# Nonlinear Optical Characterization of InP@ZnS Core-Shell Colloidal Quantum Dots Using 532 nm, 10 ns Pulses

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{−12}cm

^{2}W

^{−1}, β = 4 × 10

^{−8}cm W

^{−1}) of these CQDs were determined using 10 ns, 532 nm pulses. The saturable absorption (β = −1.4 × 10

^{−9}cm W

^{−1}, I

_{sat}= 3.7 × 10

^{8}W cm

^{−2}) in the 3.5 nm CQDs dominated at small intensities of the probe pulses (I ≤ 7 × 10

^{7}W cm

^{−2}) followed by reverse saturable absorption at higher laser intensities. We report the optical limiting studies using these CQDs showing the suppression of propagated nanosecond radiation in the intensity range of 8 × 10

^{7}–2 × 10

^{9}W cm

^{−2}. The role of nonlinear scattering is considered using off-axis z-scan scheme, which demonstrated the insignificant role of this process along the whole range of used intensities of 532 nm pulses. We discuss the thermal nature of the negative nonlinear refraction in the studied species.

## 1. Introduction

_{2}S-CuS, Ag

_{2}S-CdS, Ag

_{2}S-ZnS, Ag

_{2}S-graphene, etc. [9,10,11]).

## 2. Synthesis and Characterization of InP@ZnS CQDs

_{3}(0.9 mmol), ZnCl

_{2}(0.9 mmol) and amine (15.2 mmol) was placed in a reaction vessel and degassed at 110 °C for 40 min. After that the temperature of the mixture was increased to 220 °C in an argon atmosphere and then the phosphorus precursor (TDMAP, 1.4 mmol) was added to the mixture. In the presence of this reagent, nuclei with an average diameter of 3 nm were formed within 7 min. To grow the ZnS shell, sulfur precursor (DDT, 10.6 mmol) was introduced into the prepared mixture.

^{−1}), dried, dispersed in chloroform, and filtered through membranes with a pore diameter of 450 nm.

^{2}M). The intensity distribution of laser beam was close to the Gaussian shape. M

^{2}value was calculated to be 1.4. The beam waist diameter was 60 μm. The 1-mm-thick fused silica cell containing CQDs was moved along the z-axis through the focal point using a translating stage controlled by a computer. The energies of the initial and propagated laser pulses were measured using the calibrated photodiodes. The closed-aperture (CA) and open-aperture (OA) schemes allowed determination of the nonlinear refraction indices (γ) and nonlinear absorption coefficients (β) of the samples, respectively.

## 3. Z-Scans of InP@ZnS CQDs

^{−6}M, Figure 2, and C = 5 × 10

^{−6}M, Figure 3). We show that the 2.5-fold difference in concentration leads, from one hand, to the growth of SA and, from other hand, to the growth and saturation of the refractive nonlinearities and RSA.

^{−6}M). In the case of OA measurements, the saturable absorption manifesting the growth of CQD transmittance in the vicinity of the focal plane in the case of small energies of probe pulses (E = 0.005 mJ, Figure 2a, red filled circles) gradually decreased with the growth of the energy of 532 nm radiation (see red filled circles in Figure 2b–d). The saturation of this process of negative nonlinear absorption follows with the appearance of the valley demonstrating the manifestation of the gradual influence of RSA. This modification of OA z-scans at different energies of 532 nm pulses shows the competition of two nonlinear absorptive processes (SA and RSA) when, at the highest used energies (E = 0.16 mJ, Figure 2d) the valley attributed to the latter process goes down to T = 0.7, while the former process becomes less pronounced.

^{−6}M, Figure 3). The error bars for Figure 2 and Figure 3 were estimated to be 10% for each presented value of normalized transmittance, which represents the averaging of 20 separate measurements. The main difference in these two groups of measurements (Figure 2 and Figure 3) is a growing influence of SA in the latter case. The approximate similarity of OA and CA dependences in Figure 2d and Figure 3d points out the suppression of the nonlinear optical response of studied species at the higher energies of probe pulses.

^{9}W cm

^{−2}. This value of optical damage was more than one order of magnitude larger than the intensities used during our measurements of the optical nonlinearities of samples.

## 4. Optical Limiting and Nonlinear Scattering Studies

^{−6}M) using 10 ns, 532 nm probe radiation (Figure 4, blue empty squares). Initially, the linear dependence between the input and output pulses was sustained up to the manifestation of SA (7 × 10

^{6}W cm

^{−2}). At relatively small range of intensities (7 × 10

^{6}–4 × 10

^{7}W cm

^{−2}) the OL curve shown in Figure 4 demonstrates an increase of transmittance with the growth of laser intensity. Then, starting from I = 8 × 10

^{7}W cm

^{−2}, a gradual decay of transmittance with the increase of 532 nm probe pulse intensity up to 2 × 10

^{9}W cm

^{−2}was observed, which then was slowed down until the maximal used intensity during OL experiments (5 × 10

^{9}W cm

^{−2}). This intensity was close to the optical damage of QDs. The limiting of propagated 532 nm radiation can be attributed to the influence of RSA and/or nonlinear scattering. At stronger intensities of probe pulses, some additional nonlinear optical processes can probably play important role. Another reason for the decrease of the OL slope at higher intensities can be the additional process of saturable absorption on the higher-excited states at the intensities I > 10

^{9}W cm

^{−2}. The role of main liquid component in OL of CQDs suspension (chloroform) was analyzed at different intensities of the probe pulses (Figure 4, red filled circles). One can see that, along the whole range of used intensities of 532 nm pulses, the normalized transmittance remained unchanged, thus manifesting the absence of nonlinear absorption in the chloroform.

## 5. Determination of the Nonlinear Optical Parameters of InP@ZnS CQDs

^{−6}M) at two pulse energies (red filled circles at 0.005 mJ, Figure 3a and 0.02 mJ, Figure 3c). At small energies of probe pulses (Figure 5a, blue empty triangles), the dominating nonlinear optical process is SA, while the role of RSA is almost insignificant.

_{0}/I

_{sat}× (1 + z

^{2}/z

_{o}

^{2})]

^{0.5}

_{o}and I

_{sat}are the laser radiation intensity at the focal plane and saturation intensity and z

_{o}is the Rayleigh length of the focused radiation, z

_{o}= π(w

_{o})

^{2}/λ, w

_{o}is the beam waist radius, and λ is the wavelength of probe radiation.

_{0}/I

_{sat}= 0.08 and I

_{sat}to be ~3.7 × 10

^{8}W cm

^{−2}taking into account the intensity of probe radiation in the focal plane (3 × 10

^{7}W cm

^{−2}).

^{−1}ln [1 + q(z)]

_{eff}/[1 + (z

_{o}

^{2}/z

^{2})], L

_{eff}= [1 − exp (−α

_{o}L)]/α

_{o}is the effective length of the sample, α

_{o}is the linear absorption coefficient, and L is the thickness of the studied sample (L = 1 mm in our case).

_{0}/I

_{sat}× (1 + z

^{2}/z

_{0}

^{2})]

^{0.5}× q(z)

^{−1}× ln [1 + q(z)]

^{−8}cm W

^{−1}) attributed to the influence of RSA.

_{2}Te

_{3}nanoparticles suspension (blue filled squares). The latter species served for comparison of different mechanisms leading to the nonlinear refraction. The discussion and calculation of the nonlinear refractivity will be presented in Section 6.

## 6. Discussion

_{o}/ʋ, where w

_{o}is the beam waist radius and ʋ is the velocity of sound in the colloidal suspension. Commonly, this period is of the order of 1 to 10 ns, which points out that, during propagation of used pulse (10 ns), the acoustic wave can decrease the density of medium. In that case the trailing part of pulse can underwent the influence of the acoustic wave induced variation of density on the refractive properties of the medium.

_{o}): ΔZ ≈ 1.7z

_{o}[23]). Such a relation was maintained in the case when Kerr-related nonlinearity showed a prevailing influence over the thermal-induced refractive nonlinearity (Figure 5b, blue filled squares showing our separate CA z-scan experiments using 532 nm, 10 ns pulses and bismuth telluride nanoparticles suspension at similar focusing conditions). In those experiments with Bi

_{2}Te

_{3}nanoparticles suspension we observed the positive nonlinear refraction and saturable absorption of 532 nm, 10 ns pulses. ΔZ in that case was equal to 7 mm, which almost obeyed the above relation between the Rayleigh length and valley-to-peak distance along the Z axis for the Kerr-induced refractive nonlinearities (ΔZ ≈ 1.75z

_{o}in our case, z

_{o}during our experiments was equal to 4 mm). This study showed that the fast (electronic) nonlinearity leading to positive nonlinear refractivity was notably larger than the slow (thermal) nonlinearity inducing the self-defocusing of propagated nanosecond pulse.

_{o}. In accordance with studies [25], such a relation is attributed to the thermo-optical nonlinearity. Thus we can attribute the observed process of self-defocusing in InP@ZnS core-shell quantum dots to the thermal effect. Notice the absence of thermal lens building in the case of the pure chloroform representing the main liquid component of the studied suspension. Meantime, the role of Kerr effect in the case of InP@ZnS core-shell quantum dots is hardly can be separated from the thermal process, though in the case of molecular structures the role of other Kerr-related effects, such as molecular orientational process, can be notably increased in the case of nanosecond pulses with regard to the pure electronic Kerr effect. We assume that our quantum dots have a symmetric shape and cannot be treated as the anisotropic structures allowing the reorientation during laser pulse and thus do not further consider this process.

_{g}= 0.69 (ħ is the Planck’s constant, ω is the frequency of laser radiation, and E

_{g}is the band gap energy of semiconductor). Particularly, once this parameter becomes larger than 0.69 the medium starts showing the self-defocusing properties. In this connection, the sign of nonlinear refraction can be changed once one considers bulk material and nanoparticles of the same elemental consistence. Correspondingly these species demonstrate the negative sign of γ. However, smaller nanocrystallites may demonstrate a large blue shift in the absorption edge that leads to the variations in effective band gap. Thus the parameter ħω/E

_{g}becomes less than 0.69 and the smaller nanoparticles can demonstrate the self-focusing since their band gap became notably increased. This reversion of optical nonlinearities can be understood in terms of quantum size effect resulting from the confinement of an electron-hole pair in a small volume.

_{g}value for InP@ZnS core-shell quantum dots at the used wavelength of probe pulses was calculated to be notably larger than 0.69 (ħω/E

_{g}= 1.23). Thus, one can expect a negative sign of γ in these QD containing suspensions, once one considers only fast (Kerr-related) processes in the case of 532 nm probe pulses.

_{g}close to 0.69 demonstrate strong Kerr-related nonlinear refraction and vice verse. In our case (ħω/E

_{g}= 1.23) one can hardly expect the large Kerr-related γ of studied species. Earlier, the conclusion on the prevailing role of heat-related process in InP@ZnS core-shell quantum dots was reported in [27] in the case of 4 ns, 532 nm probe pulses. Notice their finding of the positive sign of γ at the same wavelength of InP@ZnS core-shell quantum dots dissolved in toluene in the case of femtosecond probe pulses was attributed to the prevailing influence of the toluene, which modifies the negative sign of nonlinear refraction of InP@ZnS core-shell quantum dots towards the positive sign in the case of InP@ZnS+toluene suspension.

_{2}Te

_{3}nanoparticles and InP@ZnS QDs. Since in both cases the duration of used nanosecond pulses was close to the recombination time of electron and hole, one can attribute the self-defocusing to the thermal effect. Our calculations of γ (−2 × 10

^{−12}cm

^{2}W

^{−1}; see below) showed that this parameter was one order of magnitude smaller than the measurements of InP@ZnS QDs presented in [27] (−1.6 × 10

^{−11}cm

^{2}W

^{−1}), which can be attributed to rather larger molar concentration of the used colloidal suspension in the latter case (0.1 mg/mL in the toluene solvent).

_{o}. Notice a difference between this separation and the one obtained for the cubic nonlinearity (ΔZ ≈ 1.7z

_{o}). The “purely” thermal effects related with linear absorption normally show a separation larger than the 1.1z

_{o}value [28]. Thus one can consider the higher-order process resulting from a nonlinear absorption giving rise to the thermooptical nonlinearity. The question is: what could be a possible mechanism of positive nonlinear absorption in our case? Present measurements show that the only process, which can cause the nonlinear absorption, is RSA. The positive nonlinear absorption starts appearing on this graph (Figure 5b, red empty circles) at 0.02 mJ pulse energy. Another question is: how to fit this experimental result? And is it necessary to fit our data with some thermo-optics-related theoretical curve to determine γ or there is a way to determine this parameter by simpler method?

^{(3)}effect) [29]. Meanwhile, a simplified equation (ΔT

_{pv}≈ 0.4(1 − S)

^{0.25}|ΔΦ

_{o}|) is commonly used for the direct calculation of the nonlinear refractive index at the conditions when the role of nonlinear absorptive effects becomes insignificant [26]. Here ΔT

_{pv}is the normalized difference between peak and valley transmissions, S is the transmission of the aperture in the case of CA scheme, ΔΦ

_{o}= kγI

_{0}L

_{eff}and k = 2π/λ. A similar analysis was performed for higher-order nonlinearities [23]. Authors of [23] treated the nonlinearities encountered in semiconductors where the index of refraction is altered through charge carriers generated by TPA or RSA as a sequential χ

^{(3)}: χ

^{(1)}effect, which can be considered as a fifth-order nonlinearity [30]. Authors of [23] found that, for a fifth-order effect, the peak and valley should be separated by 1.2z

_{o}as compared to 1.7z

_{o}obtained for the third-order effect. The process observed in our case (i.e., nonlinear refraction as a consequence of the thermal lens formation induced by RSA) can also be treated as a sequential effect. Thus our CA z-scan, approximately obeying the above-mentioned peak-to-valley separation rule (ΔZ ≈ 1.2z

_{o}) for such sequential effect, can be attributed to the fifth-order process.

_{pv}≈ 0.21|ΔΦ

_{o}|. Here ΔΦ

_{o}= kηI

_{o}

^{2}L

_{eff}and η is the fifth-order nonlinear refractive index, η = γ/I

_{o}. The third-order nonlinear refractive index calculated using this formula and data presented in Figure 5b for InP@ZnS QDs was equal to γ = −2 × 10

^{−12}cm

^{2}W

^{−1}. The corresponding figure of merit for the studied colloidal suspension of quantum dots is |γ/C| = 1 × 10

^{−6}cm

^{2}W

^{−1}M

^{−1}.

_{SA}attributed to SA was determined to be −1.4 × 10

^{−9}cm W

^{−1}, which is larger than the same parameter measured using the 527 nm, 100 fs pulses (−5.9 × 10

^{−10}cm W

^{−1}, [14]). Additionally, the heat-induced negative nonlinear refractive index of InP@ZnS CQDs retrieved during our studies (−2 × 10

^{−12}cm

^{2}W

^{−1}) was a few orders of magnitude larger than the Kerr-induced index determined at 800 nm in the case of 100 fs pulses (−7.1 × 10

^{−16}cm

^{2}W

^{−1}). Thus one can assume the importance of the temporal and spectral characteristics of the probe radiation in determination of the nonlinear optical characteristics of studied species. Particularly, the difference in the nonlinear refractive properties of core-shell structure can be attributed to the closeness of the probe pulse’s wavelength and excitonic band in the case of 532 nm pulses compared with the 800 nm probe pulses. Another reason in the difference of the nonlinear refractive response of InP@ZnS CQDs in the reported and our cases can be attributed to different experimental conditions (sizes of QDs, molar concentration, specific defects of core-shell structures, etc.) as well as the involvement of additional mechanisms, other than the pure electronic Kerr effect responsible for the nonlinear refraction under the action of ultrashort laser pulses [32,33].

## 7. Conclusions

^{−12}cm

^{2}W

^{−1}, β = 4 × 10

^{−8}cm W

^{−1}) of these CQDs were determined using 10 ns, 532 nm pulses. The saturable absorption (β

_{SA}= −1.4 × 10

^{−9}cm W

^{−1}, I

_{sat}= 3.7 × 10

^{8}W cm

^{−2}) in the 3.5-nm-sized CQDs dominated at small intensities of the probe pulses (I ≤ 7 × 10

^{7}W cm

^{−2}) followed by reverse saturable absorption at higher laser intensities. We have reported the optical limiting studies using these CQDs showing the suppression of propagated nanosecond radiation in the intensity range of 8 × 10

^{7}–2 × 10

^{9}W cm

^{−2}. The role of nonlinear scattering is considered using off-axis z-scan scheme, which demonstrated the insignificant role of this process along the whole range of used intensities of 532 nm pulses. We have discussed the thermal related processes of nonlinear refraction in studied CQD samples.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) TEM image of InP@ZnS QDs. (

**b**) Absorption (blue curve) and photoluminescence (red curve) spectra of InP@ZnS CQDs. The absorption spectrum of InP@ZnS shows first excitonic peak at ~575 nm. The emission band excited by 400 nm radiation was centered at 607 nm, with full width at half-maximum of 70 nm. Inset: High resolution TEM image of QD.

**Figure 2.**Open-aperture (OA, red filled circles) and closed-aperture (CA, blue empty squares) z-scans of InP@ZnS CQDs (C = 2 × 10

^{−6}M) measured at different energies of 532 nm pulses. (

**a**) 0.005 mJ, (

**b**) 0.01 mJ, (

**c**) 0.02 mJ, (

**d**) 0.16 mJ.

**Figure 3.**Open-aperture (OA, red filled circles) and closed-aperture (CA, blue empty squares) z-scans of InP@ZnS CQDs using 2.5 times larger concentration of QDs (C = 5 × 10

^{−6}M) compared with the case shown in Figure 2. These z-scans were measured at different energies of 532 nm pulses. (

**a**) 0.005 mJ, (

**b**) 0.01 mJ, (

**c**) 0.02 mJ, (

**d**) 0.16 mJ.

**Figure 4.**Optical limiting of 532 nm emission at different intensities of probe pulses. Red filled circles: intensity-dependent transmittance of chloroform. Blue empty squares: the same for InP@ZnS CQDs. Inset: dependence of scattered emission on the position of the 1-mm thick cell with regard to the focal plane of the focused probe pulses.

**Figure 5.**(

**a**) Fitting of OA z-scans of core-shell QDs at two energies of probe pulses. Blue solid curve and red dotted curve correspond to the 0.005 and 0.02 mJ pulse energies, respectively. (

**b**) CA z-scans of Bi

_{2}Te

_{3}nanoparticles suspension (blue filled squares) and 3.5 nm InP@ZnS core-shell QDs (red empty circles) using 0.02 mJ probe pulses. The corresponding distances between peaks and valleys of these scans were 7 and 4.4 mm.

**Table 1.**Summary of the nonlinear optical measurements of InP@ZnS CQDs. λ is the wavelength of probe pulse (532 nm), ħ is the Planck’s constant, ω is the frequency of laser radiation, E

_{g}is the energy band gap of studied QDs, γ is the nonlinear refractive index, C is the molar concentration, β

_{SA}is the nonlinear absorption coefficient attributed to saturable absorption, β is the nonlinear absorption coefficient attributed to reverse saturable absorption, I

_{sat}is the saturated intensity, and Reχ

^{(3)}is the real part of third-order nonlinear susceptibility.

λ | Size of QDs | ħω/E_{g} | γ | |γ/C| | β_{SA}(SA) | β (RSA) | I_{sat} | Reχ^{(3)} |
---|---|---|---|---|---|---|---|---|

532 nm | 3.5 nm | 1.23 | −2 × 10^{−12} cm^{2} W^{−1} | 1 × 10^{−6} cm^{2} W^{−1} M^{−1} | −1.4 × 10^{−9} cm W^{−1} | 4 × 10^{−8} cm W^{−1} | 3.7 × 10^{8} W cm^{−2} | 3 × 10^{−13} esu |

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**MDPI and ACS Style**

Ganeev, R.A.; Zvyagin, A.I.; Shuklov, I.A.; Spirin, M.G.; Ovchinnikov, O.V.; Razumov, V.F.
Nonlinear Optical Characterization of InP@ZnS Core-Shell Colloidal Quantum Dots Using 532 nm, 10 ns Pulses. *Nanomaterials* **2021**, *11*, 1366.
https://doi.org/10.3390/nano11061366

**AMA Style**

Ganeev RA, Zvyagin AI, Shuklov IA, Spirin MG, Ovchinnikov OV, Razumov VF.
Nonlinear Optical Characterization of InP@ZnS Core-Shell Colloidal Quantum Dots Using 532 nm, 10 ns Pulses. *Nanomaterials*. 2021; 11(6):1366.
https://doi.org/10.3390/nano11061366

**Chicago/Turabian Style**

Ganeev, Rashid A., Andrey I. Zvyagin, Ivan A. Shuklov, Maksim G. Spirin, Oleg V. Ovchinnikov, and Vladimir F. Razumov.
2021. "Nonlinear Optical Characterization of InP@ZnS Core-Shell Colloidal Quantum Dots Using 532 nm, 10 ns Pulses" *Nanomaterials* 11, no. 6: 1366.
https://doi.org/10.3390/nano11061366