and (b) the high-magnification TEM image of Bi2Te3 lattice fringes; (c) Topographic 3D AFM images of the single Bi2Te3 nanosheet and (d) the corresponding height profiles (inset: topographic 2D AFM images, left: 10 scale, right: 1.2 scale); (e) Low-magnification FESEM image of Bi2Te3 nanosheets and (f) the high-magnification FESEM image of Bi2Te3 nanosheets.
3. Experimental results and discussions
Z-scan technique was employed to characterize the nonlinear response of the TI nanosheets with broadband ultrafast laser centered about 800 nm, 1560 nm and 1930 nm, and the schematic diagram of the experimental setup was shown in Fig. 3. The TI nanosheets were mounted onto a motorized translating stage and the transmitted ultrafast laser power was monitored by appropriate power detector. The measurement was performed simultaneously in two parts, an open aperture part wherein all transmitted laser through the sample is collected by the detector (D2) and a closed aperture part wherein a small aperture is added before the detector (D1) to collect partial on-axis transmitted beam. The open aperture measurement can investigate the nonlinear absorption, while the closed aperture measurement is a combined consequence of the nonlinear absorption and the nonlinear phase effect induced by the optical Kerr nonlinearity. With the division of the closed aperture data by the open-aperture results, the nonlinear absorption and the nonlinear phase effect can be separated [30,31]. To ensure the validity of the nonlinear system, we use the carbon disulfide (CS2) solution to calibrate it. With CS2 contained in a cuvette with 1 mm in thick and 800 nm ultrafast laser operating at 1 kHz repetition rate and 100 fs pulse duration, the third-order nonlinear parameter was extracted to be n2 = 2.66 × 10−19 m2/W, very close to the value of (3 ± 0.6) × 10−19 m2/W measured by another group [32].
Fig. 3 Schematic diagram of the Z-scan experimental setup. (BS: beam splitter, L0, L1: lens; D0, D1, D2: power detector; Sample: Bi2Te3 nanosheets)
By replacing the CS2 sample with the TI nanosheets while other parameters kept unchanged, the nonlinear measurement was carried out. A typical open aperture trace is shown in Fig. 4(a), which shows a sharp and narrow peak located at the beam focus, manifesting the characteristics of saturable absorption. The typical close aperture measurement is shown in Fig. 4(b). Upon dividing the curve in Fig. 4(b) by the curve in Fig. 4(a), we could unambiguously verify the nonlinear phase change, as shown in Fig. 4(c). The latter has the typical shape of a Z-scan trace for Kerr nonlinearity. The pre-focal valley and the post-focal peak suggest the positive sign of the complex nonlinear refractive index, indicating the self-focusing effect in TI. Fitting the trace by the formula [30]
where T(x) is the normalized transmittance, x = z/z0 and ΔΦ is the on-axis nonlinear phase shift at the focus. The nonlinear phase change ΔΦ is fitted to be about 0.65. Based on n2 = ΔΦ / (k0I0L), where k0 = 2π / λ, is the wavelength number, I0 is the peak intensity at the focus and L is the sample thickness. By assuming the average thickness of Bi2Te3 to be 20 nm, a value of n2 = 0.97 × 10−10 cm2/W is obtained.Fig. 4 Z-scan traces for Bi2Te3 nanosheet at 800nm wavelength. (a) open aperture (OA); (b) closed aperture (CA); and (c) divide CA by OA, which obtain typical shape of a Z-scan curve.
The nonlinear measurements under variable optical powers have been investigated too. The open aperture measurement result shows that the transmittance has a power dependent characteristic of saturable absorption. We fitted the curve in Fig. 5(a) by [22]
where T is the transmittance, is the modulation depth, I is the input intensity and Is is the saturation intensity. The fitted values of and Is are 11.56% and 11.99 GW/cm2, respectively. The modulation depth indicates that Bi2Te3 can be a suitable passive saturable absorber for the generation of ultrashort pulse. Figure 5(b) shows the nonlinear refractive index under different input powers. With the laser intensity increasing, n2 decreases then reaches at a constant value. We controlled the incident laser intensity below the optical damage threshold of the sample to make sure the OA curve corresponds to the nonlinear responses of the nanosheet, because a sharp and narrow peak of open aperture measurement can also occur when sample is damaged [33].Fig. 5 (a) Relation between transmittance and input peak intensity for Bi2Te3 at 800 nm; (b) Dependence of n2 on peak intensity for Bi2Te3 at 800 nm.
The parallel ultrafast laser experiments were carried out based on lasers with different operating wavelength to validate the broadband nonlinear response of the TI nanosheets, as can be seen in Fig. 6. We used 2 μm mode-locked ultrafast fiber laser source from AdValue Photonics with the center wavelength 1930 nm, pulse repetition rate 32.3 MHz, pulse duration 2.8 ps to implement the nonlinear measurements. We use CaF2 lens of 150 mm focus length and power meter (Newport 818P-001-12) at 2 μm. In addition, we also measured the same sample with a self-built mode-locked 1562 nm fiber laser with pulse repetition rate 20.8 MHz and pulse duration 1.5 ps. These pulses emitted from the fiber laser has been amplified through a commercial EDFA, and then focused by a 20 times microscope objective. During this wavelength we use N-BK7 lens of 150 mm focus length and power meter (Newport 918D-IR). To guarantee the accuracy of the measurement and calculation, we measured the nonlinear refractive index of silicon oxide to be 2.32 × 10−16 cm2/W, which is the same order to value of 2.98 × 10−16 cm2/W [34]. A value of n2 2.12 × 10−8 cm2/W and 0.86 × 10−8 cm2/W for Bi2Te3 nanosheets were obtained at 1930 nm and 1562 nm, respectively. The ratio of n2 at 1.93 μm and 1.56 μm is about 2.46, which approximately satisfy the wavelength-dependent relationship by λ4 like graphene [35]. The transmittance as a function of intensity at 1562 nm and 1930 nm was also analyzed, as shown in Fig. 7.
Fig. 6 (a) OA Z-scan measurement of TI at 1562 nm and 1930 nm, respectively; (b) CA/OA Z-scan measurement of TI at 1562 nm and 1930 nm, respectively.
Fig. 7 Nonlinear optical absorption of Bi2Te3 nanosheets, measured via an open-aperture Z-scan at: (a) 1562 nm and (b) 1930 nm, respectively.
There are some deviations from the experimental results and the theoretical model, which can be attributed to the experimental errors, such as the determination of beam waist, the slow response of the different power detectors, and the TI’s performance, such as doping [36]. In the mid-IR regime, the slow response of pyroelectric power detector will introduce about 10~15% error. We argue that these errors in the experimental measurement may result in the asymmetry. We change the position of sample slightly and the incident intensity and repeatable results have been observed, which convince both the uniformity and the accuracy of the measurements. During the Z-scan measurement, the samples was moved from + Z to -Z, and then -Z to + Z for the same sample. In addition, we spatially changed the sample illumination area, repeatable results could be obtained. We compared the modulation depth, saturation intensity, non-saturable losses and the nonlinear refractive index at different wavelengths, as shown in Table 1. Moreover, the adopted experimental methods (Z-scan to four-wave mixing) and conditions (i.e. pulse width) may also contribute to the differences. The detailed theoretical work to uncover the nonlinear response mechanism and the experimental work to improve the TI’s quality is under way.
Table 1. Nonlinear parameters of the measured sample at different wavelengths.
With the improved preparation method or hybrid structures, the band-gap and the Fermi energy level of TI could be engineered, and thus may lead to the tunable third-order nonlinear optical properties. Various optoelectronic devices, such as broadband wavelength converter, optical switcher, optical modulator, could be explored for the future optoelectronic applications, especially at low (far-infrared, terahertz) frequencies.
4. Conclusions
As a summary, high quality Bi2Te3 nanosheets were prepared employing bottom-up method. Broadband nonlinear optical properties have been investigated by both open- and close- aperture Z-scan technique with ultrafast laser in picosecond and femtosecond time regimes. The wavelength-dependent third order nonlinear optical response of Bi2Te3 was experimentally reported and the third-order nonlinear coefficient n2 was measured with a peak value of 2.12 × 10−8 cm2/W at a wavelength of 1.93 µm. Our experimental results verify that Bi2Te3 nanosheets is not only a broadband nonlinear optical absorption material, but a broadband Kerr nonlinear material, especially the potential in mid-infrared, even up to microwave or terahertz range [16]. The ultra-thin TI film could be potentially developed as the novel TI based optoelectronic devices or on-chip signal processing components.
Acknowledgments
The authors acknowledge E. J. R. Kelleher and R. I. Woodward for useful discussions. The work is supported by the National 973 Program of China (Grant No. 2012CB315701), the National Natural Science Fund Foundation of China (Grant Nos. 61475102 and 11574079), Ph.D. Programs Foundation of Ministry of Education of China (20120161120027), the Open Research Fund of Key Laboratory of Fiber Optic Sensing & Communications (Education Ministry of China)(Grant No. A03011023801005) and China Schorlaship Council.
References and links
1. J. E. Moore, “The birth of topological insulators,” Nature 464(7286), 194–198 (2010). [CrossRef] [PubMed]
2. X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83(4), 1057–1110 (2011). [CrossRef]
3. H. J. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S. C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys. 5(6), 438–442 (2009). [CrossRef]
4. D. Kong, W. Dang, J. J. Cha, H. Li, S. Meister, H. Peng, Z. Liu, and Y. Cui, “Few-layer nanoplates of Bi2 Se3 and Bi2Te3 with highly tunable chemical potential,” Nano Lett. 10(6), 2245–2250 (2010). [CrossRef] [PubMed]
5. F. Bonaccorso and Z. Sun, “Solution processing of graphene, topological insulators and other 2d crystals for ultrafast photonics,” Opt. Mater. Express 4(1), 63–78 (2014). [CrossRef]
6. F. Bernard, H. Zhang, S. P. Gorza, and P. Emplit, “Towards mode-locked fiber laser using topological insulators,” in Nonlinear Photonics, OSA Technical Digest (online) (Optical Society of America, 2012), paper NTh1A.5. [CrossRef]
7. D. D. Wu, Z. P. Cai, Y. L. Zhong, J. Peng, J. Weng, Z. Q. Luo, N. Chen, and H. Y. Xu, “635-nm Visible Pr3+-Doped ZBLAN Fiber Lasers Q-Switched by Topological Insulators SAs,” IEEE Photonics Technol. Lett. 27(22), 2379–2382 (2015). [CrossRef]
8. Z. Luo, Y. Huang, J. Weng, H. Cheng, Z. Lin, B. Xu, Z. Cai, and H. Xu, “1.06 μm Q-switched ytterbium-doped fiber laser using few-layer topological insulator Bi₂Se₃ as a saturable absorber,” Opt. Express 21(24), 29516–29522 (2013). [CrossRef] [PubMed]
9. J. Li, H. Luo, L. Wang, C. Zhao, H. Zhang, H. Li, and Y. Liu, “3-μm Mid-infrared pulse generation using topological insulator as the saturable absorber,” Opt. Lett. 40(15), 3659–3662 (2015). [CrossRef] [PubMed]
10. P. H. Tang, M. Wu, Q. K. Wang, L. L. Miao, B. Huang, J. Liu, C. J. Zhao, and S. C. Wen, “2.8 μm-Pulsed Er3+: ZBLAN Fiber Laser Modulated by Topological Insulator,” IEEE Photonics Technol. Lett. 28(14), 1573–1576 (2016). [CrossRef]
11. C. J. Zhao, H. Zhang, X. Qi, Y. Chen, Z. T. Wang, S. C. Wen, and D. Y. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett. 101(21), 211106 (2012). [CrossRef]
12. J. Sotor, G. Sobon, W. Macherzynski, P. Paletko, K. Grodecki, and K. M. Abramski, “Mode-locking in Er-doped fiber laser based on mechanically exfoliated Sb2Te3 saturable absorber,” Opt. Mater. Express 4(1), 1–6 (2014). [CrossRef]
13. Z. C. Luo, M. Liu, H. Liu, X. W. Zheng, A. P. Luo, C. J. Zhao, H. Zhang, S. C. Wen, and W. C. Xu, “2 GHz passively harmonic mode-locked fiber laser by a microfiber-based topological insulator saturable absorber,” Opt. Lett. 38(24), 5212–5215 (2013). [CrossRef] [PubMed]
14. S. Q. Chen, C. J. Zhao, Y. Li, H. H. Huang, S. B. Lu, H. Zhang, and S. C. Wen, “Broadband optical and microwave nonlinear response in topological insulator,” Opt. Mater. Express 4(4), 587–596 (2014). [CrossRef]
15. S. Lu, C. Zhao, Y. Zou, S. Chen, Y. Chen, Y. Li, H. Zhang, S. Wen, and D. Tang, “Third order nonlinear optical property of Bi₂Se₃,” Opt. Express 21(2), 2072–2082 (2013). [CrossRef] [PubMed]
16. S. Q. Chen, L. L. Miao, X. Chen, Y. Chen, C. J. Zhao, S. Datta, Y. Li, Q. L. Bao, H. Zhang, Y. Liu, S. C. Wen, and D. Y. Fan, “Few-Layer Topological Insulator for All-Optical Signal Processing Using the Nonlinear Kerr Effect,” Adv. Opt. Mater. 3(12), 1769–1778 (2015). [CrossRef]
17. C. Tan, Q. K. Wang, and X. Q. Fu, “Topological insulator Sb2Te3 as an optical media for the generation of ring-shaped beams,” Opt. Mater. Express 4(10), 2016–2025 (2014). [CrossRef]
18. B. X. Shi, L. L. Miao, Q. K. Wang, J. Du, P. H. Tang, J. Liu, C. J. Zhao, and S. C. Wen, “Broadband ultrafast spatial self-phase modulation for topological insulator Bi2Te3 dispersions,” Appl. Phys. Lett. 107(15), 151101 (2015). [CrossRef]
19. M. Liu, Z. R. Cai, S. Hu, A. P. Luo, C. J. Zhao, H. Zhang, W. C. Xu, and Z. C. Luo, “Dissipative rogue waves induced by long-range chaotic multi-pulse interactions in a fiber laser with a topological insulator-deposited microfiber photonic device,” Opt. Lett. 40(20), 4767–4770 (2015). [CrossRef] [PubMed]
20. Y. Chen, M. Wu, P. Tang, S. Chen, J. Du, G. Jiang, Y. Li, C. Zhao, H. Zhang, and S. Wen, “The formation of various multi-soliton patterns and noise-like pulse in a fiber laser passively mode-locked by a topological insulator based saturable absorber,” Laser Phys. Lett. 11(5), 055101 (2014). [CrossRef]
21. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010). [CrossRef]
22. Q. L. 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]
23. H. Zhang, D. Y. Tang, R. J. Knize, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Graphene mode locked wavelength-tunable dissipative soliton fiber laser,” Appl. Phys. Lett. 96(11), 111112 (2010). [CrossRef]
24. J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband Nonlinear Optical Response of Graphene Dispersions,” Adv. Mater. 21(23), 2430–2435 (2009). [CrossRef]
25. 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]
26. 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] [PubMed]
27. R. I. Woodward, R. C. T. Howe, T. H. Runcorn, G. Hu, F. Torrisi, E. J. R. Kelleher, and T. Hasan, “Wideband saturable absorption in few-layer molybdenum diselenide (MoSe2) for Q-switching Yb-, Er- and Tm-doped fiber lasers,” Opt. Express 23(15), 20051–20061 (2015). [CrossRef] [PubMed]
28. L. Ren, X. Qi, Y. D. Liu, G. L. Hao, Z. Y. Huang, X. H. Zou, L. W. Yang, J. Li, and J. X. Zhong, “Large-scale production of ultrathin topological insulator bismuth telluride nanosheets by a hydrothermal intercalation and exfoliation route,” J. Mater. Chem. 22(11), 4921–4926 (2012). [CrossRef]
29. Q. Wang, Y. Chen, L. Miao, G. Jiang, S. Chen, J. Liu, X. Fu, C. Zhao, and H. Zhang, “Wide spectral and wavelength-tunable dissipative soliton fiber laser with topological insulator nano-sheets self-assembly films sandwiched by PMMA polymer,” Opt. Express 23(6), 7681–7693 (2015). [CrossRef] [PubMed]
30. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]
31. L. L. Miao, Y. Q. Jiang, S. B. Lu, B. X. Shi, C. J. Zhao, H. Zhang, and S. C. Wen, “Broadband ultrafast nonlinear optical response of few-layers graphene: toward the mid-infrared regime,” Photon. Res. 3(5), 214–219 (2015). [CrossRef]
32. M. Reichert, H. Hu, M. R. Ferdinandus, M. Seidel, P. Zhao, T. R. Ensley, D. Peceli, J. M. Reed, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. van Stryland, “Temporal, spectral, and polarization dependence of the nonlinear optical response of carbon disulfide,” Optica 1(6), 436–445 (2014). [CrossRef]
33. B. M. Patterson, W. R. White, T. A. Robbins, and R. J. Knize, “Linear optical effects in z-scan measurements of thin films,” Appl. Opt. 37(10), 1854–1857 (1998). [CrossRef] [PubMed]
34. T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. H. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21(26), 32192–32198 (2013). [CrossRef] [PubMed]
35. E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010). [CrossRef] [PubMed]
36. Y. H. Lin, S. F. Lin, Y. C. Chi, C. L. Wu, C. H. Cheng, W. H. Tseng, J. H. He, C. I. Wu, C. K. Lee, and G. R. Lin, “Using n- and p-Type Bi2Te3 topological insulator nanoparticles to enable controlled femtosecond mode-locking of fiber lasers,” ACS Photonics 2(4), 481–490 (2015). [CrossRef]
