1. Introduction

In addition to their outstanding linear optical properties [1–3], emerging metal halide perovskites (MHP) materials also exhibit striking nonlinear optical properties [4–7], resulting from their unique photoelectric features, such as strong spin-orbit coupling, high defect-tolerance, and direct p-p optical transitions, etc., making the advances in this research fundamental to the development of photonic devices of the next generation. Normally, both organic and inorganic MHP materials exhibit predominantly third-order optical nonlinearity (TONL) in their structural centrosymmetry, thus suitable and desirable for those advanced TONL-based devices [8–10] such as all-optical switches, terahertz generation, bio-imaging, up-conversion laser, etc. However, basic research with respect to the TONL mechanisms of MHP materials remains quite limited, so that this research area is still in its infancy [11–13].

On the other hand, chalcogenide glasses (ChGs), are also excellent optical materials with large TONL, high infrared transmittance and easy shaping and molding etc., rendering them a high-performance platform for both nonlinear and infrared photonics [14,15]. More importantly, ChGs are friendly hosts for a variety of nano-particles which in turn enhance the various properties of their host ChGs [16], thus one can expect superior TONL performance via a hybrid of MHPs and ChGs. Furthermore, although not so robust as oxide glasses, ChG packages can still protect the MHPs from moisture and oxygen in ambient atmosphere, and a unique advantage over oxide glasses is that the vacuum melting process of ChGs can prohibit volatilization of the original metal halide during preparation. However, as far as we know, studies with respect to the TONL properties of MHPs in ChGs or even in oxide glasses are scarce. The main contribution to this specific research topic came from Xiang’s group [17–20], who showed that the incorporation of inorganic MHP (CsPbX₃ (X = Cl, Br, I) or mutants) nano-crystals in oxide glasses could overcome the intrinsic defects of MHP (especially the unstable nature) and improve PL and TONL performances. Recently, Liu et al [21] also characterized the nonlinear properties of CsPbBr₃ NCs in borosilicate glasses and discovered strong two-photon process induced up-conversion PL from the MHP NCs.

Our latest series of work [22–24] established an in-situ nanocrystallization strategy for the precipitation of inorganic MHP (CsPbX₃) NCs within GeS₂-Sb₂S₃ ChG system, demonstrating the exceptional compatibility between these MHP NCs and ChGs. In this paper, an in-depth and thorough investigation with respect to the TONL attributes of the MHP-ChG composites (including composition, excitation wavelength and intensity dependencies) is present, in order to fill the gaps in this research realm.

2. Experiment

The molar compositions of the MHP-ChGs are 79.2GeS₂−15.8Sb₂S₃−5CsPbBr_x/I_3-x (x = 1, 2, 3, abbreviated as Br1, Br2, Br3 respectively) and 83.4GeS₂−16.6Sb₂S₃ for host ChG. The detailed glass preparation and nanocrystallization processes have been described in our previous paper [24]. The batch were all polished to thickness of 1 mm and mirror-like on both sides for the follow-up optical tests.

Transmission spectra from 0.4 to 2.5 µm were recorded via Perkin-Elmer Lambda 950 spectrometer, those from 2.5 to 25 µm via Nicolet381 Fourier transform IR spectrometer. The optical nonlinear attributes in wavelength range from 700 to 920 nm for the MHP-ChGs were investigated via Z-scan technique. The laser beam was generated from Coherent Chameleon Ultra II femtosecond laser (140 ± 10 fs laser pulse and 80 MHz repetition rate), and the laser power was detected by Si photodiodes. In close-aperture (CA) Z-scan measurements, for the purpose of extract the signal from the nonlinear refraction (n₂), the linear transmittance was kept at 10% through the aperture. In open-aperture (OA) Z-scan measurements, removing the aperture to access the full transmitted light and the nonlinear absorption coefficient (β). The detailed fitting formulas for the CA and OA data were given in Eq. (S1) and Eq. (S2) of Supplement 1.

The incident laser focused on the sample surface via convex lens which has focal distance of 7.5 mm and beam waist estimated at 16 ± 0.5 µm. The laser power (P) was varied from 3.65 to 43.75 mW, corresponding to a laser density at the focal point (I₀) from 0.028 to 1.29 GW/cm², aiming to explore the irradiation dependence of n₂ and β as well as the corresponding mechanism. It should be noted that the laser power is so small that the cumulative thermo-optic effect is absent in the Z-scan measurements. The mentioned optical tests were performed under room temperature.

3. Results and discussion

The broad-band transmission spectra as well as a photograph of the three MHP-ChG composites with host ChG are given in Fig. 1, showing that the composites are dark red in color and a little bit visible transparent. According to their scanning electron microscope images (Fig. S1 in supplemental document), the mean diameter of the spherical MHP NCs embedded in Br1, Br2, Br3 are estimated to be 38.6 ± 4 nm, 43.4 ± 4 nm, 59.3 ± 6 nm respectively, thus the NCs in such sizes do not affect the IR transparency near the 12 µm cut-off. The overall optical transmittance of the composites reached >80% in flat region, indicating negligible optical scattering at the interfaces between the glass matrix and crystals. Given that the tested linear refractive index n₀ for the GeS₂-Sb₂S₃ ChG of 2.302 at 632.8 nm and the estimated n₀ values of 2.2 ± 0.1 for CsPbBr₃ and 2.4 ± 0.1 for CsPbI₃ via an empirical formula [25]: n₀² = 1 + 8.32/E_g, where E_g is the bandgap energy, 2.4 ± 0.1 eV and 1.8 ± 0.1 eV for CsPbBr₃ and CsPbI₃ respectively, the matched n₀ between the host ChG and the CsPb(Br/I)₃ NCs minimized the optical scattering, which resulted in high optical transparency of the MHP-ChG composites.

 

Fig. 1. Broad-band transmission spectra of the three MHP-ChGs and the host ChG. The inset is a photograph of the four samples.

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Figure 2 is the absorption spectra of the MHP-ChG samples, showing that the bandgap edges are red-shifted as bromine is substituted by iodine, with the theoretical positions (defined as the linear absorption coefficient α at 10 cm⁻¹ [26,27]) estimated at 626, 573 and 541 nm for Br1, Br2 and Br3, corresponding to bandgap energies E_g of 1.985, 2.168 and 2.296 eV respectively. It should be noted that the E_g is a complex value mainly contributed from the ChG host and influenced by the MHP NCs, thus E_g of the sample with pristine CsPbBr₃ NCs (Br3) is smaller than the those for the CsPbBr₃ NCs dispersed colloidal solutions as well as in oxide glasses (given in Table 1), due to the inherent large number of lone-pair electrons from the GeS₂-Sb₂S₃ host ChG that have occupied the conduction band minimum [26]. Besides, below the bandgap edge, only Br3 exhibits obvious exciton absorption from the MHP NCs, as a result of its diversity in crystal sizes and larger crystal number as can be judged from the strongest diffraction intensity in the X-ray diffraction patterns Fig. S2 in the Supplement 1.

 

Fig. 2. Absorption spectra of the three MHP-ChGs. The definition of E_g and excitation wavelengths for Z-scan measurements are noted.

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Table 1. Host material, style, bandgap energy and nonlinear optical parameters of the CsPbBr₃ MHP materials in this work and others’ reports

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The broad spectral TONL properties of the MHP-ChGs were explored via Z-scan method in the wavelength range from 700 to 920 nm. The excitation wavelength region is noted in the absorption spectra, showing that all the three samples have sub-bandgap absorption from the Urbach tail (defect states) at the excitation-onset wavelengths, whereas Br3 has additional linear absorption throughout the entire excitation region due to exciton interactions, such that it may exhibit a stronger nonlinear response from both the photon-generated free carrier effects and exciton effects, as detailed below.

Figure 3(a)-(c) shows 21 representative CA Z-scan traces of the three MHP-ChGs tested at seven wavelengths under a laser power of 10 ± 1 mW. Note that all the CA profiles are valley-following-peak shaped, suggesting the self-focusing behavior namely, the positive n₂ sign is a commonality for the MHP-ChGs from 700 to 920 nm. At similar excitation wavelengths, this result is in contrast to the n₂ sign of CsPbBr₃ colloidal quantum dots in n-hexane solvent [28] and CsPbBr₃ nano-cubes/rods on glass substrates [29], but is consistent with the n₂ sign of CsPb(Br/I)₃ cubic NCs in anhydrous toluene [30] and hexane solvent [31], manifesting the highly variable TONL attributes of MHPs, related to composition, size, shape and substrate related. Besides, as can be judged from the naked eyes, the size of the peaks and valleys in the CA profiles, more specifically, the transmittance difference between peaks and valleys (ΔT_p-v), shrinks at longer excitation wavelength. In general, a smaller ΔT_p-v represents a smaller nonlinear phase shift, resulting in a smaller n₂ value for the same laser intensity. Hence, a normal n₂ dispersion for the MHP-ChGs can be concluded.

 

Fig. 3. CA and OA Z-scans under laser power of 10 ± 1 mW at wavelengths from 700 to 920 nm for Br1 (a) and (d), Br2 (b) and (e), Br3 (c) and (f), respectively. The data points are obtained from the experiments, and the solid lines represent the theoretical fits.

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The specific n₂ values were calculated by using Kwak’s fitting procedure [32] proposed for large nonlinear phase shift (ΔT_p-v > 1) in the CA traces, and all n₂ values are given in Table S1 of the supplemental document. By plotting the n₂ values against laser power (P) for the seven tested wavelengths as illustrated in Fig. S3-S9 in the supplemental document, it can be seen that the n₂-P relations exhibit a general overall negative dependence, although in some cases rather weak and insignificant. This observation is similar to the TONL attribute of the organic-inorganic hybrid MHPs [33], demonstrating that the nonlinear refraction of the present MHP-ChGs also arises in part from a photon-induced carrier effect which is suppressed at high laser intensities, the so-called Pauli blocking effect. The calculations do confirm that Br3 exhibits larger n₂ values compared to the other two samples. Therefore, as a representative, its minimum and maximum n₂ values along with those of the other CsPbBr₃ counterparts in various styles and hosts in previous reports are summarized in Table 1. The comparison among these n₂ values shows that the n₂ behavior of the present CsPbBr₃ NCs embedded ChG is remarkably stronger than those of the CsPbBr₃ NCs embedded borosilicate glass [19] and hexane [31], comparable to quantum dots dispersed in n-hexane [28], but weaker than those of mixed-phase NCs dispersed in anhydrous toluene [30] and shaped NC films coated on silica glass [29]. Furthermore, it is noted that the CsPbBr₃ nanoparticles dispersed hexane [35] has n₂ values at 1064 nm larger than ours, which can be assigned to the strong accumulated free-carrier effect due to the use of nanosecond pulse laser.

Figure 3(d)-(f) shows the 21 OA Z-scan traces corresponding to their CA counterparts. It is evident that a single valley is present in the central of each profile, signifying reverse saturation absorption (RSA, positive β) as a commonality for MHP-ChGs in this wavelength region. A continuous reduction of the valley size (transmittance depth ΔT_v) at longer wavelength can be observed, which manifests β attenuation, in analogy to the positive dispersion of the n₂ value. In details, the photon energy E_p of excitation wavelength is from 1.35 eV (920 nm) to 1.78 eV (700 nm), giving the range of normalized photon energy (E_p/E_g) from 0.58 to 0.9 meet the criterion for two-photon absorption (2PA, 0.5 < E_p/E_g< 1), thus the RSA can be attributed to 2PA. It should be noted that 2PA dominates under the entire excitation densities from 0.028 to 1.29 GW/cm², without the presence of sub-bandgap absorption saturation (SAS) that observed in many other MHP materials [21,28,33,40,41] at both low power and high power ends. The absent SAS for the MHP-ChGs, especially Br3 with considerable sub-bandgap absorption is simply because it is submerged by the strong 2PA of the host ChG. An analogous observation had been reported in the CsPb(Cl/Br)₃ NCs embedded oxide glasses [20] which exhibit persistent 2PA under incident laser densities from 25.5 to 332 GW/cm² at a wavelength of 800 nm.

The concrete 2PA coefficient β_2PA was calculated via a fit to the OA Z-scan trajectory by using the proven 2PA model [42], and all the values are listed in Table S1. The β_2PA-P relations at each excitation wavelength are illustrated in Fig. S3-S9, again they exhibit a general overall negative correlation, confirming the presence of Pauli blocking effect. Table 1 lists the minimum and maximum β_2PA value for Br3 as well as those of CsPbBr₃ materials in different styles and hosts from others’ reports. Notably, the β_2PA magnitude for the present CsPbBr₃ embedded ChG is outstanding, it is remarkably larger than those of the majority of its counterparts, similar to those of CsPbBr₃ nanosheets [38], but smaller than that of CsPbBr₃ quantum dots film coated on silicon substrates [34], which might exhibit inherently large 2PA at the testing wavelength of 720 nm.

The significant larger n₂ and β_2PA values of the CsPbBr₃ NCs embedded ChG compared to the identical NCs embedded oxide glasses and organic solvents demonstrated the strong impact of host (or substrate) upon the TONL attribute of MHP materials. In this regard, a direct comparison of the OA and CA Z-scans between the host ChG and three MHP-ChGs under similar laser power of 3.75 ± 0.1 mW at 700 nm are illustrated in Fig. 4, which clearly shows that the host ChG exhibits distinct n₂ and β_2PA signals represented in the CA (ΔT_p-v) and OA (ΔT_v) profile respectively, but is weaker than the MHP-ChGs, indicating the advance of the intrinsic large ChG TONL after the inorganic MHP NCs incorporation. Besides, in previous study [43] with respect to the TONL properties of ChGs within GeS₂-Sb₂S₃ system, the researchers found that the n₂ value of the ChGs depends on Sb₂S₃ content and the maximum n₂ obtained from a 60GeS₂−40Sb₂S₃ (in mol%) glass is 6.65 × 10⁻¹⁴ cm²/W at excitation wavelength of 800 nm. In this study, molar composition of the host ChG is 83.4GeS₂−16.6Sb₂S₃, but the average n₂ value at 800 nm for the three MHP-ChGs are 10.56 × 10⁻¹⁴ cm²/W (Br1), 7.77 × 10⁻¹⁴ cm²/W (Br2) and 12.86 × 10⁻¹⁴ cm²/W (Br3) respectively, all of them are remarkably larger than that of the 60GeS₂−40Sb₂S₃ glass. A major reason for such overall augment is the enhanced light-mater interactions via irradiation of femtosecond laser induced dielectric confinement effect due to the large dielectric difference between the amorphous host ChG composed of covalent bonds and these crystalline MHP NCs composed of ionic bonds.

 

Fig. 4. CA (a) and OA (b) Z-scans of the three MHP-ChGs and the host ChG under laser power of 3.75 ± 0.1 mW at 700 nm. The data points are obtained from the experiments, and the solid lines represent the theoretical fits.

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For data analysis, the n₂ and β_2PA values measured at same excitation wavelength but different laser powers were averaged and plotted against the E_p/E_g in Fig. 5, represented as the n₂ and β_2PA spectra for the MHP-ChGs. First of all, it is clear that no general overall n₂-E_p/E_g and β_2PA-E_p/E_g relationships regardless of the MHP composition exists, confirming that each MHP-ChG has an individual band structure, being a mixture of direct type of valence to conduction band transitions from the MHP NCs and indirect-type transitions of the amorphous host ChG. However, both n₂ and β_2PA values exhibit an increasing trend with increasing E_p/E_g. For the n₂ spectra, this trend demonstrates that approaching excitation wavelength to bandgap edge would remarkably enhance n₂ value of the material, which confirmed that free carriers generated at the sub-bandgap (namely Urbach band or defect states) region via 1PA process is a significant contribution. In particular, Br3 is explicitly higher n₂ spectrum than the other two samples which are nearly overlapped. Such profile is the almost identical to the absorption spectra (scaled by E_p/E_g) as illustrated in inset of Fig. 5(a), and this is a direct support that the existence of exciton-phonon coupling [6,44] is an additional effect leading to the n₂ enhancement for Br3. For the β_2PA spectra, the three β_2PA-E_p/E_g profiles are almost identical, and all of them equally exhibit a rapid increase of β_2PA at E_p/E_g beyond 0.7. Such trend is analogous to the relativistic effects induced two-step upward trend in the 2PA spectra of MHP materials [7], which implies that the MHP NCs in ChG also have conduction bands split due to spin-orbit coupling of the heavy metal atoms, with heavy and light electronic states (HLES) above the secondary gap. As schematically indicated in inset of Fig. 5(b), the conduction band is an intermediate state for the electron transitions from the valence band to HLES with a rapidly enhancing 2PA process in the spectral region.

 

Fig. 5. (a) n₂ versus E_p/E_g for the three MHP-ChG samples, inset is the corresponding absorption spectra in the same E_p/E_g range; (b) β_2PA versus E_p/E_g for the three MHP-ChG samples, inset is schematic showing 2PA processes in conditions of E_p1 < ∼0.7E_g < E_p2, VB and CB are abbreviations for valence band and conduction band, respectively.

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On the other hand, it can be clearly distinguished from Fig. 5 that both n₂ and β_2PA values of the three samples at same E_p/E_g follow a spectral order of Br3 > Br2 > Br1. For β_2PA, such compositional dependency is consistent with that of the CsPb(Br/I)₃ NCs dispersed hexane at the excitation wavelength of 1064 nm [35]. For n₂, such compositional dependency is consistent with the CsPb(Br/I)₃ NCs dispersed anhydrous toluene in similar excitation wavelengths from 750 to 920 nm [30], but deviated from that of the CsPb(Br/I)₃ NCs dissolved hexane at an excitation wavelength of 1064 nm [35] which is attributed to the different underlying mechanism for n₂ at different excitation wavelength. Excitation at short wavelengths, i.e., this study and Ref. 30, resonant free carrier nonlinearity via 1PA process at sub-bandgap is the dominant contribution to the n₂ value, thus stoichiometric MHPs with fewer carrier trapping defects exhibits higher n₂ as compared to their non-stoichiometric counterparts. Excitation at long wavelength, i.e., Ref. 35, non-resonant bound electronic charge nonlinearity is the dominant contribution to the n₂ value, thus MHPs with higher iodine content exhibit higher n₂ because polarizability of iodine is higher than bromine.

At last, it is necessary to judge the functionality of the MHP-ChGs for the TONL-based applications via figure of merit (FOM), defined as the following express:

 

Fig. 6. FOM versus E_p/E_g for the three MHP-ChG samples, the arrows note the FOM maximum in each spectrum.

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4. Conclusion

In summary, we prepared stable CsPb(Br/I)₃ MHP NCs by packaging them in a GeS₂-Sb₂S₃ ChG matrix, and characterized the TONL attribute (including n₂ and β_2PA) of the nano-composites via femtosecond Z-scan technique at excitation wavelengths from 700 to 920 nm. The experimental results demonstrate that the optical nonlinear attributes of MHP-ChGs are highly adjustable by exploiting the flexible tunability of the MHP composition as well as the excitation conditions. Firstly, the addition of MHP NCs could advance the intrinsic large optical nonlinearity of the host ChG, which is due the dielectric confinement induced local filing enhancement between the amorphous host ChG composed of covalent bonds and these crystalline MHP NCs composed of ionic bonds, and the nonlinear performance is much higher as compared to those of the MHP NCs embedded oxide glasses. Secondly, changing the composition of the MHP NCs from Br/I mixture to pristine Br further enhances the optical nonlinearity, as a result of the reduced carrier trapping defects in the stoichiometric MHP NCs. Thirdly, in the samples with pristine Br NCs, exciton-phonon coupling effect were discovered to promote its optical nonlinearity. Fourthly, the optical nonlinearity of all MHP-ChGs exhibits an overall decreasing trend with increasing excitation wavelength and power, which is attributed to spin-orbit coupling effects and Pauli blocking effects respectively. Finally, estimates of FOM manifested that the MHP-ChGs possess stronger 2PA than nonlinear refraction in the wavelength ranges from 700 to 920 nm, suggesting that they are promising materials for β_2PA-based applications, such as optical limiting.