Large and ultrafast third-order optical nonlinearities in Ag-doped bismuthate glasses which are prepared by incorporating Ag ions into bismuthate glasses to form Ag nanoparticles through a consecutive melting–quenching–annealing technique are reported. Due to the high refractive index of bismuthate glass, surface plasmon resonance (SPR) of Ag nanoparticles is extendable to 1400 nm, resulting in a higher nonlinear refractive index than bismuthate glass. Femtosecond Z-scans show that the nonlinear refractive index, as high as 9.4 × 10−17 and 5.6 × 10−18 m2 W−1 at 800 and 1300 nm, respectively, can be achieved by selecting an optimized concentration of Ag nano-sized particles. And two-photon absorption at 800 nm is suppressed due to a blue shift in the band-gap of Ag-doped bismuthate glasses, as compared to pristine bismuthate glasses. Optical Kerr shutter technique reveals that these nonlinearities have a relaxation time of < 1 ps.
© 2014 Optical Society of America
Transparent glassy materials possessing high and ultrafast third-order non-linearity (χ(3)) have attracted considerable attention because of their potential applicability in ultra-fast optical processing devices . Bismuth-oxide-based (Bi2O3-based), heavy-metal-oxide (HMO) glasses, namely, bismuthate glasses , are promising within this context. It was reported that a bismuthate glass within the Bi2O3–B2O3–SiO2 (BBS) pseudo-ternary system exhibits the highest χ(3) nonlinearity, as compared to other oxide glasses , and it also has a ultrafast response time (< 200 fs) [4,5]. Our previous investigation demonstrated that the substitution of SiO2 with titanium dioxide (TiO2) can enhance χ(3)-response . And we also showed that Bi2O3–B2O3–TiO2 (BBT) micro-sized crystals prepared by using the TiO2 as a nucleating agent possess a large χ(3)-value . Here, we report our observation of large and ultrafast third-order optical nonlinearity at 800 and 1300 nm in bismuthate glasses doped with silver nanoparticles.
Noble metallic (e.g., Au, Ag, and Cu) nanoparticles are known to possess large χ(3) nonlinearity at light wavelengths close to surface plasmon resonance (SPR), which originates from dipolar electron oscillations in the conduction bands of these metal particles . Singh and Karmakar reported the synthesis of bismuth-coated silver nanoparticles (Ag-NPs) in bismuthate glasses by introducing silver ions (Ag+) , which capitalizes on the reducing capacity of defect structures, e.g., Bi2+, Bi+, and Bi0, within the HMO glasses. We also preformed the characterization of χ(3) nonlinearity in bismuthate glasses doped with Ag-NPs and Au-NPs [10,11]; and observed a significant increase in the χ(3) nonlinearity as the light wavelength approaches their SPR.
More importantly, we observed that the SPR band of Ag-NPs in bismuthate glasses exhibits a significant red-shift, as compared to its typical location (~400 nm) in silica glass, resulting from the high refractive index of the host medium (n0 > 2). We also noticed that the SPR band of Ag-NPs in bismuthate glasses extends to the near infrared region (~1400 nm). With such an extension, a SPR-enhancement in χ(3) nonlinearity should be anticipated at 800 and 1300 nm , and 1300-nm window one of the two important telecom windows. However, to our best knowledge, there is no report in literature on χ(3) nonlinearity at 1300 nm in glasses doped with Ag-NPs, though there are reports on χ(3) nonlinearity at 800 nm or less in Ag-doped glasses [12–16].
In this work, we report both the synthesis of silver nanoparticles composited bismuthate (SNCB) glasses within the BBT ternary system using a consecutive melting–quenching–annealing process and the investigation into the dependence of their optical properties on the Ag-NP density. We present the linear and nonlinear optical characterization of the as-synthesized glasses. It should be pointed out that, for the first time, a large χ(3) nonlinearity in SNCB glasses is achieved at 1300 nm.
The host glass was composed of 60Bi2O3–30B2O3–10TiO2 (in mol%), and these glasses were doped with 0.05, 0.1, 0.15, 0.2, and 0.3 wt% AgNO3 (referred to as BBT-Agx, x = 5, 10, 15, 20, and 30), which were prepared using reagent-grade Bi2O3, H3BO3, TiO2 and AgNO3 chemicals. The raw materials were carefully weighed (30 g) and placed inside high-purity alumina crucibles. The materials were then melted in a muffle furnace at 1200 °C for 30 min in air with stirring. The melt was quenched on a stainless steel plate and annealed at 400 °C for 2 h and then cooled to room temperature at a rate of 10 °C/h. The sample plates were cut and polished to a thickness of 0.7 mm for further optical measurement.
The linear absorption spectra of the samples were measured using a Perkin-Elmer-Lamda 950UV/VIS/NIR spectrophotometer. The morphology images of the nanoparticles were obtained using transmission electron microscopes (TEM, FEI, Tecnai F20, 200 kV). The nonlinear optical properties of the samples were investigated using the single-beam Z-scan and optical Kerr shutter (OKS) techniques. In the Z-scan measurements, 120-fs laser pulses at 800 nm were produced by a mode-locked Ti: sapphire laser (Coherent, OperA) operated at a repetition rate of 1 k Hz. 150-fs laser pulses at 1300 nm were generated by an Optical Parametric Generator (Light Conversion TOPAZ) which was pumped by the above-said Ti:sapphire laser. The incident energy of single laser pulse was kept at 10 ± 1 nJ. The nonlinear refractive index, γ of the sample was extracted from the Z-scan theoretical fit to the closed-aperture (CA) Z-scan measurement, which corresponded to the transmittance of a tightly focused Gaussian beam through a finite aperture S (linear transmission, S = 50%) in the far field as a function of sample position Z with respect to the focal plane. Open-aperture (OA) Z-scans were obtained by removing the aperture and the theoretical Z-scan fit to obtain the nonlinear absorption (NA) coefficient β. These theoretical Z-scan fits were calculated based on well-established, nonlinear curve fitting procedures .
For the OKS measurement, a Ti: sapphire laser (Coherent Mira 900-D) with pulse duration of 200 fs at 76 MHz repetition rate was used as excitation source, and the operating wavelength λ was set at 800 nm. The average power of probe and pump pulses were set at 5 ± 0.5 mW and 30 ± 3 mW, respectively. The measurements were calibrated by the host glass and CS2. As shown in Fig. 1, the host bismuthate glass and CS2 has nonlinear response time (τ) < 200 fs and > 1 ps, respectively, in good agreement with previous study . The OKS curves of the SNCB glasses were fitted using exponential decay convolved with 200 fs Gaussian pulse, and the τ value was obtained. All of the above measurements were conducted at room temperature.
3. Results and discussion
The linear absorption spectra of the samples are shown in Fig. 2. An evident difference in the SNCB glasses spectra is the band-gap wavelength (or UV cut-off) that blue-shifts from ~500 nm to below 400 nm after Ag+ ions are added, signaling the presence of Ag-NP SPRs . The formation of Ag-NPs caused the presence of Femi level above the conduction band of host glass , which opened up the energy band gap and led to the blue-shifting of UV cut-off. Besides, the consumption of defect structures (e.g., Bi2+, Bi+, and Bi0) by Ag-NPs decreased their absorption at short wavelengths, which also contributed to the blue-shifting. All silver-doped sample spectra exhibit an absorption peak similar to typical Ag-NP SPR absorption, and tail of the absorption band extended to ~1400 nm, indicating the local field effect induced by SPR would have an impact at near infrared region. The single SPR peak is a result of intraband electronic transitions in silver atom clusters , which occur at a longer wavelength than that of the interband transition band (at 300 nm). These intraband electronic transitions may overlap with the UV absorption edges because of the strong electronic transitions in bismuth ions.
The SPR peak wavelength (λmax = 466 nm to 575 nm) of Ag-NPs within the BBT glass was significantly red-shifted, as compared with their original location (~400 nm) either in liquid or in conventional silica glass (n0 ≈1.5) . This is a result of the high refractive index (n0 = 2.166 and 2.0821 at 632.8 and 1310 nm, respectively) of the host medium and the dielectric variation, consistent with the Mie theory . The strongest SPR intensity was observed in BBT-Ag15, which has the longest SPR peak wavelength at 524 mm among all of the samples containing AgNO3 below 0.3 wt%. The increased size and number of Ag-NPs is thus obtained from this sample. The SPR of BBT-Ag30 sample, which was doped with the highest AgNO3 content among all the samples, was dramatically weakened and the corresponding λmax red-shifted to 575 nm, the longest among all of the SNCB glasses. This finding reveals that the mean size of the silver particles in BBT-Ag30 should reach the size confinement effect (SCE) threshold value [18,21]. The λmax of the SNCB glasses shows a nonlinear dependence on silver concentration as indicated in Table 1, which would yield the relationships among the silver concentration, SPR, and SCE. The resultant curve from plotting λmax versus silver doping quantity, as shown in Fig. 3, this continuous process was well-fitted by a third-order polynomial function. This curve indicates that the silver concentration threshold for SCE attenuation is approximately 0.23 wt%, whereas the optimum silver concentration that results in the broadest band of SPR among all of the samples and a strong SCE is approximately 0.13 wt%.
The TEM technique was used to gain more insights on Ag-NP variation in SNCB glasses doped with different amounts of silver ions. First, no microscopic structure can be observed within the pure BBT glass as shown in Fig. 4(a), thus confirming the amorphous nature of the host medium. TEM images obtained from SNCB glasses show that the samples consist of large numbers of gray and dark particle structures that are uniformly distributed, thus confirming the formation of Ag-NPs in SNCB glasses after the incorporation of silver ions. The average size of the Ag-NP histograms of BBT-Ag10 is approximately 3.1 nm in diameter as calculated by Gaussian fitting when the particle diameter is plotted against its number in the TEM image in Fig. 4(b). BBT-Ag15 has stronger and 10 nm red-shifted SPR as compared to that of BBT-Ag10, indicating the number and mean size of Ag-NPs in the former are larger than those in the later. Since the logical size for Ag-NPs with strong SCE is in the range of 3 to10 nm , we believed that the Ag-NPs in BBT-Ag15 are in this range as indicated by its strongest SPR absorption spectrum. The TEM images obtained from BBT-Ag30 show that the Ag-NP size in this sample is evidently larger compared with the previous sample, as shown in Fig. 4(c). This observation was verified by the calculated size of 15.5 nm for Ag-NPs in the BBT-Ag30 sample.
The Mie theory shows that the increase in the size of metallic nanoparticles gives rise to the increase in the peak wavelength of SPR. The average size of Ag-NPs in BBT-Ag30 is largest, and thus the SPR of BBT-Ag30 is located at the longest wavelength among all of the SNCB glasses. Particle aggregation as a result of the Ostwald ripening process was significant in BBT-Ag30 as a result of its high Ag+ content , as shown in Fig. 4(c). There are rod-shaped particles with size over 100 nm, and their long electron mean free paths caused a weak confinement effect, thus resulting in a considerably broad but weak SPR absorption band.
Figure 5 presents the CA Z-scans of the SNCB glasses at 800 and 1300 nm, and the peak of each curve following valley configuration displays positive signs of γ, which is evidence of self-focusing behavior in both two wavelengths. The CA signal (difference between valley and peak) increases with initial increase of silver content and reaches the maximum intensity in the sample BBT-Ag15, and then it decreases as the AgNO3 doping quantity reaches 0.3 wt%. The variation of the CA signal with silver concentration is evidently consistent with that of the SPR tail intensities in the samples.
The γ-values of the samples were obtained by fitting the CA curves, and the values are listed in Table 1. It can be seen that the γ-value of the nanocomposites obtained in 1300 nm is one order lower than those obtained at 800 nm, indicating their significant dependence on SPR intensity. The largest γ-value was obtained from BBT-Ag15 at 800 nm, which reaches 9.4 × 10−17 m2 W−1 and is about 30 times larger than that of the host. This result gives an optimum Ag-NP concentration for the maximum of γ. Interestingly, the γ of BBT-Ag5 at 1300 nm is smaller than that of the host glass, indicating that the SPR enhancement in this sample is absent at this wavelength and its CA signal is merely from the medium which has larger band gap energy than the pure bismuthate glass as indicated from Fig. 2.
The OA Z-scan of the host glass shows a valley in the center at 800 nm as depicted in Fig. 6, thus illustrating the presence of two-photon absorption (TPA). This observation agrees with previous study on pure bismuthate glasses . However, TPA signal is not observed in the Z-scans of our samples, thus indicating that the formation of Ag-NPs suppresses the TPA in the host medium. As displayed in Fig. 2, the UV cut-off of the host glass absorption spectra significantly blue-shifted to below 400 nm after the introduction of silver, which caused the half-band gap energy (1/2Eopg) of the samples to exceed incident photon energy (1.55 eV at 800 nm). The TPA from the host glass was consequently suppressed . At 1300 nm, both OA signal of host glass and Ag-NPs doped glasses was not observed as a result of the low photon energy at this wavelength (0.95 eV at 1300 nm) which is too small to bridge to the 1/2Eopg of all the samples .
The nonlinear susceptibility χ(3) of the samples can be obtained based on their γ- and β-values using the following formula :Table 1. This result is consistent with the enhancement in the measured γ-magnitude. The Ag-NP parameters related to γ or Re[χ(3)]) in the current BBT glass are larger than those obtained in lead-based oxide glass (composed of PbO–GeO2) , silica glass , and chalcogenide glass (composed of GeS2–Ga2S3–KBr) . However, the Ag-NP NR parameters in the BBT glass are one order lower than those obtained in periodic Ag-NP arrays and iron-contained float glasses [15,16], but the former one exhibited enormous TPA coefficient at 800 nm and the later one was measured by laser pulse of 76 MHz repetition rate. The relatively high γ or Re[χ(3)] obtained from the current Ag-NP-embedded bismuthate glass indicate that the localized field effect had extended to near infrared by capitalizing on the red-shifted SPR band, which is a result of the high refractive index of the host glass. For the NR parameters obtained at 1300 nm, they are still benefited from SPR but the amplification is significantly reduced since 1300 nm locates at the edge of SPR band of the present materials. The maximum γ of SNCB glasses is over two times larger than that of silicon at 1300 nm , and it is comparable to that of pure chalcogenide glass (As2S3) which has moderate TPA coefficient of 1.6 × 10−12 m W−1 at the telecom wavelength .
Mizrahi’s study demonstrated that TPA mainly limits the applicability of nonlinear materials in all optical switching-related nonlinear devices . TPA is absent at 800 and 1300 nm in our work as a result of Ag-NP formation, as discussed in the section above. The TPA figure of merit (T = γ/βλ) of the samples is an infinite value that makes them ideal for the above-mentioned devices working near infrared. However, the linear absorption induced by SPR becomes another problem for the materials to be applied in practical applications. To evaluate the influence the linear absorption, we evaluate the one photon figure of merit (W) that is defined as :Fig. 7, the W values at 800 and 1300 nm in all cases are above one.
Figure 8(a) presents the OKS signals of SNCB glasses at 800 nm, from which we obtain the response time τ and third-order nonlinear susceptibility χ(3). First of all, as shown in the figure, BBT-Ag15 with the highest χ(3) shows the strongest OKS signal while that of BBT-Ag30 is the weakest. Accordingly, the χ(3) value of the SNCB glasses can be obtained by using CS2 as reference :Figure 8(b) shows the comparison of χ(3) values that obtained from the OKS signals and Z-scan calculation, and the Ag-concentration dependence of OKS signals is in good agreement with those calculated from Z-scans. On the other hand, by fitting the normalized curves using exponential decay convolved with 200 fs Gaussian pulse as shown in the inset of Fig. 8(a), OKS response time (τ) of the SNCB glasses are obtained, which are faster than 1 ps but slower than that of the host glass, indicating interband electric-dipole transition between d-valence band and quantum confined electron states of the s-p conduction band is the main contribution to the enhanced nonlinearity . For BBT-Ag15 with strongest SPR absorption at 800 nm, its τ value is the longest because the number of Ag-NPs that participated in the nonlinear excitation-relaxation process is larger than those in other samples. Similarly, the fastest τ is obtained in BBT-Ag30 as a result of aggregation that significantly reduced the number of Ag-NPs. The response time of present SNCB glasses can be considered as fast (< 1 ps) that makes them ideal for ultrafast optical switching. However, the preparation of present SNCB glasses into waveguide forms that can be applied practically remains a challenge, and research work that addresses this issue is presently in process.
In conclusion, we have reported large and ultrafast third-order optical nonlinearities in Ag-doped bismuthate glasses, which are prepared by incorporating Ag ions into bismuthate glasses to form Ag nanoparticles through a consecutive melting–quenching–annealing technique. Due to the high refractive index of bismuthate glass, surface plasmon resonance (SPR) of Ag nanoparticles is extendable to 1400 nm, resulting in a higher nonlinear refractive index than bismuthate glass. Our femtosecond Z-scans show that the nonlinear refractive index, as high as 9.4 × 10−17 and 5.6 × 10−18 m2 W−1 at 800 and 1300 nm, respectively, can be achieved by selecting an optimized concentration of Ag nano-sized particles. And two-photon absorption at 800 nm is suppressed due to a blue shift in the band-gap of Ag-doped bismuthate glasses, as compared to pristine bismuthate glasses. Optical Kerr shutter technique reveals that these nonlinearities have a relaxation time of < 1 ps. Therefore, we believe that Ag-doped bismuthate glasses have great potential for ultrafast nonlinear optical devices.
This work was partially supported by the International Science & Technology Cooperation Program of China (Grant No. 2011DFA12040), National Program on Key Basic Research Project (973 Program) (Grant No. 2012CB722703), Program for Innovative Research Team of Ningbo City (Grant No. 2009B21007), the National Natural Science Foundation of China (Grant No. 61308094), the Open Fund of the State Key Laboratory of Luminescent Materials and Devices (South China University of Technology), the Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ12F05003). It was also sponsored by K.C. Wong Magna Fund in Ningbo University.
References and links
1. G. Agrawal, Applications of Nonlinear Fiber Optics (Academic, 2008).
2. W. H. Dumbaugh and J. C. Lapp, “Heavy-metal oxide glasses,” J. Am. Ceram. Soc. 75(9), 2315–2326 (1992). [CrossRef]
3. T. Hasegawa, T. Nagashima, and N. Sugimoto, “Z-scan study of third-order optical nonlinearities in bismuth-based glasses,” Opt. Commun. 250(4–6), 411–415 (2005). [CrossRef]
4. N. Sugimoto, H. Kanbara, S. Fujiwara, K. Tanaka, and K. Hirao, “Ultrafast response of third-order optical nonlinearity in glasses containing Bi2O3,” Opt. Lett. 21(20), 1637–1639 (1996). [CrossRef] [PubMed]
5. N. Sugimoto, “Ultrafast optical switches and wavelength division multiplexing (WDM) amplifiers based on bismuth oxide glasses,” J. Am. Ceram. Soc. 85(5), 1083–1088 (2002). [CrossRef]
6. T. Xu, F. Chen, S. Dai, Q. Nie, X. Shen, and X. Wang, “Third-order optical nonlinear characterizations of Bi2O3-B2O3-TiO2 ternary glasses,” Physica B 404(14–15), 2012–2015 (2009). [CrossRef]
7. F. Chen, T. Xu, S. Dai, Q. Nie, X. Shen, X. Wang, and B. Song, “Preparation and optical nonlinearities of transparent bismuth-based glass ceramics embedded with Bi2O3 microcrystals,” J. Non-Cryst. Solids 356(50–51), 2786–2789 (2010). [CrossRef]
8. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
9. S. P. Singh and B. Karmakar, “Single-step synthesis and surface plasmons of bismuth-coated spherical to hexagonal silver nanoparticles in dichroic ag:bismuth glass nanocomposites,” Plasmonics 6(3), 457–467 (2011). [CrossRef]
10. F. Chen, S. Dai, T. Xu, X. Shen, C. Lin, Q. Nie, C. Liu, and J. Heo, “Surface-plasmon enhanced ultrafast third-order optical nonlinearities in ellipsoidal gold nanoparticles embedded bismuthate glasses,” Chem. Phys. Lett. 514(1–3), 79–82 (2011). [CrossRef]
11. T. Xu, F. Chen, X. Shen, S. Dai, Q. Nie, and X. Wang, “Observation of surface plasmon resonance of silver particles and enhanced third-order optical nonlinearities in AgCl doped Bi2O3-B2O3-SiO2 ternary glasses,” Mater. Res. Bull. 45(10), 1501–1505 (2010). [CrossRef]
12. L. De Boni, E. C. Barbano, T. A. de Assumpção, L. Misoguti, L. R. P. Kassab, and S. C. Zilio, “Femtosecond third-order nonlinear spectra of lead-germanium oxide glasses containing silver nanoparticles,” Opt. Express 20(6), 6844–6850 (2012). [CrossRef] [PubMed]
13. B. Ghosh and P. Chakraborty, “Large third-order optical nonlinearity of silver colloids in silica glasses synthesized by ion implantation,” Nucl. Instrum. Methods B 269(11), 1321–1326 (2011). [CrossRef]
14. Q. Liu, X. He, X. Zhou, F. Ren, X. Xiao, C. Jiang, H. Zhou, X. Zhao, L. Lu, and S. Qian, “Third-order nonlinearity in Ag-nanoparticles embedded 56GeS2–24Ga2S3–20KBr chalcohalide glasses,” J. Non-Cryst. Solids 357(11-13), 2320–2323 (2011). [CrossRef]
15. B. H. Yu, D. L. Zhang, Y. B. Li, and Q. B. Tang, “Nonlinear optical behaviors in a silver nanoparticle array at different wavelengths,” Chin. Phys. B 22(1), 014212 (2013). [CrossRef]
16. J. Rönn, L. Karvonen, S. Kujala, A. Säynätjoki, A. Tervonen, and S. Honkanen, “Third-order optical nonlinearities of Ag nanoparticles fabricated by two-step ion exchange in glass,” Proc. SPIE 8434, 84341K (2012). [CrossRef]
17. N. Sugimoto, “Ultrafast optical switches and wavelength division multiplexing (WDM) amplifiers based on bismuth oxide glasses,” J. Am. Ceram. Soc. 85(5), 1083–1088 (2002). [CrossRef]
18. F. Hache, D. Ricard, and C. Flytzanis, “Optical nonlinearities of small metal particles: surface-mediated resonance and quantum size effects,” J. Opt. Soc. Am. B 3(12), 1647–1655 (1986). [CrossRef]
19. S. Qu, Y. Zhang, H. Li, J. Qiu, and C. Zhu, “Nanosecond nonlinear absorption in Au and Ag nanoparticles precipitated glasses induced by a femtosecond laser,” Opt. Mater. 28(3), 259–265 (2006). [CrossRef]
20. H. Kozuka, “Metal nanoparticles in gel-derived oxide coating films: control and application of surface plasma resonance,” Proc. SPIE 3136, 304–314 (1997). [CrossRef]
21. K.-C. Lee, S.-J. Lin, C.-H. Lin, C.-S. Tsai, and Y.-J. Lu, “Size effect of Ag nanoparticles on surface plasmon resonance,” Surf. Coat. Tech. 202(22-23), 5339–5342 (2008). [CrossRef]
22. T. Som and B. Karmakar, “Nanosilver enhanced upconversion fluorescence of erbium ions in Er3+: Ag-antimony glass nanocomposites,” J. Appl. Phys. 105(1), 013102 (2009). [CrossRef]
23. Y. Watanabe, S. Sakata, T. Watanabe, and T. Tsuchiya, “Two-photon absorption in binary Bi2O3-B2O3 glass at 532 nm,” J. Non-Cryst. Solids 240(1–3), 212–220 (1998). [CrossRef]
25. M. Sheik-Bahae, D. J. Hagan, and E. W. Van 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]
26. 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 GeS2-Sb2S3-CdS chalcogenide glasses,” Opt. Express 18(22), 23275–23284 (2010). [CrossRef] [PubMed]
27. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]
28. J. M. Harbold, F. Ö. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett. 27(2), 119–121 (2002). [CrossRef] [PubMed]
29. V. Mizrahi, K. W. Delong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14(20), 1140–1142 (1989). [CrossRef] [PubMed]
30. B. L. Yu, C. S. Zhu, and F. X. Gan, “Optical nonlinearity of Bi2O3 nanoparticles studied by Z-scan technique,” J. Appl. Phys. 82(9), 4532–4537 (1997). [CrossRef]
31. H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO2 composite films on femtosecond and picosecond time scales,” Opt. Lett. 23(5), 388–390 (1998). [CrossRef] [PubMed]