Abstract

We report on a kind of self-assembled volume grating in silica glass induced by tightly focused femtosecond laser pulses. The formation of the volume grating is attributed to the multiple microexplosion in the transparent materials induced by the femtosecond pulses. The first order diffractive efficiency is in dependence on the energy of the pulses and the scanning velocity of the laser greatly, and reaches as high as 30%. The diffraction pattern of the fabricated grating is numerically simulated and analyzed by a two dimensional FDTD method and the Fresnel Diffraction Integral. The numerical results proved our prediction on the formation of the volume grating, which agrees well with our experiment results.

© 2010 OSA

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  1. Y. Li, Y. Dou, R. An, H. Yang, and Q. Gong, “Permanent computer-generated holograms embedded in silica glass by femtosecond laser pulses,” Opt. Express 13(7), 2433–2438 (2005).
    [CrossRef] [PubMed]
  2. S. Qu, C. Zhao, Q. Zhao, J. Qiu, C. Zhu, and K. Hirao, “One-off writing of multimicrogratings on glass by two interfered femtosecond laser pulses,” Opt. Lett. 29(17), 2058–2060 (2004).
    [CrossRef] [PubMed]
  3. Z. Guo, S. Qu, L. Ran, Y. Han, and S. Liu, “Formation of two-dimensional periodic microstructures by a single shot of three interfered femtosecond laser pulses on the surface of silica glass,” Opt. Lett. 33(20), 2383–2385 (2008).
    [CrossRef] [PubMed]
  4. T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
    [CrossRef]
  5. Z. Guo, S. Qu, and S. Liu, “Generating optical vortex with computer-generated hologram fabricated inside glass by femtosecond laser pulses,” Opt. Commun. 273(1), 286–289 (2007).
    [CrossRef]
  6. S. Kanehira, J. H. Si, J. R. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett. 5(8), 1591–1595 (2005).
    [CrossRef] [PubMed]
  7. X. Hu, B. Qian, P. Zhang, X. Wang, L. Su, J. Qiu, and C. Zhu, “Self-organized microvoid array perpendicular to the femtosecond laser beam in CaF2 crystals,” Laser Phys. Lett. 5(5), 394–397 (2008).
    [CrossRef]
  8. J. Song, X. Wang, J. Xu, H. Sun, Z. Xu, and J. Qiu, “Microstructures induced in the bulk of SrTiO3 crystal by a femtosecond laser,” Opt. Express 15(5), 2341–2347 (2007).
    [CrossRef] [PubMed]
  9. E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
    [CrossRef]
  10. S. Hirono, M. Kasuya, K. Matsuda, Y. Ozeki, K. Itoh, H. Mochizuki, and W. Watanabe, “Increasing diffraction efficiency by heating phase gratings formed by femtosecond laser irradiation in poly (methyl methacrylate),” Appl. Phys. Lett. 94(24), 241122 (2009).
    [CrossRef]
  11. S. Sowa, W. Watanabe, J. Nishii, and K. Itoh, “Filamentary cavity formation in poly (methyl methacrylate) by single femtosecond pulse,” Appl. Phys., A Mater. Sci. Process. 81(8), 1587–1590 (2005).
    [CrossRef]
  12. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  13. Q. Z. Zhao, J. R. Qiu, X. W. Jiang, E. W. Dai, C. H. Zhou, and C. S. Zhu, “Direct writing computer-generated holograms on metal film by an infrared femtosecond laser,” Opt. Express 13(6), 2089–2092 (2005).
    [CrossRef] [PubMed]
  14. J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
    [CrossRef]
  15. A. Brodeur, F. Ilkov, and S. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 96(3-4), 193–198 (1996).
    [CrossRef]
  16. Q. Zhao, J. Qiu, X. Jiang, C. Zhao, and C. Zhu, “Mechanisms of the refractive index change in femtosecond laser-irradiated Au3+-doped silicate glasses,” J. Appl. Phys. 129(12), 7122 (2004).
    [CrossRef]

2009 (1)

S. Hirono, M. Kasuya, K. Matsuda, Y. Ozeki, K. Itoh, H. Mochizuki, and W. Watanabe, “Increasing diffraction efficiency by heating phase gratings formed by femtosecond laser irradiation in poly (methyl methacrylate),” Appl. Phys. Lett. 94(24), 241122 (2009).
[CrossRef]

2008 (3)

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

Z. Guo, S. Qu, L. Ran, Y. Han, and S. Liu, “Formation of two-dimensional periodic microstructures by a single shot of three interfered femtosecond laser pulses on the surface of silica glass,” Opt. Lett. 33(20), 2383–2385 (2008).
[CrossRef] [PubMed]

X. Hu, B. Qian, P. Zhang, X. Wang, L. Su, J. Qiu, and C. Zhu, “Self-organized microvoid array perpendicular to the femtosecond laser beam in CaF2 crystals,” Laser Phys. Lett. 5(5), 394–397 (2008).
[CrossRef]

2007 (2)

J. Song, X. Wang, J. Xu, H. Sun, Z. Xu, and J. Qiu, “Microstructures induced in the bulk of SrTiO3 crystal by a femtosecond laser,” Opt. Express 15(5), 2341–2347 (2007).
[CrossRef] [PubMed]

Z. Guo, S. Qu, and S. Liu, “Generating optical vortex with computer-generated hologram fabricated inside glass by femtosecond laser pulses,” Opt. Commun. 273(1), 286–289 (2007).
[CrossRef]

2005 (5)

S. Kanehira, J. H. Si, J. R. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett. 5(8), 1591–1595 (2005).
[CrossRef] [PubMed]

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[CrossRef]

Y. Li, Y. Dou, R. An, H. Yang, and Q. Gong, “Permanent computer-generated holograms embedded in silica glass by femtosecond laser pulses,” Opt. Express 13(7), 2433–2438 (2005).
[CrossRef] [PubMed]

S. Sowa, W. Watanabe, J. Nishii, and K. Itoh, “Filamentary cavity formation in poly (methyl methacrylate) by single femtosecond pulse,” Appl. Phys., A Mater. Sci. Process. 81(8), 1587–1590 (2005).
[CrossRef]

Q. Z. Zhao, J. R. Qiu, X. W. Jiang, E. W. Dai, C. H. Zhou, and C. S. Zhu, “Direct writing computer-generated holograms on metal film by an infrared femtosecond laser,” Opt. Express 13(6), 2089–2092 (2005).
[CrossRef] [PubMed]

2004 (2)

Q. Zhao, J. Qiu, X. Jiang, C. Zhao, and C. Zhu, “Mechanisms of the refractive index change in femtosecond laser-irradiated Au3+-doped silicate glasses,” J. Appl. Phys. 129(12), 7122 (2004).
[CrossRef]

S. Qu, C. Zhao, Q. Zhao, J. Qiu, C. Zhu, and K. Hirao, “One-off writing of multimicrogratings on glass by two interfered femtosecond laser pulses,” Opt. Lett. 29(17), 2058–2060 (2004).
[CrossRef] [PubMed]

2003 (1)

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[CrossRef]

1996 (1)

A. Brodeur, F. Ilkov, and S. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 96(3-4), 193–198 (1996).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

An, R.

Brodeur, A.

A. Brodeur, F. Ilkov, and S. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 96(3-4), 193–198 (1996).
[CrossRef]

Cheng, Y.

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

Chin, S.

A. Brodeur, F. Ilkov, and S. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 96(3-4), 193–198 (1996).
[CrossRef]

Dai, E. W.

Dai, Y.

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

Dou, Y.

Fujita, K.

S. Kanehira, J. H. Si, J. R. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett. 5(8), 1591–1595 (2005).
[CrossRef] [PubMed]

Gong, Q.

Guo, Z.

Z. Guo, S. Qu, L. Ran, Y. Han, and S. Liu, “Formation of two-dimensional periodic microstructures by a single shot of three interfered femtosecond laser pulses on the surface of silica glass,” Opt. Lett. 33(20), 2383–2385 (2008).
[CrossRef] [PubMed]

Z. Guo, S. Qu, and S. Liu, “Generating optical vortex with computer-generated hologram fabricated inside glass by femtosecond laser pulses,” Opt. Commun. 273(1), 286–289 (2007).
[CrossRef]

Han, Y.

Hirao, K.

S. Kanehira, J. H. Si, J. R. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett. 5(8), 1591–1595 (2005).
[CrossRef] [PubMed]

S. Qu, C. Zhao, Q. Zhao, J. Qiu, C. Zhu, and K. Hirao, “One-off writing of multimicrogratings on glass by two interfered femtosecond laser pulses,” Opt. Lett. 29(17), 2058–2060 (2004).
[CrossRef] [PubMed]

Hirono, S.

S. Hirono, M. Kasuya, K. Matsuda, Y. Ozeki, K. Itoh, H. Mochizuki, and W. Watanabe, “Increasing diffraction efficiency by heating phase gratings formed by femtosecond laser irradiation in poly (methyl methacrylate),” Appl. Phys. Lett. 94(24), 241122 (2009).
[CrossRef]

Hu, X.

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

X. Hu, B. Qian, P. Zhang, X. Wang, L. Su, J. Qiu, and C. Zhu, “Self-organized microvoid array perpendicular to the femtosecond laser beam in CaF2 crystals,” Laser Phys. Lett. 5(5), 394–397 (2008).
[CrossRef]

Ilkov, F.

A. Brodeur, F. Ilkov, and S. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 96(3-4), 193–198 (1996).
[CrossRef]

Itoh, K.

S. Hirono, M. Kasuya, K. Matsuda, Y. Ozeki, K. Itoh, H. Mochizuki, and W. Watanabe, “Increasing diffraction efficiency by heating phase gratings formed by femtosecond laser irradiation in poly (methyl methacrylate),” Appl. Phys. Lett. 94(24), 241122 (2009).
[CrossRef]

S. Sowa, W. Watanabe, J. Nishii, and K. Itoh, “Filamentary cavity formation in poly (methyl methacrylate) by single femtosecond pulse,” Appl. Phys., A Mater. Sci. Process. 81(8), 1587–1590 (2005).
[CrossRef]

Jiang, X.

Q. Zhao, J. Qiu, X. Jiang, C. Zhao, and C. Zhu, “Mechanisms of the refractive index change in femtosecond laser-irradiated Au3+-doped silicate glasses,” J. Appl. Phys. 129(12), 7122 (2004).
[CrossRef]

Jiang, X. W.

Juodkazis, S.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[CrossRef]

Kamata, M.

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[CrossRef]

Kanehira, S.

S. Kanehira, J. H. Si, J. R. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett. 5(8), 1591–1595 (2005).
[CrossRef] [PubMed]

Kasuya, M.

S. Hirono, M. Kasuya, K. Matsuda, Y. Ozeki, K. Itoh, H. Mochizuki, and W. Watanabe, “Increasing diffraction efficiency by heating phase gratings formed by femtosecond laser irradiation in poly (methyl methacrylate),” Appl. Phys. Lett. 94(24), 241122 (2009).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kondo, T.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[CrossRef]

Li, Y.

Liu, S.

Z. Guo, S. Qu, L. Ran, Y. Han, and S. Liu, “Formation of two-dimensional periodic microstructures by a single shot of three interfered femtosecond laser pulses on the surface of silica glass,” Opt. Lett. 33(20), 2383–2385 (2008).
[CrossRef] [PubMed]

Z. Guo, S. Qu, and S. Liu, “Generating optical vortex with computer-generated hologram fabricated inside glass by femtosecond laser pulses,” Opt. Commun. 273(1), 286–289 (2007).
[CrossRef]

Matsuda, K.

S. Hirono, M. Kasuya, K. Matsuda, Y. Ozeki, K. Itoh, H. Mochizuki, and W. Watanabe, “Increasing diffraction efficiency by heating phase gratings formed by femtosecond laser irradiation in poly (methyl methacrylate),” Appl. Phys. Lett. 94(24), 241122 (2009).
[CrossRef]

Matsuo, S.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[CrossRef]

Misawa, H.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[CrossRef]

Mizeikis, V.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[CrossRef]

Mochizuki, H.

S. Hirono, M. Kasuya, K. Matsuda, Y. Ozeki, K. Itoh, H. Mochizuki, and W. Watanabe, “Increasing diffraction efficiency by heating phase gratings formed by femtosecond laser irradiation in poly (methyl methacrylate),” Appl. Phys. Lett. 94(24), 241122 (2009).
[CrossRef]

Nishii, J.

S. Sowa, W. Watanabe, J. Nishii, and K. Itoh, “Filamentary cavity formation in poly (methyl methacrylate) by single femtosecond pulse,” Appl. Phys., A Mater. Sci. Process. 81(8), 1587–1590 (2005).
[CrossRef]

Obara, M.

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[CrossRef]

Ozeki, Y.

S. Hirono, M. Kasuya, K. Matsuda, Y. Ozeki, K. Itoh, H. Mochizuki, and W. Watanabe, “Increasing diffraction efficiency by heating phase gratings formed by femtosecond laser irradiation in poly (methyl methacrylate),” Appl. Phys. Lett. 94(24), 241122 (2009).
[CrossRef]

Qian, B.

X. Hu, B. Qian, P. Zhang, X. Wang, L. Su, J. Qiu, and C. Zhu, “Self-organized microvoid array perpendicular to the femtosecond laser beam in CaF2 crystals,” Laser Phys. Lett. 5(5), 394–397 (2008).
[CrossRef]

Qiu, J.

X. Hu, B. Qian, P. Zhang, X. Wang, L. Su, J. Qiu, and C. Zhu, “Self-organized microvoid array perpendicular to the femtosecond laser beam in CaF2 crystals,” Laser Phys. Lett. 5(5), 394–397 (2008).
[CrossRef]

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

J. Song, X. Wang, J. Xu, H. Sun, Z. Xu, and J. Qiu, “Microstructures induced in the bulk of SrTiO3 crystal by a femtosecond laser,” Opt. Express 15(5), 2341–2347 (2007).
[CrossRef] [PubMed]

S. Qu, C. Zhao, Q. Zhao, J. Qiu, C. Zhu, and K. Hirao, “One-off writing of multimicrogratings on glass by two interfered femtosecond laser pulses,” Opt. Lett. 29(17), 2058–2060 (2004).
[CrossRef] [PubMed]

Q. Zhao, J. Qiu, X. Jiang, C. Zhao, and C. Zhu, “Mechanisms of the refractive index change in femtosecond laser-irradiated Au3+-doped silicate glasses,” J. Appl. Phys. 129(12), 7122 (2004).
[CrossRef]

Qiu, J. R.

Qu, S.

Ran, L.

Si, J. H.

S. Kanehira, J. H. Si, J. R. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett. 5(8), 1591–1595 (2005).
[CrossRef] [PubMed]

Song, J.

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

J. Song, X. Wang, J. Xu, H. Sun, Z. Xu, and J. Qiu, “Microstructures induced in the bulk of SrTiO3 crystal by a femtosecond laser,” Opt. Express 15(5), 2341–2347 (2007).
[CrossRef] [PubMed]

Sowa, S.

S. Sowa, W. Watanabe, J. Nishii, and K. Itoh, “Filamentary cavity formation in poly (methyl methacrylate) by single femtosecond pulse,” Appl. Phys., A Mater. Sci. Process. 81(8), 1587–1590 (2005).
[CrossRef]

Su, L.

X. Hu, B. Qian, P. Zhang, X. Wang, L. Su, J. Qiu, and C. Zhu, “Self-organized microvoid array perpendicular to the femtosecond laser beam in CaF2 crystals,” Laser Phys. Lett. 5(5), 394–397 (2008).
[CrossRef]

Sun, H.

Toratani, E.

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[CrossRef]

Wang, X.

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

X. Hu, B. Qian, P. Zhang, X. Wang, L. Su, J. Qiu, and C. Zhu, “Self-organized microvoid array perpendicular to the femtosecond laser beam in CaF2 crystals,” Laser Phys. Lett. 5(5), 394–397 (2008).
[CrossRef]

J. Song, X. Wang, J. Xu, H. Sun, Z. Xu, and J. Qiu, “Microstructures induced in the bulk of SrTiO3 crystal by a femtosecond laser,” Opt. Express 15(5), 2341–2347 (2007).
[CrossRef] [PubMed]

Watanabe, W.

S. Hirono, M. Kasuya, K. Matsuda, Y. Ozeki, K. Itoh, H. Mochizuki, and W. Watanabe, “Increasing diffraction efficiency by heating phase gratings formed by femtosecond laser irradiation in poly (methyl methacrylate),” Appl. Phys. Lett. 94(24), 241122 (2009).
[CrossRef]

S. Sowa, W. Watanabe, J. Nishii, and K. Itoh, “Filamentary cavity formation in poly (methyl methacrylate) by single femtosecond pulse,” Appl. Phys., A Mater. Sci. Process. 81(8), 1587–1590 (2005).
[CrossRef]

Xu, J.

Xu, Z.

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

J. Song, X. Wang, J. Xu, H. Sun, Z. Xu, and J. Qiu, “Microstructures induced in the bulk of SrTiO3 crystal by a femtosecond laser,” Opt. Express 15(5), 2341–2347 (2007).
[CrossRef] [PubMed]

Yang, H.

Zhang, P.

X. Hu, B. Qian, P. Zhang, X. Wang, L. Su, J. Qiu, and C. Zhu, “Self-organized microvoid array perpendicular to the femtosecond laser beam in CaF2 crystals,” Laser Phys. Lett. 5(5), 394–397 (2008).
[CrossRef]

Zhao, C.

S. Qu, C. Zhao, Q. Zhao, J. Qiu, C. Zhu, and K. Hirao, “One-off writing of multimicrogratings on glass by two interfered femtosecond laser pulses,” Opt. Lett. 29(17), 2058–2060 (2004).
[CrossRef] [PubMed]

Q. Zhao, J. Qiu, X. Jiang, C. Zhao, and C. Zhu, “Mechanisms of the refractive index change in femtosecond laser-irradiated Au3+-doped silicate glasses,” J. Appl. Phys. 129(12), 7122 (2004).
[CrossRef]

Zhao, Q.

Q. Zhao, J. Qiu, X. Jiang, C. Zhao, and C. Zhu, “Mechanisms of the refractive index change in femtosecond laser-irradiated Au3+-doped silicate glasses,” J. Appl. Phys. 129(12), 7122 (2004).
[CrossRef]

S. Qu, C. Zhao, Q. Zhao, J. Qiu, C. Zhu, and K. Hirao, “One-off writing of multimicrogratings on glass by two interfered femtosecond laser pulses,” Opt. Lett. 29(17), 2058–2060 (2004).
[CrossRef] [PubMed]

Zhao, Q. Z.

Zhou, C. H.

Zhu, C.

X. Hu, B. Qian, P. Zhang, X. Wang, L. Su, J. Qiu, and C. Zhu, “Self-organized microvoid array perpendicular to the femtosecond laser beam in CaF2 crystals,” Laser Phys. Lett. 5(5), 394–397 (2008).
[CrossRef]

S. Qu, C. Zhao, Q. Zhao, J. Qiu, C. Zhu, and K. Hirao, “One-off writing of multimicrogratings on glass by two interfered femtosecond laser pulses,” Opt. Lett. 29(17), 2058–2060 (2004).
[CrossRef] [PubMed]

Q. Zhao, J. Qiu, X. Jiang, C. Zhao, and C. Zhu, “Mechanisms of the refractive index change in femtosecond laser-irradiated Au3+-doped silicate glasses,” J. Appl. Phys. 129(12), 7122 (2004).
[CrossRef]

Zhu, C. S.

Appl. Phys. Lett. (4)

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[CrossRef]

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[CrossRef]

S. Hirono, M. Kasuya, K. Matsuda, Y. Ozeki, K. Itoh, H. Mochizuki, and W. Watanabe, “Increasing diffraction efficiency by heating phase gratings formed by femtosecond laser irradiation in poly (methyl methacrylate),” Appl. Phys. Lett. 94(24), 241122 (2009).
[CrossRef]

J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (1)

S. Sowa, W. Watanabe, J. Nishii, and K. Itoh, “Filamentary cavity formation in poly (methyl methacrylate) by single femtosecond pulse,” Appl. Phys., A Mater. Sci. Process. 81(8), 1587–1590 (2005).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

J. Appl. Phys. (1)

Q. Zhao, J. Qiu, X. Jiang, C. Zhao, and C. Zhu, “Mechanisms of the refractive index change in femtosecond laser-irradiated Au3+-doped silicate glasses,” J. Appl. Phys. 129(12), 7122 (2004).
[CrossRef]

Laser Phys. Lett. (1)

X. Hu, B. Qian, P. Zhang, X. Wang, L. Su, J. Qiu, and C. Zhu, “Self-organized microvoid array perpendicular to the femtosecond laser beam in CaF2 crystals,” Laser Phys. Lett. 5(5), 394–397 (2008).
[CrossRef]

Nano Lett. (1)

S. Kanehira, J. H. Si, J. R. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett. 5(8), 1591–1595 (2005).
[CrossRef] [PubMed]

Opt. Commun. (2)

Z. Guo, S. Qu, and S. Liu, “Generating optical vortex with computer-generated hologram fabricated inside glass by femtosecond laser pulses,” Opt. Commun. 273(1), 286–289 (2007).
[CrossRef]

A. Brodeur, F. Ilkov, and S. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 96(3-4), 193–198 (1996).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

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Figures (5)

Fig. 1
Fig. 1

(a) the sketch of the experimental setup for the generation of periodic voids, Side view of the voids array induced in silica glass by femtosecond laser pulses,(b) different number of with pulse energy of 20 μ J , (c) single pulse with different energies, (d) double pulses with different energies. The scale bars in the Figure are 20 μ m . The arrows show the direction of the pulses propagation, and the lop lines express the focus place.

Fig. 2
Fig. 2

the fabricated grating: (a) top view, (b) side view; diffraction pattern of the grating obtained under different conditions: (c) E = 1.76 μJ , v = 1000 μm/s , (d) E = 7.38 μJ , v = 1000 μm/s

Fig. 3
Fig. 3

(a) Variational tendency of the transmittance efficiency (TE) with the different pulse of energy and scanning velocity, (b) Variational tendency of the first order diffraction efficiency (FODE) with the different pulse of energy and scanning velocity, (c) Variational tendency of the normalized first order diffraction efficiency (NFODE) with the different pulse of energy and scanning velocity

Fig. 4
Fig. 4

(a) A simple sketch of our numerical method, (b) A typical example of the distribution of the amplitude of the electric field inside the sample. (c) Distribution of the amplitude of the Electric filed in the silicate glass sample.

Fig. 5
Fig. 5

The far field diffraction of the distribution of Electric filed along the x ' direction, (a) d r e c = 10 μm, δ n = 0.007 and the three curves correspond to different depths of the induced gratings: h c = 5(solid red), 20(dotted blue) and 40 μm (dashed black) respectively; (b) h c = 40 μm , δ n = 0.007 and the three curves correspond to different width of the filaments: d r e c = 5(solid red), 10(dotted blue) and 15 μm (dashed black) respectively; (c) d r e c = 10 μm , h c = 40 μm and the three curves correspond to different RICs: δ n = 0.002 (solid red), 0.007 (dotted blue) and 0.012(dashed black) respectively.

Equations (1)

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E ( x ' ) = C j λ + E ( x ) exp ( i k r ) r cos θ + 1 2 d x ,

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