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Abstract
We report the wavelength-dependent third-order optical nonlinearity of two-dimensional halide organic-inorganic perovskite (PEA)2PbI4 film experimentally. The high-quality two-dimensional (PEA)2PbI4 film prepared via confinement-assisted drop-casting process exhibits ultrafast optical response and large third-order optical nonlinearities, and the measured nonlinear refractive index is closer to the quantum perturbation model accounting for the excitonic effect. In addition, the wavelength-dependent optical response transition from self-focusing to self-defocusing, saturable absorption to reverse saturable absorption has been observed and investigated. The experimental results confirm the large third-order optical nonlinearities in (PEA)2PbI4 film and may make inroads toward developing cost-effective high-performance optoelectronic devices.
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1. Introduction
Nonlinear optical materials with large third-order nonlinear optical (NLO) responses and explicit wavelength-dependent properties are highly required for applications in the field of on-chip integration and all-optical devices [1–5]. The NLO properties of conventional semiconductors, such as silicon [6–8] and gallium arsenide [9,10], have been extensively studied. However, they cannot meet the demand for cost-effective NLO devices with large and broadband NLO responses. With the evolvement of optical materials, the low-dimensional materials have shown extraordinary broadband NLO effects, but nevertheless they suffer from relatively weak optical modulation and unsatisfied stability. Recently, solution-processed two-dimensional (2D) halide organic-inorganic perovskite (HOIP) semiconductors have attracted increasing attention as one of the most attractive next-generation optoelectronic materials for their excellent optoelectronic properties, ease of preparation, and improved stability compared to their three-dimensional counterparts [11]. (PEA)2PbI4, as a member of HOIP materials, has a 2D quantum-well construction made up of inorganic semiconductor layers interposed between organic dielectric layers PEA+, and the organic layers have a larger bandgap and lower dielectric constant than the inorganic layers, which can endow the HOIP strong quantum and dielectric confinement effects, such as strong exciton–photon coupling, short exciton decay time, and large nonlinear response [12,13].
As a consequence of the concern for the NLO response of 2D HOIPs, giant two-photon absorption (TPA) coefficients have been obtained in 2D HOIP nanosheets [14], heterostructures [15], and films [16], respectively. Moreover, enhanced three-photon absorption (3 PA) has also been demonstrated in layered (C4H9NH3)2PbBr4 perovskites by the critical role of 2D excitons [17]. With the excellent nonlinear absorption (NLA) characteristics of the 2D HOIPs, the efficient polarization-resolved sub-bandgap photodetector in the near-IR regime [14], sensitive photodetectors in the infrared regime [15], and ultrafast fiber lasers operating in both near- and mid-infrared regimes have been investigated experimentally [18]. Apart from the NLA, the nonlinear refraction (NLR) behavior plays an important role in nonlinear optoelectronic devices. Saouma et al. explored the large third-order NLO response of HOIPs (PEA2(CH3NH3)n−1PbnI3n + 1 (n = 1−4) under mid-infrared excitation via THG process, which exhibits four times stronger THG in mid-infrared wavelength compared with the three-dimensional (CH3NH3)PbI3 [19]. The exciton–exciton interactions in the HOIP quantum wells can lead to a situation where the excitons cannot be modeled as non-interacting ideal bosons, which leads to a more complicated NLO mechanism in 2D HOIPs. Abdelwahab et al. reported the tunable optical nonlinearity of 2D HOIPs at 400 nm-700 nm, observing unprecedentedly large NLR and NLA coefficients near excitonic resonances [20]. Wang et al. observed the conversion of NLA with varying irradiance in quasi-2D perovskite films, which can result from the competition between excitonic absorption enhancement and non-thermalized carrier induced bleaching [21]. As a consequence of interest in perovskites and especially in the nonlinear interactions in perovskites, it has become increasingly important to explore novel 2D HOIPs with large optical nonlinearity and possess the nonlinear susceptibilities within a broad spectral range. However, current studies focus on the optical nonlinearity of perovskite systems at specific wavelengths, while the wavelength-dependent optical nonlinearity of 2D HOIPs has received less attention [22–26].
Here, we have prepared the high-quality 2D HOIP (PEA)2PbI4 thin film and obtained the broadband NLO response of the 2D (PEA)2PbI4 in the spectral range from 450 nm to 800 nm with femtosecond Z-scan technique and transient absorption spectroscopy experimentally. The nonlinear optical characteristics and mechanisms of the 2D (PEA)2PbI4 have been examined by measuring the wavelength-dependent NLO coefficients in the resonant and non-resonant regions. The measured nonlinear refractive index (n2) is closer to a quantum perturbation model that accounts for the excitonic effect. The obtained experimental results can help us deepen the photophysical understanding of the dispersion behavior of the optical nonlinearities and may extend the nonlinear optics applications of the low-dimensional perovskites.
2. Fabrication and characterization of 2D (PEA)2PbI4 film
The high-quality 2D HOIP (PEA)2PbI4 film has been synthesized through a confinement-assisted drop-casting process with the following specific steps in an ambient environment [27,28]. Firstly, 149.4 mg (0.6 mol) of PEAI and 138.3 mg (0.3 mol) of PbI2 were dissolved into 1 mL of DMF solution. The solution was added to a vortex shaker to make it clear and transparent and filtered through a nylon filter (0.22 µm) afterward. Secondly, 15 μL of precursor solution was transferred to a glass substrate, then the upper glass was immediately covered and slowly removed. With the evaporation of the DMSO, (PEA)2PbI4 perovskite tends to crystallize on the quartz substrates. Finally, an annealing process was performed at 100°C for about 15 minutes to improve the film quality.
We have characterized the morphology and structure of the 2D (PEA)2PbI4 film, as shown in Fig. 1. The scanning electron microscope (SEM) image of (PEA)2PbI4 is shown in Fig. 1(a), which demonstrates the smooth surface morphology of the sample. Figure 1(b) shows the atomic force microscopy (AFM) pattern of the prepared 2D (PEA)2PbI4 films, and the thickness of the sample is about 33 nm with an edge thickness of about 120 nm. The grain size and the roughness of the films are 0.3∼1 µm and 5.57 nm, respectively. The X-ray diffraction (XRD) pattern of the (PEA)2PbI4 is presented in Fig. 1(c), and the well-defined diffraction patterns conform to the (00 h) series of reflections, indicating the good crystallinity as well as the preferred orientation, which matches well with the previously reported 2D HOIPs [29]. The linear absorption characteristic of the 2D (PEA)2PbI4 film has been obtained with the spectrophotometer (Shimadzu Corporation, UV3600), as shown in Fig. 1(d), and the peak occurring at 516 nm wavelength corresponds to the excitonic absorption. According to the Tauc plot, the bandgap of the perovskite can be extracted to be about 2.3 eV, which is consistent with the previous report [30].
Fig. 1. Characterization of the (PEA)2PbI4. (a) The SEM image of (PEA)2PbI4. (b) The AFM pattern and (c) XRD pattern of the (PEA)2PbI4. (d) The normalized linear absorbance of the (PEA)2PbI4. Inset: The Tauc plot illustrates that the bandgap is 2.3 eV.
3. Results and discussions
3.1 Ultrafast carrier dynamics
To investigate the photophysical mechanism and NLO application potential of 2D perovskites, the ultrafast carrier dynamics of (PEA)2PbI4 have been studied with a 400 nm pump laser from an optical parametric amplifier (OPA), and the probe light obtained by focusing the Ti: sapphire laser (repetition rate: 6 kHz, pulse duration: 190 fs) onto the sapphire crystal. Figure 2 shows the differential absorption (ΔOD) results by 400 nm pump excitation, and probe at 485 nm, 530 nm, 750 nm, and 800 nm wavelengths with the same fluence of 1.1 mJ/cm2, respectively. The positive ΔOD at all probe wavelengths from resonance to non-resonance regime has been observed during the hot-carrier cooling process of the perovskite [31]. Furthermore, a double exponential decay function is used to extract the time component [32]. With the increasing probe wavelength, the 2D (PEA)2PbI4 experienced a rapid decay in the range of τ1 = 3-6 ps, and then a slow cooling process on the scale of tens of picoseconds. For the (PEA)2PbI4 perovskites in the absorption resonance region (485 nm, 530 nm), the positive decay signal can be derived from the variation of the imaginary part of the refractive index, where photo-induced absorption (PIA) and band gap renormalization dominate the decay process [33,34]. While in the non-resonant region (750 nm, 800 nm), the (PEA)2PbI4 exhibits a positive decay signal and a faster response time, contributing to the transition between excited state energy levels. The ultrafast behavior on the picosecond scale (16 ± 0.8 ps∼26 ± 2.5 ps) can be obtained via the global fit, indicating the potential for ultrafast nonlinear applications of (PEA)2PbI4.
Fig. 2. The temporal evolution of ΔOD and fitting curves of (PEA)2PbI4 at different probe wavelengths using the femtosecond nondegenerate pump-probe measurements. The solid lines (red) represent the fits to a biexponential decay function. The Error values for decay time derived from global fitting are labeled.
3.2 Wavelength-dependent third-order nonlinearities in the 2D (PEA)2PbI4 film
The wavelength-tunable femtosecond laser was employed to carry out the open- and close- aperture (OA and CA) Z-scan measurements of the 2D (PEA)2PbI4 film with an OPA system (Coherent, USA) with the repetition rate of 1 kHz and the pulse duration of 35 fs, as shown in Fig. 3(a). The NLO measurements were performed in the ambient environment and the untested samples were kept in the inert gas glove box. During the experiments, the light intensity ranges from 1.0 to 27.3 GW/cm2, and no significant variation has been observed for the quartz substrate, which suggests that the nonlinear response results from the perovskite. We have selected four wavelengths above/below the bandgap of the 2D (PEA)2PbI4 film as excitations to investigate the nonlinear behavior from visible to near-IR region. The variations of the real and imaginary parts of the NLO susceptibility have been observed with the Z-scan technique. As shown in Fig. 3(b), (PEA)2PbI4 exhibits saturable absorption (SA) behavior for excitation wavelength above the bandgap photon energy (480 nm and 530 nm), while it shows a typical reverse saturable absorption (RSA) behavior for excitation below the bandgap photon energy (750 nm and 800 nm), indicating the TPA characteristics of the (PEA)2PbI4. The OA trajectories of the 2D (PEA)2PbI4 film are given as follows [35],
Fig. 3. (a) Schematic diagram of the Z-scan experimental setup. (b) OA and (c) CA Z-scan measurements of the 2D (PEA)2PbI4 under different wavelengths of excitation, and the gray hollow dots are the scanning traces of the substrate. (d) Log-log plot of the scaled n2 vs. bandgap, and the solid line represents the theoretical result with a slope of -4.
At the same time, Fig. 3(c) depicts the CA/OA Z-scan experimental results at the same excitation wavelengths, suggesting the self-defocusing behavior with n2 < 0 for long wavelength excitation and the self-focusing behavior with n2 > 0 for short wavelength excitation. The fitting equation for the CA/OA trace is given as follows,
where the NLO phase shift ΔΦ=kn2I0Leff, the Rayleigh range z0 = 2πω0/λ, and the wave number k = 2π/λ. By fitting the curves, the n2 for 2D (PEA)2PbI4 film are 2.1 × 10−10 cm2/W (480 nm), 6.80 × 10−10 cm2/W (530 nm), -0.19 × 10−10 cm2/W (750 nm), and -1.56 × 10−10 cm2/W (800 nm), respectively. We have compared the n2 of the 2D (PEA)2PbI4 film with the reported typical semiconductors by plotting the scaled n2 in terms of $\frac{{{n_2}{n_0}}}{{K^{\prime}G({\hbar \omega /{E_g}} )}}$ and the corresponding energy gap Eg, where n0, G(${\hbar}$ω/Eg) and K’ are linear refractive index, dispersion function, and K'=3.4 × 10−8 respectively, as shown in Fig. 3(d) [36]. It can be seen that the 2D HOIP shows three orders of magnitude larger n2 than that in typical semiconductors [36], which defies the bandgap scaling rule [19].3.3 Discussion
To visualize the evolution of the wavelength-dependent nonlinear properties, we performed the Z-scan measurements under different excitations, and obtained the dispersion of the NLA and NLR of the perovskite (PEA)2PbI4, as shown in Fig. 4. It should be noted that the NLA and the Kerr effect vary with the pump intensity in the resonant absorption region [21]. The (PEA)2PbI4 exhibits SA behavior under resonant excitation with large negative β benefiting from the strong single-photon resonance absorption. While in the non-resonant regime, the 2D (PEA)2PbI4 film shows RSA behavior, where the β decreases as well as the sign turns positive, indicating TPA. From Fig. 4(b), the sign of n2 changes from positive in the resonant region to negative in the non-resonant region. Table 1 illustrates the reported coefficients of the NLO response of the 2D perovskites. By comparing the experimental results with the 2D (PEA)2PbI4 film, it can be seen that the film exhibits a large n2 and the values can reach 6.80 × 10−10 cm2/W near the resonance region, which is 3-4 orders of magnitude larger than those of silicon and typical low-dimensional materials [37–39]. While in the non-resonant region, the n2 values of the HOIPs are superior to that of traditional semiconductor materials like GaAs [37], which are also comparable to or larger than those of typical perovskite materials [20,23–26,40].
Fig. 4. Dispersion of NLA index β (a) and NLR index n2 (b) of the 2D (PEA)2PbI4. The color bars indicate the different light irradiances. (c) Comparison of n2 predicted by the two-band and exciton models for 2D HOIPs, with solid spheres for experimental data.
Table 1. Comparison of the NLO properties of the typical perovskite materialsa
The nonlinearity of the 2D (PEA)2PbI4 benefits from the strong resonance enhancement in the resonant region. While in the non-resonant regime, the NLA and the Kerr effect can be partially predicted by the two-band model, which relates the NLA to NLR via the Kramers-Kronig relations [41]. However, we find the trend of n2 is still negative when hν/Eg < 0.74, which in this case defies the two-band model with positive n2, and the experimentally measured n2 is 4 orders of magnitude larger than the n2 calculated with the model [36]. Lu et al. and Krishnakanth et al. have also observed the negative n2 at hν/Eg ≈ 0.6 of CsPbBr3 and CH3NH3PbBr3, respectively [42,43]. Based on the discrepancy between theoretical and experimental results, we employ a semi-empirical expression that takes into account 2D exciton features, instead of the traditional two-band model, to predict n2 dispersion: ${n_2}({h\nu } )= \frac{{{{Z^{\prime}}_2}{{({n_0^2 + 2} )}^4}}}{{E_{2p}^2}}G(x )\; $[44], where ${Z^{\prime}_2} = 1 \times {10^{ - 14}}$, $G(x )= \frac{{0.5 - x}}{{{{({0.5 - x} )}^2} + 0.3{{\left( {\frac{{h\gamma }}{{{E_{2p}}}}} \right)}^2}}}$, and the E2p represents the energy level of 2p excitonic state, and hγ represents half of its linewidth, respectively. The envelopes in the green area have been obtained with hγ/E2p = 0.05 and 0.15, as depicted in Fig. 4(c). The experimental data can match the predicted n2 curve, indicating the non-negligible contribution of exciton effects to NLR due to the unique multi-quantum-well structure of the (PEA)2PbI4, and the corresponding Kramers-Kronig conjugation is significantly enhanced by the 2D quantum effects [19,45,46].
4. Conclusion
In conclusion, the wavelength-dependent NLO properties of high-quality 2D (PEA)2PbI4 film have been investigated via ultrafast pump-probe and nonlinear Z-scan measurements experimentally. The ultrafast third-order nonlinear response of 2D perovskite from resonance to non-resonance region has been observed and investigated, including the transition from SA to RSA, self-focusing to self-defocusing. The large NLA and NLR coefficients of the 2D (PEA)2PbI4 film have been extracted to be ∼10−7 m/W and ∼10−10 cm2/W, respectively, which can be attributed to the quantum confinement effect of the 2D structure. The results can deepen the photophysical understanding of the 2D organic-inorganic perovskite, and future studies will further exploit the enormous nonlinear coefficients of 2D perovskites and potentially lead to advances in practical applications of the perovskite-based nonlinear photonics devices.
Funding
National Natural Science Foundation of China (61805076, 61975055).
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.
References
1. J. Xu, X. Li, J. Xiong, et al., “Halide Perovskites for Nonlinear Optics,” Adv. Mater. 32(3), 1806736 (2020). [CrossRef]
2. A. S. Berestennikov, P. M. Voroshilov, S. V. Makarov, et al., “Active meta-optics and nanophotonics with halide perovskites,” Appl. Phys. Rev. 6(3), 031307 (2019). [CrossRef]
3. P. Zhang, G. Yang, F. Li, et al., “Direct in situ photolithography of perovskite quantum dots based on photocatalysis of lead bromide complexes,” Nat. Commun. 13(1), 6713 (2022). [CrossRef]
4. J. Tian, G. Adamo, H. Liu, et al., “Optical Rashba Effect in a Light-Emitting Perovskite Metasurface,” Adv. Mater. 34(12), 2109157 (2022). [CrossRef]
5. P. Tonkaev, K. Koshelev, M. A. Masharin, et al., “Observation of Enhanced Generation of a Fifth Harmonic from Halide Perovskite Nonlocal Metasurfaces,” ACS Photonics 10(5), 1367–1375 (2023). [CrossRef]
6. O. Tokel, A. Turnalı, G. Makey, et al., “In-chip microstructures and photonic devices fabricated by nonlinear laser lithography deep inside silicon,” Nat. Photonics 11(10), 639–645 (2017). [CrossRef]
7. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010). [CrossRef]
8. Z. Zhou, X. Ou, Y. Fang, et al., “Prospects and applications of on-chip lasers,” eLight 3(1), 1–25 (2023). [CrossRef]
9. M. Davanco, J. Liu, L. Sapienza, et al., “Heterogeneous integration for on-chip quantum photonic circuits with single quantum dot devices,” Nat. Commun. 8(1), 889 (2017). [CrossRef]
10. A. Osada, Y. Ota, R. Katsumi, et al., “Strongly Coupled Single-Quantum-Dot-Cavity System Integrated on a CMOS-Processed Silicon Photonic Chip,” Phys. Rev. Appl. 11(2), 024071 (2019). [CrossRef]
11. G. Wang, S. Mei, J. Liao, et al., “Advances of Nonlinear Photonics in Low-Dimensional Halide Perovskites,” Small 17(43), 2100809 (2021). [CrossRef]
12. X. Gong, O. Voznyy, A. Jain, et al., “Electron-phonon interaction in efficient perovskite blue emitters,” Nat. Mater. 17(6), 550–556 (2018). [CrossRef]
13. J. C. Blancon, J. Even, C. C. Stoumpos, et al., “Semiconductor physics of organic-inorganic 2D halide perovskites,” Nat. Nanotechnol. 15(12), 969–985 (2020). [CrossRef]
14. F. Zhou, I. Abdelwahab, K. Leng, et al., “2D Perovskites with Giant Excitonic Optical Nonlinearities for High-Performance Sub-Bandgap Photodetection,” Adv. Mater. 31(48), 1904155 (2019). [CrossRef]
15. J. Wang, Y. Mi, X. Gao, et al., “Giant Nonlinear Optical Response in 2D Perovskite Heterostructures,” Adv. Opt. Mater. 7(15), 1900398 (2019). [CrossRef]
16. W. Liu, J. Xing, J. Zhao, et al., “Giant Two-Photon Absorption and Its Saturation in 2D Organic-Inorganic Perovskite,” Adv. Opt. Mater. 5(7), 1601045 (2017). [CrossRef]
17. S. Lu, F. Zhou, Q. Zhang, et al., “Layered Hybrid Perovskites for Highly Efficient Three-Photon Absorbers: Theory and Experimental Observation,” Adv. Sci. 6(4), 1801626 (2019). [CrossRef]
18. Y. He, N. Li, Y. Feng, et al., “Broadband Nonlinear Optical Modulator With 2D Organic-Inorganic Hybrid Perovskite Nanocrystals,” IEEE J. Sel. Top. Quantum Electron. 29(6), 1–8 (2023). [CrossRef]
19. F. O. Saouma, C. C. Stoumpos, J. Wong, et al., “Selective enhancement of optical nonlinearity in two-dimensional organic-inorganic lead iodide perovskites,” Nat. Commun. 8(1), 742 (2017). [CrossRef]
20. I. Abdelwahab, P. Dichtl, G. Grinblat, et al., “Giant and Tunable Optical Nonlinearity in Single-Crystalline 2D Perovskites due to Excitonic and Plasma Effects,” Adv. Mater. 31(29), 1902685 (2019). [CrossRef]
21. G. Wang, T. Liu, B. Wang, et al., “Hot-carrier tunable abnormal nonlinear absorption conversion in quasi-2D perovskite,” Nat. Commun. 13(1), 6935 (2022). [CrossRef]
22. D. Sirbu, H. C. L. Tsui, N. Alsaif, et al., “Wide-Band-Gap Metal-Free Perovskite for Third-Order Nonlinear Optics,” ACS Photonics 8(8), 2450–2458 (2021). [CrossRef]
23. C. Kriso, M. Stein, T. Haeger, et al., “Nonlinear refraction in CH3NH3PbBr3 single crystals,” Opt. Lett. 45(8), 2431–2434 (2020). [CrossRef]
24. B. S. Kalanoor, L. Gouda, R. Gottesman, et al., “Third-Order Optical Nonlinearities in Organometallic Methylammonium Lead Iodide Perovskite Thin Films,” ACS Photonics 3(3), 361–370 (2016). [CrossRef]
25. R. A. Ganeev, K. S. Rao, Z. Yu, et al., “Strong Nonlinear Absorption in Perovskite Films,” Opt. Mater. Express 8(6), 1472–1483 (2018). [CrossRef]
26. R. Ketavath, N. K. Katturi, S. G. Ghugal, et al., “Deciphering the Ultrafast Nonlinear Optical Properties and Dynamics of Pristine and Ni-Doped CsPbBr3 Colloidal Two-Dimensional Nanocrystals,” J. Phys. Chem. Lett. 10(18), 5577–5584 (2019). [CrossRef]
27. Y. Liu, Y. Zhang, Z. Yang, et al., “Multi-inch single-crystalline perovskite membrane for high-detectivity flexible photosensors,” Nat. Commun. 9(1), 5302 (2018). [CrossRef]
28. W. Wu, X. Han, J. Li, et al., “Ultrathin and Conformable Lead Halide Perovskite Photodetector Arrays for Potential Application in Retina-Like Vision Sensing,” Adv. Mater. 33(9), 2006006 (2021). [CrossRef]
29. V. S. Chirvony, I. Suárez, J. Rodríguez Romero, et al., “Inhomogeneous Broadening of Photoluminescence Spectra and Kinetics of Nanometer-Thick (Phenethylammonium)2PbI4 Perovskite Thin Films: Implications for Optoelectronics,” ACS Appl. Nano Mater. 4(6), 6170–6177 (2021). [CrossRef]
30. Y. Zhao, Q. Ma, B. Liu, et al., “Layer-dependent transport and optoelectronic property in two-dimensional perovskite: (PEA)2PbI4,” Nanoscale 10(18), 8677–8688 (2018). [CrossRef]
31. C. Qin, L. Xu, Z. Zhou, et al., “Carrier dynamics in two-dimensional perovskites: Dion–Jacobson vs. Ruddlesden–Popper thin films,” J. Mater. Chem. A 10(6), 3069–3076 (2022). [CrossRef]
32. J. Fu, M. Li, A. Solanki, et al., “Electronic States Modulation by Coherent Optical Phonons in 2D Halide Perovskites,” Adv. Mater. 33(11), 2006233 (2021). [CrossRef]
33. J. Yin, R. Naphade, P. Maity, et al., “Manipulation of hot carrier cooling dynamics in two-dimensional Dion-Jacobson hybrid perovskites via Rashba band splitting,” Nat. Commun. 12(1), 3995 (2021). [CrossRef]
34. M. B. Price, J. Butkus, T. C. Jellicoe, et al., “Hot-carrier cooling and photoinduced refractive index changes in organic-inorganic lead halide perovskites,” Nat. Commun. 6(1), 8420 (2015). [CrossRef]
35. M. Sheik-Bahae, A. A. Said, T. H. Wei, et al., “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]
36. M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990). [CrossRef]
37. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]
38. S. Lu, C. Zhao, Y. Zou, et al., “Third order nonlinear optical property of Bi2Se3,” Opt. Express 21(2), 2072–2082 (2013). [CrossRef]
39. X. Zheng, Y. Zhang, R. Chen, et al., “Z-scan measurement of the nonlinear refractive index of monolayer WS2,” Opt. Express 23(12), 15616–15623 (2015). [CrossRef]
40. W. Y. Liang, F. Liu, Y. J. Lu, et al., “High optical nonlinearity in low-dimensional halide perovskite polycrystalline films,” Opt. Express 28(17), 24919–24927 (2020). [CrossRef]
41. M. S. Bahae, D. C. Hutchings, D. J. Hagan, et al., “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991). [CrossRef]
42. K. N. Krishnakanth, S. Seth, A. Samanta, et al., “Broadband femtosecond nonlinear optical properties of CsPbBr3 perovskite nanocrystals,” Opt. Lett. 43(3), 603–606 (2018). [CrossRef]
43. W. Lu, C. Chen, D. Han, et al., “Nonlinear Optical Properties of Colloidal CH3NH3PbBr3 and CsPbBr3 Quantum Dots: A Comparison Study Using Z-Scan Technique,” Adv. Opt. Mater. 4(11), 1732–1737 (2016). [CrossRef]
44. F. Zhou, C. J. Nieva, D. Fan, et al., “Superior optical Kerr effects induced by two-dimensional excitons,” Photonics Res. 10(3), 834 (2022). [CrossRef]
45. D. Cotter, M. G. Burt, and R. J. Manning, “Below-band-gap third-order optical nonlinearity of nanometer-size semiconductor crystallites,” Phys. Rev. Lett. 68(8), 1200–1203 (1992). [CrossRef]
46. D. Giovanni, W. K. Chong, H. A. Dewi, et al., “Tunable room-temperature spin-selective optical Stark effect in solution-processed layered halide perovskites,” Sci. Adv. 2(6), 1600477 (2016). [CrossRef]
