## Abstract

The optical limiting properties of alloyed Cd_{0.5}Zn_{0.5}S quantum dots associated with erythrosine dye are analyzed using 532 nm, 40 ps pulses. We show that joint influence of saturable absorption, reverse saturable absorption and two-photon absorption cause the optical limiting of 532 nm radiation at the pulse energies exceeding 1 mJ. The nonlinear refraction and nonlinear absorption of these quantum dots associated with different organic dyes were studied using 1064 nm and 532 nm radiation. The nonlinear refraction index and nonlinear absorption coefficient of Cd_{0.5}Zn_{0.5}S quantum dots were measured at *λ* = 1064 nm to be 2 × 10^{−13} cm^{2} W^{−1} and 1.2 × 10^{−8} cm W^{−1}, while the reverse saturable absorption of Cd_{0.5}Zn_{0.5}S quantum dots and erythrosine at *λ* = 532 nm was almost two orders larger. The potential applications of these quantum dots for high-order harmonic generation are discussed.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Optical limiting is one of the potential applications of the materials’ optical nonlinearities. It aimed in protecting eyes and sensitive registration devices from damaging. Previously, small-sized species, like nanoparticles and quantum dots (QDs), have shown the advantages in their use for optical limiting [1,2]. Among various QDs the metal sulfides took special attention due to their advanced nonlinear optical properties. Silver sulfide is the most studied QD sample [3]. The nonlinear optical characterization of these QDs has revealed that, in the 532 nm spectral region, it possesses large nonlinear refraction and nonlinear absorption. The structure of those QDs, their Z-scans and the pump-probe characterization have been reported in numerous studies. Other most frequently studied metal sulfide samples include CdS and ZnS QDs. Those species showed large nonlinear refractive indices (*γ*) and nonlinear absorption coefficients (*β*) depending on the conditions of experiments [4,5]. The development of the principles of formation of metal sulfide QDs with desired low-order nonlinear optical properties for different applications, particularly for generation of coherent extreme ultraviolet radiation through high-order harmonic generation during propagation of ultrashort pulses through the plasmas containing such QDs, is one of important tasks of nonlinear optics.

The interest in small-sized species is caused by enhancement of the nonlinear optical response near their surface plasmon resonances [6]. The variation of quantum size effect in QDs can be achieved by doping with other semiconductor materials. The tuning of band gap energy of QDs without changing their size can be achieved by varying the alloyed QDs composition. This opportunity has spurred the fabrication of several varieties of alloyed QDs (CdSeTe, CdZnS, ZnCdSe and CdSSe) with tunable optical properties [7]. Those alloyed semiconductor QDs with both homogeneous and gradient internal structures have been developed to achieve continuous tuning of the optical properties without changing the particle size.

The nonlinear optical studies of CdSe_{0.8}S_{0.2} QDs using the Nd:YAG laser second harmonic radiation (*λ* = 532 nm, *t* = 35 ps) were reported by Wu *et al* [8]. Those studies have shown that CdSe_{0.8}S_{0.2} QDs possess strong reverse saturable absorption (RSA) and weak saturable absorption (SA), while the nonlinear absorption coefficient was measured to be three orders of magnitude larger than that of CdSeS-doped glasses. In [9], Danilov *et al* have reported similar studies using 532 nm nanosecond laser pulses. The composition-dependent nonlinear optical properties of CdSe* _{x}*S

_{1−}

*alloyed QDs were analyzed by the Z-scan technique using 532 nm laser radiation [10]. The 4 to 10 fold growth of nonlinear optical characteristics, particularly two-photon absorption (2PA), in CdSe*

_{x}*S*

_{x}_{1−}

*depending on*

_{x}*x*values (from 0 to 1) has been shown.

The aqueous synthesis of mixed cadmium and zinc sulfide colloidal QDs has been successfully realized and the method for preparation of colloidal Cd_{x}Zn_{1−x}S QDs in a cubic crystal lattice with particle size of ∼2 nm has been demonstrated by Klyuev *et al* [11]. In those studies the blueshift of optical absorption maximum from 420 to 295 nm and the recombination photoluminescence (PL) from 646 to 483 nm with increasing zinc content in QDs was observed. Those results have prompted the preparation of CdZnS QDs films and the studies of the PL properties of CdZnS QD suspensions for solar cells applications. Meanwhile, one can note the absence of the optical limiting studies of alloyed Cd_{1-x}Zn_{x}S QDs and its associates with various molecules in the visible range. Notice that these monodisperse wurtzite nanoalloys possess superior optical properties with PL quantum yields of 25-50% [12].

The absorption spectra of synthesized Cd_{1−x}Zn_{x}S reveal that their optical bandgaps are in good agreement with the values found by calculating the interband emission energy [13]. It was predicted that investigation of Cd_{1-x}Zn_{x}S QDs and their associates with molecules, such as dyes, will prompt the application of the attractive properties of those materials in the future. The interest in such QD-containing systems has raised due to expectations for simultaneous application of the attractive properties of each of components for different potential applications. Moreover, the QDs associated with different dyes may further amend the optical and nonlinear optical response of newly developed species. In this connection the Cd_{1−x}Zn_{x}S QDs associates with organic dyes may demonstrate the advanced optical limiting in the visible range. One has to carefully analyze different conditions of the formation of such associates from the point of view of their advanced optical limiting properties, as well as to study their nonlinear optical characteristics, such as *γ*, *β*, 2PA, SA, and RSA.

In this paper, we analyze these parameters and demonstrate the optical limiting in the Cd_{0.5}Zn_{0.5}S + erythrosine associates dissolved in water. We present the measurements of *γ* and *β* at different combinations of QD + dye associates using infrared and visible laser pulses of picosecond duration. We also show the potential applications of QDs for strong field laser-matter interactions. Particularly, we discuss the ablation of those species for plasma formation and high-order harmonic generation during propagation of ultrashort laser pulses through the plasmas containing QDs.

## 2. Experimental arrangements

The preparation of zinc-cadmium sulfide QDs was described by Klyuev et al [11]. Briefly, colloidal Cd_{0.5}Zn_{0.5}S QDs were prepared through the water synthesis in gelatin. Water solutions of CdCl_{2}, ZnBr_{2}, and Na_{2}S precursors were inserted in the thermostatic reactor at appropriate ratio by maintaining constant speed and steering at 40°C. The concentration of QDs was equal to 2% of mass of gelatin. Associates were prepared by mixing the water solutions of dyes and QDs at the molar ratio of 0.03:1.

The TEM of QDs are shown in Fig. 1(a). The mean size of Cd_{0.5}Zn_{0.5}S QDs was about 2 nm (see inset). The absorption spectra of Cd_{0.5}Zn_{0.5}S QDs and its associates with dyes are shown in Fig. 1(b). Three dyes of different classes (thiazine (thionine), xanthene (erythrosine), and carbocyanine (3,3′-di-(γ-sulfopropyl) - 4,4’,5,5′ - dibenzo-9 – ethylthiacarbocyaninebetaine pyridinium salt; further this dye will be dubbed as DEC)) were used as the associative molecules. We chose these dyes to change the linear absorption peaks of the mixtures of Cd_{0.5}Zn_{0.5}S QDs + dyes near the wavelength of the second harmonic (532 nm) of Nd:YAG laser radiation.

The nonlinear optical processes in QD + dye associates were analyzed at the wavelengths of 1064 nm and 532 nm using picosecond pulses. The experimental set-up contained the picosecond Nd:YAG laser, which generated a single pulse (*τ* = 40 ps) at 2 Hz repetition rate and closed-aperture (CA) and open-aperture (OA) Z-scan schemes for nonlinear optical characterization of associates. Laser radiation (*λ* = 1064 nm), or its second harmonic (*λ* = 532 nm) generated in KDP crystal, was focused by a 25 cm focal length lens [see inset in Fig. 1(b)]. The beam waist diameters were 80 *μ*m and 60 *μ*m (at half width of 1/e^{2} maximum of the spatial distribution at the focal plane) in the case of fundamental and second harmonic beams respectively. The laser pulse energy was measured by a calibrated photodiode. The 2-mm-thick fused silica cells containing QDs or QD + dye associates were moved along the z-axis through the focal point using a translating stage controlled by a computer. Attention was given to prevent optical breakdown of the studied medium. The intensities of the optical breakdown of QD + dye associates were measured to be 2.5 × 10^{11} W cm^{−2} and 1 × 10^{11} W cm^{−2} at the wavelengths of the fundamental and second harmonic radiation respectively, while the maximum intensities of radiation in the experiments did not exceed 1 × 10^{11} W cm^{−2} (1064 nm) and 3 × 10^{10} W cm^{−2} (532 nm). The Z-scan scheme was calibrated using the known values of the nonlinear optical parameters of 1-mm-thick fused silica slides. The error bars for Z-scans were ± 5%. The error bars of the definition of the absolute values of nonlinear optical parameters were estimated to be ± 25% due to the uncertainty in the measurements of the intensities of laser pulses in the focal plane.

The optical limiting studies were carried out by varying the energy of the pulses propagating through the cells. The energy was changed using the calibrated filters. The sample was placed on the path of focused radiation at the position when energy density was sufficient for observation of optical limiting.

## 3. Optical limiting in QD + dye associates

The optical limiting was demonstrated using the 532 nm, 40 ps pulses propagated through the Cd_{0.5}Zn_{0.5}S QDs + erythrosine associates in water. This solution was placed close to the focal plane of 400 mm focal length lens. We gradually increased the energy of 532 nm pulses and measured the output radiation propagated through the 1-mm-thick cell contained QD + dye associates. The linear dependence between input and output pulses was maintained up to the input pulse energy of ~1.1 mJ [Fig. 2]. Further grow of input pulse energy led to the optical limiting of the energy of propagated laser radiation (filled circles).

This process was maintained up to the maximal available energy of 532 nm pulses (~2.5 mJ), which allowed stabilization of output energy at the level of 0.65 mJ along the 1.1 – 2.5 mJ energy range of input pulses. Note that optical limiting effect has previously been reported in different dyes [14] and the competitive contribution of SA, as well as joint influence of 2PA and RSA, on the optical limiting in thionine was analyzed.

In present studies, the contribution of QDs on the optical limiting in QD + dye associates played a decisive role, since at high pulse energies the joint influence of 2PA and RSA becoming stronger than the influence of SA. Similar conclusion has been reported by Valligatla *et al* [15], which have shown that optical limiting in CdSe QD was based on RSA. This process dominated over SA at higher intensities of 532 nm laser radiation. Similar optical limiting properties in the solution contained ZnS nanostructures using 532 nm nanosecond pulses were reported by Divyasree *et al* [16]. In their studies, the optical limiting was also attributed to the nonlinear absorption properties of ZnS nanostructures. Our observations of the optical limiting in QD + dye associates were also mostly attributed to the RSA. The optical limiting occurred at the pulse energy much higher than the energy of laser radiation at which the SA became a dominating process at similar focusing conditions (1.1 and 0.1 mJ respectively).

Similar, though less pronounced, optical limiting properties were observed in QD + thionine and QD + DEC associates. As for QD water solution without dyes, we obtained the optical limiting at narrower range of limitation of the output pulses (1.5 – 2.5 mJ). In the case of QD + erythrosine we achieved ~2.1 fold decrease of output pulse energy compared with input radiation. One can compare the expected energy of output pulses without limiting effect depicted from the dashed line (~1.4 mJ) and actual energy of those pulses [0.65 mJ, Fig. 2] at the input pulse energy of 2.5 mJ. At similar conditions, pure QDs in water showed the ~1.8 fold decrease of output energy [Fig. 2, empty triangles]. These observations point out the relative influence of dye molecules attached to QDs on the optical limiting properties of QD + dye associates.

To quantitatively analyze different nonlinear optical processes responsible for optical limiting in QDs and QD + dye associates, one has to measure *γ* and *β* using standard Z-scan technique. Below we describe the results of those studies.

## 4. Z-scan measurements

The Z-scans showing normalized transmittances of Cd_{0.5}Zn_{0.5}S QDs in water using 1064 and 532 nm pulses are presented in Fig. 3. The Cd_{0.5}Zn_{0.5}S QD-containing solution was consisted on 19.5 g of distilled water, 0.05 g of QDs and 0.5 g of gelatin. The gelatin was added to restrict the aggregation of QDs.

The nonlinear refraction and nonlinear absorption were observed in this water solution of QDs at the wavelength of 1064 nm [Fig. 3(a)]. In the case of CA Z-scan we observed the positive sign of *γ*. The *γ* and *β* were determined using the standard fitting procedure using the relations of Z-scan theory [17]. The nonlinear refractive index and nonlinear absorption coefficient of this solution at *λ* = 1064 nm were found to be 5.5 × 10^{−16} cm^{2} W^{−1} and 3.2 × 10^{−11} cm W^{−1} respectively. The *γ* and *β* of QDs were calculated to be 2 × 10^{−13} cm^{2} W^{−1} and 1.2 × 10^{−8} cm W^{−1} taking into account their volume part in this solution (2.7 × 10^{−3}). The application of different intensities of 1064 nm pulses did not lead to the change of *β*, which points out the third-order process of 2PA as the main mechanism responsible for nonlinear absorption. We also analyzed the nonlinear absorption in the case of two energies (0.034 and 0.047 mJ) of 532 nm pulses [Fig. 3(b)]. The minimal normalized transmittances in these cases were *T*_{0.034 mJ} = 0.86 and *T*_{0.047 mJ} = 0.64. The corresponding *β* of solution were found to be 1 × 10^{−10} and 1.5 × 10^{−10} cm W^{−1} at two different energies of laser pulses. This discrepancy in measurements of nonlinear absorption using different probe pulses point out on some additional nonlinear absorptive processes alongside the 2PA. Most expected mechanism of the variation of nonlinear absorption in that case is the involvement of RSA in overall decrease of propagation of stronger 532 nm pulses through the medium, rather than high-order nonlinear optical processes like 3PA.

Next set of studies was carried out using two associates of QDs and different dyes. Figure 4 presents the results of nonlinear refraction and nonlinear absorption studies of the Cd_{0.5}Zn_{0.5}S QD + DEC associates in water. In that case the QD-contained solution consisted of 0.008 g Cd_{0.5}Zn_{0.5}S QDs, 2.9 g of distilled water, and 0.08 g of gelatin. The weight concentration of DEC in this suspension was 10^{−3}. The positive nonlinear refraction was observed using 1064 nm pulses [Fig. 4(a)]. The nonlinear absorption was demonstrated at two wavelengths (1064 and 532 nm) of picosecond Nd:YAG laser radiation [Figs. 4(a) and 4(b)]. The *γ* and *β* of this solution at *λ* = 1064 nm were calculated using fitting procedure to be 4.6 × 10^{−16} cm^{2} W^{−1} and 3.4 × 10^{−11} cm W^{−1} respectively. One can see that the influence of DEC on the values of *γ* and *β* of this dye-contained solution of QDs was almost insignificant compared with the *γ* and *β* measured in the water solution of QDs. Meanwhile, in the case of 532 nm the *β* of QD + dye associates was approximately two times larger than in the case of QD solution without dye. The values of nonlinear refraction indices and 2PA, SA, and RSA coefficients at the wavelengths of 1064 and 532 nm are collected in Table 1.

Similar results were obtained in the case of adding another dye (thionine) in water solution of Cd_{0.5}Zn_{0.5}S QDs. In Fig. 5(a), we present the dependence of normalized transmittance on the position of thionine-contained QD solution using OA Z-scan. We observed weak nonlinear absorption at the wavelength of 1064 nm, while strong nonlinear absorption was obtained at the wavelength of 532 nm. The decrease of normalized transmittance of this solution at the valley was Δ*T*_{1064 nm} = 0.21 and Δ*T*_{532 nm} = 0.36 respectively using 1064 nm (*E* = 0.63 mJ) and 532 nm (*E* = 0.028 mJ) pulses. The *β* of this solution were calculated to be 1.0 × 10^{−11} cm W^{−1} (1064 nm) and 2.3 × 10^{−10} cm W^{−1} (532 nm).

The nonlinear absorption and SA in the Cd_{0.5}Zn_{0.5}S QD + erythrosine associates was also analyzed at 1064 nm and 532 nm radiation. In Fig. 5(b), the OA Z-scans demonstrating different types of nonlinear absorption in this solution are presented. The absorption spectra of this solution show strong linear absorption band centered at the wavelength of 520 nm [Fig. 1]. In this sample, we did not observe nonlinear refraction at both used wavelengths. Meanwhile, it demonstrated strong 2PA, SA and RSA. The 2PA was the main mechanism of nonlinear absorption at the fundamental wavelength of Nd:YAG laser (empty squares). At the same time, SA and RSA were dominated at the wavelength of second harmonic of laser radiation at different energies of focused beam (empty circles and filled circles). Standard OA Z-scan fitting allowed determining the sign and magnitude of positive and negative nonlinear absorption coefficients of this solution, as well as saturation intensity (*I*_{sat}) of SA.

One can see that SA, which dominates over RSA at relatively small energies of 532 nm pulses [E = 0.034 mJ, empty circles in Fig. 5(b)], becomes less pronounced at higher pulse energies (E = 0.085 mJ, filled circles) with regard to significantly stronger RSA effect. This difference in the involvement of SA and RSA is clearly seen in the area close to the focal plane of focusing lens (i.e. near z = 0 mm where laser radiation had largest intensity). Further growth of pulse energy led to appearance of deeper valley and larger decrease of normalized transmittance in the vicinity of z = 0 mm (down to *T* ≈0.45). The intensity of laser pulses at these conditions was close to the one at which largest value of optical limiting (~2.1) was achieved (see section 3).

The nonlinear absorption processes at *λ* = 532 nm in the cases including SA and RSA were analyzed by the *α(I) = α _{0} × 1/(1 + I/I_{sat}) + β × I = α_{SA} + α_{RSA}* relation for intensity-dependent absorption coefficient [18]. Here

*α*is the linear absorption coefficient and

_{0}*I*is the intensity of laser pulse. The nonlinear optical coefficients were consisted on two parts: one related with saturable absorption (

*α*

_{SA}) and another related with reverse saturable absorption (

*α*

_{RSA}). Using this model we found the saturation intensity (

*I*

_{sat}= 3 × 10

^{10}W cm

^{−2}) for our QD + dye associates. Meanwhile, the

*β*of this solution associated with RSA was calculated to be 3 × 10

^{−9}cm W

^{−1}(at

*λ*= 532 nm). One can estimate the

*β*of QD + dye associates at these conditions to be ~1 × 10

^{−6}cm W

^{−1}taking into account the volume part of those species in the solution. This strong nonlinear absorption was responsible for optical limiting of 532 nm radiation [Fig. 2].

## 5. Discussion

QDs and dye molecules allow both resonance excitation of energetic levels and resonance transfer of energy. Most probably the observed effect of optical limiting was caused by photosensibilization of these associates due to presence of the dyes possessing larger effective cross-section of the two-photon transition of QDs compared with the cross-section of photoionization. Additionally, the transfer of electrons from erythrosine onto the conduction zone has larger probability, due to small ionization potential, which increases the cross-section of the population of upper state, thus increasing the RSA of 532 nm picosecond radiation in the QD + dye associates. Pure dye solutions, though demonstrating some minor optical limiting, were notably less efficient while one compares this effect with regard to the QD + dye associates. We carried out the Z-scan measurements using pure gelatin solution in water. The nonlinear response in that case was negligible in the range of used intensities of laser radiation (up to 1 × 10^{11} W cm^{−2}). Increasing of intensity above some threshold led to optical breakdown in the gelatin solution in water.

Below we address the usefulness of analysis and variations of the nonlinear optical parameters in small-sized QDs with respect to larger nanoparticles and discuss the potential applications of studied alloyed QDs in the formation of optimal conditions for short-wavelength generation using the high-order harmonic generation in these species. An interest in the synthesis, characterization, and application of such quantum dot materials has grown markedly since early studies of these materials [19,20] due to the strong size-related dependence of their optical and electronic properties. The studies of QD solutions [21,22] have shown a change of the sign of nonlinear optical processes due to size-related features of CdS and As_{2}S_{3} nanoparticles. Some analogous properties can be expected in the case of alloyed QDs embedded in sol–gel thin films. The variations of QD’s sizes lead to a change of absorption spectra compared to the bulk semiconductors (CdS, ZnS) [23]. QDs with sizes less than 4 nm can play a predominant role in the nonlinear refraction of such structures due to the quantum confinement effects. The positive sign of *γ* attributed to small QDs can prevail with respect to the negative sign of *γ* in the case of larger-sized nanoparticles. This peculiarity can lead to the difference in the nonlinear optical properties of bulk materials, large-sized nanoparticles, and small-sized QDs. A detailed consideration of this phenomenon has been analyzed by Ganeev *et al* [21].

Our observations of the optical limiting in QD + dye associates were also mostly attributed to the RSA at the 532 nm. Meanwhile, RSA can play important role at the conditions when absorption cross sections of the excited states become greater than those of the ground states [24]. The efficiency of optical limiting can be estimated by the ratio of cross section of excited state and ground states, which is a function of wavelength, and the populations of the states that evolve in time during the pulse. In the meantime, the optical limiting threshold reduces when the sizes of nanoparticle increase [25]. In our case, we analyzed probabilities of optical limiting in the pure QDs and associates of QD and dye. The nonlinear absorption coefficient of RSA was larger than the coefficient of 2PA of QD + erythrosine at 532 nm. From other hand, 2PA was stronger than RSA in the cases of pure QDs, QD + thionine and QD + DEC solutions.

As has already been mentioned, formation of alloyed QDs with desired low-order nonlinear optical properties may be useful for high-order harmonic generation during propagation of ultrashort pulses through the plasmas containing such QDs. The fundamental task in the context of this problem is the determination of the optimal applications of QDs and nanoparticles as the effective emitters of the high-order harmonics of femtosecond pulses. At the first stage one has to develop different alloyed QDs (particularly Cd_{x}Zn_{1-x}S) satisfying the requirements for efficient high-order harmonic generation in laser-produced plasmas. This task includes (a) the formation of alloyed Zn_{x}Cd_{1-x}S QDs satisfying by their sizes and dispersion, as well as structural and low-order nonlinear optical properties, the conditions of efficient harmonic generation in plasma torches, (b) the morphological, absorptive, and luminescence analysis of the synthesized samples of QDs, and (c) the studies of the nonlinear optical characteristics of QDs by Z-scan technique to determine the influence of low-order optical nonlinearities on the higher orders of nonlinearities, particularly during generation of high-order harmonics.

How many atoms in the nanoparticle become optimal for efficient generation of coherent extreme ultraviolet radiation using a whole ensemble of particles, which allows to increase the number of photons of high-order harmonics, remains a puzzle despite the fact that to date numerous experiments using the gas clusters [26–31], as well as the ablated nanoparticles [32–34] were conducted. Qualitative assessments predict that presence of the particles containing a few hundred to a few thousand atoms in the area of interaction with strong laser field may lead to the maximal growth of generated harmonics. This problem is expected to explore in future studies using the ablated alloyed particles of different sizes. The knowledge of nonlinear absorptive and nonlinear refractive properties of those small-sized structures will allow defining the optimal conditions of excitation of these alloyed QDs during formation of plasma plumes for harmonic generation. The research will be aimed to show that the dimensions of alloyed QDs of the order of a few nanometers are optimal for amendment of harmonic generation efficiency. Those studies should lead to the understanding of the processes occurring during harmonic generation in small-sized ensembles of atoms. In this connection, present studies allow determining the role of impeding effects associated with the low-order nonlinearities in the restriction of high-order nonlinear optical processes.

## 6. Conclusions

In conclusion, we have demonstrated the optical limiting in Cd_{0.5}Zn_{0.5}S + erythrosine associates. The stabilization of propagated radiation at the level of 0.65 mJ of 532 nm, 40 ps pulses was achieved. We studied the nonlinear optical processes in the solutions containing Cd_{0.5}Zn_{0.5}S QDs and their associates with three types of dyes using 1064 nm and 532 nm pulses, to determine the mechanisms of observed optical limiting. These studies allowed calculating the nonlinear optical parameters associated with the two-photon absorption, saturable absorption, reverse saturable absorption, as well as nonlinear refraction in those solutions. We have shown that the nonlinear refraction of studied solutions was due to the Kerr nonlinearity in the field of picosecond laser pulses. In the meantime, the nonlinear absorption was attributed to the two-photon absorption, saturable absorption, and reverse saturable absorption.

We have performed the analysis of the nonlinear optical properties of QDs in order to determine the effect of influence of the low-order nonlinearity on the high-order one. In particular, the generation of high-order harmonics in those QDs can be performed with the use of femtosecond and picosecond laser pulses. We have presented the quantitative analysis of the nonlinear optical parameters of QD + dye associates. Particularly, we have analyzed the normalized transmittances of alloyed QDs in the case of the open and closed aperture Z-scan schemes and discussed the potential role of nonlinear absorption during high-order harmonic studies using those species. The analysis of these dependences allowed calculating the basic low-order optical nonlinearities (i.e. nonlinear refraction indices and nonlinear absorption coefficients). The nonlinear refraction index and nonlinear absorption coefficient of Cd_{0.5}Zn_{0.5}S QDs were measured at *λ* = 1064 nm to be 2 × 10^{−13} cm^{2} W^{−1} and 1.2 × 10^{−8} cm W^{−1} taking into account their volume parts in the solutions, while the reverse saturable absorption of the Cd_{0.5}Zn_{0.5}S QDs and erythrosine at *λ* = 532 nm was almost two orders larger (~1 × 10^{−6} cm W^{−1}).

The novelty of this research is related with the potential applications of alloyed quantum dots in their future applications as the media suitable for efficient high-order harmonic generation and creation of the sources of coherent extreme ultraviolet radiation. To define best conditions of plasma formations containing such alloyed quantum dots for harmonic generation one has to carefully study the low-order nonlinear optical processes in these species. This knowledge will help to restrict the impeding processes influencing the conversion efficiency of infrared pulses towards the short wavelength region. Thus the performed calculations of the nonlinear refractive and absorptive properties of alloyed quantum dots allow the application of those features for optimization of higher-order nonlinear optical processes, such as high-order harmonic generation.

## Funding

Russian Fund for Basic Research (RFBR Grant Nº 17-52-12034 ННИО_а); The Postdoctoral Management Committee of Hubei Province; Chinese Academy of Sciences President’s International Fellowship Initiative (Grant No. 2018VSA0001).

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