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Yb3+ in the nonlinear refractive spectrum of CaLiBO glasses
Journal of Non-Crystalline Solids 524 (2019) 119637
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Effect of Tb3+/Yb3+ in the nonlinear refractive spectrum of CaLiBO glasses a,⁎
a
S.N.C. Santos , K.T. Paula , J.M.P. Almeida a b
a,b
a
, A.C. Hernandes , C.R. Mendonça
T
a
São Carlos Institute of Physics, University of São Paulo, PO Box 369, 13560-970 São Carlos, SP, Brazil Department of Materials Engineering, São Carlos School of Engineering, University of São Paulo, Av. João Dagnone, 1100, 13563-120 São Carlos, SP, Brazil
A R T I C LE I N FO
A B S T R A C T
Keywords: Femtosecond laser Z-scan technique Nonlinear refractive index Rare earths CaLiBO glass BGO model
This paper reports a study on linear and nonlinear optical properties in a series of lithium‑calcium tetraborate (CaLiBO) glasses in the presence of two rare earth ions, Tb3+ and Yb3+. The nonlinear index of refraction (n2) was determined in a wide wavelength range (470–1500 nm) through femtosecond Z-scan technique. Such results were modeled by BGO approach, in which the optical nonlinearity was related to the oxygens present in the glasses. Also, the molar electronic polarizability evidenced that there is a strong influence of the polarizability of the rare earth ions in the nonlinear optical properties. Thus, we can infer that the cooperation of oxygens and the polarizability of rare earth ions are responsible for the nonlinearity present in the investigated vitreous system.
1. Introduction Research in nonlinear optics is fundamental for the development of new photonic devices with applications in areas of specific interest, such as optical limiting [1,2], all-optical switching [3–5] and photodetectors [6,7]. It has been reported a variety of studies evaluating the nonlinear optical properties of silicate [8], germanate [9], phosphate [10], borate [11,12] tellurite [13] and oxyfluoride glasses [14]. Among these kinds of glasses, the borate ones are known for having low melting point, good thermal stability and easiness in the manufacturing process [15,16]. Due to their high hygroscopicity, the incorporation of modifying ions, such as alkaline, alkaline earth and transition metals, helps to reduce this problem, without changing its properties significantly [17,18]. Furthermore, they are matrices that have excellent solubility of rare earth ions because they present a set of borate groups that constitute the three-dimensional random network [19,20]. For example, boron-based glasses doped with ytterbium (Yb3+) and terbium (Tb3+) ions have been studied for the down-conversion process [21,22] and quantum cutting [23–25]. Also, waveguides with broad emission in the visible spectrum were demonstrated in barium borate glass containing dysprosium (Dy3+) and europium (Eu3+) ions [26]. In spite of the scientific and technological interests on rare earths doped borate glasses, little attention has been given to their optical nonlinearities. Although, borate glasses generally display the lowers optical nonlinearities among the different classes of glass, in this study we show that the addition of rare earth ions can improve such properties, favoring their use in nonlinear optical devices. The investigation was carried out with a lithium calcium tetraborate (CaLiBO) glass system,
⁎
containing ytterbium and terbium ions, which showed to be relevant as down-converter material for the near-infrared region and for applications in solar cells [21]. The nonlinear refraction spectra of the glass with different Tb content were investigated in a wide wavelength range (470–1500 nm) at femtosecond regime. Experimental data obtained through the Z-scan technique were modeled by the BGO approach, in which the optical nonlinearity is related to the oxygen ions present in the glasses. The molar electronic polarizability given by the LorentzLorenz relation showed that there is a strong influence of the polarizability of the rare earth ions on the nonlinear optical properties. We infer that the cooperation of both oxygen ions and the polarizability of rare earth ions are responsible for the nonlinearity present in this vitreous system. 2. Experimental The glasses studied here have composition (99% - x) CaLiBO +1% Yb2O3 + x%Tb4O7 with x = 0.1; 1.0 and 2.0 (mol%) and were synthesized by melt-quenching technique, using platinum crucible and electric furnace open to the atmosphere. High purity B2O3 (Alfa Aesar 97.5%), Li2O3 (Carlo Erba 99%), CaCO3 (Alfa Aesar 99.5%), Tb4O7 (Alfa Aesar 99.9%) and Yb2O3 (Alfa Aesar 99.9%) were used as raw materials. Initially, CaLiBO glass matrix, composed by 60% B2O3 + 30%CaO + 10%Li2O (mol%) (CaLiBO), was prepared. Its reagents were heated at 850 °C for 40 min to allow decarbonation. The temperature was slowly increased to 1100 °C and after 2 h the melt was quenched into a stainless-steel mold at room temperature. Terbium and Ytterbium codoped glass was obtained by melting of the CaLiBO matrix
Corresponding author. E-mail address: [email protected] (S.N.C. Santos).
https://doi.org/10.1016/j.jnoncrysol.2019.119637 Received 17 April 2019; Received in revised form 12 August 2019; Accepted 20 August 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
Journal of Non-Crystalline Solids 524 (2019) 119637
S.N.C. Santos, et al.
together rare earth oxides at 1100–1300 °C during 30–100 min, depending on the composition. The samples were quenched at the same conditions that CaLiBO matrix and annealing at 590 °C for 9 h. Polished flat samples with ~1.4 mm of thickness, free of inclusions or cords were used for the optical measurements. The nonlinear refractive index (n2) and the two-photon absorption (β) spectra were analyzed using closedand open-aperture Z-scan technique, respectively [27,28]. An optical parametric amplifier (OPA) was employed as excitation light source and provides 120-fs pulses from 470 to 1500 nm. The OPA is pumped by a Ti:Sapphire laser amplified system (CPA 2001, Clark MXR®) at 775 nm with 150-fs pulses at 1 kHz repetition rate. Fused silica has been used as reference material, whose nonlinear refractive index was found to be approximately 2.1 × 10−20 m2/W from visible to infrared, which is in accordance with the literature [29]. The experimental error associated with the n2 determination is 20%, being related to the pulse intensity fluctuation, and experimental error on the determination of pulse duration and beam waist. A Pulfrich refractometer (Carl Zeiss Jena Pulfrich Refractometer PR2®) and m-line technique were employed to measure the linear refractive index.
Fig. 2. Linear refractive index of CaLiBO (a), x = 0.1 (b), x = 1.0 (c) and x = 2.0 (d) glasses. The solid lines represent the fitting with Sellmeier equation (Eq. (1)), while symbols are the experimental data with error of the order of 4 × 10−4.
3. Results Absorption spectra of the samples are shown in Fig. 1. CaLiBO presents a wide transmission window, from 350 nm to λ > 1100 nm. Besides that, it is possible to observe absorption peaks that are characteristic of the Yb3+ and Tb3+ ions in the doped samples. The transitions of Tb+3 ion are located at 317 nm (7F6 → 5D1); 338 nm (7F6 → 5 D0); 350 nm (7F6 → 5L9); 368 nm (7F6 → 5L10); 377 nm (7F6 → 5 G6 + 5D3) and 484 nm (7F6 → 5D4) [30,31], and the transition at 975 nm (2F7/2 → 2F5/2) is due to Yb3+ ion [32,33]. The linear refractive index (n0) is an important optical characteristic of the glass which is related to the electronic polarizability [34], as well as the nonlinear index of refraction. In Fig. 2, we present the linear refractive index values measured at 404.7, 435.8, 546.1, 632.8 and 1538 nm (symbols) for all samples. These experimental values were fitted using the bipolar Sellmeier (Eq. (1)) dispersion equation [35],
n02 =
A+
Bλ2 Dλ2 + 2 λ2 − C λ −E
refractive index (continuous line). The Sellmeier coefficients obtained through the fitting are presented in Table 1. The spectrum of n2 (nonlinear refraction spectrum) for the samples CaLiBO, x = 0.1, x = 1.0, and x = 2.0, obtained from closed-aperture (refractive) Z-scan technique are shown in Fig. 3(a), (b), (c) and (d), respectively. The insets of Fig. 3 display a typical Z-scan signature to CaLiBO with x = 0.1, x = 1.0, and x = 2.0 at 950, 700, 750 and 600 nm, respectively, obtained at each wavelength. The nonlinear refraction spectra show a nearly constant behavior as a function of the wavelength, within the experimental error. The mean values of n2 obtained for CaLiBO, x = 0.1, x = 1.0, and x = 2.0 are 4.2, 4.5, 4.6 and 4.7 × 10−20 m2/W, respectively. Such values are about twice higher than the ones reported for fused silica [29]. In addition, for openaperture Z-scan measurements no nonlinear absorption signal was observed, indicating the absence of two-photon absorption in the wavelength range analyzed. The nonlinear refraction spectra displayed in Fig. 3 were modeled using the BGO (Boling, Glass, and Owyoung) approach [36], which is a semi-empirical model based on a classical nonlinear oscillator. It assumes that the second hyperpolarizability is proportional to the square of the linear polarizability, and considers that the incident light frequency is far from resonance (ω ≪ ω0). According to this model, the nonlinear refractive index, in SI (m2/W), is written as [36],
(1)
where A, B, C, D and E are Sellmeier's coefficients and λ is the wavelength in micrometers, in order to obtain the spectra of the linear
n2 (BGO) =
5(n 02 + 2)2 (n 02 − 1)2 (gs ) 6n 02 c ћω0 (Ns )
(2)
in which g is a dimensionless anharmonicity parameter, s is the effective oscillator strength, c is the speed light, ћ is the Planck's constant, N is the composition-dependent ion density, and n0 is the linear refractive index of light at the wavelength λ. The product Ns, as well as the resonance frequency ω0 can be obtained by using
m (ω02 − ω2) 4π (n02 + 2) = 2 3 2(n0 − 1) e 2 (Ns )
(3)
in which m and e are the mass and electron charge, respectively. By evaluating Eq. (3) at two frequencies ω, at which the linear index of refraction n0 is known (through the results in Fig. 2), one are able to determine the parameters Ns and ω0 for each sample. Furthermore, the dispersion of n0 can be included in the BGO model (Eq. (2)) using the Sellmeier equation (Eq. (1)), with the corresponding coefficients displayed in Table 1. The effective oscillator strength, s, was estimated from the ratio
Fig. 1. Linear absorption coefficient spectra of CaLiBO (a), x = 0.1 (b), x = 1.0 (c) and x = 2.0 (d) samples. They were vertically shifted for better visualization of the Yb+3 and Tb+3 absorption peaks. 2
Journal of Non-Crystalline Solids 524 (2019) 119637
S.N.C. Santos, et al.
Table 1 Sellmeier coefficients for CaLiBO glasses obtained from the fitting shown in Fig. 2. Samples glass
A
CaLiBO x = 0.1 x = 1.0 x = 2.0
2.27 2.43 2.49 2.56
± ± ± ±
0.06 0.01 0.09 0.02
B
C
D
0.24 ± 0.02 0.123 ± 0.007 0.11 ± 0.08 0.095 ± 0.008
0.056 ± 0.008 0.085 ± 0.005 0.09 ± 0.03 0.093 ± 0.007
0.6 0.9 1.2 1.3
E ± ± ± ±
0.6 0.5 0.3 0.5
80 ± 30 100 ± 20 100 ± 10 100 ± 20
reason why an almost flat behavior is observed for the n2 dispersion, as seen in Fig. 3. Studies on the n2 of SAL (SiO2-Al2O3-La2O3) glasses were investigated as a function of the content of the rare earth La3+ ion by using the Z-scan technique. In such work, it was observed an increase of n2 with the concentration of the rare earth, which is also related to the oxygen ions [37]. Similarly, the nonlinear refractive index of zinc borotellurite glass was studied for different concentrations of Gd3+. The authors observed an increase in n2 with the rare earth ion concentration, which was attributed to Gd3+ ion inducing a high polarizability of the glass network [38]. The electronic polarizability is another important property that influences optical nonlinearities [39]. The electronic molar polarizability in (Å3) is given by
between the density of nonlinear oscillators (Ns) and the density of oxygen ions in the samples (Nox), considering that oxygen plays the major role in the nonlinearities of oxide glasses [36]. From such procedures, we determined s = 2. Therefore, the only free parameter to be obtained by fitting the experimental data with the BGO model is the anharmonicity parameter g. The red line along the data points in Fig. 3 corresponds to the fitting obtained with the BGO model, according to the procedure described previously, from which the parameter g was determined as being 0.82, 0.84, 0.85, and 0.86 for CaLiBO, x = 0.1, x = 1.0 and x = 2.0, respectively. As it can be seen, there is a good agreement between the experimental data and the model. The mean nonlinear refractive index values obtained from the BGO model to CaLiBO, x = 0.1, x = 1.0 and x = 2.0 are 4.2, 4.5, 4.6 and 4.7 × 10−20 m2/W, which are in good agreement with the experimental ones. Therefore, according to the BGO model, the major contribution for the nonlinear index of refraction of the samples studied here are related to the glass matrix, whose main electronic transitions are located in the UV region of the spectrum,
3 ⎞ RM αM = ⎛ 4 πN A⎠ ⎝ ⎜
⎟
(4)
in which NA is Avogadro's number and RM is the molar refraction value,
Fig. 3. Spectra of the nonlinear refractive index (n2) of CaLiBO (a), x = 0.1 (b), x = 1.0 (c) and x = 2.0 (d). The symbols correspond to the experimental data and solid lines represent the fit obtained with the BGO model, with parameters given in the text. The inserts show the typical Z-signature measured for all samples, while the line is the adjustment from which n2 is extracted. 3
Journal of Non-Crystalline Solids 524 (2019) 119637
S.N.C. Santos, et al.
4. Conclusion
Table 2 Density (ρ), molecular weight (M) and molar electronic polarizability (αM) for the CaLiBO glasses. Samples glass
M(g/mol)
ρ(g/cm3)
αM(Å3)
CaLiBO x = 0.1 x = 1.0 x = 2.0
61.6 65.6 72.3 79.8
2.5743 ± 0.0009 2.732 ± 0.002 2.9269 ± 0.0008 3.131 ± 0.002
3.27 3.32 3.49 3.65
± ± ± ±
The nonlinear refractive index of CaLiBO glasses containing different concentrations of rare earth ions were characterized by the Zscan technique and interpreted using the empirical BGO model. The addition of Tb3+ and Yb3+ ions do not affect the spectral behavior of the nonlinear refractive index, which exhibited a nearly constant value for the spectral window between 470 and 1500 nm, within the experimental error, for all investigated samples. This behavior was confirmed by the BGO model, which also showed that the oxygen ions present in the glass matrix play a role in its third-order nonlinearities. Nonetheless, the n2 of CaLiBO glasses increased with the addition of Tb3+ and Yb3+, indicating that the combination of the oxygen ions present in the matrix and the polarizability of the rare earth ions contributed to the increase of the nonlinear response. This study presents a progress in the understanding of the nonlinear properties of borate glass and the influence that rare earth ions have on these properties, especially those related to third-order susceptibility, contributing for the development of new optical devices.
0.07 0.07 0.08 0.08
Declaration of Competing Interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors gratefully acknowledge financial support from the CNPq, FAPESP (2018/11283-7) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001.
Fig. 4. Nonlinear refractive index as a function of the electronic molar polarizability, evidencing that the increase depends on the addition of the rare earth ions.
References given by the Lorentz -Lorenz equation as [40–42]:
n2 − 1⎤ M RM = ⎡ 02 ⎢ n0 + 2 ⎥ ρ ⎣ ⎦
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(5)
where n0 is the linear refractive index, M is molecular weight and ρ is density (see Table 2). The values for the molar electronic polarizability determined using Eq. (4) are shown in Table 2. In Fig. 4 it can be observed that the mean values of the nonlinear refractive index display a clear increasing tendency, with the molar electronic polarizability, which in turn is related to the increase in the concentration of Tb3+ ion. The increase of the electronic polarizability values is probably due to the presence of Yb3+ (0.86 Å3) ions, as well as the addition and increase of the Tb3+ (1.04 Å3) ion concentration, whose polarizabilities are greater than B3+ (0.003 Å3), Ca2+ (0.47 Å3) and Li+ (0.024 Å3) ions [43,44]. The same behavior has been observed in BiCl3-Li2O-B2O3Er2O3 glasses, in which the polarizability presented a gradual increase with the increase of the Er3+ content [45]. A study of the CaO-B2O3Al2O3-CaF2 system doped with Nd3+ revealed that the electronic polarizability increased as a function of the rare earth concentration, which was attributed to an increase of nonbonding oxygen caused by the rare earth addition since these are more polarizable than the oxygens that are connected [46]. The comparison of the reported observations is in agreement with our results, which demonstrated an increase in both the nonlinear refractive index and the electronic polarizability values for glasses containing rare earth ions. Therefore, our results indicate a cooperative effect between the glass matrix (major effect) and the electronic polarizability of the rare earth contributions to the optical nonlinearity of CaLiBO glasses.
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Effect of Tb3+/Yb3+ in the nonlinear refractive spectrum of CaLiBO glasses a,⁎
a
S.N.C. Santos , K.T. Paula , J.M.P. Almeida a b
a,b
a
, A.C. Hernandes , C.R. Mendonça
T
a
São Carlos Institute of Physics, University of São Paulo, PO Box 369, 13560-970 São Carlos, SP, Brazil Department of Materials Engineering, São Carlos School of Engineering, University of São Paulo, Av. João Dagnone, 1100, 13563-120 São Carlos, SP, Brazil
A R T I C LE I N FO
A B S T R A C T
Keywords: Femtosecond laser Z-scan technique Nonlinear refractive index Rare earths CaLiBO glass BGO model
This paper reports a study on linear and nonlinear optical properties in a series of lithium‑calcium tetraborate (CaLiBO) glasses in the presence of two rare earth ions, Tb3+ and Yb3+. The nonlinear index of refraction (n2) was determined in a wide wavelength range (470–1500 nm) through femtosecond Z-scan technique. Such results were modeled by BGO approach, in which the optical nonlinearity was related to the oxygens present in the glasses. Also, the molar electronic polarizability evidenced that there is a strong influence of the polarizability of the rare earth ions in the nonlinear optical properties. Thus, we can infer that the cooperation of oxygens and the polarizability of rare earth ions are responsible for the nonlinearity present in the investigated vitreous system.
1. Introduction Research in nonlinear optics is fundamental for the development of new photonic devices with applications in areas of specific interest, such as optical limiting [1,2], all-optical switching [3–5] and photodetectors [6,7]. It has been reported a variety of studies evaluating the nonlinear optical properties of silicate [8], germanate [9], phosphate [10], borate [11,12] tellurite [13] and oxyfluoride glasses [14]. Among these kinds of glasses, the borate ones are known for having low melting point, good thermal stability and easiness in the manufacturing process [15,16]. Due to their high hygroscopicity, the incorporation of modifying ions, such as alkaline, alkaline earth and transition metals, helps to reduce this problem, without changing its properties significantly [17,18]. Furthermore, they are matrices that have excellent solubility of rare earth ions because they present a set of borate groups that constitute the three-dimensional random network [19,20]. For example, boron-based glasses doped with ytterbium (Yb3+) and terbium (Tb3+) ions have been studied for the down-conversion process [21,22] and quantum cutting [23–25]. Also, waveguides with broad emission in the visible spectrum were demonstrated in barium borate glass containing dysprosium (Dy3+) and europium (Eu3+) ions [26]. In spite of the scientific and technological interests on rare earths doped borate glasses, little attention has been given to their optical nonlinearities. Although, borate glasses generally display the lowers optical nonlinearities among the different classes of glass, in this study we show that the addition of rare earth ions can improve such properties, favoring their use in nonlinear optical devices. The investigation was carried out with a lithium calcium tetraborate (CaLiBO) glass system,
⁎
containing ytterbium and terbium ions, which showed to be relevant as down-converter material for the near-infrared region and for applications in solar cells [21]. The nonlinear refraction spectra of the glass with different Tb content were investigated in a wide wavelength range (470–1500 nm) at femtosecond regime. Experimental data obtained through the Z-scan technique were modeled by the BGO approach, in which the optical nonlinearity is related to the oxygen ions present in the glasses. The molar electronic polarizability given by the LorentzLorenz relation showed that there is a strong influence of the polarizability of the rare earth ions on the nonlinear optical properties. We infer that the cooperation of both oxygen ions and the polarizability of rare earth ions are responsible for the nonlinearity present in this vitreous system. 2. Experimental The glasses studied here have composition (99% - x) CaLiBO +1% Yb2O3 + x%Tb4O7 with x = 0.1; 1.0 and 2.0 (mol%) and were synthesized by melt-quenching technique, using platinum crucible and electric furnace open to the atmosphere. High purity B2O3 (Alfa Aesar 97.5%), Li2O3 (Carlo Erba 99%), CaCO3 (Alfa Aesar 99.5%), Tb4O7 (Alfa Aesar 99.9%) and Yb2O3 (Alfa Aesar 99.9%) were used as raw materials. Initially, CaLiBO glass matrix, composed by 60% B2O3 + 30%CaO + 10%Li2O (mol%) (CaLiBO), was prepared. Its reagents were heated at 850 °C for 40 min to allow decarbonation. The temperature was slowly increased to 1100 °C and after 2 h the melt was quenched into a stainless-steel mold at room temperature. Terbium and Ytterbium codoped glass was obtained by melting of the CaLiBO matrix
Corresponding author. E-mail address: [email protected] (S.N.C. Santos).
https://doi.org/10.1016/j.jnoncrysol.2019.119637 Received 17 April 2019; Received in revised form 12 August 2019; Accepted 20 August 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
Journal of Non-Crystalline Solids 524 (2019) 119637
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together rare earth oxides at 1100–1300 °C during 30–100 min, depending on the composition. The samples were quenched at the same conditions that CaLiBO matrix and annealing at 590 °C for 9 h. Polished flat samples with ~1.4 mm of thickness, free of inclusions or cords were used for the optical measurements. The nonlinear refractive index (n2) and the two-photon absorption (β) spectra were analyzed using closedand open-aperture Z-scan technique, respectively [27,28]. An optical parametric amplifier (OPA) was employed as excitation light source and provides 120-fs pulses from 470 to 1500 nm. The OPA is pumped by a Ti:Sapphire laser amplified system (CPA 2001, Clark MXR®) at 775 nm with 150-fs pulses at 1 kHz repetition rate. Fused silica has been used as reference material, whose nonlinear refractive index was found to be approximately 2.1 × 10−20 m2/W from visible to infrared, which is in accordance with the literature [29]. The experimental error associated with the n2 determination is 20%, being related to the pulse intensity fluctuation, and experimental error on the determination of pulse duration and beam waist. A Pulfrich refractometer (Carl Zeiss Jena Pulfrich Refractometer PR2®) and m-line technique were employed to measure the linear refractive index.
Fig. 2. Linear refractive index of CaLiBO (a), x = 0.1 (b), x = 1.0 (c) and x = 2.0 (d) glasses. The solid lines represent the fitting with Sellmeier equation (Eq. (1)), while symbols are the experimental data with error of the order of 4 × 10−4.
3. Results Absorption spectra of the samples are shown in Fig. 1. CaLiBO presents a wide transmission window, from 350 nm to λ > 1100 nm. Besides that, it is possible to observe absorption peaks that are characteristic of the Yb3+ and Tb3+ ions in the doped samples. The transitions of Tb+3 ion are located at 317 nm (7F6 → 5D1); 338 nm (7F6 → 5 D0); 350 nm (7F6 → 5L9); 368 nm (7F6 → 5L10); 377 nm (7F6 → 5 G6 + 5D3) and 484 nm (7F6 → 5D4) [30,31], and the transition at 975 nm (2F7/2 → 2F5/2) is due to Yb3+ ion [32,33]. The linear refractive index (n0) is an important optical characteristic of the glass which is related to the electronic polarizability [34], as well as the nonlinear index of refraction. In Fig. 2, we present the linear refractive index values measured at 404.7, 435.8, 546.1, 632.8 and 1538 nm (symbols) for all samples. These experimental values were fitted using the bipolar Sellmeier (Eq. (1)) dispersion equation [35],
n02 =
A+
Bλ2 Dλ2 + 2 λ2 − C λ −E
refractive index (continuous line). The Sellmeier coefficients obtained through the fitting are presented in Table 1. The spectrum of n2 (nonlinear refraction spectrum) for the samples CaLiBO, x = 0.1, x = 1.0, and x = 2.0, obtained from closed-aperture (refractive) Z-scan technique are shown in Fig. 3(a), (b), (c) and (d), respectively. The insets of Fig. 3 display a typical Z-scan signature to CaLiBO with x = 0.1, x = 1.0, and x = 2.0 at 950, 700, 750 and 600 nm, respectively, obtained at each wavelength. The nonlinear refraction spectra show a nearly constant behavior as a function of the wavelength, within the experimental error. The mean values of n2 obtained for CaLiBO, x = 0.1, x = 1.0, and x = 2.0 are 4.2, 4.5, 4.6 and 4.7 × 10−20 m2/W, respectively. Such values are about twice higher than the ones reported for fused silica [29]. In addition, for openaperture Z-scan measurements no nonlinear absorption signal was observed, indicating the absence of two-photon absorption in the wavelength range analyzed. The nonlinear refraction spectra displayed in Fig. 3 were modeled using the BGO (Boling, Glass, and Owyoung) approach [36], which is a semi-empirical model based on a classical nonlinear oscillator. It assumes that the second hyperpolarizability is proportional to the square of the linear polarizability, and considers that the incident light frequency is far from resonance (ω ≪ ω0). According to this model, the nonlinear refractive index, in SI (m2/W), is written as [36],
(1)
where A, B, C, D and E are Sellmeier's coefficients and λ is the wavelength in micrometers, in order to obtain the spectra of the linear
n2 (BGO) =
5(n 02 + 2)2 (n 02 − 1)2 (gs ) 6n 02 c ћω0 (Ns )
(2)
in which g is a dimensionless anharmonicity parameter, s is the effective oscillator strength, c is the speed light, ћ is the Planck's constant, N is the composition-dependent ion density, and n0 is the linear refractive index of light at the wavelength λ. The product Ns, as well as the resonance frequency ω0 can be obtained by using
m (ω02 − ω2) 4π (n02 + 2) = 2 3 2(n0 − 1) e 2 (Ns )
(3)
in which m and e are the mass and electron charge, respectively. By evaluating Eq. (3) at two frequencies ω, at which the linear index of refraction n0 is known (through the results in Fig. 2), one are able to determine the parameters Ns and ω0 for each sample. Furthermore, the dispersion of n0 can be included in the BGO model (Eq. (2)) using the Sellmeier equation (Eq. (1)), with the corresponding coefficients displayed in Table 1. The effective oscillator strength, s, was estimated from the ratio
Fig. 1. Linear absorption coefficient spectra of CaLiBO (a), x = 0.1 (b), x = 1.0 (c) and x = 2.0 (d) samples. They were vertically shifted for better visualization of the Yb+3 and Tb+3 absorption peaks. 2
Journal of Non-Crystalline Solids 524 (2019) 119637
S.N.C. Santos, et al.
Table 1 Sellmeier coefficients for CaLiBO glasses obtained from the fitting shown in Fig. 2. Samples glass
A
CaLiBO x = 0.1 x = 1.0 x = 2.0
2.27 2.43 2.49 2.56
± ± ± ±
0.06 0.01 0.09 0.02
B
C
D
0.24 ± 0.02 0.123 ± 0.007 0.11 ± 0.08 0.095 ± 0.008
0.056 ± 0.008 0.085 ± 0.005 0.09 ± 0.03 0.093 ± 0.007
0.6 0.9 1.2 1.3
E ± ± ± ±
0.6 0.5 0.3 0.5
80 ± 30 100 ± 20 100 ± 10 100 ± 20
reason why an almost flat behavior is observed for the n2 dispersion, as seen in Fig. 3. Studies on the n2 of SAL (SiO2-Al2O3-La2O3) glasses were investigated as a function of the content of the rare earth La3+ ion by using the Z-scan technique. In such work, it was observed an increase of n2 with the concentration of the rare earth, which is also related to the oxygen ions [37]. Similarly, the nonlinear refractive index of zinc borotellurite glass was studied for different concentrations of Gd3+. The authors observed an increase in n2 with the rare earth ion concentration, which was attributed to Gd3+ ion inducing a high polarizability of the glass network [38]. The electronic polarizability is another important property that influences optical nonlinearities [39]. The electronic molar polarizability in (Å3) is given by
between the density of nonlinear oscillators (Ns) and the density of oxygen ions in the samples (Nox), considering that oxygen plays the major role in the nonlinearities of oxide glasses [36]. From such procedures, we determined s = 2. Therefore, the only free parameter to be obtained by fitting the experimental data with the BGO model is the anharmonicity parameter g. The red line along the data points in Fig. 3 corresponds to the fitting obtained with the BGO model, according to the procedure described previously, from which the parameter g was determined as being 0.82, 0.84, 0.85, and 0.86 for CaLiBO, x = 0.1, x = 1.0 and x = 2.0, respectively. As it can be seen, there is a good agreement between the experimental data and the model. The mean nonlinear refractive index values obtained from the BGO model to CaLiBO, x = 0.1, x = 1.0 and x = 2.0 are 4.2, 4.5, 4.6 and 4.7 × 10−20 m2/W, which are in good agreement with the experimental ones. Therefore, according to the BGO model, the major contribution for the nonlinear index of refraction of the samples studied here are related to the glass matrix, whose main electronic transitions are located in the UV region of the spectrum,
3 ⎞ RM αM = ⎛ 4 πN A⎠ ⎝ ⎜
⎟
(4)
in which NA is Avogadro's number and RM is the molar refraction value,
Fig. 3. Spectra of the nonlinear refractive index (n2) of CaLiBO (a), x = 0.1 (b), x = 1.0 (c) and x = 2.0 (d). The symbols correspond to the experimental data and solid lines represent the fit obtained with the BGO model, with parameters given in the text. The inserts show the typical Z-signature measured for all samples, while the line is the adjustment from which n2 is extracted. 3
Journal of Non-Crystalline Solids 524 (2019) 119637
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4. Conclusion
Table 2 Density (ρ), molecular weight (M) and molar electronic polarizability (αM) for the CaLiBO glasses. Samples glass
M(g/mol)
ρ(g/cm3)
αM(Å3)
CaLiBO x = 0.1 x = 1.0 x = 2.0
61.6 65.6 72.3 79.8
2.5743 ± 0.0009 2.732 ± 0.002 2.9269 ± 0.0008 3.131 ± 0.002
3.27 3.32 3.49 3.65
± ± ± ±
The nonlinear refractive index of CaLiBO glasses containing different concentrations of rare earth ions were characterized by the Zscan technique and interpreted using the empirical BGO model. The addition of Tb3+ and Yb3+ ions do not affect the spectral behavior of the nonlinear refractive index, which exhibited a nearly constant value for the spectral window between 470 and 1500 nm, within the experimental error, for all investigated samples. This behavior was confirmed by the BGO model, which also showed that the oxygen ions present in the glass matrix play a role in its third-order nonlinearities. Nonetheless, the n2 of CaLiBO glasses increased with the addition of Tb3+ and Yb3+, indicating that the combination of the oxygen ions present in the matrix and the polarizability of the rare earth ions contributed to the increase of the nonlinear response. This study presents a progress in the understanding of the nonlinear properties of borate glass and the influence that rare earth ions have on these properties, especially those related to third-order susceptibility, contributing for the development of new optical devices.
0.07 0.07 0.08 0.08
Declaration of Competing Interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors gratefully acknowledge financial support from the CNPq, FAPESP (2018/11283-7) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001.
Fig. 4. Nonlinear refractive index as a function of the electronic molar polarizability, evidencing that the increase depends on the addition of the rare earth ions.
References given by the Lorentz -Lorenz equation as [40–42]:
n2 − 1⎤ M RM = ⎡ 02 ⎢ n0 + 2 ⎥ ρ ⎣ ⎦
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(5)
where n0 is the linear refractive index, M is molecular weight and ρ is density (see Table 2). The values for the molar electronic polarizability determined using Eq. (4) are shown in Table 2. In Fig. 4 it can be observed that the mean values of the nonlinear refractive index display a clear increasing tendency, with the molar electronic polarizability, which in turn is related to the increase in the concentration of Tb3+ ion. The increase of the electronic polarizability values is probably due to the presence of Yb3+ (0.86 Å3) ions, as well as the addition and increase of the Tb3+ (1.04 Å3) ion concentration, whose polarizabilities are greater than B3+ (0.003 Å3), Ca2+ (0.47 Å3) and Li+ (0.024 Å3) ions [43,44]. The same behavior has been observed in BiCl3-Li2O-B2O3Er2O3 glasses, in which the polarizability presented a gradual increase with the increase of the Er3+ content [45]. A study of the CaO-B2O3Al2O3-CaF2 system doped with Nd3+ revealed that the electronic polarizability increased as a function of the rare earth concentration, which was attributed to an increase of nonbonding oxygen caused by the rare earth addition since these are more polarizable than the oxygens that are connected [46]. The comparison of the reported observations is in agreement with our results, which demonstrated an increase in both the nonlinear refractive index and the electronic polarizability values for glasses containing rare earth ions. Therefore, our results indicate a cooperative effect between the glass matrix (major effect) and the electronic polarizability of the rare earth contributions to the optical nonlinearity of CaLiBO glasses.
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