Low- and high-order nonlinear optical properties of Ag₂S quantum dot thin films

3.1 Z-scans and TA measurements of Ag₂S QD films

Figure 2A shows the absorption spectra of two QD films of different thickness (80 and 500 nm). The absorption band between 300 and 400 nm (>2.0 eV) can be ascribed to the band gap of the Ag₂S QDs, which was blue-shifted compared with that of bulk Ag₂S (0.9~1.1 eV) [33]. The absorption spectra of Ag₂S QDs thin films were in agreement with the tendency of the suspension, illustrating the QDs thin film we got. The linear increase with the absorption of different thickness suggests that amounts of Ag₂S QDs were absorbed after being spin-coated with different speeds, resulting in a buildup of homogeneous films. The inset in Figure 2A shows the transmission electron microscopy (TEM) image of Ag₂S QDs. The average size of QDs was ~4 nm (JEOL-JEM-2100F, Japan). High-resolution TEM image of Ag₂S QDs with well-developed lattice fringes shows good crystallinity of all the samples in Figure 2B. Atomic planes with d-spacing of 0.225 nm are indexed to the (122) facet of monoclinic α-Ag₂S, suggesting the synthesis of Ag₂S QDs. Energy-dispersive X-ray spectroscopy (EDS) (S-4800, Hitachi, Japan) was carried out to further characterize the composition of QDs. Ag and S elements were with an atomic ratio of 2.11:1 in the synthesized QDs, which is similar to the bulk Ag₂S (Figure 2C,D). So that the combined TEM and EDS results reveal that the thin film we manufactured was indeed Ag₂S QDs thin film. Figure 3 shows the CA Z-scans of two Ag₂S QD films using 30 fs pulses at λ=800 nm. The pulse energy was 0.36 μJ. The maximum fluence at the beam waist during these Z-scans was 7×10⁻³ J cm⁻² and the peak intensity was I₀=2×10¹¹ W cm⁻².

Figure 2:

(A) Absorption spectra of thin (80 nm) and thick (500 nm) Ag₂S films. Inset: transmission electron microscopy (TEM) image of synthesized Ag₂S quantum dots (QDs) with the 5 nm scale plate. (B) High-resolution TEM image of Ag₂S QDs. (C) Energy-dispersive X-ray spectroscopy (EDS) of Ag₂S QDs thin film. (D) EDS of Ag₂S bulk target.

Figure 3:

Z-scan measurements at 800 nm.

Closed aperture (CA) Z-scans of (A) 80 nm and (B) 500 nm thick films. Solid curves show the fits using (2).

In the general case of joint contribution of nonlinear refraction and absorption the normalized transmittance of samples along z-axis, T(z), can be presented as follows [34]:

where ΔΦ₀=kγI₀L_eff and Δψ₀=βI₀L_eff/2 are the phase variations due to nonlinear refraction and nonlinear absorption, respectively, x=z/z₀, z₀=k(w₀)²/2 is the Rayleigh length, k=2π/λ is the wave number, w₀ is the beam waist radius at the 1/e² level of intensity distribution, I₀ is the intensity in focal plane, L_eff=[1–exp(–α₀L)]/α₀ is the effective length of the medium, α₀ is the linear absorption coefficient, and L is the thickness of sample.

By making the substitution ρ=β/2kγ one can get the relation between ΔΦ₀ and Δψ₀(Δψ₀=ρΔΦ₀). In that case (1) can be re-written as follows:

This formula was fitted with experimental CA data. The fitting of experimental curves allowed to extract phase changing due to the change of the refractive and absorptive properties of the transparent materials. The measurement of nonlinear refractive index and nonlinear absorption coefficients was based on the determination of phase change of probe pulses.

Thinner film had higher values of γ and β. The β values of the 80 and 500 nm films were measured to be −1×10⁻⁷ and −3.2×10⁻⁸ cm W⁻¹. The negative nonlinear absorption was attributed to saturable absorption (SA). The nonlinear refractive index of thicker film (γ=1×10⁻¹² cm² W⁻¹) was 11 times smaller than that of the thin film (γ=1.1×10⁻¹¹ cm² W⁻¹). Notice that the Z-scan measurements of the dissolved in the hexane Ag₂S QDs showed that the nonlinear absorption coefficient of this suspension at λ=800 nm was 8.8×10⁻¹² cm W⁻¹, and the nonlinear refractive index was 3×10⁻¹⁶ cm² W⁻¹ [35] that was correspondingly 10⁴ and 10⁵ times smaller than the same parameters of 80 nm film. Many reasons can account for the improved nonlinear absorption in the Ag₂S QDs thin films such as improved electronic passivation of the QDs surface, the smaller Ag₂S QDs size, contribution from Ag₂S two-photon absorption.

In the case of 400 nm, 30 fs probe pulses the nonlinear refraction was larger than in the case of 800 nm pulses. The CA Z-scan of 80 nm film showed the positive nonlinear refraction and positive nonlinear absorption, when the valley was deeper than the peak (Figure 4A). The nonlinear refraction index of this thin film was calculated to be γ=3.3×10⁻¹⁰ cm² W⁻¹, while in the case of thicker film (500 nm) it was 25 times smaller (γ=1.3×10⁻¹¹ cm² W⁻¹).

Figure 4:

Z-scan measurement at 400 nm.

Normalized transmittances in the case of (A) CA Z-scan of 80 nm film and (B) Open-aperture (OA) Z-scans of 80 and 500 nm films measured using the 400 nm, 30 fs pulses. Theoretical curves are the fits deduced from Eqs. (2), (4), and (5).

For the OA Z-scans the normalized transmittance is given by [32]

This formula can be presented in a simplified form

where q=βI0Leff/(1+z2/z02).

In the case of SA, the nonlinear absorption coefficient and absorption coefficient are determined by the relations

Here I_sat is the saturation intensity for the SA, which is related with the concentration of the active centers in the medium, the effective cross-sections of involved transitions and the lifetimes of excited states. In the case of low intensity, the SA at λ=800 nm dominated over other nonlinear optical processes in the used samples.

The fitting of the experimental data allows to extract a phase shift of the probe laser pulses. If the phase shift is positive (i.e. self-focusing occurs), then the peak will trail the valley. If the phase shift is negative, then the valley will trail the peak (i.e. self-defocusing). The magnitude of the phase shift can be determined from the change in normalized transmittance between peak and valley, ΔT_pv, using the relation

Here S is the fraction of beam transmitted through the aperture. The nonlinear index, n₂, can then be determined from phase change.

Contrary to the 800 nm probe pulses, the use of 400 nm radiation led to variation of nonlinear absorption from SA to reverse saturable absorption (RSA). The CA measurements revealed the high value of nonlinear absorption coefficient in the case of 80 nm film (β=4×10⁻⁵ cm W⁻¹). Almost similar value was obtained during OA Z-scan of this film (β=3×10⁻⁵ cm W⁻¹, Figure 4B). Note that simultaneously with this process we observed the growth of normalized transmittance at the highest intensities that can be attributed to the higher-order SA effect (see the variation of normalized absorption in the vicinity of z=0, Figure 4B). The nonlinear absorption in thicker (500 nm) film (β=1.2×10⁻⁶ cm W⁻¹, in the case of OA Z-scan, and β=1.6×10⁻⁶ cm W⁻¹, in the case of CA Z-scan) was 25 times smaller compared with the β of thin film. The two positive γ values reveal that the Ag₂S QDs films show a self-focusing behavior at both 400 and 800 nm wavelengths. The β values are positive (at 400 nm) and negative (at 800 nm), indicating that the Ag₂S QDs thin film behave as strong excited-state absorbers and optical bleachers, respectively, at the corresponding wavelengths. The measured relaxation time of Ag₂S QDs thin films at 400 nm was short enough for them to be applied for optical switching devices.

In order to understand the observed difference in the Z-scan profile for Ag₂S QD thin film with different thickness, optical density of these films can provide the valuable reasoning. As reported in the literature, Ag₂S QD exhibit weak surface plasmon resonance at 440 nm. Moreover the excitation at 400 nm using moderate intensity of femtosecond laser pulses in our experiment suggest the nonlinear absorption originating from multiple excitons generation in single QD through nonradiative auger recombination process. However, the ground state bleaching (GSB) for the Ag₂S is already reported at 3.2 E_g for the Ag₂S QD by the Sun et al. [36], where E_g is the band gap energy. The GSB process leads to the increase in the transmittance as the intensity of laser pulse increases which occurs in the vicinity of the focal region. For thinner film of 80 nm, the threshold for the GSB happened to be smaller due to the density of the Ag₂S QD in the vicinity of the irradiated area whereas for thicker film of 500 nm, this threshold is much higher due to the number density of the Ag₂S QD. There are few reports on the Ag₂S nanocrystal (NC) in suspensions suggesting the two-photon absorption process at reasonably high fluence of incidence photons. The obtained β in Ag₂S QD was found to be much larger as compared to the Ag₂S NC at 532 nm (β=5.5×10⁻⁸ cm W⁻¹, [37]).

There are various reports on the TA phenomenon in the Ag₂S QDs and NCs measured in the near-infrared region [36], [38], which was attributed to the Auger recombination process. Meantime, the decay time constant for Ag₂S QDs was reported neither at 800 nm nor at 400 nm wavelength regions. We measured the TA in the 80 and 500 nm thin films containing the Ag₂S QDs deposited on the glass substrates using the 400 nm, 30 fs pulses. The energy of the pump pulse was used to be 30 nJ to excite the films. Prior to the measurements of the TA of films, similar measurements of the glass substrate were performed, to separate its contribution from the TA data obtained in the case of Ag₂S QD thin films, which showed the absence of the change in transmittance with time delay in the case of substrates.

Figure 5A shows the temporal evolution of transmittance in the case of the 80 nm Ag₂S QD thin film. The TA profile demonstrated the transient bleaching due to SA as compared to the reverse process in the 500 nm thick Ag₂S QD film (Figure 5B). In the case of 500 nm Ag₂S QD film, transient transmittance decreases with delay time, which is due to RSA during the temporal overlap of pump and probe pulses. In order to confirm the RSA at 400 nm wavelength, we analyzed the OA Z-scans of these two films (Figure 4B), which depicted the positive nonlinear absorption at employed pulse energy and at the area out from the maximal intensity region (i.e. out from the focal area). However, as already mentioned, in the vicinity of focal area, the transmittance of laser pulses increased for 80 nm Ag₂S QD thin film, which is probably due to the dominance of SA phenomenon over RSA, contrary to the case of the 500 nm film showing the RSA at these conditions. Thus our TA measurements (Figure 5) were found to be consistent with the OA Z-scan studies of two films. The decay time constants were determined to be 150 and 245 fs in the case of 80 and 500 nm films respectively. The difference of the decay times for these two films was attributed to different life times of excited states and absorption probabilities in the case of thin and thick Ag₂S QD films.

Figure 5:

Temporal evolution of probe pulse transmittance through the Ag₂S films in the case of 400 nm, 30 fs pulses. (A) 80 nm thick film and (B) 500 nm thick film.

3.2 HHG in the plasmas produced on the Ag₂S QD films

A search for new applications of QDs is an important task for the optical community. One of the ideas is to find the optimal conditions in application of such QDs as effective emitters of the high-order harmonics of femtosecond pulses for the development of the efficient sources of coherent XUV radiation. To study the high-order nonlinear optical properties through HHG the Ag₂S QD suspension was dried on the quartz substrates and placed in the vacuum chamber for creation of the plasma plume by laser ablation of this film. We analyzed the influence of the delay between the heating and the driving pulses and application of different energies of heating pulses on the harmonics yield.

Figure 6 shows the spectra of the high-order harmonics in the spectral range of 30–80 nm generated from the ablated QD thin film. The optimal delay between the heating and the driving pulses was found to be 400–500 ns. This figure also shows the plasma emission spectrum of ablated Ag₂S QD film. Note that the conditions of ablation at relatively high pulse energy of the heating radiation (E_ns=9 mJ), when the plasma emission shown in Figure 6C dominates in the XUV spectra, are unsuitable for efficient HHG due to the presence of a large amount of free electrons, which prevent the maintenance of optimal phase relation between the generated harmonics.

Figure 6:

Harmonics emission spectrum.

(A) Harmonics emission spectrum in the case of Ag₂S QD ablation of thin films using 3 mJ, 5 ns pulses. (B) Harmonics emission spectrum in the case of Ag₂S QD ablation of thin films using 5 mJ, 5 ns pulses. (C) Plasma emission spectrum in the case of Ag₂S QD ablation of thin films using 9 mJ, 5 ns pulses. Dashed lines show the similarity in plasma emission lines in these three conditions of plasma formation.

Lesser excitation of the QD-containing films (by 3 and 5 mJ pulses) allowed formation of the plasmas suitable for HG (Figure 6A,B). Odd harmonics of 800 nm radiation up to the 23rd order (H23) were achieved using the Ag₂S QD plasmas. The appearance of strong harmonics emission did not coincide with the plasma emission from highly charged particles in the studied spectral range (30–80 nm) that confirmed that these experiments were carried out in a soft regime of ablation of QD-containing targets. The driving pulse [I≈(2–5)×10¹⁴ W cm⁻²] did not cause the appearance of strong ionic emission from higher charged molecules and QDs as well.

The estimate of HHG conversion efficiency was carried out using the comparison with known results from other plasmas (silver and carbon [39], [40]). In the case of silver plasma at similar conditions of experiments, we observed the almost three times smaller conversion efficiency with regard to Ag₂S QD plasma. By knowing the conversion efficiency from previous measurements of harmonic generation in the plasmas produced on the surface of bulk Ag at similar experimental conditions (8×10⁻⁶ [39]) we deduced that HHG conversion efficiency in Ag₂S QD plasmas was ~2×10⁻⁵.

The application of two electronically separated pulses from different lasers synchronized by a digital delay generator allows to analyze the involvement of various ablated species in the HHG process. Application of this approach for HHG in multi-particle plasmas, alongside with other methods of harmonic enhancement, requires the analysis of the ablated species, to temporally match them with the propagation of driving femtosecond pulses through the plasma.

The highest harmonics yield was observed in the plasmas of ablated Ag₂S QD thin film (atomic weight 247.8 amu) after 400–500 ns delay from the beginning of ablation. Note that the use of carbon plasma (atomic weight 12 amu) allowed maximal harmonic intensity after a significantly smaller delay (about 30–50 ns between the heating and the driving pulses using similar pulse energies). Further increase of the delay led to a gradual decrease of the HHG efficiency from Ag₂S QDs plasmas (see variations of 13th and 17th harmonic yields at different delays, Figure 7). The harmonics almost disappeared once the delay exceeded 2 μs. No harmonics were observed after the maximum delays explored in these studies (25 μs).

Figure 7:

The 13th and the 17th harmonics emission variations at different delays between heating nanosecond pulses and driving femtosecond pulses.

Experiments using ablated Ag₂S bulk target led to similar dependence of the harmonics yield on the delay between the heating and the driving pulses. These studies showed that, independently on whether molecules or QDs spread out from the target surface of the same material, they appear in the area of femtosecond beam propagation at approximately the same time. The harmonics cut-off was higher for the ablated bulk Ag₂S (H33) with regard to the QD species. Plasma from the ablated Ag₂S QD thin film allowed generation of up to H19 at similar experimental conditions of ablation (Figure 8). In the meantime, the conversion efficiency for the lowest orders in that case was three to four times larger compared with the ablation of bulk Ag₂S. For the QDs thin films have a higher intensity of the harmonic generation within 500 ns than the same bulk material. The HHG during ablation of QDs-containing targets has revealed the advantages of using such species for frequency conversion in the XUV range. Due to the larger cross-section of recombination, possibility of recombination of accelerated electron with parent multi-atomic particles through either recombination with the same atom or the neighbor atom and the multi-atomic particle as a whole were considered as the most probable reasons in the growth of HHG yield from such plasmas. However, the conditions of experiments, particularly the delay between heating and driving pulses, were not optimized.

Figure 8:

Comparison of harmonics spectra in the case of ablation of the Ag₂S bulk target (thick curve) and Ag₂S QD thin film (thin curve).

The developed method for the analysis of multi-particle plasma formation using two laser sources for HHG using laser ablation can be considered a promising approach for materials science. Its application will expand the possibilities of optimizing HHG in laser-produced plasma plumes, allow to implement new approaches for the study of large molecules and clusters undergoing ablation, and significantly increase the range of the objects of study compared with HHG in gases.