The nonlinear refractive index for 10 types of recently developed new soft glasses was measured under the same conditions using a pulsed Nd:YAG laser operating at 1064 nm with a 35 ps pulse duration. The study included various types of oxide-based soft glasses commonly used for nonlinear fiber optics, such as lead silicate, borosilicate, phosphatate, tellurite and heavy metal oxide glasses. All studied glasses have good rheological properties, and are suitable for further multi-step thermal processing, including fabrication of nonlinear photonic crystal fibers. As reference samples, standard fused silica glass and commercially available lead silicate glasses were used. The standard Z-scan setup was employed, with both “open-” and “closed-aperture” types of measurement. We show that nonlinearities of some benchmarked thermally stable heavy metal oxide glasses are comparable to more expensive and very fragile chalcogenide glasses.
© 2017 Optical Society of America
In recent years, the ever-increasing applications using nonlinear optics such as optical fibers, waveguide gratings or photonic crystals motivate research on glasses with increased nonlinear refractive indices. In order to synthesize glasses with ever higher nonlinearity, the generally accepted approach is incorporating new compounds into the glass matrix . An important criterion for fiber optic applications of nonlinear glasses is recrystallization resistance. Qualifying a given glass for photonic crystal fiber fabrication by multiple thermal processing steps is a critical parameter [2,3]. Among materials suitable for fabrication of photonic crystal fibers (PCF), the highest nonlinear refractive index values so far have been reported for the chalcogenide group of glasses, typically two orders of magnitude larger than in fused silica . Various compositions of chalcogenide glasses have been shown to enable fabrication of optical fibers including all-solid photonic crystal fibers and step index fibers [5,6]. Another glass type widely used for nonlinear applications are fluoride glasses. They also have a broad transmittance window spanning from ultraviolet to mid-infrared up to 8 μm, but their nonlinear refractive indices are comparable to silica . Still, low refractive index and low attenuation allows for introducing high power pulses generating supercontinuum light [8,9]. However, synthesis and processing of these materials is challenging, since protective atmosphere is required. On the other hand, fused silica shows well-known low attenuation, but the transmission window in optical fibers is limited up to about 2.4 µm, and the nonlinear refractive index is very low . Progress in this area could involve fibers based on step index silica-germanium fibers . A compromise between high nonlinear refractive index, broad transmission and easy synthesis are the heavy metal oxide glasses. Their attenuation is higher than silica, which limits the allowable length of fiber in an application. However, the transmission window of soft glasses based on silicon dioxide extends up to 5.5 µm. In addition, the possibility to include in their composition various heavy metal oxides can lead to a significant increase of the nonlinear refractive index. This enables fabrication of photonic crystal fibers for various nonlinear applications such as supercontinuum generation [12,13] or in broadband micro-optical elements . In particular, these glasses can be optimized for fabrication of all-solid photonic crystal fibers, where total fiber dispersion is determined, aside from waveguide dispersion, by the material dispersion contributions of the used glasses. As a result, fibers with ultra-flat, ultra-broadband dispersion characteristics (normal or anomalous) or birefringent fibers can be fabricated [13,14]. Another type of glasses widely used for nonlinear applications are tellurite glasses with relatively high nonlinear refractive indices comparable to those of silicate glasses with high concentration of heavy metal oxides . Combining this property with broad transmission window allows for generation of supercontinuum spanning over 4000 nm .
In this work, we report on a comprehensive study of the third-order nonlinear optical (NLO) response of a range of heavy metal soft glasses encompassing different types of glasses and compositions. Among several other techniques that have been extensively used for nonlinear optical measurements (e.g. four-wave mixing, optical Kerr effect, third harmonic generation etc.) the Z-scan technique was chosen because it allows not only for the simultaneous determination of both the third-order nonlinear refraction and absorption from a single measurement using only one beam, but it also provides information on the sign of the nonlinear refraction . The same experimental conditions were maintained for all studied samples, which afforded the direct comparison of the nonlinear refraction as a function of the key parameters such as chemical composition, type and percentage of heavy metals present in the glass and the linear index of refraction. The laser excitation source was a 35 ps pulsed, mode-locked Nd:YAG laser operating at a repetition rate of 10 Hz at its fundamental wavelength of 1064 nm. The investigated set of glasses included borosilicate-based compositions, heavy metal oxides silicate glasses, tellurite glasses and phosphate glasses, each of which offers specific advantages in different areas of fiber optics technology.
Silicate glasses containing alkali oxides offer only slightly modified nonlinear refraction. Thus, besides good rheological properties, they are not that interesting as bulk materials . However, in applications involving fabrication of all-solid glass PCFs, even small change of the nonlinear index of refraction n2 is important, as the light propagating in the core is confined by photonic crystal lattice elements made from more than one type of glass. Lead silicate glasses are very interesting, because they can be modified in a wide range of lead oxide concentration. Furthermore, high refractive index changes which result from introduction of various oxide dopants are also possible . Most lead oxide glasses are also suitable for multiple thermal processing, such as in PCF fabrication or thermal molding, e.g. in the hot embossing technique . Bismuth oxide-based glasses are very interesting for their increased nonlinearity compared to that of lead oxide glasses . Novel glass systems based on silica or boron oxide offer a wide range of modifiable concentrations to obtain a high nonlinear refractive index and additionally exhibit good solubility of rare earth metal oxides for optical amplification . Tellurite glasses offer wide transmission windows with average nonlinearities; however, for applications in the mid-infrared range, the water peak becomes an issue due to its wide absorption extending from 3 to 4 µm [21,22]. Phosphate glasses are commonly used for fiber lasers. Their main advantage is their good solubility of rare earth metal oxides with very small nonlinearity, which is crucial for fiber laser applications .
2. Measurement of nonlinear refractive index with the Z-scan technique
For the determination of the nonlinear refractive indices the Z-scan technique was employed . In the Z-scan technique – shown schematically in Fig. 1, the measurement of the transmittance (T) of a sample is performed, as the sample is moved along the laser propagation of a focused laser beam (e.g., along the z-axis). Thus the sample experiences a continuously varying intensity at each z-position. The transmittance measurement is performed in two different ways, either just after the sample, where all the transmitted laser light is collected and measured, or after the transmitted laser beam has passed through a small aperture placed in the far field. The former measurement is defined as the “open-aperture” Z-scan, whereas the latter is the “closed-aperture” Z-scan. From the “open-aperture” measurement the magnitude of the nonlinear absorption coefficient β of the sample, which is related to the imaginary part of the third-order susceptibility [Imχ(3)] can be determined by fitting the obtained curve with the following equation :1]:24]:
The laser beam was focused onto the samples by means of a 20 cm focal length plano-convex lens, while the beam spot radius at focus (i.e. half width at 1/e2 of the maximum of irradiance) was determined to be about 30 μm, using a CCD camera.
3. Chemical composition and optical properties of selected glasses
We studied different types of glasses. All of the used glasses except the commercial ones, were in-house synthetized using conventional melt and quench technique. Moreover we chose only these compositions which are suitable for multi-thermal processing, such as the stack and draw method for PCFs fabrication. NC21A and UV-710 borosilicate glasses are specially designed for fabrication of all-solid photonic crystal fibers with high contrast of refractive indices . Their thermomechanical properties are maintained to match either the SF6 and F2 glasses or the PBG81 glass, respectively. Lead-bismuth-gallium silicate glasses exhibit high linear refractive index and broad transmittance from visible up to 5.5 µm . Additionally, as they have softening points close to 500 °C, they are suitable for fabrication of micro-optical elements by the hot embossing technique . Phosphate glass IRF-16/02 was designed especially for microstructured fiber lasers. Previous works proved that it is possible to incorporate large amount of ytterbium oxide – up to 6% mol. into its chemical composition . PBS-57A is a lead silicate modification of SF57 glass with improved thermal stability, preserving all the thermomechanical and optical properties, especially for optical fiber drawing. The chemical compositions of all investigated glasses are given in Table 1.
PBG81 and PBG-08 have the same initial composition but differ in synthetic conditions. PBG81 is melted from dry materials, and incorporate bubbling procedure with ultra-dry oxygen during melting. The purpose of this modification is to reduce hydroxyl groups concentration in the bulk material, as well as to improve the homogeneity of the glass. OH groups are responsible for strong absorption at 2.8 µm. This absorption band is very inconvenient, since it limits the mid-infrared applications of this material. The comparison of transmittance in bulk sample of this modification is presented in Fig. 2. To obtain further removal of hydroxyl groups contamination in the glass, the chemical removal by adding halides and performing synthesis in glove box is necessary .
As reference samples, four commercially available lead-silicate Schott’s glasses were used, namely LLF1, F2, SF6 and SF57. These materials are suitable for fiber drawing.
The composition of raw materials in pure oxides and salts with minimum purity of 99.5% or higher, was weighted and grinded to obtain homogenous powder with desired final composition. All glasses except tellurite and phosphate glasses were melted in platinum crucibles to obtain best homogeneity. Tellurite glass was melted in a gold crucible, while a quartz crucible was used for melting of the phosphate glass. Standard furnaces with resistance heating elements were used for melting glasses. All melts were stirred during the melting, and poured onto a preheated graphite form followed by annealing at cooling rate of 0.5°C per minute to room temperature. From obtained glass bars, plates with 1 mm thickness were cut and polished to optical quality for the measurements.
4. Experimental results
In Fig. 3 the representative “closed-aperture” Z-scan curves are presented for the glasses which exhibited the largest nonlinearities. As shown in all cases, the glasses revealed important nonlinear refraction of positive sign, as indicated by the “valley-peak” configuration of all the “closed-aperture” Z-scans, suggesting clear self-focusing behavior. At the same time, all the studied glasses were found to exhibit negligible nonlinear absorption as suggested by the “open-aperture” Z-scan traces (not shown here), at least for the range of laser energies/intensities that were employed for the determination of the nonlinear refractive index. However, it is important to notice that at very high laser intensities (> 46 GW/cm2), the “open-aperture” Z-scans of the glasses showed a minimum in the transmittance at the focal plane position, suggesting the presence of either multi-photon absorption (MPA) and/or nonlinear scattering (NLS).
Figure 4 shows the variation of the ΔTp-v parameter as a function of laser energy for the different glasses. The values of the ΔTp-v for all glasses were found to scale linearly with the laser energy, as can be seen by the least-squares fits also shown in Fig. 4 . From the slope of the fitting lines, the nonlinear refractive index parameter n2 was deduced for each sample. Similar graphs have been prepared for all the studied glasses. The results obtained for all glasses are summarized in Table 2.
Transmittance of the investigated glasses are shown in Fig. 5. At the laser operating wavelength 1064 nm no absorbance was recorded. From the obtained data, the Tauc plots were drawn to obtain optical band gap . Tauc plot is presented in Fig. 6, and the energies of the bandaps of glasses are summarized in Table 3. Obtained transmittance and optical bandgaps proves that observed nonlinear refractive index is not disturbed by any presence of absorption at 1064nm or two photon absorption.
In Fig. 7 the plot of the refractive index versus the nonlinear refractive index for the different types of glasses is shown. The nearly proportional relation that is found to hold between these two values is similar to data obtained by other groups [29,30].
Lead-bismuth-gallium silicate glass (labeled here as CS-1030) was found to have the largest n2 value, of 11.42 ± 0.56 × 10−19 m2/W. Comparing it to PBG-08 glass, increased concentration of heavy metal oxides caused nearly three-fold increase of the nonlinear refractive index. This is explained by the reduction in concentration of silica with the simultaneous increase of concentration of specific heavy metal oxides, including gallium, bismuth and cadmium oxides. This result highlights the fabrication of thermally stable glasses based on silicon and heavy metal oxides, with high nonlinear refractive index. The nonlinearity of CS-1030 exceeds even that of tellurite glass TWPN/I/6. Comparing silicate glasses in a system of SiO2-ZnO-Bi2O3 studied by Bala et al., and some ternary tellurite glasses, the obtained refractive index was found in the range of 4-5 × 10−19 m2W−1 [20,22]. Thus, results for the PBG glass series prove that silicate glasses with high concentration of heavy metal oxides can obtain as high nonlinear refractive index as tellurite glasses. Moreover, the CS-1030 has better mechanical properties, and synthesis of this material is easier, due to better resistance to crystallization. If we consider development of highly nonlinear fibers, the tellurite glass TWPN/I/6 and the heavy metal oxide CS-1030 have properties which are an ideal combination between the glass mechanical-chemical reliability and the strength of the nonlinear optical response.
The PBG glass series including PBG-08, PBG-81 and PBG89 exhibited nonlinear refractive indices of the same order of magnitude. Moreover, it is worth noting that the obtained value for PBG-08 4.3 × 10−19 m2W−1 is in very good agreement with previous measurements of 4.13 × 10−19 m2W−1, which were performed at 1240 nm wavelength . Furthermore, it is very interesting that thee dehydration process of PBG81 resulted in an unexpected decrease of n2 comparing to PBG-08 with higher absorption level caused by hydroxyl groups. We speculate that this decrease could have been caused by the increased evaporation of components with lower melting temperatures, which is connected with the observed decrease of the refractive index from 1.900 to 1.889. Simultaneously, we suspect that the internal structure of dehydrated glass is also changed, which could be a topic for further investigation. Similar behavior was observed also for the SF57 and PBS-57A glasses. Commercial SF57 glass exhibited a lower nonlinear refractive index than PBS-57A. However, both glasses have the same linear refractive indices and comparable chemical composition. Thus, it is probable that the parameters of the melting process became very important issues not only in obtaining high quality optical glasses, but also in modifying the nonlinear properties of glasses.
The lowest values of nonlinear refractive indices in multicomponent glasses were obtained in borosilicate glasses NC-21A, NC-25, UV-710, low lead oxide content lead silicate glasses LLF1 and F2, and in phosphate glass IRF-16/02. The nonlinear refractive indices of these glasses can be effectively used to design novel photonic crystal fibers, especially all-solid photonic crystal fibers. This approach allows development of fibers with broadband flat, normal or anomalous, dispersion characteristics highly demanded for supercontinuum generation . In these fibers, a high refractive index core is surrounded by photonic cladding made from low refractive index glass. Despite the fact, that the nonlinear refractive index of the core is the dominant parameter in shaping of the nonlinear processes in the fiber, the cladding also has significant impact on fiber nonlinear coefficient and its dispersion characteristics.
We have also compared obtained results with previously reported values of n2 for soft glasses. Nonlinear refractive index vary from each other by using different method. As observed in case of PBG-08 and PBG81, also synthesis conditions have significant influence on nonlinear refractive indices. Thus present experiment allows to direct comparison of n2 for several types of soft glasses, obtained under same measuring conditions. Gathered nonlinear refractive indices values obtained in the present experiments and in other works are listed in Table 4.
We measured the nonlinear refractive index in a series of oxide soft glasses for optical fiber drawing, including the commercially available lead-silicate based glasses, as well as a series of in-house made glasses with well-known chemical compositions. All investigated glasses enable drawing of photonic crystal fibers, including the all-solid structures, which require multiple thermal processing in the stack-and-draw approach. Experimental conditions of the Z-scan technique (i.e. laser wavelength, pulse duration, repetition rate) were maintained across the entire range of the glass samples used for characterization, enabling direct comparison of the nonlinear response. Results showed for the first time that some compositions of heavy metal oxide silicate glasses, especially the presented CS-1030 glass could exceed n2 values for tellurite glasses used for novel PCFs fabrication . Obtained refractive index as high as 1.14 × 10−18 m2/W, is comparable to some chalcogenide and fluorotellurite glasses [4,35]. We anticipate the present results will motivate further investigation of new nonlinear glasses based on silicon oxide, leading to the design and fabrication of improved nonlinear photonic crystal fibers.
TEAM TECH/2016-1/1 project awarded by the Foundation for Polish Science Team Programme from the funds of European Regional Development Fund under Smart Growth Operational Programme; SONATA project UMO-2013/11/D/ST7/03156 awarded by National Science Centre in Poland; MPNS COST Action MP1205 Advances in Optofluidics: Integration of Optical Control and Photonics with Microfluidics.
References and links
1. A. D. Sontakke, K. Biswas, A. Tarafder, R. Sen, and K. Annapurna, “Broadband Er3+ emission in highly nonlinear Bismuth modified Zinc-Borate glasses,” Opt. Mater. Express 1(3), 344–356 (2011). [CrossRef]
2. R. Stępień, D. Pysz, I. Kujawa, and R. Buczyński, “Development of silicate and germanate glasses based on lead, bismuth and gallium oxides for midIR microstructured fibers and microoptical elements,” Opt. Mater. 35(8), 1587–1594 (2013). [CrossRef]
3. R. Kasztelanic, I. Kujawa, R. Stȩpień, J. Cimek, K. Haraśny, M. Klimczak, A. J. Waddie, M. R. Taghizadeh, and R. Buczyński, “Fabrication and characterization of microlenses made of tellurite and heavy metal oxide glass developed with hot embossing technology,” Opt. Quantum Electron. 46(4), 541–552 (2014). [CrossRef]
4. F. Smektala, C. Quemard, V. Couderc, and A. Barthelemy, “Non-linear optical properties of chalcogenide glasses measured by Z-scan,” J. Non-Cryst. Solids 274(1–3), 232–237 (2000). [CrossRef]
6. B. Zhang, Y. Yu, C. Zhai, S. Qi, Y. A. Wang, X. Gai, R. Wang, Z. Yang, and B. Luther-Davies, “High Brightness 2.2-12 μm Mid-Infrared Supercontinuum Generation in a Nontoxic Chalcogenide Step-Index Fiber,” J. Am. Ceram. Soc. 99(8), 2565–2568 (2016). [CrossRef]
7. J. M. Parker, “Fluoride Glasses,” Annu. Rev. Mater. Sci. 19(1), 21–41 (1989). [CrossRef]
8. R. Salem, Z. Jiang, D. Liu, R. Pafchek, D. Gardner, P. Foy, M. Saad, D. Jenkins, A. Cable, and P. Fendel, “Mid-infrared supercontinuum generation spanning 1.8 octaves using step-index indium fluoride fiber pumped by a femtosecond fiber laser near 2 µm,” Opt. Express 23(24), 30592–30602 (2015). [CrossRef] [PubMed]
9. X. Jiang, N. Y. Joly, M. A. Finger, F. Babic, G. K. L. Wong, J. C. Travers, and P. St. J. Russell, “Deep-ultraviolet to mid-infrared supercontinuum generated in solid-core ZBLAN photonic crystal fibre,” Nat. Photonics 9(2), 133–139 (2015). [CrossRef]
11. L. Yang, B. Zhang, K. Yin, J. Yao, G. Liu, and J. Hou, “0.6-3.2 μm supercontinuum generation in a step-index germania-core fiber using a 4.4 kW peak-power pump laser,” Opt. Express 24(12), 12600–12606 (2016). [CrossRef] [PubMed]
12. A. V. Husakou and J. Herrmann, “Supercontinuum generation in photonic crystal fibers made from highly nonlinear glasses,” Appl. Phys. B 77(2), 227–234 (2003). [CrossRef]
13. M. Klimczak, B. Siwicki, P. Skibiński, D. Pysz, R. Stępień, A. Heidt, C. Radzewicz, and R. Buczyński, “Coherent supercontinuum generation up to 2.3 µm in all-solid soft-glass photonic crystal fibers with flat all-normal dispersion,” Opt. Express 22(15), 18824–18832 (2014). [CrossRef] [PubMed]
14. G. Stępniewski, I. Kujawa, M. Klimczak, T. Martynkien, R. Kasztelanic, K. Borzycki, D. Pysz, A. Waddie, B. Salski, R. Stępień, M. R. Taghizadeh, and R. Buczyński, “Artificially anisotropic core fiber with ultra-flat high birefringence profile,” Opt. Mater. Express 6(5), 1464–1479 (2016). [CrossRef]
15. E. Yousef, M. Hotzel, and C. Russel, “Effect of ZnO and Bi2O3 addition on linear and non-linear optical properties of tellurite glasses,” J. Non-Cryst. Solids 353(4), 333–338 (2007). [CrossRef]
16. P. Domachuk, N. A. Wolchover, M. Cronin-Golomb, A. Wang, A. K. George, C. M. B. Cordeiro, J. C. Knight, and F. G. Omenetto, “Over 4000 nm Bandwidth of Mid-IR Supercontinuum Generation in sub-centimeter Segments of Highly Nonlinear Tellurite PCFs,” Opt. Express 16(10), 7161–7168 (2008). [CrossRef] [PubMed]
17. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]
18. M. Grehn, T. Seuthe, W. Tsai, M. Höfner, A. Achtstein, A. Mermillod-Blondin, M. Eberstein, H. Eichler, and J. Bonse, “Nonlinear absorption and refraction of binary and ternary alkaline and alkaline earth silicate glasses,” Opt. Mater. Express 3(12), 2132–2140 (2013). [CrossRef]
19. S. R. Friberg and P. W. Smith, “Nonlinear optical glasses for ultrafast optical switches,” IEEE J. Quantum Electron. 23(12), 2089–2094 (1987). [CrossRef]
20. R. Bala, A. Agrawal, S. Sanghi, and N. Singh, “Effect of Bi2O3 on nonlinear optical properties of ZnO-Bi2O3-SiO2 glasses,” Opt. Mater. 36(2), 352–356 (2013). [CrossRef]
21. X. Feng, J. Shi, M. Segura, N. M. White, P. Kannan, L. Calvez, X. Zhang, L. Brilland, and W. H. Loh, “Towards Water-Free Tellurite Glass Fiber for 2–5 μm Nonlinear Applications,” Fibers 1(3), 70–81 (2013). [CrossRef]
22. S. Manning, H. Ebendorff-Heidepreim, and T. M. Monro, “Ternary tellurite glasses for the fabrication of nonlinear optical fibres,” Opt. Mater. Express 2(2), 140–152 (2012). [CrossRef]
23. R. Stępień, M. Franczyk, D. Pysz, I. Kujawa, M. Klimczak, and R. Buczyński, “Ytterbium-phosphate glass for microstructured fiber laser,” Materials (Basel) 7(6), 4723–4738 (2014). [CrossRef] [PubMed]
24. J. E. Aber, M. C. Newstein, and B. A. Garetz, “Femtosecond optical Kerr effect measurements in silicate glasses,” J. Opt. Soc. Am. B 17(1), 120–127 (2000). [CrossRef]
25. J. Cimek, R. Stępień, M. Klimczak, I. Kujawa, D. Pysz, and R. Buczyński, “Modification of borosilicate glass composition for joint thermal processing with lead oxide glasses for development of photonic crystal fibers,” Opt. Quantum Electron. 47(1), 27–35 (2015). [CrossRef]
26. M. Boivin, M. El-Amraoui, S. Poliquin, R. Vallée, and Y. Messaddeq, “Advances in methods of purification and dispersion measurement applicable to tellurite-based glasses,” Opt. Mater. Express 6(4), 1079–1086 (2016). [CrossRef]
27. S. Couris, E. Koudoumas, A. A. Ruth, and S. Leach, “Concentration and Wavelength Dependence of the Effective Third-Order Susceptibility and Optical Limiting of C60 in Toluene Solution,” J. Phys. At. Mol. Opt. Phys. 28(20), 4537–4554 (1995). [CrossRef]
28. J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi 15(2), 627–637 (1966). [CrossRef]
29. X. Feng, A. K. Mairaj, D. W. Hewak, and T. M. Monro, “Nonsilica Glasses for Holey Fibers,” J. Lightwave Technol. 23(6), 2046–2054 (2005). [CrossRef]
30. X. Feng, F. Poletti, A. Camerlingo, F. Parmigiani, P. Petropoulos, P. Horak, G. M. Ponzo, M. Petrovich, J. Shi, W. H. Loh, and D. J. Richardson, “Dispersion controlled highly nonlinear fibers for all-optical processing at telecoms wavelengths,” Spec. Fiber Struct. Appl. 16(6), 378–391 (2010).
31. D. Lorenc, M. Aranyosiova, R. Buczyński, R. Stępień, I. Bugar, A. Vincze, and D. Velic, “Nonlinear refractive index of multicomponent glasses designed for fabrication of photonic crystal fibers,” Appl. Phys. B 93(2–3), 531–538 (2008). [CrossRef]
32. M. Klimczak, G. Soboń, R. Kasztelanic, K. M. Abramski, and R. Buczyński, “Direct comparison of shot-to-shot noise performance of all normal dispersion and anomalous dispersion supercontinuum pumped with sub-picosecond pulse fiber-based laser,” Sci. Rep. 6(1), 19284 (2016). [CrossRef] [PubMed]
33. R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index measurements of glasses using three-wave frequency mixing,” J. Opt. Soc. Am. B 4(6), 875–881 (1987). [CrossRef]
34. M. J. Moran, C. She, and R. L. Carman, “Interferometric Measurements of the Nonlinear Refractive-Index Coefficient Relative to CS in Laser-System-Related Materials,” IEEE J. Quantum Electron. 11(6), 259–263 (1975). [CrossRef]
35. F. Wang, K. Wang, C. Yao, Z. Jia, S. Wang, C. Wu, G. Qin, Y. Ohishi, and W. Qin, “Tapered fluorotellurite microstructured fibers for broadband supercontinuum generation,” Opt. Lett. 41(3), 634–637 (2016). [CrossRef] [PubMed]