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The glass forming region of chalcogenide glasses in a germanium-tin-sulfur (Ge-Sn-S) ternary system is depicted. Three series of Ge-Sn-S glasses in different compositions are selected and synthesized in order to investigate the dependence of structural, optical and third-order nonlinear properties on chemical composition. Spectroscopy analyses demonstrate that Ge and Sn have similar structural behavior in the glass network, while the introduction of Sn decreases the optical bandgap energy and improves the infrared transmittance of the glasses. Third-order nonlinear properties of the glasses are investigated by the Z-scan technique at a mid-infrared wavelength of 3.3 μm. The experimental results demonstrate that the nonlinear absorption at the mid-infrared wavelength is absent due to the large optical bandgap energy of the glasses, while the nonlinear refractive behavior is evident and can be improved by reducing number of [GeS4] tetrahedrons in the glass network.
© 2016 Optical Society of America
Corrections
7 September 2016: A correction was made to Fig. 6.
1. Introduction
Chalcogenide glasses (GhGs) known as an amorphous infrared (IR) material possess IR transparency from visible to far infrared region, covering the widely used atmospheric IR windows of 3-5 and 8-14 µm. Besides, ChGs possess low phonon energy (150-450 cm−1), high refractive index (>2), as well as the large third-order optical nonlinearity (TONL, χ(3) ~2-3 orders higher than that of silica) with ultra-fast response time (<200 fs), which make them the perfect candidates for IR photonic devices, such as IR imaging, IR laser, chemical sensing and optical communication [1–4].
Among various ChGs systems, the sulfide ChGs based on germanium-sulfur (Ge-S) and arsenic-sulfur (As-S) binary systems have the unique visible transmittance property, while the former is nontoxic as well as exhibits larger band-gap energy which helps photonic devices to overcome optical loss originated from two-photon absorption (TPA) at the optical communication wavelengths (e.g. 1310 and 1550 nm) [5–8]. In addition, the Ge-S ChGs also have high rear-earth solubility, desirable chemical and mechanical stability as well as low thermal-photon coefficient due to the existence of germanium. Previous studies on Ge-S ChGs focused on property modification of the glasses by various methods, e.g. composition changing, heat treatment, laser irradiation etc, in order to optimize their performance in the corresponding photonic devices. For examples, Zhang’s study [9] had found the enhanced mechanical strength of Sb-contained Ge-S ChGs after thermal treatment; Ivanova [10] discovered that incorporation of Ga to Ge-S glasses could enhance the rare earth solubility; in Qu’s work [11], Pb was introduced to Ge-S glasses for the precipitation of PbS quantum dots in the glass matrix; our previous work [12] had found the enhancement of TONL properties of Ge-Ga-S glasses by gold doping. Accordingly, introduction of an third component to Ge-S based glasses can be considered as a simple but effective method to improve various properties of the ChGs.
Tin (Sn) is a “green” element, and previous study [13] had reported that introduction of Sn to Ge-Se ChGs could remove the Ge-O impurity in the glasses which resulted in improvement of the infrared transmittance. Our recent work [14] has discovered the enhancement of TONL properties of Ge-Se ChGs by Sn doping. However, little effort had been made to the study of Sn doped Ge-S glasses, and the glass forming, optical and TONL properties of ChGs in Ge-Sn-S (GSS) ternary system remain unclear. In this work, we have present the glass forming region of GSS system along with the dependence of optical properties on glass structure and composition. Further, mid-infrared TONL properties of the GSS ChGs have been investigated by Z-scan technique at 3.3 μm, and its correlation with network structure of the GSS ChGs has been given.
2. Experimental procedure
Bulk GSS glasses were prepared in 10 g batches by melt-quenching method. Highly pure starting elemental materials (Ge, Sn, and S, 5N) were weighed carefully and placed into pre-cleaned quartz ampoules. Prior to sealing and melting, the ampoules containing the starting materials were pre-heated at 100 °C for 4 h in order to remove surface moisture from the quartz ampoule and the raw materials. Then, the ampoules were sealed under vacuum (10−4 Pa). The sealed ampoules were introduced into a rocking furnace, melted at 850 °C for 12 h to guarantee the full reaction. The melts were removed from the furnace and rapidly quenched in water to form bulk glasses. All samples were then annealed at 10 °C below glass transition temperature (Tg) for 5 h to minimize the inner stress and slowly cooled to room temperature with a rate of 10 °C /h. Finally, the obtained glass rods were cut into disks with a thickness of 1 mm and polished to mirror smoothness on both sides by using the CeO2 polishing powder (average size of 1~10μm) together with a lambskin for further testing.
To measure the glass transition temperature (Tg), thermo-mechanical analysis (TMA, Netzsch, DIL402, GERMANY) was carried out at a heating rate of 5 °C/min from 50 to 500 °C with the protection of nitrogen gas flux. The amorphous nature of samples was confirmed by X-ray diffraction method using a diffractometer (Bruker D2 phaser, Karlsruhe. λ = 0.15406 nm, 30 kV, 10 mA, CuKα). Vicker's hardness (Hv) of the glass samples was measured by using a Vickers micro-indenter (Everone MH-3, Everone Enterprise Ltd., Shanghai, China) with a charge of 100 g for 5 seconds, and each Hv is the average value of 5 measurements. The Vis-NIR absorption spectra of samples were recorded in the range of 400-1000 nm using Perkin–Elmer Lambda 950 UV–VIS–NIR spectrophotometer. The infrared transmission spectra in the range of 2.5–13 μm were obtained using Nicolet 381 Fourier Transform Infrared spectrometer (FTIR). Raman scattering spectra were measured using a Renishaw Invia Raman Microscope (Renishaw, Gloucestershire, UK) with the excited wavelength of 785 nm. Z-scan method was employed to measure the nonlinear refraction index at MIR wavelength of 3.3 μm and the optical parametric amplifier (OPA, Coherent, Mira 900, Legend Elite and Opera Solo) was adopted as laser source with the pulse width of 100 fs and repetition frequency of 1 KHz. The transmitted power through the samples was detected by the highly sensitive power probe (Laser Probe, Rkp-575, 0.2-20 μm). All above optical testing were conducted at room temperature.
3. Results and discussion
3.1 Glass forming region
To depict the glass forming region of the GSS ternary system, three glass series in molar compositions of GexSn5S95-x (series A), Ge25-ySnyS75 (series B) and Ge20SnzS80-z (series C) that kept Sn, S and Ge content constant were selected and prepared by melt-quenching method. Figure 1(a) gives the XRD patterns of samples in series C, it shows that no obvious crystallization peak appears until the Sn content reaches 13.5 mol%, confirming that the maximum Sn concentration kept samples of series C amorphous is ~13 mol%. The opal sample Ge20Sn13.5 is partially crystallized, and the assignment of the small diffraction peaks in its XRD pattern is the combination of GeS2 phase (JCPDF No.27-238) and SnS2 phase (JCPDF No.40-1466), as present in Fig. 1(b).
Fig. 1 (a) XRD patterns of GSS samples of series C; (b) identification of the crystal phases in crystallized sample with molar composition of Ge20Sn13.5
Similarly, the maximum S and Ge content in series A and series B is found to be 75 and 27.5 mol% respectively, thus the glass forming region of Ge-Sn-S ternary system was consequently obtained and given in Fig. 2. It can be seen that the GSS ternary system has a small glass forming region which locates in the sulfur-rich part (S content > 65 mol%). Accordingly, nine GSS glass samples (compositions are listed in Table 1) were chosen and applied to the subsequent measurements.
Table 1. Composition, physical, optical and TONL parameters of Ge-Sn-S glass samples
3.2 Thermal and mechanical properties
Glass transition temperature (Tg) of the GSS glasses measured by TMA method are shown in Table 1. In series A of the ChGs, the gradual substitution of S by Ge resulted in increase of Tg, and the similar variation tendency can be observed in series C in which S is replaced by Sn. In series B that both Ge and Sn content varies, Tg of the ChGs shows a decreasing tendency as Ge is substituted by Sn. It is known that the Tg value of glass materials is considered to be proportional to mean bond energy of the glass network [15–17]. Therefore, variation of Tg of the ChGs is dominated by the number of Ge-S bonds which has the largest bond energy in the glass system (Ge-S bond: 556 kJ/mol, Sn-S bond: 467 kJ/mol, S-S bond: 425 kJ/mol) [18]. On the other hand, Tg of the ChGs is also related to the network structure which can be described by mean coordination number (Z). For the present GSS glasses, the Z value can be calculated by using coordination number (CN) of Ge (CN = 4), Sn (CN = 4) and S (CN = 2), respectively. By plotting the Z value versus the Tg (as shown in Fig. 3), two conclusions can be extracted: (1) Tg of the GSS glasses has a positive dependence on the Z value, indicating that transition of GSS glass network to a rigid state would promote the thermal threshold of glass transition; (2) Tg of the GSS glasses is sensitive to the variation of Z value, the four glass samples (Ge20Sn5, Ge25Sn0, Ge22.5Sn2.5 and Ge17.5Sn7.5) with the same Z value (Z = 2.5) show close Tg to each other (< 10 °C), while small increase of Z would cause a significant increase of the Tg value: increase of Z by 0.05 would promote Tg of 18 °C (average value in Series A) and 34 °C (average value in Series C), which can be attributed to the larger bonding energy of Ge-S and Sn-S bonds as compared to that of the S-S bonds.
Mechanical strength of the ChGs presented by Vicker's hardness (Hv) is given in Table 1. It can be seen that Ge could significantly increase the Hv of the ChGs while the introduction of Sn to the glass resulted in weakening of the mechanical strength. Besides, the density (ρ) of samples shows a monotonously increasing tendency with the increase of molar mass of ChGs, namely both increase content of Ge and Sn could increase the ρ value.
3.3 Absorption and FTIR spectra
Absorption spectra of the GSS ChGs are present in Fig. 4. It can be seen that fundamental absorption edge of samples in series A manifests a blue-shifting with the increase of Ge content, while it red-shifts from 460 to 520 nm with the gradual substitution of Ge by Sn in series B. In series C with constant Ge content, a slight red-shifting tendency of the absorption edge with increase of Sn content can be observed in inset of Fig. 4. By employing the well-known Tauc’s method [19], shifting of the absorption edge can be numerically represented by optical bandgap energy (Eopg) by using the formula as follow:
where α is the linear absorption coefficient, hv is the incident photon energy, B is a constant related to the electronic transition probability and m is a parameter which can have two values 2 and 0.5 in the case of indirect and direct optical transitions respectively. For glassy materials (GSS ChGs in this work) that have anomalous band structure, m = 2 presenting indirect allowed transition is preferable. Eopg of the GSS ChGs were calculated and summarized in Table 1, and an evident variation of the Eopg value can be observed in series B with constant S content: both the maximum and minimum Eopg were present in this series, indicating the contrast of Ge and Sn to band structure of the GSS glasses. Previous studies [20–22] had reported that Eopg of glass materials depend negatively on the polarizability of structural units that built the glass network. For ChGs, the variation of Eopg is associated with the polarizability of the structural units linked by covalent bonds. The increase of Eopg in series A indicated that the increase of Ge-related structural units could decrease the total polarizability, while the variation of Eopg in series B and C manifested the increasing number of Sn-related and S-related units could increase the total polarizability of the GSS glasses. The identification of the above-mentioned structural units would be discussed in Raman spectra as present in the following section.Figure 5 presents the FTIR spectra of the GSS glasses. It can be seen that the GSS glasses have infrared transmittance over 70 % and the maximum transmission is maintained up to 10.5-11 µm. The most evident variation of the spectra after the introduction of Sn is the disappearance of absorption band belonging to impurity vibration of Ge-O bonds at ~9 μm (as the red arrow noted in series B), even in sample with Sn doping level of 2.5 mo%, which is in good agreement with the experimental results reported in Sn-doped Ge-Se glasses [13]. Therefore, introduction of Sn can be considered as an effective method to improve infrared transmittance of the Ge-S based glasses.
3.4 Raman spectra
To investigate the evolution of GSS glass structure after composition modification, as well as to correlate properties of the ChGs to glass structure, Raman spectra of the GSS glasses were measured and given in Fig. 6. As seen in the spectra, the Raman signal of the GSS ChGs is located at region between 100 and 600 cm−1, in good agreement with those reported in other Ge-S based ChGs [23,24]. The main Raman band of the GSS ChGs located at ~330 cm−1 belongs to symmetrical stretching vibration mode of [Ge(Sn)S4] tetrahedron units [23]. In series B and series C, shifting of the main Raman peak from 340 to 320 cm−1 with increase of Sn content can be clearly observed, indicating the increasing number of [SnS4] tetrahedron units in the glass network. It should be noted that only 7.5 mol% Sn could make Raman intensity of the characteristic band of [SnS4] tetrahedrons maximum in the spectra, illustrating large Raman gain coefficient of the [SnS4] tetrahedron units.
In the spectral region below the main band (<300 cm−1), Raman bands at 150 and 216 cm−1 can be observed, and they belong to characteristic vibration of S8 molecules [24] which decreased significantly in intensity when S was replaced by Ge or Sn as can be seen in series A and series C, respectively. In the spectra of series B with constant S content, replacement of Ge by Sn caused a slight increase of the S8 vibration, indicating that the Sn in GSS glass network has a lower coordination number (2-coordinated in [SnS2] links) [25] and more S8 rings would ‘survive’ after the substitution of Ge by Sn. On the other hand, two Raman bands can be observed above the main Raman band (> 400 cm−1), and the one at ~470 cm−1 belongs to vibration mode of S-S bonds in S8 ring which has the same variation tendency to the Raman bands at 150 and 216 cm−1. For the band at 430 cm−1, it can be assigned to vibration modes of edge-shared and corner-shared [GeS4] tetrahedrons [24]. In the spectra of series A and series B, intensity of this band exhibits positively dependence on Ge content, and it keeps in constant intensity in the spectra of series C with constant Ge concentration.
According to above analysis of the Raman spectra as summarized in Fig. 7, structure of the GSS glass network can be described: all the ChSs are in S-rich state, and [GeS4] tetrahedrons isolated by S8 rings is the main frame of the Ge-S glass network; as Sn was introduced, part of Ge in the [GeS4] tetrahedrons were replaced by Sn and the S-S bonds in S8 rings were broken, leading to the presence of [SnS4] tetrahedrons and [SnS2] links. On the other hand, as referred from the variation tendency of the Eopg values, polarizability of the structural units in GSS network can be ordered in following sequence: [SnS4(2)] units ≥ S8 rings > [GeS4] tetrahedrons.
Fig. 7 Structural units in the GSS network according to Raman spectra taken from three glass samples.
3.5 Third-order optical nonlinearity
Third-order optical nonlinearity (TONL) of the GSS ChGs is investigated by femtosecond Z-scan technique at a mid-infrared (MIR) wavelength of 3.3 μm, which is the first study of MIR-TONL properties of Ge-S based ChGs to the best of our knowledge. Nonlinear absorption and nonlinear refraction behavior of the GSS ChGs at the MIR wavelength are present by open-aperture (OA) and closed-aperture (CA) Z-scans, respectively. Figure 8(a) presents the OA Z-scans of the representative GSS glass samples selected from each series, the line-type signal indicated the absence of nonlinear absorption at the MIR wavelength. The incident photon energy is 0.38 eV at 3.3 μm which is nearly one sixth of Eopg of the GSS glasses, indicating that nonlinear absorption behavior could be originated from six-photon absorption [26]. The incident laser power (10 µW) used in present experiments is too low to generate such multiple-photon absorption which requires high excitation energy to satisfy phase matching. Therefore, no signal of nonlinear absorption was observed from the GSS glasses in OA Z-scan measurements. As a result, the nonlinear refractive behavior of the GSS ChGs in present experimental condition is contributed from pure distortion of electron cloud of the structural units in the glasses without the resonant contribution from multiple-photon absorption.
Fig. 8 (a) open-aperture Z-scans of the GSS glasses; (b) closed-aperture Z-scans of GSS glasses in series B.
Figure 8(b) gives the CA Z-scans of four GSS samples, which qualitatively represent typical behavior in the CA Z-scan measurements on all the glasses prepared in this study. The signal of the CA Z-scans exhibit a valley following peak configuration, indicating self-focusing behavior, namely positive sign of nonlinear refraction (γ) of the ChGs at the MIR wavelength, which is in agreement with Sheik-Bahae’s theory [27] predicting that the sigh of nonlinear refraction of dielectric materials would keep positive at wavelength far below the bandgap energy. By fitting the CA Z-scans with the well-established calculation process [28] as the red curves noted in Fig. 8(b), γ values of the GSS glasses were obtained. As the data given in Table 1, value of the γ at 3.3 μm is in magnitude of 10−19 m2/W, one order lower than those of the Ge-S based ChGs measured at near-infrared wavelengths [5–8], due to the dispersion property of the nonlinear refractive behavior. The minimum γ of present GSS ChGs is the sample without Sn, demonstrating the improvement of Sn-doping to TONL properties of the Ge-S binary glass. However, considering the experimental error ( ± 10%), the increase of Sn content in glass series C (substituting for S) actually kept the nonlinear refractive behavior unchanged, indicating the contribution of Sn-related structural units ([SnS4] tetrahedrons and [SnS2] links) to TONL properties is equal to that of the S-related units (S8 chains and rings). On the other hand, in Series A with constant Sn content, decrease of the γ value took place as S was replaced by Ge, indicating that the S-related structural units (S-S chains and rings) have larger contribution to TONL property than those of Ge-related units ([GeS4] tetrahedrons). In Series B with constant S content, increase of the γ value as Ge was replaced by Sn can be observed, indicating that the Sn-related structural units ([SnS4] tetrahedrons and [SnS2] links) also have larger contribution to TONL property than that of Ge-related units ([GeS4] tetrahedrons). Accordingly, the [GeS4] tetrahedrons have smallest contribution to TONL properties of the GSS glasses as compared with other structural units. The experimental result that maximum γ obtained in GSS sample with the lowest Ge content could prove this conclusion as well. Thus, in order to improve TONL properties of the GSS ChGs, the Ge content needs to be decreased, and decreased Ge concentration could also reduce the cost of the ChGs.
According to the experimental results from the Z-scan measurements, absence of multi-photon absorption (i.e. nonlinear absorption coefficient β = 0) which would cause optical loss is beneficial to fabrication of nonlinear optical devices, because the figure of merit (F = γ/βλ, λ is wavelength of incident laser) [5,7] defined the TONL performance of optical materials would be infinite at mid-infrared wavelength. In other words, the GSS ChGs can be considered as a promising candidate to nonlinear optical devices operating at mid-infrared region.
4. Conclusions
In summary, glass forming region of chalcogenide glasses (ChGs) in Ge-Sn-S (GSS) ternary system was depicted. It located in sulfur-rich region, and the maximum doping level of Sn could reach 13 mol%. The introduction of Sn eliminated the optical absorption from impurity of Ge-O bonds, which improved the infrared transmittance of the GSS ChGs. Measurement of the Raman spectra manifested that introduction of Sn could replace part of Ge in the [GeS4] tetrahedrons and break the S8 rings forming [SnS4] tetrahedrons and [SnS2] links in the glass network, which resulted in the increase of transition temperature and optical bandgap energy of the GSS ChGs. Mid-infrared (3.3 μm) third-order optical nonlinearities of the GSS ChGs were studied by Z-scan technique. Absence of nonlinear absorption due to the large optical bandgap energy of the glasses was observed, while nonlinear refractive behavior was evident at the mid-infrared wavelength. Nonlinear refraction (γ) of the GSS glasses at 3.3 μm is in magnitude of 10−19 m2/W, and can be promoted by reducing the number of [GeS4] tetrahedrons in the glass network.
Acknowledgments
This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 61435009, 61675106 and 61308094). It was also sponsored by K.C. Wong Magna Fund in Ningbo University.
References and links
1. B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5(3), 141–148 (2011).
2. L. Li, H. Lin, S. Qiao, Y. Zou, S. Danto, K. Richardson, J. D. Musgraves, N. Lu, and J. Hu, “andJ. Hu, “Integrated flexible chalcogenide glass photonic devices,” Nat. Photonics 8(8), 643–649 (2014). [CrossRef]
3. J. Hu, J. Meyer, K. Richardson, and L. Shah, “Feature issue introduction: mid-IR photonic materials,” Opt. Mater. Express 3(9), 1571–1575 (2013). [CrossRef]
4. C. R. Petersen, U. Møller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4–13.3 μm molecular fingerprint region using ultra-high NA chalcogenide step-index fibre,” Nat. Photonics 8(11), 830–834 (2014). [CrossRef]
5. T. Wang, X. Gai, W. Wei, R. Wang, Z. Yang, X. Shen, S. Madden, and B. Luther-Davies, “Systematic z-scan measurements of the third order nonlinearity of chalcogenide glasses,” Opt. Mater. Express 4(5), 1011–1022 (2014). [CrossRef]
6. H. Guo, C. Hou, F. Gao, A. Lin, P. Wang, Z. Zhou, M. Lu, W. Wei, and B. Peng, “Third-order nonlinear optical properties of GeS(2)-Sb(2)S(3)-CdS chalcogenide glasses,” Opt. Express 18(22), 23275–23284 (2010). [CrossRef] [PubMed]
7. L. Petit, N. Carlie, K. Richardson, A. Humeau, S. Cherukulappurath, and G. Boudebs, “Nonlinear optical properties of glasses in the system Ge/Ga-Sb-S/Se,” Opt. Lett. 31(10), 1495–1497 (2006). [CrossRef] [PubMed]
8. D. Marchese, M. De Sario, A. Jha, A. K. Kar, and E. C. Smith, “Highly nonlinear GeS2-based chalcohalide glass for all-optical twin-core-fiber switching,” J. Opt. Soc. Am. B 15(9), 2361–2370 (1998). [CrossRef]
9. X. Zhang, M. A. Hongli, and J. Lucas, “A new class of infrared transmitting glass-ceramics based on controlled nucleation and growth of alkali halide in a sulphide based glass matrix,” J. Non-Cryst. Solids 337(2), 130–135 (2004). [CrossRef]
10. Z. G. Ivanova, V. S. Vassilev, E. Cernoskova, and Z. Cernosek, “Physicochemical, structural and fluorescence properties of Er-doped Ge–S–Ga glasses,” J. Phys. Chem. Solids 64(1), 107–110 (2003). [CrossRef]
11. G. Qu, S. Zhai, Y. Xu, S. Dai, H. Tao, S. Gu, and C. Lin, “The effect of PbS on crystallization behavior of GeS2-Ga2S3-based chalcogenide glasses,” J. Am. Ceram. Soc. 97(11), 3469–3474 (2014). [CrossRef]
12. F. Chen, S. Dai, C. Lin, Q. Yu, and Q. Zhang, “Performance improvement of transparent germanium-gallium-sulfur glass ceramic by gold doping for third-order optical nonlinearities,” Opt. Express 21(21), 24847–24855 (2013). [CrossRef] [PubMed]
13. I. Haruvi-Busnach, J. Dror, and N. Croitoru, “Chalcogenide glasses Ge-Sn-Se, Ge-Se-Te, and Ge-Sn-Se-Te for infrared optical fibers,” J. Mater. Res. 5(6), 1215–1223 (1990). [CrossRef]
14. B. Qiao, S. Dai, Y. Xu, P. Zhang, X. Shen, T. Xu, Q. Nie, W. Ji, and F. Chen, “Third-order optical nonlinearities of chalcogenide glasses within Ge-Sn-Se ternary system at a mid-infrared window,” Opt. Mater. Express 5(10), 2359 (2015). [CrossRef]
15. H. Tao, S. Mao, W. Tong, and X. Zhao, “Formation and properties of the GeS2–In2S3–KCl new chalcohalide glassy system,” Mater. Lett. 60(6), 741–745 (2006). [CrossRef]
16. V. Vassilev, K. Tomova, V. Parvanova, and S. Parvanov, “New chalcogenide glasses in the GeSe2–Sb2Se3–PbSe system,” Mater. Chem. Phys. 103(2-3), 312–317 (2007). [CrossRef]
17. G. Saffarini, J. M. Saiter, and J. Matthiesen, “Thermal stability and percolation threshold of Ge–Se–Fe glasses,” Mater. Lett. 61(2), 432–436 (2007). [CrossRef]
18. Y. R. Luo, Comprehensive Handbook of Chemical Bond Energies (CRC Press, 2007).
19. J. Tauc and A. Menth, “States in the gap,” J. Non-Cryst. Solids 8(10), 569–585 (1972). [CrossRef]
20. Y. Chen, Q. Nie, T. Xu, S. Dai, X. Wang, and X. Shen, “A study of nonlinear optical properties in Bi2O3-WO3-TeO2 glasses,” J. Non-Cryst. Solids 354(29), 3468–3472 (2008). [CrossRef]
21. S.-H. Kim, T. Yoko, and S. Sakka, “Linear and nonlinear optical properties of TeO2 glass,” J. Am. Ceram. Soc. 76(10), 2486–2490 (1993). [CrossRef]
22. G. Saffarini, J. M. Saiter, and H. Schmitt, “The composition dependence of the optical band gap in Ge-Se-In thin films,” Opt. Mater. 29(9), 1143–1147 (2007). [CrossRef]
23. C. Lin, H. Tao, Z. Wang, B. Wang, H. Zang, X. Zheng, and X. Zhao, “Defect configurations in Ge–S chalcogenide glasses studied by Raman scattering and positron annihilation technique,” J. Non-Cryst. Solids 355(7), 438–440 (2009). [CrossRef]
24. X. F. Wang, S. X. Gu, J. G. Yu, X. J. Zhao, and H. Z. Tao, “Structural investigations of GeS2–Ga2S3–CdS chalcogenide glasses using Raman spectroscopy,” Solid State Commun. 130(7), 459–464 (2004). [CrossRef]
25. S. A. Fayek, “The effects of Sn addition on properties and structure in Ge–Se chalcogenide glass,” Infrared Phys. Technol. 46(3), 193–198 (2005). [CrossRef]
26. T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21(26), 32192–32198 (2013). [CrossRef] [PubMed]
27. M. Sheik-Bahae, D. J. Hagan, and E. W. V. Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990). [CrossRef] [PubMed]
28. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. V. Stryland, ““Dispersion of bound electron nonlinear refraction in solids,” IEEE. J Quantum Electron. 27(6), 1296–1309 (1991). [CrossRef]
