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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 13 — Jun. 22, 2009
  • pp: 10970–10975
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Femtosecond third-order optical nonlinearity of polycrystalline BiFeO3

Bing Gu, Yang Wang, John Wang, and Wei Ji  »View Author Affiliations


Optics Express, Vol. 17, Issue 13, pp. 10970-10975 (2009)
http://dx.doi.org/10.1364/OE.17.010970


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Abstract

We report both linear and nonlinear optical properties of a ferroelectric thin film of polycrystalline BiFeO3 deposited on a quartz substrate. The linear refraction index and absorption coefficient of the film are determined as a function of light wavelength by optical transmittance measurements. By performing Z-scan experiments with femtosecond laser pulses at a wavelength of 780 nm, the third-order nonlinear refraction index and two-photon absorption (2PA) coefficient are measured to be 1.5×10-4 cm2/GW and 16 cm/GW, respectively. The results indicate that the thin film of polycrystalline BiFeO3 is a promising candidate for applications in nonlinear photonic devices.

© 2009 Optical Society of America

1. Introduction

As a new multifunctional material, thin films of BiFeO3 (BFO) have recently received particularly attention due to their potential applications in data storage, spintronics, sensors, actuators, nonvolatile random access memory, and microelectromechanical systems [1

1. J. Wang, J. B. Neaton, H. Zheng, V. Nagarajan, S. B. Ogale, B. Liu, D. Viehland, V. Vaithyanathan, D. G. Schlom, U. V. Waghmare, N. A. Spaldin, K. M. Rabe, M. Wuttig, and R. Ramesh, “Epitaxial BiFeO3 multiferroic thin film heterostructures,” Science 299, 1719–1722 (2003). [CrossRef] [PubMed]

]. Researchers have reported the notable physical characteristics of BFO thin films, such as prominent ferroelectricity [2

2. K. Y. Yun, M. Noda, and M. Okuyama, “Prominent ferroelectricity of BiFeO3 thin films prepared by pulsed-laser deposition,” Appl. Phys. Lett. 83, 3981–3983 (2003). [CrossRef]

], photoconductivity [3

3. S. R. Basu, L. W. Martin, Y. H. Chu, M. Gajek, R. Ramesh, R. C. Rai, X. Xu, and J. L. Musfeldt, “Photoconductivity in BiFeO3 thin films,” Appl. Phys. Lett. 92, 091905 (2008). [CrossRef]

], magnetic and electrical properties [4

4. A. K. Pradhan, K. Zhang, D. Hunter, J. B. Dadson, G. B. Loutts, P. Bhattacharya, R. Katiyar, J. Zhang, D. J. Sellmyer, U. N. Roy, Y. Cui, and A. Burger, “Magnetic and electrical properties of single-phase multiferroic BiFeO3,” J. Appl. Phys. 97, 093903 (2005). [CrossRef]

], ferroelectric and dielectric characteristics [5

5. Y. Wang, R. Y. Zheng, C. H. Sim, and J. Wang, “Charged defects and their effects on electrical behavior in Bi1-xLaxFeO3 thin films,” J. Appl. Phys. 105, 016106 (2009). [CrossRef]

], and large second-order optical nonlinearities [6

6. A. Kumar, R. C. Rai, N. J. Podraza, S. Denev, M. Ramirez, Y. H. Chu, L. W. Martin, J. Ihlefeld, T. Heeg, J. Suchubert, D. G. Schlom, J. Orenstein, R. Ramesh, R. W. Collins, J. L. Musfeldt, and V. Gopalan, “Linear and nonlinear optical properties of BiFeO3,” Appl. Phys. Lett. 92, 121915 (2008). [CrossRef]

]. It has been demonstrated that ferroelectric thin films are promising for applications in nonlinear photonic devices because of their high optical transparency and remarkable optical nonlinearity [7

7. H. Shin, H. J. Chang, R. W. Boyd, M. R. Choi, and W. Jo, “Large nonlinear optical response of polycrystalline Bi3.25La0.75Ti3O12 ferroelectric thin films on quartz substrates,” Opt. Lett. 32, 2453–2455 (2007). [CrossRef] [PubMed]

11

11. S. W. Liu, J. Xu, D. Guzun, G. J. Salamo, C. L. Chen, Y. Lin, and M. Xiao, “Nonlinear optical absorption and refraction of epitaxial Ba0.6Sr0.4TiO3 thin films on (001) MgO substrates,” Appl. Phys. B 82, 443–447 (2006). [CrossRef]

]. However, most of these investigations have been carried out with nanosecond and picosecond laser pulses [7

7. H. Shin, H. J. Chang, R. W. Boyd, M. R. Choi, and W. Jo, “Large nonlinear optical response of polycrystalline Bi3.25La0.75Ti3O12 ferroelectric thin films on quartz substrates,” Opt. Lett. 32, 2453–2455 (2007). [CrossRef] [PubMed]

10

10. T. Ning, C. Chen, Y. Zhou, H. Lu, D. Zhang, H. Ming, and G. Yang, “Large optical nonlinearity in CaCu3Ti4O12 thin films,” Appl. Phys. A 94, 567–570 (2009). [CrossRef]

]; and the full understanding on the ultrafast nonlinear optical responses of ferroelectric films is seldom in the literature [11

11. S. W. Liu, J. Xu, D. Guzun, G. J. Salamo, C. L. Chen, Y. Lin, and M. Xiao, “Nonlinear optical absorption and refraction of epitaxial Ba0.6Sr0.4TiO3 thin films on (001) MgO substrates,” Appl. Phys. B 82, 443–447 (2006). [CrossRef]

]. Here, we present our experimental investigations into the linear optical properties of a polycrystalline BFO ferroelectric thin film on a quartz substrate and its third-order nonlinear response to femtosecond laser pulses.

2. Experiments and results

The BFO ferroelectric thin film was deposited on the quartz substrate at 650°C by radio-frequency magnetron sputtering. The relevant ceramic target was prepared using conventional solid state reaction method starting with high-purity (>99 %) oxide powders of Bi2O3 and Fe2O3. It is noted that 10 wt % excess bismuth was utilized to compensate for bismuth loss during the preparation. During magnetron sputtering, the Ar/O2 ratio was controlled at 7 : 1. The detailed experimental procedure can be found elsewhere [5

5. Y. Wang, R. Y. Zheng, C. H. Sim, and J. Wang, “Charged defects and their effects on electrical behavior in Bi1-xLaxFeO3 thin films,” J. Appl. Phys. 105, 016106 (2009). [CrossRef]

]. The X-ray diffraction analysis demonstrated that the sample was a polycrystalline structure of perovskite phase. The observation from the scanning electron microscopy showed that the BFO film and the substrate were distinctive and no evident inter-diffusion occurred between them.

The linear optical properties of the BFO film were studied by optical transmittance measurements. The optical transmittance spectrum of the BFO thin film on the quartz substrate was recorded at room temperature with a spectrophotometer (Shimadzu UV-3600). As shown in Fig. 1, it is clear that the BFO thin film is highly transparent with transmittances between 58% and 91% in the visible and near-infrared wavelength region. Furthermore, the pronounced oscillation in the transmittance spectrum indicates that the BFO thin film has a flat surface and good homogeneity. With these desired qualities, the BFO thin film should be a promising candidate for applications in photonic devices.

Fig. 1. Optical transmittance spectrum of the BFO thin film on the quartz substrate (solid line) and its envelope (dotted lines).
Fig. 2. Wavelength dependence of (a) the linear refractive index and (b) the absorption coefficient of the BFO thin film. The circles are the calculated data and the solid lines are the theoretical fittings by the improved Sellmeier-type formulae [13].

Figure 2 presents both linear refractive index n 0 and absorption coefficient α 0 of the BFO film obtained from the transmittance curve using the envelope technique [12

12. R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E: Sci. Instrum. 16, 1214–1222 (1983). [CrossRef]

]. The film thickness calculated in this way is determined to be 510±23 nm. At 780 nm, we obtain n 0=2.60 and α 0=1.07×104 cm−1 though the Sellmeier-type dispersion fitting [13

13. N. A. Barboza and R. S. Cudney, “Improved Sellmeier equation for congruently grown lithium tantalate,” Appl. Phys. B 95, 453–458 (2009). [CrossRef]

], respectively. The optical bandgap (Eg) of the film can be estimated using Tauc’s formulae (α 0 )2/n=Const(hν-Eg), where is the photon energy of incident light, n is determined by the characteristics of electron transitions in a material [14

14. J. Tauc, R. Grigorovici, and A. Vancu, “Optical Properties and Electronic Structure of Amorphous Germanium,” Phys. Stat. Sol. 15, 627–637 (1966). [CrossRef]

]. From the data displayed in Fig. 3, we obtain n=1 and extrapolate Eg=2.80 eV, indicating that the BFO has a direct bandgap at 443-nm wavelength. The observation is very close to the reported one [6

6. A. Kumar, R. C. Rai, N. J. Podraza, S. Denev, M. Ramirez, Y. H. Chu, L. W. Martin, J. Ihlefeld, T. Heeg, J. Suchubert, D. G. Schlom, J. Orenstein, R. Ramesh, R. W. Collins, J. L. Musfeldt, and V. Gopalan, “Linear and nonlinear optical properties of BiFeO3,” Appl. Phys. Lett. 92, 121915 (2008). [CrossRef]

].

Fig. 3. (α0)2 is plotted as a function of photon energy, , or wavelength for the BFO thin film.

The nonlinear-optical measurements were conducted by using conventional Z-scan technique [15

15. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990). [CrossRef]

] with 780-nm, 350-fs laser pulses at 1 kHz repetition rate. The laser pulses were generated by a Ti:sapphire regenerative amplifier (Quantronix, Titan) and focused onto the sample with a minimum beam waist of 31 µm. The transmitted pulse energies in the presence or absence of an aperture placed in front of the detector at the far field were monitored as the sample was moved along the propagation direction of the laser pulses, giving rise to the closed-aperture (CA) and open-aperture (OA) Z-scans, respectively. For the CA Z-scans, the linear transmittance of the far-field aperture was fixed at 15% by adjusting the aperture radius. The measurement system was calibrated with carbon disulfide. In addition, neither laser-induced damage nor significant scattering signal was observed from our Z-scan measurements.

To exclude the optical nonlinearity from the substrate, we first performed Z-scans on the 1.0-mm-thick quartz substrate. The nonlinear absorption coefficient of α sub 2⋍0 and the third-order refractive index of n sub 2=3.26×10−7 cm2/GW are extracted from the best fittings between the femtosecond-pulsed Z-scan theory [16

16. B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed z scans on instantaneous nonlinearity,” Appl. Opt. 47, 1187–1192 (2008). [CrossRef] [PubMed]

] and the experimental data illustrated in Fig. 4(a) at I 0=156 GW/cm2. The measured n sub 2 value is independent of I 0 under our experimental conditions and is consistent with the reported one [17

17. S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001). [CrossRef] [PubMed]

]. It should be noted that I0 is the peak intensity within the sample and can be evaluated through the relation I 0=I 00(1-R 1), where I 00 is the peak intensity just before the sample surface and R 1=(n 0−1)2/(n 0+1)2 is the Fresnel reflection coefficient at the air-sample interface. The peak intensity within the substrate for a cascade nonlinear medium of sample and substrate can be yielded from I0=I 0(1-R 2), where R 2=(n 0n sub 0)2/(n 0+n sub 0)2 is the Fresnel reflection coefficient at the sample-substrate interface.

Figure 4(b) displays typical OA and CA Z-scans for the 510-nm-thick BFO thin film on the 1.0-mm-thick quartz substrate at I 0=156 GW/cm2, showing positive signs for both absorptive and refractive nonlinearities, respectively. It should be pointed out that such Z-scan signals arise from the resultant nonlinear response contributed by both the BFO film and the substrate. To separate each contribution, a rigorous analysis of Z-scan data for a cascaded nonlinear medium [18

18. W. P. Zang, J. G. Tian, Z. B. Liu, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, “Study on Z-scan characteristics of cascaded nonlinear media,” Appl. Phys. B 77, 529–533 (2003). [CrossRef]

] is adopted as follows. Firstly, under the assumption that both the BFO film and the substrate only exhibit third-order nonlinearities, we evaluate the total nonlinear response of absorptive nonlinearity, q 0, and refractive nonlinearity, Δϕ 0, from the best fittings to the measured Z-scans for the composite system of BFO and quartz with the femtosecond-pulsed Z-scan theory, which is described in detail elsewhere [16

16. B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed z scans on instantaneous nonlinearity,” Appl. Opt. 47, 1187–1192 (2008). [CrossRef] [PubMed]

]. Such evaluations are carried out for the Z-scans measured at different levels of I 0. Secondly, the nonlinear absorption coefficient α 2 and the nonlinear refraction index n 2 for the BFO film can then be obtained from the following relations: α 2=[q 0/I0-(1-R 2)α sub 2 L sub eff]/L eff and n 2=[Δϕ 0 λ/2πI 0−(1−R 2)n sub 2 L sub eff]/L eff, respectively, where L eff=[1−exp(−α 0 L)]/α 0 is the effective length of the BFO film, λ is the laser wavelength, and R 2 is the Fresnel reflection coefficient at the BFO-substrate interface. As such, the nonlinear coefficients of α 2 and n 2 for the BFO film at different values of I 0 are determined unambiguously and rigorously.

Fig. 4. Examples of Z-scans measured at I 0=156 GW/cm2 for (a) the 1.0-mm-thick quartz substrate and (b) the 510-nm-thick BFO film deposited on the 1.0-mm-thick quartz substrate. Filled and open circles are the OA and CA Z-scans, respectively; and the solid lines are the best-fit curves calculated by the femtosecond-pulsed Z-scan theory [16].
Fig. 5. Intensity independence of (a) 2PA coefficient α 2 and (b) nonlinear refraction index n 2 for the BFO film.

As displayed in Fig. 5, the values of α 2 and n 2 are independent of the intensity, clearly indicating that the observed nonlinearities are of cubic nature; and α 2=16.0±0.6 cm/GW and n 2=(1.46±0.06)×10−4 cm2/GW at 780 nm. It should be emphasized that the above-said nonlinear coefficients are average values due to the polycrystalline, multi-domain nature of the BFO film. For comparison, Table I lists the nonlinear coefficients of several thin films in the near infrared region under the excitation of femtosecond laser pulses. It suggests that the BFO thin film should have a greater potential for nonlinear photonic devices, compared to the other films.

Table 1. Femtosecond optical nonlinearities of several thin films in the near infrared region.

table-icon
View This Table

From Fig. 4(b), we conclude that the positive nonlinear absorption mainly originates from the 2PA process because (i) the Z-scan theory on two-photon absorbers fits our OA Z-scans well; and (ii) both excitation photon energy (=1.60 eV) and bandgap (Eg=2.80 eV) of the BFO film fulfill the 2PA requirement (<Eg<2). It is also known that the ultrafast femtosecond pulses can eliminate the contribution to the refractive nonlinearity from electrostriction, molecular reorientation, and population redistribution since those effects have a response time much longer than 350 fs [22

22. with contributions by R. L. SutherlandD. G. McLean and S. Kikpatrick, Handbook of Nonlinear Optics, 2nd ed. (Marcel Dekker, New York, 2003). [CrossRef]

]. Moreover, accumulative thermal effects are negligible because the experiments were conducted at a low repetition rate of 1 kHz. Consequently, the measured n 2 should directly result from the electronic origin of the refractive nonlinearity in the BFO thin film.

3. Conclusion

In summary, we have investigated the linear optical properties of polycrystalline BFO thin film and its third-order nonlinear response to femtosecond laser pulses. The high optical transparency and large third-order optical nonlinearity show that the BFO thin film is a promising candidate for applications in nonlinear photonic devices.

Acknowledgements

This work was supported in part by the National Science Foundation of China (Grant Number: 10704042) and the National University of Singapore (Grant Number: R-144-000-213-112). Dr Wang Yang is supported by the Singapore Millennium Foundation.

References and links

1.

J. Wang, J. B. Neaton, H. Zheng, V. Nagarajan, S. B. Ogale, B. Liu, D. Viehland, V. Vaithyanathan, D. G. Schlom, U. V. Waghmare, N. A. Spaldin, K. M. Rabe, M. Wuttig, and R. Ramesh, “Epitaxial BiFeO3 multiferroic thin film heterostructures,” Science 299, 1719–1722 (2003). [CrossRef] [PubMed]

2.

K. Y. Yun, M. Noda, and M. Okuyama, “Prominent ferroelectricity of BiFeO3 thin films prepared by pulsed-laser deposition,” Appl. Phys. Lett. 83, 3981–3983 (2003). [CrossRef]

3.

S. R. Basu, L. W. Martin, Y. H. Chu, M. Gajek, R. Ramesh, R. C. Rai, X. Xu, and J. L. Musfeldt, “Photoconductivity in BiFeO3 thin films,” Appl. Phys. Lett. 92, 091905 (2008). [CrossRef]

4.

A. K. Pradhan, K. Zhang, D. Hunter, J. B. Dadson, G. B. Loutts, P. Bhattacharya, R. Katiyar, J. Zhang, D. J. Sellmyer, U. N. Roy, Y. Cui, and A. Burger, “Magnetic and electrical properties of single-phase multiferroic BiFeO3,” J. Appl. Phys. 97, 093903 (2005). [CrossRef]

5.

Y. Wang, R. Y. Zheng, C. H. Sim, and J. Wang, “Charged defects and their effects on electrical behavior in Bi1-xLaxFeO3 thin films,” J. Appl. Phys. 105, 016106 (2009). [CrossRef]

6.

A. Kumar, R. C. Rai, N. J. Podraza, S. Denev, M. Ramirez, Y. H. Chu, L. W. Martin, J. Ihlefeld, T. Heeg, J. Suchubert, D. G. Schlom, J. Orenstein, R. Ramesh, R. W. Collins, J. L. Musfeldt, and V. Gopalan, “Linear and nonlinear optical properties of BiFeO3,” Appl. Phys. Lett. 92, 121915 (2008). [CrossRef]

7.

H. Shin, H. J. Chang, R. W. Boyd, M. R. Choi, and W. Jo, “Large nonlinear optical response of polycrystalline Bi3.25La0.75Ti3O12 ferroelectric thin films on quartz substrates,” Opt. Lett. 32, 2453–2455 (2007). [CrossRef] [PubMed]

8.

B. Gu, Y. H. Wang, X. C. Peng, J. P. Ding, J. L. He, and H. T. Wang, “Giant optical nonlinearity of a Bi2Nd2Ti3O12 ferroelectric thin film,” Appl. Phys. Lett. 85, 3687–3689 (2004). [CrossRef]

9.

W. Leng, C. Yang, H. Ji, J. Zhang, J. Tang, H. Chen, and L. Gao, “Linear and nonlinear optical properties of RF sputtered (Pb,La)(Zr,Ti)O3 ferroelectric thin films,” J. Mater. Sci: Mater. Electron. 18, 887–892 (2007). [CrossRef]

10.

T. Ning, C. Chen, Y. Zhou, H. Lu, D. Zhang, H. Ming, and G. Yang, “Large optical nonlinearity in CaCu3Ti4O12 thin films,” Appl. Phys. A 94, 567–570 (2009). [CrossRef]

11.

S. W. Liu, J. Xu, D. Guzun, G. J. Salamo, C. L. Chen, Y. Lin, and M. Xiao, “Nonlinear optical absorption and refraction of epitaxial Ba0.6Sr0.4TiO3 thin films on (001) MgO substrates,” Appl. Phys. B 82, 443–447 (2006). [CrossRef]

12.

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E: Sci. Instrum. 16, 1214–1222 (1983). [CrossRef]

13.

N. A. Barboza and R. S. Cudney, “Improved Sellmeier equation for congruently grown lithium tantalate,” Appl. Phys. B 95, 453–458 (2009). [CrossRef]

14.

J. Tauc, R. Grigorovici, and A. Vancu, “Optical Properties and Electronic Structure of Amorphous Germanium,” Phys. Stat. Sol. 15, 627–637 (1966). [CrossRef]

15.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990). [CrossRef]

16.

B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed z scans on instantaneous nonlinearity,” Appl. Opt. 47, 1187–1192 (2008). [CrossRef] [PubMed]

17.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001). [CrossRef] [PubMed]

18.

W. P. Zang, J. G. Tian, Z. B. Liu, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, “Study on Z-scan characteristics of cascaded nonlinear media,” Appl. Phys. B 77, 529–533 (2003). [CrossRef]

19.

H. I. Elim, W. Ji, G. H. Ma, K. Y. Lim, C. H. Sow, and C. H. A. Huan, “Ultrafast absorptive and refractive nonlinearities in multiwalled carbon nanotube films,” Appl. Phys. Lett. 85, 1799–1801 (2004). [CrossRef]

20.

D. Rativa, R. E. de Araujo, C. B. de Araújo, A. S. L. Gomes, and L. R. P. Kassab, “Femtosecond nonlinear optical properties of lead-germanium oxide amorphous films,” Appl. Phys. Lett. 90, 231906 (2007). [CrossRef]

21.

R. Lopez, R. F. Haglund Jr., L. C. Feldman, L. A. Boatner, and T. E. Haynes, “Optical nonlinearities in VO2 nanoparticles and thin films,” Appl. Phys. Lett. 85, 5191–5193 (2004). [CrossRef]

22.

with contributions by R. L. SutherlandD. G. McLean and S. Kikpatrick, Handbook of Nonlinear Optics, 2nd ed. (Marcel Dekker, New York, 2003). [CrossRef]

OCIS Codes
(160.2260) Materials : Ferroelectrics
(190.3270) Nonlinear optics : Kerr effect
(190.4180) Nonlinear optics : Multiphoton processes

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 7, 2009
Revised Manuscript: June 2, 2009
Manuscript Accepted: June 2, 2009
Published: June 16, 2009

Citation
Bing Gu, Yang Wang, John Wang, and Wei Ji, "Femtosecond third-order optical nonlinearity of BiFeO3," Opt. Express 17, 10970-10975 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-13-10970


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References

  1. J. Wang, J. B. Neaton, H. Zheng, V. Nagarajan, S. B. Ogale, B. Liu, D. Viehland, V. Vaithyanathan, D. G. Schlom, U. V. Waghmare, N. A. Spaldin, K. M. Rabe, M. Wuttig, and R. Ramesh, "Epitaxial BiFeO3 multiferroic thin film heterostructures," Science 299, 1719-1722 (2003). [CrossRef] [PubMed]
  2. K. Y. Yun, M. Noda, and M. Okuyama, "Prominent ferroelectricity of BiFeO3 thin films prepared by pulsed-laser deposition," Appl. Phys. Lett. 83, 3981-3983 (2003). [CrossRef]
  3. S. R. Basu, L. W. Martin, Y. H. Chu, M. Gajek, R. Ramesh, R. C. Rai, X. Xu, and J. L. Musfeldt, "Photoconductivity in BiFeO3 thin films," Appl. Phys. Lett. 92, 091905 (2008). [CrossRef]
  4. A. K. Pradhan, K. Zhang, D. Hunter, J. B. Dadson, G. B. Loutts, P. Bhattacharya, R. Katiyar, J. Zhang, D. J. Sellmyer, U. N. Roy, Y. Cui, and A. Burger, "Magnetic and electrical properties of single-phase multiferroic BiFeO3," J. Appl. Phys. 97, 093903 (2005). [CrossRef]
  5. Y. Wang, R. Y. Zheng, C. H. Sim, and J. Wang, "Charged defects and their effects on electrical behavior in Bi1−xLaxFeO3 thin films," J. Appl. Phys. 105, 016106 (2009). [CrossRef]
  6. A. Kumar, R. C. Rai, N. J. Podraza, S. Denev, M. Ramirez, Y. H. Chu, L. W. Martin, J. Ihlefeld, T. Heeg, J. Suchubert, D. G. Schlom, J. Orenstein, R. Ramesh, R. W. Collins, J. L. Musfeldt, and V. Gopalan, "Linear and nonlinear optical properties of BiFeO3," Appl. Phys. Lett. 92, 121915 (2008). [CrossRef]
  7. H. Shin, H. J. Chang, R. W. Boyd, M. R. Choi, and W. Jo, "Large nonlinear optical response of polycrystalline Bi3.25La0.75Ti3O12 ferroelectric thin films on quartz substrates," Opt. Lett. 32, 2453-2455 (2007). [CrossRef] [PubMed]
  8. B. Gu, Y. H. Wang, X. C. Peng, J. P. Ding, J. L. He, and H. T. Wang, "Giant optical nonlinearity of a Bi2Nd2Ti3O12 ferroelectric thin film," Appl. Phys. Lett. 85, 3687-3689 (2004). [CrossRef]
  9. W. Leng, C. Yang, H. Ji, J. Zhang, J. Tang, H. Chen, and L. Gao, "Linear and nonlinear optical properties of RF sputtered (Pb,La)(Zr,Ti)O3 ferroelectric thin films," J. Mater. Sci: Mater. Electron. 18, 887-892 (2007). [CrossRef]
  10. T. Ning, C. Chen, Y. Zhou, H. Lu, D. Zhang, H. Ming, G. Yang, "Large optical nonlinearity in CaCu3Ti4O12 thin films," Appl. Phys. A 94, 567-570 (2009). [CrossRef]
  11. S. W. Liu, J. Xu, D. Guzun, G. J. Salamo, C. L. Chen, Y. Lin, and M. Xiao, "Nonlinear optical absorption and refraction of epitaxial Ba0.6Sr0.4TiO3 thin films on (001) MgO substrates," Appl. Phys. B 82, 443-447 (2006). [CrossRef]
  12. R. Swanepoel, "Determination of the thickness and optical constants of amorphous silicon," J. Phys. E: Sci. Instrum. 16, 1214-1222 (1983). [CrossRef]
  13. N. A. Barboza and R. S. Cudney, "Improved Sellmeier equation for congruently grown lithium tantalate," Appl. Phys. B 95, 453-458 (2009). [CrossRef]
  14. J. Tauc, R. Grigorovici, and A. Vancu, "Optical Properties and Electronic Structure of Amorphous Germanium," Phys. Stat. Sol. 15, 627-637 (1966). [CrossRef]
  15. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990). [CrossRef]
  16. B. Gu, W. Ji, and X. Q. Huang, "Analytical expression for femtosecond-pulsed z scans on instantaneous nonlinearity," Appl. Opt. 47, 1187-1192 (2008). [CrossRef] [PubMed]
  17. S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, "Self-guided propagation of ultrashort IR laser pulses in fused silica," Phys. Rev. Lett. 87, 213902 (2001). [CrossRef] [PubMed]
  18. W. P. Zang, J. G. Tian, Z. B. Liu, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, "Study on Z-scan characteristics of cascaded nonlinear media," Appl. Phys. B 77, 529-533 (2003). [CrossRef]
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