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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 6 — Mar. 17, 2008
  • pp: 3912–3917
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Femtosecond laser-induced oriented precipitation of Ba2TiGe2O8 crystals in glass

Ye Dai, Hongliang Ma, Bo Lu, Bingkun Yu, Bin Zhu, and Jianrong Qiu  »View Author Affiliations


Optics Express, Vol. 16, Issue 6, pp. 3912-3917 (2008)
http://dx.doi.org/10.1364/OE.16.003912


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Abstract

Ba2TiGe2O8 crystals were selectively precipitated on femtosecond laser irradiated BaO-TiO2-GeO2 glass surface. Furthermore, the crystal could grow from the surface of glass to the interior towards the laser movement direction when the laser focus was continuously moved. The laser-induced crystal was confirmed to be Ba2TiGe2O8 phase by x-ray diffraction analysis and micro-Raman spectra. We also observed blue light due to double-frequency conversion of the 800nm incident laser in the crystallized regions. We propose the observed phenomena resulted from the femtosecond laser-assisted orientation of precipitation of crystal.

© 2008 Optical Society of America

1. Introduction

Ba2TiGe2O8, a fresnoite-type (Ba2TiSi2O8) crystal [1

1. P. B. Moore and J. Louisnathan, “Fresnoite: Unusal Titanium Coordination,” Science 156, 1361–1362 (1967). [CrossRef] [PubMed]

], possesses an acentric structure with a space group of Cmm2 at room temperature [2

2. M. Kimura, K. Doi, S. Nanamatsu, and T. Kawamura, “A new piezoelectric crystal: Ba2Ge2TiO8,” Appl. Phys. Lett. 23, 531–532 (1973). [CrossRef]

]. Due to its permanent polarity along the c axis, Ba2TiGe2O8 crystal exhibits attractive ferroelastic, pyroelectric and piezoelectric properties [3

3. H. Schmid, P. Genequand, H. Tippmann, G. Pouilly, and H. Guédu, “Pyroelectricity and Related Properties in the Fresnoite Pseudobinary System Ba2Ti Ge2O8- Ba2Ti Si2O8,” J. Mater. Sci. 13, 2257–2265 (1978). [CrossRef]

]. Recently, glass-ceramic consisting of Ba2TiGe2O8 through the crystallization of BaO-TiO2-GeO2 (BTG) optical glass show excellent second-order nonlinearities [4–6

4. Y. Takahashi, Y. Benino, T. Fujiwara, and T. Komatsu, “Optical second order nonlinearity of transparent Ba2TiGe2O8 crystallized glass,” Appl. Phys. Lett. 81, 223–225 (2002). [CrossRef]

]. Especially, the second-order optical susceptibility d 33 of the Ba2TiGe2O8 surface crystallized glass could reach 24 pm/V through accurate heat treatment process [6

6. H. Masai, T. Fujiwara, Y. Benino, and T. Komatsu, “Large second-order optical non-linearity in 30BaO-15TiO2-55GeO2 surface crystallized glass with strong orientation,” J. Appl. Phys.100, 023526/1–023526/4 (2006). [CrossRef]

]. This d 33 value is comparable to that of LiNbO3 single crystal. Therefore, it would be of great interest for application in integrated optics if Ba2TiGe2O8 crystallized regions could be selectively induced inside a bulk glass. However, so far, there are few reports concerning the spatial precipitation of laser-induced Ba2TiGe2O8 crystals because most of the laser energy can not penetrate into the interior of bulk glass due to the limitation of linear absorption [7

7. T. Honma, Y. Benino, T. Fujiwara, and T. Komatsu, “Transition metal atom heat processing for writing of crystal lines in glass,” Appl. Phys. Lett.88, 231105/1–231105/3 (2006). [CrossRef]

].

2. Experiments

The glass composition studied in our experiment was 33.3BaO-16.7TiO2-50GeO2 (mol%). Reagent grade GeO2, BaCO3 and TiO2 were used as starting materials. A mixed batch about 20g was melted in a Pt crucible at 1250°C for 30 minutes. Then the melt was poured onto a steel plate and cooled down to room temperature. The transparent glass was annealed to release stress at 400°C for 2h. After that, it was mechanically cut and polished to get mirror surfaces with a size of 10mm×10mm×2mm.

A commercial Ti:sapphire regenerative amplifier (RegA 900, Coherent Inc) was used to generate 150fs, 800nm, 250 kHz laser pulses. The laser beam passes through a Glans polarizer to change pulse energy continuously. Then it was focused normally by a 100× objective lens with a numerical aperture of 0.8 into the interior of the glass that was fixed on a computer-controlled 3D XYZ stage. Second harmonic spectra were recorded by a spectrometer (Ocean Optics: USB2000-VIS-NIR). A Rigaku D/MAX-RA diffractometer with Cu as the incident radiation was used to characterize the induced Ba2TiGe2O8 phase in the femtosecond laser irradiated regions. Micro-Raman spectra for the structure modifications were also measured by a Raman spectrometer (Renishaw inVia) and a laser microscopy system with a 514nm Ar+ laser excitation. All the measurements were carried out at room temperature.

3. Results and discussion

Fig. 1. Microscopic images of the focal point (a) after and (b) during the laser irradiation on the surface of the glass sample; (c), (d) the depths of the focal point were 30 µm and 100µm respectively, the blue light in the images due to second harmonic generation; (e) the laser-induced crystallization pattern for x-ray diffraction analysis and micro-Raman spectra, the detailed scanning process was described in text. The scaling bars under the images (d) and (e) denoted 20 µm and 50 µm, respectively.

Figure 1 shows the microscopic images of the focal point after and during the femtosecond laser irradiation on the BTG glass. The spot size of the focused beam was about 2 µm with a 1/e2 radius in the focal point, and the focused laser intensity was about 5.1 × 1018 W/cm2, that was more than the ablation threshold of the glass surface. In Fig. 1(b), an obvious blue light emerged from the focal region immediately after the femtosecond laser irradiation on the glass surface. After 10s irradiation, the sample stage was controlled to move up at 5 µm/s in order that the focal point of the femtosecond laser could penetrate into the interior of the bulk glass. In this process, the blue light could keep going along with the laser focus. As one can see in Fig. 1(c) and (d), the depth of the blue light even exceeded 100 µm below the surface. We measured the emission spectra from the irradiated regions during the blue light emerging. The spectra clearly proved second harmonic generation of the incident 800nm laser. Therefore, there existed a possibility of phase transformation from glass to nonlinear optical crystal in the irradiated regions, and these induced crystals could preferentially grow along the laser focus moving direction. It was also found that the double frequency light would not occur if the femtosecond laser were firstly focused into the interior of the bulk glass. This result indicated that femtosecond laser-induced nucleation on the surface of BTG glass could be more effective in comparison with laser-induced internal nucleation, and the newly formed seeds on the surface could highly promote subsequent crystal growth in the process of temperature rise due to absorption of the laser energy [12

12. A. A. Cabral, V. M. Fokin, and E. D. Zanotto, “Nanocrystallization of fresnoite glass. ‖. Analysis of homogeneous nucleation kinetics,” J. Non-Cryst. Solids 343, 85–90 (2000). [CrossRef]

, 13

13. I. Gutzow, R. Pascova, A. Karamanov, and J. Schmelzer, “The kinetics of surface induced sinter crystallization and the formation of glass-ceramic materials,” J. Mater. Sci. 33, 5265–5273 (1998). [CrossRef]

].

Fig. 2. X-ray diffraction pattern for the femtosecond laser-induced crystals.
Fig. 3. Micro-Raman spectra for the femtosecond laser-induced crystals and the BaO-TiO2-GeO2 glass respectively.

Recently, the grain-oriented Ba2TiGe2O8 crystals were intensively studied in surface crystallized glass by heat treatment [4–6

4. Y. Takahashi, Y. Benino, T. Fujiwara, and T. Komatsu, “Optical second order nonlinearity of transparent Ba2TiGe2O8 crystallized glass,” Appl. Phys. Lett. 81, 223–225 (2002). [CrossRef]

], but it was well known that this method was unavailable to control the spatially precipitated regions of the formed crystals, especially in the interior of bulk glass. In this experiment, since the energy injection was a multiphoton process, the heat accumulation effect was limited three-dimensionally in the focused region where the local temperature may exceed the glass crystallization temperature Tc (Tc~700K, please refer to [4

4. Y. Takahashi, Y. Benino, T. Fujiwara, and T. Komatsu, “Optical second order nonlinearity of transparent Ba2TiGe2O8 crystallized glass,” Appl. Phys. Lett. 81, 223–225 (2002). [CrossRef]

]) [16

16. S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Y. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13, 4708–4716 (2005). [CrossRef] [PubMed]

]. Hence, it was considered that the heat accumulation effect was an important force influencing the formation of crystallization. Fig.4 shows a cross-section image of a femtosecond laser-induced crystallized region parallel to the laser focus moving direction. It seemed as if the Ba2TiGe2O8 crystallites may continuously grow from the already-crystallized region to the laser-irradiating region, with up going speed at 5 µm/s. So, it was believed that femtosecond laser accelerated the oriented precipitation of Ba2TiGe2O8 crystallites because these heated seeds were easier to grow in the vicinity of the heat source. Since the femtosecond laser-irradiated region was flawed and even rough, it only demonstrated large frequency-conversion capability in some parts. For example, when the 800nm incident laser was side-focused in this long crystallization structure, the 400nm light intensity fluctuated from surface to region (a). We think the beam deviation loss and the light scattering effect should be two negative reasons for this phenomenon. After that region, the light became stable from region (a) to (b). Additionally, in the region (c) (the end of the laser-irradiated region), the local temperature was failure to exceed Tc on account of light scattering effect, therefore no crystallization occurred. No frequency-conversion light was observed in (c). It indicated that the glass matrix did not have second-order optical nonlinearity and the crystallization was difficult to occur inside the glass interior because of the absence of the corresponding seed.

Fig. 4. A cross-section image of femtosecond laser-induced oriented crystallization region. The blue light shown in (a) and (b) due to second harmonic generation, whereas no nonlinear optical crystals precipitated in the region (c). The scaling bar denoted 50 µm.

Generally, the glass will transform to plasma state via multiphoton ionization due to the ultrahigh field intensity of the focused femtosecond laser, the optically dense plasma will also absorb the laser energy effectively, so a nucleation due to the heat effect was brought in the laser-irradiated regions [17

17. G. J. Lee, J. Park, E. K. Kim, Y. P. Lee, K. M. Kim, H. Cheong, C. S. Yoon, Y. D. Son, and J. Jang, “Microstructure of femtosecond laser-induced grating in amorphous silicon,” Opt. Express 13, 6445–6453 (2005). [CrossRef] [PubMed]

, 18

18. J. Y. Yang, H. L. Ma, G. H. Ma, B. Lu, and H. Ma, “Phase transformation at the surface of TiO2 single crystal irradiated by femtosecond laser pulse,” Applied Physics A 88, 801–804 (2007). [CrossRef]

]. Next, the surrounding glass medium would be heated and formed a low-viscous melt in a very short time. This process initiated the growth of crystallites in the following irradiation. According to the classic nucleation theory, the value of the surface energy is responsible for the nucleation rate of glass [19

19. J. W. Mullin, Crystallization, 3rd ed. (World scientific, Beijing, China, 2000).

]. Especially, the surface energy on the glass surface or heterogeneous interface is more than that in the homogenous medium, therefore the crystallites preferred to form on the laser-irradiated glass surface to the glass interior. Besides that, the formed seeds began their growths under the thermodynamic driving force if the increasing temperature exceeds the crystallization temperature Tc. Consequently, under current conditions, the Ba2TiGe2O8 crystallites precipitated on the glass surface through heat nucleation firstly. After that, the irradiated glass was heated to a melt through absorbing the laser energy, and then there exists a transition layer at the solid-liquid interface between the glass and the melt. If this layer temperature exceeded Tc, the melt at the interface began to transform into crystal. The process of the crystallization during the femtosecond laser irradiation is schematically illustrated in Fig. 5, where the yellow region and the white arrows indicated the crystallized part enlarged with irradiation time increasing. Hardly did there construct a balance between the absorbed laser energy and the heat dissipation from the laser affect regions, when the heated volume stopped swelling.

Here we give an explanation on the laser-induced internal nucleation. When the heat diffused from the focus to the outer, the threshold of internal nucleation became lower due to the interface energy effect [19

19. J. W. Mullin, Crystallization, 3rd ed. (World scientific, Beijing, China, 2000).

]. Therefore, the subsequent crystallites may continuously extract from the heated melts as long as the heat nucleation can provide the seeds. According to the above discussions, two important conditions were indispensable for the formations of Ba2TiGe2O8 crystals, i.e., the seeds from laser-induced surface/interface nucleation and the heated temperature above Tc due to the heat accumulation effect.

Fig. 5. Schematic illustration of the femtosecond laser-assisted crystal precipitation.

Although the morphology of the formed crystal in this experiment was rough and fractional, the predominant feature of femtosecond laser-induced crystallization technique compared with those of other kinds of lasers is the laser-assisted interior crystal precipitation. It is well known that glass surface is the preferred site for the start of crystallization and the surface induced nucleation is more active because the specific surface energy at the foreign substrate/crystal interface is lowers [19

19. J. W. Mullin, Crystallization, 3rd ed. (World scientific, Beijing, China, 2000).

]. So most laser-induced crystallization techniques only wrote nonlinear optical crystal patterns on the glass surface, and they were difficult to achieve selectively internal nucleation and subsequently controllable crystal precipitation. High repetition femtosecond laser irradiation offers an effective method for rapid heat accumulation inside 3D volumes, therefore, it is of great interest for developing femtosecond laser-induced space-selectively crystallization technique.

4. Conclusions

In this paper, we reported femtosecond laser-induced oriented precipitation of Ba2TiGe2O8 crystals in a nearly stoichiometric glass material. X-ray diffraction pattern and micro-Raman spectra confirmed the precipitated crystals were with Ba2TiGe2O8 phase. The precipitated crystals could further grow along the laser moving direction from the surface of the glass to the interior. We think the seeds from laser-induced surface nucleation and the heated temperature above Tc due to the heat accumulation effect are two important contributions for the precipitation of Ba2TiGe2O8 crystals.

Acknowledgments

This work was financially supported by National Basic Research Program of China (2006CB806000b), National High Technology Program of China (2006AA03Z304), National Natural Science Foundation of China (Grants No. 50672087) and Shanghai Leading Academic Discipline Project T0104.

References and links

1.

P. B. Moore and J. Louisnathan, “Fresnoite: Unusal Titanium Coordination,” Science 156, 1361–1362 (1967). [CrossRef] [PubMed]

2.

M. Kimura, K. Doi, S. Nanamatsu, and T. Kawamura, “A new piezoelectric crystal: Ba2Ge2TiO8,” Appl. Phys. Lett. 23, 531–532 (1973). [CrossRef]

3.

H. Schmid, P. Genequand, H. Tippmann, G. Pouilly, and H. Guédu, “Pyroelectricity and Related Properties in the Fresnoite Pseudobinary System Ba2Ti Ge2O8- Ba2Ti Si2O8,” J. Mater. Sci. 13, 2257–2265 (1978). [CrossRef]

4.

Y. Takahashi, Y. Benino, T. Fujiwara, and T. Komatsu, “Optical second order nonlinearity of transparent Ba2TiGe2O8 crystallized glass,” Appl. Phys. Lett. 81, 223–225 (2002). [CrossRef]

5.

Y. Takahashi, Y. Benino, T. Fujiwara, and T. Komatsu, “Formation mechanism of ferroelastic Ba2TiGe2O8 and second order optical non-linearity in transparent crystallized glasses,” J. Non-Cryst. Solids 316, 320–330 (2003). [CrossRef]

6.

H. Masai, T. Fujiwara, Y. Benino, and T. Komatsu, “Large second-order optical non-linearity in 30BaO-15TiO2-55GeO2 surface crystallized glass with strong orientation,” J. Appl. Phys.100, 023526/1–023526/4 (2006). [CrossRef]

7.

T. Honma, Y. Benino, T. Fujiwara, and T. Komatsu, “Transition metal atom heat processing for writing of crystal lines in glass,” Appl. Phys. Lett.88, 231105/1–231105/3 (2006). [CrossRef]

8.

K. Miura, J. Qiu, T. Mitsuyu, and K. Hirao, “Space-selective growth of frequency-conversion crystals in glasses with ultrashort infrared laser pulses,” Opt. Lett. 25, 408–410 (2000). [CrossRef]

9.

Y. Yonesaki, K. Miura, R. Araki, K. Fujita, and K. Hirao, “Space-selective precipitation of non-linear optical crystals inside silicate glasses using near-infrared femtosecond laser,” J. Non-Cryst. Solids 351, 885–892 (2005). [CrossRef]

10.

Y. Dai, B. Zhu, J. Qiu, H. Ma, B. Lu, S. Cao, and B. Yu, “Direct writing three-dimensional Ba2TiSi2O8 crystalline pattern in glass with ultrashort pulse laser,” Appl. Phys. Lett.90, 181109/1–181109/3 (2007). [CrossRef]

11.

B. Zhu, Y. Dai, H. Ma, S. Zhang, G. Lin, and J. Qiu, “Femtosecond laser induced space-selective precipitation of nonlinear optical crystals in rare-earth-doped glasses,” Opt. Express 15, 6069–6074 (2007). [CrossRef] [PubMed]

12.

A. A. Cabral, V. M. Fokin, and E. D. Zanotto, “Nanocrystallization of fresnoite glass. ‖. Analysis of homogeneous nucleation kinetics,” J. Non-Cryst. Solids 343, 85–90 (2000). [CrossRef]

13.

I. Gutzow, R. Pascova, A. Karamanov, and J. Schmelzer, “The kinetics of surface induced sinter crystallization and the formation of glass-ceramic materials,” J. Mater. Sci. 33, 5265–5273 (1998). [CrossRef]

14.

S. A. Markgraf, S. K. Sharma, and A. S. Bhalla, “Raman study of fresnoite-type materials: Polarized single crystal, crystalline powers, and glasses,” J. Mater. Res. 8, 635–648 (1993). [CrossRef]

15.

Th. G. Mayerhöfer and H. H. Dunken, “Single-crystal IR spectroscopic investigation on fresnoite, Sr-fresnoite and Ge-fresnoite,” Vib. Spectrosc. 25, 185–195 (2001). [CrossRef]

16.

S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Y. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13, 4708–4716 (2005). [CrossRef] [PubMed]

17.

G. J. Lee, J. Park, E. K. Kim, Y. P. Lee, K. M. Kim, H. Cheong, C. S. Yoon, Y. D. Son, and J. Jang, “Microstructure of femtosecond laser-induced grating in amorphous silicon,” Opt. Express 13, 6445–6453 (2005). [CrossRef] [PubMed]

18.

J. Y. Yang, H. L. Ma, G. H. Ma, B. Lu, and H. Ma, “Phase transformation at the surface of TiO2 single crystal irradiated by femtosecond laser pulse,” Applied Physics A 88, 801–804 (2007). [CrossRef]

19.

J. W. Mullin, Crystallization, 3rd ed. (World scientific, Beijing, China, 2000).

OCIS Codes
(140.3390) Lasers and laser optics : Laser materials processing
(140.6810) Lasers and laser optics : Thermal effects
(160.2750) Materials : Glass and other amorphous materials
(160.4330) Materials : Nonlinear optical materials

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: November 20, 2007
Revised Manuscript: January 21, 2008
Manuscript Accepted: January 22, 2008
Published: March 10, 2008

Citation
Ye Dai, Hongliang Ma, Bo Lu, Bingkun Yu, Bin Zhu, and Jianrong Qiu, "Femtosecond laser-induced oriented precipitation of Ba2TiGe2O8 crystals in glass," Opt. Express 16, 3912-3917 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-6-3912


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References

  1. P. B. Moore and J. Louisnathan, "Fresnoite: Unusal Titanium Coordination," Science 156, 1361-1362 (1967). [CrossRef] [PubMed]
  2. M. Kimura, K. Doi, S. Nanamatsu, and T. Kawamura, "A new piezoelectric crystal: Ba2Ge2TiO8," Appl. Phys. Lett. 23, 531-532 (1973). [CrossRef]
  3. H. Schmid, P. Genequand, H. Tippmann, G. Pouilly, and H. Guédu, "Pyroelectricity and Related Properties in the Fresnoite Pseudobinary System Ba2Ti Ge2O8- Ba2Ti Si2O8," J. Mater. Sci. 13, 2257-2265 (1978). [CrossRef]
  4. Y. Takahashi, Y. Benino, T. Fujiwara, and T. Komatsu, "Optical second order nonlinearity of transparent Ba2TiGe2O8 crystallized glass," Appl. Phys. Lett. 81, 223-225 (2002). [CrossRef]
  5. Y. Takahashi, Y. Benino, T. Fujiwara, and T. Komatsu, "Formation mechanism of ferroelastic Ba2TiGe2O8 and second order optical non-linearity in transparent crystallized glasses," J. Non-Cryst. Solids 316, 320-330 (2003). [CrossRef]
  6. H. Masai. T. Fujiwara, Y. Benino, and T. Komatsu, "Large second-order optical nonlinearity in 30BaO-15TiO2-55GeO2 surface crystallized glass with strong orientation," J. Appl. Phys. 100, 023526/1-023526/4 (2006). [CrossRef]
  7. T. Honma, Y. Benino, T. Fujiwara, and T. Komatsu, "Transition metal atom heat processing for writing of crystal lines in glass," Appl. Phys. Lett. 88, 231105/1-231105/3 (2006). [CrossRef]
  8. K. Miura, J. Qiu, T. Mitsuyu, and K. Hirao, "Space-selective growth of frequency-conversion crystals in glasses with ultrashort infrared laser pulses," Opt. Lett. 25, 408-410 (2000). [CrossRef]
  9. Y. Yonesaki, K. Miura, R. Araki, K. Fujita, and K. Hirao, "Space-selective precipitation of non-linear optical crystals inside silicate glasses using near-infrared femtosecond laser," J. Non-Cryst. Solids 351, 885-892 (2005). [CrossRef]
  10. Y. Dai, B. Zhu, J. Qiu, H. Ma, B. Lu, S. Cao, and B. Yu, "Direct writing three-dimensional Ba2TiSi2O8 crystalline pattern in glass with ultrashort pulse laser," Appl. Phys. Lett. 90, 181109/1-181109/3 (2007). [CrossRef]
  11. B. Zhu, Y. Dai, H. Ma, S. Zhang, G. Lin, and J. Qiu, "Femtosecond laser induced space-selective precipitation of nonlinear optical crystals in rare-earth-doped glasses," Opt. Express 15, 6069-6074 (2007). [CrossRef] [PubMed]
  12. A. A. Cabral, V. M. Fokin, and E. D. Zanotto, "Nanocrystallization of fresnoite glass. II. Analysis of homogeneous nucleation kinetics," J. Non-Cryst. Solids 343, 85-90 (2000). [CrossRef]
  13. I. Gutzow, R. Pascova, A. Karamanov, and J. Schmelzer, "The kinetics of surface induced sinter crystallization and the formation of glass-ceramic materials," J. Mater. Sci. 33, 5265-5273 (1998). [CrossRef]
  14. S. A. Markgraf, S. K. Sharma, and A. S. Bhalla, "Raman study of fresnoite-type materials: Polarized single crystal, crystalline powers, and glasses," J. Mater. Res. 8, 635-648 (1993). [CrossRef]
  15. Th. G. Mayerhöfer and H. H. Dunken, "Single-crystal IR spectroscopic investigation on fresnoite, Sr-fresnoite and Ge-fresnoite," Vib. Spectrosc. 25, 185-195 (2001). [CrossRef]
  16. S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Y. Arai, "Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate," Opt. Express 13, 4708-4716 (2005). [CrossRef] [PubMed]
  17. G. J. Lee, J. Park, E. K. Kim, Y. P. Lee, K. M. Kim, H. Cheong, C. S. Yoon,Y. D. Son, and J. Jang, "Microstructure of femtosecond laser-induced grating in amorphous silicon," Opt. Express 13, 6445-6453 (2005). [CrossRef] [PubMed]
  18. J. Y. Yang, H. L. Ma, G. H. Ma, B. Lu, and H. Ma, "Phase transformation at the surface of TiO2 single crystal irradiated by femtosecond laser pulse," Appl. Phys. A 88, 801-804 (2007). [CrossRef]
  19. J. W. Mullin, Crystallization, 3rd ed. (World scientific, Beijing, China, 2000).

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