Tunable nonlinear absorption and optical limiting behavior of NaBi(Mo_xW_1−xO₄)₂ single crystals with ratio of Molybdenum/Tungsten

NaBi(Mo_xW_1−xO₄)₂ single crystals for compositions of x = 0, 0.5 and 0.75 were grown by Czochralski method [13, 21]. Bi₂O₃, MoO₃, WO₃ and Na₂CO₃ starting compounds were used in the required ratios for each crystal. The starting compounds used in stoichiometric ratios were mixed and then pelleted. The pellets were heated at 700 °C–800 °C for 20–24 h to obtain a single phase. Throughout the growing process, 2 mm h⁻¹ pulling rate and 15 rpm rotation rate was applied. After the end of the crystal growth process, small rectangular prism-shaped pieces were cut from the large ingot and these pieces were polished. NaBi(Mo_xW_1−xO₄)₂ single crystals for x = 0, 0.5 and 0.75 were represented as crystals 1, 2 and 3 in this report.

X-ray diffraction (XRD) experiments are used to analysis of structural characterization of the grown crystals. Rigaku miniflex model diffractometer emitting CuK_α radiation at wavelength of 0.154049 nm from 20 to 50° with a speed of 0.02°/s was used for XRD measurements. The thicknesses of the single crystals were measured at around 0.4 cm. UV-1800 model Shimadzu UV–vis spectrophotometer was used to reveal the linear optical behavior of the NaBi(Mo_xW_1−xO₄)₂ (at x = 0, 0.5 and 0.75) single crystals. OA Z-scan experiments with Q-switched Nd:YAG (Quantel Birillant) laser (10 Hz repetition rate, 4 ns pulse duration) at 532 nm excitation wavelength were carried out to determine nonlinear optical behavior of the crystals. The beam waist radius (ω₀) at the focus was used as 22 μm, Rayleigh length were calculated to be 2.85 mm for 532 nm. The OA experiments were performed at 0.8, 2.7 and 4 μJ input energies and at 13.23, 44.10 and 66.16 MW cm⁻² the input intensities.

Figure 1 depicts the XRD patterns of NaBi(Mo_xW_1−xO₄)₂ crystals. XRD patterns show sharp peaks at 31.30° and 64.95° for crystal 1, 34.60° and 70.00° for crystal 2, 35.20° and 70.90° for crystal 3. The presence of these peaks shows that grown compounds were successfully obtained in single crystal form. The peaks seen in the XRD patterns of crystals 1 and 2 are in good accordance with the literature's previously published peaks [13]. Considering the [20], the observed peaks are related to tetragonal crystalline structure of the studied crystals and figure 1 shows the corresponding Miller indices on the peaks. When the positions of the peaks observed for each crystal in the figure were compared, it was seen that the angle position of the peaks seen at high degrees corresponded to almost twice the angle position of the peaks seen at low degrees. This shows that the planes of the respective peaks are parallel to each other. For example, the (200) plane of the peak at 35.20° observed for crystal 3 is parallel to the (400) plane of the peak at 70.90°. This can be interpreted as the orientation of crystal surfaces in a single plane. The values of particle sizes (D) were were found to be 61.02, 29.92 and 44.43 nm for 1, 2 and 3 crystals, respectively, which were calculated using the Scherrer's equation (D = 0.94λ/β cosθ) [22]. Herein, θ is the Bragg angle, β is the FWHM and λ refers to the wavelength of the x-ray.

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Figure 2(a) indicates linear absorption behavior of crystals 1, 2 and 3. The Mo/W ratios are 0, 1 and 3 for crystal 1, 2 and 3, respectively. As can be seen from this figure, the increased Mo/W ratio resulted in increased absorption with slightly shifted absorption band edge towards the longer wavelength. The energy of forbidden bandgap is obtained by the following expression [23]

$$\begin{eqnarray}&&\alpha h\nu =A{\left(h\nu -{E}_{g}\right)}^{n}\end{eqnarray} \tag{ 1 }$$

where n = 1/2 and n = 2 for direct and indirect transitions taking place between valence and conduction bands, E_g is forbidden bandgap energy, α is absorption coefficient, A is a constant and hν is photon energy. Due to the direct transition of the crystals 1, 2 and 3, (αhν)² versus hν graphs (Tauc plot) presented in figure 2(b) give the E_g values of the studied single crystals. The E_g values are found as 3.47, 3.24 and 3.13 eV for crystals 1, 2 and 3. The reported bandgap energies of the NaBi(MoO₄)₂ and NaBi(WO₄)₂ crystals are around 2.90 and 3.50 eV, respectively [14, 15]. It is clearly seen that increasing Mo/W ratio in the crystal led to decreasing bandgap energy. This also means that the E_g value of NaBi(Mo_xW_1−xO₄)₂ single crystals can be adjusted for desired optoelectronic applications by varying the Mo/W ratio. The tuning characteristics of the bandgap energy of NaBi(MoxW1-xO4)2 compounds provide a remarkable advantage for optoelectronic applications.

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Nonlinear optical behavior and nonlinear absorption mechanisms are strongly associated with the defects in the structure as well as bandgap energy of the materials [24–28]. The tail width of absorption band edge, known as the Urbach tail, is used to reveal the defects just below the conduction band using the following expression [29]

$$\begin{eqnarray}&&\alpha ={\alpha }_{0}\exp \left(hv/{E}_{U}\right)\end{eqnarray} \tag{ 2 }$$

where α₀ is a constant, E_U is the Urbach energy and α is the linear absorption coefficient. The inverse slope of the linear region of the lnα with respect to hν graphs presented in figure 3 provides the E_U values of the samples. The values of E_U are calculated as 0.37, 0.17 and 0.15 eV for crystals 1, 2 and 3, respectively. Decreasing E_U value with increase of the Mo/W ratio is the evidence of the decreasing defects in the structure [30, 31].

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OA Z-scan measurements are conducted at 532 nm irradiation wavelength under several input densities to bring out the NA properties of 1, 2 and 3 single crystals. The data of Z-scan are analyzed using a theoretical model that takes into account the contribution of one-photon absorption (OPA), two-photon absorption (TPA) and free carrier absorption (FCA) to NA.

$$\begin{eqnarray}&&\displaystyle \frac{dI}{d{z}^{\text{'}}}=\displaystyle \frac{\alpha I}{1+I/{I}_{SAT}}-\displaystyle \frac{{\beta }_{eff}{I}^{2}}{1+{I}^{2}/{I}_{SAT}^{2}}\end{eqnarray} \tag{ 3 }$$

In this model, the first term represents the OPA and its saturation, the second term represents TPA, FCA and their saturations. In equation (3), I_SAT is the saturation intensity threshold and β_eff is the effective NA coefficient and it is given as below.

$$\begin{eqnarray}&&{\beta }_{eff}=\beta +\left({\sigma }_{0}\alpha {\tau }_{0}/\hslash \omega \right)\end{eqnarray} \tag{ 4 }$$

The fitting details are given in [32]. The curves of OA Z-scan of the crystals 1, 2 and 3 at various input intensities are shown in figure 4. When the input intensity increased, the normalized transmittance for crystal 1 decreased. Contrarily, for crystals 2 and 3, the normalized transmittance increased as the input intensity increase. Due to lower energy of the incident light (2.32 eV) than that of the bandgap energies of the single crystals, the main NA mechanism is TPA for studied crystals. On the other hand, the presence of intermediate states allows the differentiation of two types of TPA: (i) genuine TPA, which involves simultaneous absorption of two photons through a virtual state, and (ii) sequential TPA also known as OPA + ESA (excited state absorption) is sequential absorption of two photons [33]. Intermediate states created by defects lead to enhanced depletion of the ground state population, resulting in increased ESA. Genuine TPA is common when the NA coefficient is independent of the input density. However, when the NA coefficient changes (increases/decreases) with increasing input density, the ESA process will become dominant. Z-scan cannot reveal the nature of TPA, therefore, intensity-dependent NA assessment is necessary to ascertain the true mechanism behind TPA. Therefore, the graph of variation β_eff by input density is presented in figure 5. According to this figure, the studied crystals have real intermediate states in the energy region of 2.32 eV. NA decreased with increasing input densities due to defect states corresponding to the energy region of 2.32 eV being filled by OPA. Therefore, the main NA mechanism is sequential TPA for these crystals.

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The normalized transmittances of single crystals at 66.16 MW cm⁻² are presented in figure 6. The obtained β_eff are found to be 3.73 ×10^–7, 2.98 ×10⁻⁷ and 1.24 ×10⁻⁷ cm W⁻¹, and the I_SAT values are obtained as 6.63 ×10⁹, 3.86 ×10⁹ and 1.80 ×10⁹ W/cm² for crystals 1, 2 and 3, respectively. Decreased β_eff is obtained for increasing Mo/W ratio and a similar trend is observed for I_SAT values. The schematic of the proposed NA mechanisms for these single crystals were given in figure 7. All of the single crystals have the same NA mechanism (sequential TPA). On the other hand, their defect states density created differences on the power of NA behaviors. Their defect states density were displayed in figure 7 as dash line. S.G. Singh et all [34] reported five defect centers around 3.1, 2.8, 2.6, 2.0 and 1.7 eV for NaBi(WO₄)₂ which is represented as crystal 1 in this study. According to figure 5, it was also said that the crystal 2 and 3 have defect states at around 2.32 eV energy region inside the band gap. The observing increasing normalized transmittance (figure 4) can be attributed to lower defect states of crystal 2 and 3 at around 2.32 eV as compared to crystal 1. These lower density of the defect states were filled by OPA and the saturable absorption effect on the NA led to weaker NA behavior as compared to crystal 1. All of the results indicated that the crystal 1 has higher β_eff among other single crystals due to its higher defect states. We reported the effect of the defect states on the NA behavior of the single crystals in our previous studies [35–37].

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An excellent optical limiter for efficient limiting at intense laser beam is composed of FCA, TPA, ESA, nonlinear refraction and nonlinear scattering [38]. As the optical limiters are essential for protecting optically sensitive equipment from hazardous laser light, their development takes great attention [39–41]. An efficient optical limiter limits the transmitted light intensity over its optical limiting threshold and holds it constant, and in this way it protects the sensitive devices. It is well known that a lower optical limiting threshold causes higher optical limiting response. Figure 8 demonstrates the normalized transmission curves as a function of fluence. The distance dependent fluence relation is given by the following equation [42],

$$\begin{eqnarray}&&I\left(z\right)=\displaystyle \frac{E}{\pi {\omega }^{2}\left(z\right)t}\end{eqnarray} \tag{ 5 }$$

where E is the input energy per pulse and t is the pulse duration, $\omega \left(z\right)$ is the beam waist as a function of distance and it can be determined by following the relation for Gaussian beam waist,

$$\begin{eqnarray}&&{\omega }^{2}\left(z\right)={\omega }_{0}^{2}\left(1+\displaystyle \frac{{z}^{2}}{{z}_{R}^{2}}\right)\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&{z}_{R}=\displaystyle \frac{\pi {\omega }_{0}^{2}}{\lambda }\end{eqnarray} \tag{ 7 }$$

where ${z}_{R}$ is the Rayleigh distance, $\lambda$ is the wavelength of the input light, and ${\omega }_{0}$ is the beam waist at focus. Optical limiting thresholds are found to be 5.19 ×10⁻², 3.39 ×10⁻¹ and 4.38 ×10⁻¹ mJ/cm² for crystals 1, 2 and 3, respectively. It is clearly seen that stronger NA behavior triggers higher optical limiting behavior. Among other crystals, crystal 1 showed stronger optical limiting behavior.

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