Abstract

We have fabricated the complicated two-dimensional subwave-length microstructures induced by the femtosecond vector light fields on silicon. The fabricated microstructures have the interval between two ripples in microstructures to be around 670–690 nm and the depth of the grooves to be about 300 nm when the pulse fluence of 0.26 J/cm2 is slightly higher than the ablated threshold of 0.2 J/cm2 for silicon under the irradiation of 100 pulses. The ripples are always perpendicular to the direction of the locally linear polarization. The designable spatial structure of polarization of the femtosecond vector light field can be used to manipulate the fabricated microstructure.

© 2011 OSA

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  1. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
    [CrossRef]
  2. C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
    [CrossRef]
  3. X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32, 3549–3551 (2007).
    [CrossRef] [PubMed]
  4. X. L. Wang, Y. N. Li, J. Chen, C. S. Guo, J. P. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18, 10786–10795 (2010).
    [CrossRef] [PubMed]
  5. M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: Optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
    [CrossRef]
  6. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  7. C. C. Sun and C. K. Liu, “Ultrasmall focusing spot with a long depth of focus based on polarization and phase modulation,” Opt. Lett. 28, 99–101 (2003).
    [CrossRef] [PubMed]
  8. Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24, 1793–1798 (2007).
    [CrossRef]
  9. H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon. 2, 501–505 (2008).
    [CrossRef]
  10. C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
    [CrossRef] [PubMed]
  11. Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pluses,” Phys. Rev. Lett. 91, 247405 (2003).
    [CrossRef] [PubMed]
  12. D. J. Hwang, C. P. Grigoropoulos, and T. Y. Choi, “Efficiency of silicon micromachining by femtosecond laser pulses in ambient air,” J. Appl. Phys. 99, 083101 (2006).
    [CrossRef]
  13. K. Okamuro, M. Hashida, Y. Miyasaka, Y. Ikuta, S. Tokita, and S. Sakabe, “Laser fluence dependence of periodic grating structures formed on metal surfaces under femtosecond laser pulse irradiation,” Phys. Rev. B 82, 165417 (2010).
    [CrossRef]
  14. E. M. Hsu, T. H. R. Crawford, H. F. Tiedje, and H. K. Haugen, “Periodic surface structures on gallium phosphide after irradiation with 150fs-7ns laser pulses at 800nm,” Appl. Phys. Lett. 91, 111102 (2007).
    [CrossRef]
  15. M. Huang, F. L. Zhao, Y. Cheng, N. S. Xu, and Z. Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano.  3, 4062–4070 (2009).
    [CrossRef] [PubMed]
  16. J. Bonse, A. Rosenfeld, and J. Krüger, “On the role of surface Plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond-laser pulses,” J. Appl. Phys. 106, 104910 (2009).
    [CrossRef]
  17. S. Sakabe, M. Hashida, S. Tokuta, S. Namba, and K. Okamuro, “Mechanism for self-formation of periodic grating structures on a metal surface by a femtosecond laser pulse,” Phys. Rev. B 79, 033409 (2009).
    [CrossRef]
  18. R. A. Ganeev, M. Baba, T. Ozaki, and H. Kuroda, “Long- and short-period nanostructure formation on semiconductor surfaces at different ambient conditions,” J. Opt. Soc. Am. B 27, 1077–1082 (2010).
    [CrossRef]
  19. R. L. Harzic, D. D. Sauer, M. Neumeier, M. Epple, H. Zimmermann, and F. Stracke, “Formation of periodic nanoripples on silicon and Germanium induced by femtosecond laser pulses,” Phys. Procedia 12, 29–36 (2011).
    [CrossRef]
  20. C. Wang, H. B. Huo, M. Johnson, M. Shen, and E. Mazur, “The thresholds of surface nano-/micro-morphology modifications with femtosecond laser pulse irradiations,” Nanotechnology 21, 075304 (2010).
    [CrossRef]
  21. J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon-modification thresholds and morphology,” Appl. Phy. A 74, 19–25 (2002).
    [CrossRef]
  22. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1760 (1996).
    [CrossRef]
  23. Y. H. Han and S. L. Qu, “The ripples and nanoparticles on silicon irradiated by femtosecond laser,” Chem. Phys. Lett. 495, 241–244 (2010).
    [CrossRef]
  24. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251 (1995).
    [CrossRef] [PubMed]
  25. A. D. Bristow, N. Rotenberg, and H. M. V. Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200nm,” Appl. Phys. Lett. 90, 191104 (2007).
    [CrossRef]
  26. M. Kraus, M. A. Ahmed, A. Michalowski, A. Voss, R. Weber, and T. Graf, “Microdrilling in steel using ultrashort pulsed laser beams with radial and azimuthal polarization,” Opt. Express 18, 22305–22313 (2010).
    [CrossRef] [PubMed]
  27. K. Venkatakrishnan and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16, 2603–2607 (2006).
    [CrossRef]
  28. W. C. Shen, C. W. Cheng, M. C. Yang, Y. Kozawa, and S. Sato, “Fabrication of novel structures on silicon with femtosecond laser pulses,” J. Laser Micro/Nanoeng. 5, 229–232 (2010).
    [CrossRef]
  29. M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
    [CrossRef] [PubMed]
  30. K. M. Romallosa, J. Bantang, and C. Saloma, “Three-dimensional light distribution near the focus of a tightly focused beam of few-cycle optical pulses,” Phys. Rev. A 68, 033812 (2003).
    [CrossRef]

2011 (2)

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
[CrossRef] [PubMed]

R. L. Harzic, D. D. Sauer, M. Neumeier, M. Epple, H. Zimmermann, and F. Stracke, “Formation of periodic nanoripples on silicon and Germanium induced by femtosecond laser pulses,” Phys. Procedia 12, 29–36 (2011).
[CrossRef]

2010 (7)

C. Wang, H. B. Huo, M. Johnson, M. Shen, and E. Mazur, “The thresholds of surface nano-/micro-morphology modifications with femtosecond laser pulse irradiations,” Nanotechnology 21, 075304 (2010).
[CrossRef]

Y. H. Han and S. L. Qu, “The ripples and nanoparticles on silicon irradiated by femtosecond laser,” Chem. Phys. Lett. 495, 241–244 (2010).
[CrossRef]

M. Kraus, M. A. Ahmed, A. Michalowski, A. Voss, R. Weber, and T. Graf, “Microdrilling in steel using ultrashort pulsed laser beams with radial and azimuthal polarization,” Opt. Express 18, 22305–22313 (2010).
[CrossRef] [PubMed]

W. C. Shen, C. W. Cheng, M. C. Yang, Y. Kozawa, and S. Sato, “Fabrication of novel structures on silicon with femtosecond laser pulses,” J. Laser Micro/Nanoeng. 5, 229–232 (2010).
[CrossRef]

K. Okamuro, M. Hashida, Y. Miyasaka, Y. Ikuta, S. Tokita, and S. Sakabe, “Laser fluence dependence of periodic grating structures formed on metal surfaces under femtosecond laser pulse irradiation,” Phys. Rev. B 82, 165417 (2010).
[CrossRef]

R. A. Ganeev, M. Baba, T. Ozaki, and H. Kuroda, “Long- and short-period nanostructure formation on semiconductor surfaces at different ambient conditions,” J. Opt. Soc. Am. B 27, 1077–1082 (2010).
[CrossRef]

X. L. Wang, Y. N. Li, J. Chen, C. S. Guo, J. P. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18, 10786–10795 (2010).
[CrossRef] [PubMed]

2009 (5)

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: Optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[CrossRef]

M. Huang, F. L. Zhao, Y. Cheng, N. S. Xu, and Z. Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano.  3, 4062–4070 (2009).
[CrossRef] [PubMed]

J. Bonse, A. Rosenfeld, and J. Krüger, “On the role of surface Plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond-laser pulses,” J. Appl. Phys. 106, 104910 (2009).
[CrossRef]

S. Sakabe, M. Hashida, S. Tokuta, S. Namba, and K. Okamuro, “Mechanism for self-formation of periodic grating structures on a metal surface by a femtosecond laser pulse,” Phys. Rev. B 79, 033409 (2009).
[CrossRef]

2008 (1)

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon. 2, 501–505 (2008).
[CrossRef]

2007 (5)

Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24, 1793–1798 (2007).
[CrossRef]

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32, 3549–3551 (2007).
[CrossRef] [PubMed]

E. M. Hsu, T. H. R. Crawford, H. F. Tiedje, and H. K. Haugen, “Periodic surface structures on gallium phosphide after irradiation with 150fs-7ns laser pulses at 800nm,” Appl. Phys. Lett. 91, 111102 (2007).
[CrossRef]

A. D. Bristow, N. Rotenberg, and H. M. V. Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200nm,” Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

2006 (2)

K. Venkatakrishnan and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16, 2603–2607 (2006).
[CrossRef]

D. J. Hwang, C. P. Grigoropoulos, and T. Y. Choi, “Efficiency of silicon micromachining by femtosecond laser pulses in ambient air,” J. Appl. Phys. 99, 083101 (2006).
[CrossRef]

2003 (4)

Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pluses,” Phys. Rev. Lett. 91, 247405 (2003).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

C. C. Sun and C. K. Liu, “Ultrasmall focusing spot with a long depth of focus based on polarization and phase modulation,” Opt. Lett. 28, 99–101 (2003).
[CrossRef] [PubMed]

K. M. Romallosa, J. Bantang, and C. Saloma, “Three-dimensional light distribution near the focus of a tightly focused beam of few-cycle optical pulses,” Phys. Rev. A 68, 033812 (2003).
[CrossRef]

2002 (1)

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon-modification thresholds and morphology,” Appl. Phy. A 74, 19–25 (2002).
[CrossRef]

1996 (1)

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1760 (1996).
[CrossRef]

1995 (1)

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251 (1995).
[CrossRef] [PubMed]

1993 (1)

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[CrossRef] [PubMed]

Ahmed, M. A.

Baba, M.

Bantang, J.

K. M. Romallosa, J. Bantang, and C. Saloma, “Three-dimensional light distribution near the focus of a tightly focused beam of few-cycle optical pulses,” Phys. Rev. A 68, 033812 (2003).
[CrossRef]

Baudach, S.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon-modification thresholds and morphology,” Appl. Phy. A 74, 19–25 (2002).
[CrossRef]

Bernet, S.

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

Bonse, J.

J. Bonse, A. Rosenfeld, and J. Krüger, “On the role of surface Plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond-laser pulses,” J. Appl. Phys. 106, 104910 (2009).
[CrossRef]

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon-modification thresholds and morphology,” Appl. Phy. A 74, 19–25 (2002).
[CrossRef]

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. V. Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200nm,” Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Chen, J.

Cheng, C. W.

W. C. Shen, C. W. Cheng, M. C. Yang, Y. Kozawa, and S. Sato, “Fabrication of novel structures on silicon with femtosecond laser pulses,” J. Laser Micro/Nanoeng. 5, 229–232 (2010).
[CrossRef]

Cheng, Y.

M. Huang, F. L. Zhao, Y. Cheng, N. S. Xu, and Z. Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano.  3, 4062–4070 (2009).
[CrossRef] [PubMed]

Choi, T. Y.

D. J. Hwang, C. P. Grigoropoulos, and T. Y. Choi, “Efficiency of silicon micromachining by femtosecond laser pulses in ambient air,” J. Appl. Phys. 99, 083101 (2006).
[CrossRef]

Chong, C. T.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon. 2, 501–505 (2008).
[CrossRef]

Crawford, T. H. R.

E. M. Hsu, T. H. R. Crawford, H. F. Tiedje, and H. K. Haugen, “Periodic surface structures on gallium phosphide after irradiation with 150fs-7ns laser pulses at 800nm,” Appl. Phys. Lett. 91, 111102 (2007).
[CrossRef]

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: Optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

Ding, J.

Ding, J. P.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Driel, H. M. V.

A. D. Bristow, N. Rotenberg, and H. M. V. Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200nm,” Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Epple, M.

R. L. Harzic, D. D. Sauer, M. Neumeier, M. Epple, H. Zimmermann, and F. Stracke, “Formation of periodic nanoripples on silicon and Germanium induced by femtosecond laser pulses,” Phys. Procedia 12, 29–36 (2011).
[CrossRef]

Feit, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1760 (1996).
[CrossRef]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251 (1995).
[CrossRef] [PubMed]

Furhapter, S.

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

Ganeev, R. A.

Graf, T.

Grigoropoulos, C. P.

D. J. Hwang, C. P. Grigoropoulos, and T. Y. Choi, “Efficiency of silicon micromachining by femtosecond laser pulses in ambient air,” J. Appl. Phys. 99, 083101 (2006).
[CrossRef]

Guo, C. S.

Han, Y. H.

Y. H. Han and S. L. Qu, “The ripples and nanoparticles on silicon irradiated by femtosecond laser,” Chem. Phys. Lett. 495, 241–244 (2010).
[CrossRef]

Harzic, R. L.

R. L. Harzic, D. D. Sauer, M. Neumeier, M. Epple, H. Zimmermann, and F. Stracke, “Formation of periodic nanoripples on silicon and Germanium induced by femtosecond laser pulses,” Phys. Procedia 12, 29–36 (2011).
[CrossRef]

Hashida, M.

K. Okamuro, M. Hashida, Y. Miyasaka, Y. Ikuta, S. Tokita, and S. Sakabe, “Laser fluence dependence of periodic grating structures formed on metal surfaces under femtosecond laser pulse irradiation,” Phys. Rev. B 82, 165417 (2010).
[CrossRef]

S. Sakabe, M. Hashida, S. Tokuta, S. Namba, and K. Okamuro, “Mechanism for self-formation of periodic grating structures on a metal surface by a femtosecond laser pulse,” Phys. Rev. B 79, 033409 (2009).
[CrossRef]

Haugen, H. K.

E. M. Hsu, T. H. R. Crawford, H. F. Tiedje, and H. K. Haugen, “Periodic surface structures on gallium phosphide after irradiation with 150fs-7ns laser pulses at 800nm,” Appl. Phys. Lett. 91, 111102 (2007).
[CrossRef]

Herman, S.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1760 (1996).
[CrossRef]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251 (1995).
[CrossRef] [PubMed]

Hirao, K.

Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pluses,” Phys. Rev. Lett. 91, 247405 (2003).
[CrossRef] [PubMed]

Hnatovsky, C.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
[CrossRef] [PubMed]

Hsu, E. M.

E. M. Hsu, T. H. R. Crawford, H. F. Tiedje, and H. K. Haugen, “Periodic surface structures on gallium phosphide after irradiation with 150fs-7ns laser pulses at 800nm,” Appl. Phys. Lett. 91, 111102 (2007).
[CrossRef]

Huang, M.

M. Huang, F. L. Zhao, Y. Cheng, N. S. Xu, and Z. Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano.  3, 4062–4070 (2009).
[CrossRef] [PubMed]

Huo, H. B.

C. Wang, H. B. Huo, M. Johnson, M. Shen, and E. Mazur, “The thresholds of surface nano-/micro-morphology modifications with femtosecond laser pulse irradiations,” Nanotechnology 21, 075304 (2010).
[CrossRef]

Hwang, D. J.

D. J. Hwang, C. P. Grigoropoulos, and T. Y. Choi, “Efficiency of silicon micromachining by femtosecond laser pulses in ambient air,” J. Appl. Phys. 99, 083101 (2006).
[CrossRef]

Ikuta, Y.

K. Okamuro, M. Hashida, Y. Miyasaka, Y. Ikuta, S. Tokita, and S. Sakabe, “Laser fluence dependence of periodic grating structures formed on metal surfaces under femtosecond laser pulse irradiation,” Phys. Rev. B 82, 165417 (2010).
[CrossRef]

Jesacher, A.

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

Johnson, M.

C. Wang, H. B. Huo, M. Johnson, M. Shen, and E. Mazur, “The thresholds of surface nano-/micro-morphology modifications with femtosecond laser pulse irradiations,” Nanotechnology 21, 075304 (2010).
[CrossRef]

Kautek, W.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon-modification thresholds and morphology,” Appl. Phy. A 74, 19–25 (2002).
[CrossRef]

Kazansky, P. G.

Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pluses,” Phys. Rev. Lett. 91, 247405 (2003).
[CrossRef] [PubMed]

Kempe, M.

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[CrossRef] [PubMed]

Kozawa, Y.

W. C. Shen, C. W. Cheng, M. C. Yang, Y. Kozawa, and S. Sato, “Fabrication of novel structures on silicon with femtosecond laser pulses,” J. Laser Micro/Nanoeng. 5, 229–232 (2010).
[CrossRef]

Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24, 1793–1798 (2007).
[CrossRef]

Kraus, M.

Krolikowski, W.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
[CrossRef] [PubMed]

Krüger, J.

J. Bonse, A. Rosenfeld, and J. Krüger, “On the role of surface Plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond-laser pulses,” J. Appl. Phys. 106, 104910 (2009).
[CrossRef]

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon-modification thresholds and morphology,” Appl. Phy. A 74, 19–25 (2002).
[CrossRef]

Kuroda, H.

Lenzner, M.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon-modification thresholds and morphology,” Appl. Phy. A 74, 19–25 (2002).
[CrossRef]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Li, Y. N.

Liu, C. K.

Lukyanchuk, B.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon. 2, 501–505 (2008).
[CrossRef]

Maurer, C.

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

Mazur, E.

C. Wang, H. B. Huo, M. Johnson, M. Shen, and E. Mazur, “The thresholds of surface nano-/micro-morphology modifications with femtosecond laser pulse irradiations,” Nanotechnology 21, 075304 (2010).
[CrossRef]

Michalowski, A.

Miyasaka, Y.

K. Okamuro, M. Hashida, Y. Miyasaka, Y. Ikuta, S. Tokita, and S. Sakabe, “Laser fluence dependence of periodic grating structures formed on metal surfaces under femtosecond laser pulse irradiation,” Phys. Rev. B 82, 165417 (2010).
[CrossRef]

Namba, S.

S. Sakabe, M. Hashida, S. Tokuta, S. Namba, and K. Okamuro, “Mechanism for self-formation of periodic grating structures on a metal surface by a femtosecond laser pulse,” Phys. Rev. B 79, 033409 (2009).
[CrossRef]

Neumeier, M.

R. L. Harzic, D. D. Sauer, M. Neumeier, M. Epple, H. Zimmermann, and F. Stracke, “Formation of periodic nanoripples on silicon and Germanium induced by femtosecond laser pulses,” Phys. Procedia 12, 29–36 (2011).
[CrossRef]

Ni, W. J.

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: Optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

Okamuro, K.

K. Okamuro, M. Hashida, Y. Miyasaka, Y. Ikuta, S. Tokita, and S. Sakabe, “Laser fluence dependence of periodic grating structures formed on metal surfaces under femtosecond laser pulse irradiation,” Phys. Rev. B 82, 165417 (2010).
[CrossRef]

S. Sakabe, M. Hashida, S. Tokuta, S. Namba, and K. Okamuro, “Mechanism for self-formation of periodic grating structures on a metal surface by a femtosecond laser pulse,” Phys. Rev. B 79, 033409 (2009).
[CrossRef]

Ozaki, T.

Padgett, M. J.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: Optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

Perry, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1760 (1996).
[CrossRef]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251 (1995).
[CrossRef] [PubMed]

Qiu, J. R.

Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pluses,” Phys. Rev. Lett. 91, 247405 (2003).
[CrossRef] [PubMed]

Qu, S. L.

Y. H. Han and S. L. Qu, “The ripples and nanoparticles on silicon irradiated by femtosecond laser,” Chem. Phys. Lett. 495, 241–244 (2010).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

Rode, A.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
[CrossRef] [PubMed]

Romallosa, K. M.

K. M. Romallosa, J. Bantang, and C. Saloma, “Three-dimensional light distribution near the focus of a tightly focused beam of few-cycle optical pulses,” Phys. Rev. A 68, 033812 (2003).
[CrossRef]

Rosenfeld, A.

J. Bonse, A. Rosenfeld, and J. Krüger, “On the role of surface Plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond-laser pulses,” J. Appl. Phys. 106, 104910 (2009).
[CrossRef]

Rotenberg, N.

A. D. Bristow, N. Rotenberg, and H. M. V. Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200nm,” Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Rubenchik, A. M.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1760 (1996).
[CrossRef]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251 (1995).
[CrossRef] [PubMed]

Rudolph, W.

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[CrossRef] [PubMed]

Sakabe, S.

K. Okamuro, M. Hashida, Y. Miyasaka, Y. Ikuta, S. Tokita, and S. Sakabe, “Laser fluence dependence of periodic grating structures formed on metal surfaces under femtosecond laser pulse irradiation,” Phys. Rev. B 82, 165417 (2010).
[CrossRef]

S. Sakabe, M. Hashida, S. Tokuta, S. Namba, and K. Okamuro, “Mechanism for self-formation of periodic grating structures on a metal surface by a femtosecond laser pulse,” Phys. Rev. B 79, 033409 (2009).
[CrossRef]

Saloma, C.

K. M. Romallosa, J. Bantang, and C. Saloma, “Three-dimensional light distribution near the focus of a tightly focused beam of few-cycle optical pulses,” Phys. Rev. A 68, 033812 (2003).
[CrossRef]

Sato, S.

W. C. Shen, C. W. Cheng, M. C. Yang, Y. Kozawa, and S. Sato, “Fabrication of novel structures on silicon with femtosecond laser pulses,” J. Laser Micro/Nanoeng. 5, 229–232 (2010).
[CrossRef]

Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24, 1793–1798 (2007).
[CrossRef]

Sauer, D. D.

R. L. Harzic, D. D. Sauer, M. Neumeier, M. Epple, H. Zimmermann, and F. Stracke, “Formation of periodic nanoripples on silicon and Germanium induced by femtosecond laser pulses,” Phys. Procedia 12, 29–36 (2011).
[CrossRef]

Shen, M.

C. Wang, H. B. Huo, M. Johnson, M. Shen, and E. Mazur, “The thresholds of surface nano-/micro-morphology modifications with femtosecond laser pulse irradiations,” Nanotechnology 21, 075304 (2010).
[CrossRef]

Shen, W. C.

W. C. Shen, C. W. Cheng, M. C. Yang, Y. Kozawa, and S. Sato, “Fabrication of novel structures on silicon with femtosecond laser pulses,” J. Laser Micro/Nanoeng. 5, 229–232 (2010).
[CrossRef]

Sheppard, C.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon. 2, 501–505 (2008).
[CrossRef]

Shi, L. P.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon. 2, 501–505 (2008).
[CrossRef]

Shimotsuma, Y.

Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pluses,” Phys. Rev. Lett. 91, 247405 (2003).
[CrossRef] [PubMed]

Shore, B. W.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1760 (1996).
[CrossRef]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251 (1995).
[CrossRef] [PubMed]

Shvedov, V.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
[CrossRef] [PubMed]

Stracke, F.

R. L. Harzic, D. D. Sauer, M. Neumeier, M. Epple, H. Zimmermann, and F. Stracke, “Formation of periodic nanoripples on silicon and Germanium induced by femtosecond laser pulses,” Phys. Procedia 12, 29–36 (2011).
[CrossRef]

Stuart, B. C.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1760 (1996).
[CrossRef]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251 (1995).
[CrossRef] [PubMed]

Sun, C. C.

Tan, B.

K. Venkatakrishnan and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16, 2603–2607 (2006).
[CrossRef]

Tiedje, H. F.

E. M. Hsu, T. H. R. Crawford, H. F. Tiedje, and H. K. Haugen, “Periodic surface structures on gallium phosphide after irradiation with 150fs-7ns laser pulses at 800nm,” Appl. Phys. Lett. 91, 111102 (2007).
[CrossRef]

Tokita, S.

K. Okamuro, M. Hashida, Y. Miyasaka, Y. Ikuta, S. Tokita, and S. Sakabe, “Laser fluence dependence of periodic grating structures formed on metal surfaces under femtosecond laser pulse irradiation,” Phys. Rev. B 82, 165417 (2010).
[CrossRef]

Tokuta, S.

S. Sakabe, M. Hashida, S. Tokuta, S. Namba, and K. Okamuro, “Mechanism for self-formation of periodic grating structures on a metal surface by a femtosecond laser pulse,” Phys. Rev. B 79, 033409 (2009).
[CrossRef]

Venkatakrishnan, K.

K. Venkatakrishnan and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16, 2603–2607 (2006).
[CrossRef]

Voss, A.

Wang, C.

C. Wang, H. B. Huo, M. Johnson, M. Shen, and E. Mazur, “The thresholds of surface nano-/micro-morphology modifications with femtosecond laser pulse irradiations,” Nanotechnology 21, 075304 (2010).
[CrossRef]

Wang, H. F.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon. 2, 501–505 (2008).
[CrossRef]

Wang, H. T.

Wang, X. L.

Weber, R.

Xu, N. S.

M. Huang, F. L. Zhao, Y. Cheng, N. S. Xu, and Z. Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano.  3, 4062–4070 (2009).
[CrossRef] [PubMed]

Xu, Z. Z.

M. Huang, F. L. Zhao, Y. Cheng, N. S. Xu, and Z. Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano.  3, 4062–4070 (2009).
[CrossRef] [PubMed]

Yang, M. C.

W. C. Shen, C. W. Cheng, M. C. Yang, Y. Kozawa, and S. Sato, “Fabrication of novel structures on silicon with femtosecond laser pulses,” J. Laser Micro/Nanoeng. 5, 229–232 (2010).
[CrossRef]

Zhan, Q.

Zhao, F. L.

M. Huang, F. L. Zhao, Y. Cheng, N. S. Xu, and Z. Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano.  3, 4062–4070 (2009).
[CrossRef] [PubMed]

Zimmermann, H.

R. L. Harzic, D. D. Sauer, M. Neumeier, M. Epple, H. Zimmermann, and F. Stracke, “Formation of periodic nanoripples on silicon and Germanium induced by femtosecond laser pulses,” Phys. Procedia 12, 29–36 (2011).
[CrossRef]

ACS Nano (1)

M. Huang, F. L. Zhao, Y. Cheng, N. S. Xu, and Z. Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano.  3, 4062–4070 (2009).
[CrossRef] [PubMed]

Adv. Opt. Photon. (1)

Appl. Phy. A (1)

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon-modification thresholds and morphology,” Appl. Phy. A 74, 19–25 (2002).
[CrossRef]

Appl. Phys. Lett. (2)

E. M. Hsu, T. H. R. Crawford, H. F. Tiedje, and H. K. Haugen, “Periodic surface structures on gallium phosphide after irradiation with 150fs-7ns laser pulses at 800nm,” Appl. Phys. Lett. 91, 111102 (2007).
[CrossRef]

A. D. Bristow, N. Rotenberg, and H. M. V. Driel, “Two-photon absorption and kerr coefficients of silicon for 850–2200nm,” Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Chem. Phys. Lett. (1)

Y. H. Han and S. L. Qu, “The ripples and nanoparticles on silicon irradiated by femtosecond laser,” Chem. Phys. Lett. 495, 241–244 (2010).
[CrossRef]

J. Appl. Phys. (2)

J. Bonse, A. Rosenfeld, and J. Krüger, “On the role of surface Plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond-laser pulses,” J. Appl. Phys. 106, 104910 (2009).
[CrossRef]

D. J. Hwang, C. P. Grigoropoulos, and T. Y. Choi, “Efficiency of silicon micromachining by femtosecond laser pulses in ambient air,” J. Appl. Phys. 99, 083101 (2006).
[CrossRef]

J. Laser Micro/Nanoeng. (1)

W. C. Shen, C. W. Cheng, M. C. Yang, Y. Kozawa, and S. Sato, “Fabrication of novel structures on silicon with femtosecond laser pulses,” J. Laser Micro/Nanoeng. 5, 229–232 (2010).
[CrossRef]

J. Micromech. Microeng. (1)

K. Venkatakrishnan and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16, 2603–2607 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nanotechnology (1)

C. Wang, H. B. Huo, M. Johnson, M. Shen, and E. Mazur, “The thresholds of surface nano-/micro-morphology modifications with femtosecond laser pulse irradiations,” Nanotechnology 21, 075304 (2010).
[CrossRef]

Nat. Photon. (1)

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon. 2, 501–505 (2008).
[CrossRef]

New J. Phys. (1)

C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Procedia (1)

R. L. Harzic, D. D. Sauer, M. Neumeier, M. Epple, H. Zimmermann, and F. Stracke, “Formation of periodic nanoripples on silicon and Germanium induced by femtosecond laser pulses,” Phys. Procedia 12, 29–36 (2011).
[CrossRef]

Phys. Rev. A (2)

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
[CrossRef] [PubMed]

K. M. Romallosa, J. Bantang, and C. Saloma, “Three-dimensional light distribution near the focus of a tightly focused beam of few-cycle optical pulses,” Phys. Rev. A 68, 033812 (2003).
[CrossRef]

Phys. Rev. B (3)

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1760 (1996).
[CrossRef]

S. Sakabe, M. Hashida, S. Tokuta, S. Namba, and K. Okamuro, “Mechanism for self-formation of periodic grating structures on a metal surface by a femtosecond laser pulse,” Phys. Rev. B 79, 033409 (2009).
[CrossRef]

K. Okamuro, M. Hashida, Y. Miyasaka, Y. Ikuta, S. Tokita, and S. Sakabe, “Laser fluence dependence of periodic grating structures formed on metal surfaces under femtosecond laser pulse irradiation,” Phys. Rev. B 82, 165417 (2010).
[CrossRef]

Phys. Rev. Lett. (4)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
[CrossRef] [PubMed]

Y. Shimotsuma, P. G. Kazansky, J. R. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pluses,” Phys. Rev. Lett. 91, 247405 (2003).
[CrossRef] [PubMed]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251 (1995).
[CrossRef] [PubMed]

Prog. Opt. (1)

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: Optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental schematic for fabricating the subwavelength microstructures by femtosecond vector fields. M1 and M2: broadband high-reflection mirrors.

Fig. 2
Fig. 2

Subwavelength microstructures induced by the femtosecond vector fields under the irradiation of 100 pulses with its laser fluence of 0.26 J/cm2. (a) Spatial distributions of intensity and polarization of the focused femtosecond radially-polarized vector field with m = 1 and φ0 = 0. (b) SEM image of the microstructure induced by the vector field shown in (a). (c) Magnified image of the central region of the SEM image shown in (b). (d) Spatial distributions of intensity and polarization of the focused femtosecond azimuthally-polarized vector field with m = 1 and φ0 = π/2. (e) SEM image of the microstructure induced by the vector field shown in (d). (f) Magnified image of the central region of the SEM image shown in (e).

Fig. 3
Fig. 3

Subwavelength microstructures induced by the femtosecond vector fields under the irradiation of 100 pulses with its laser fluence of 0.26 J/cm2. (a) Spatial distributions of intensity and polarization of the focused femtosecond radially-polarized vector field with m = −1 and φ0 = 0. (b) SEM image of the microstructure induced by the vector field shown in (a). (c) Magnified image of the central region of the SEM image shown in (b). (d) Spatial distributions of intensity and polarization of the focused femtosecond azimuthally-polarized vector field with m = −1 and φ0 = π/2. (e) SEM image of the microstructure induced by the vector field shown in (d). (f) Magnified image of the central region of the SEM image shown in (e).

Fig. 4
Fig. 4

Subwavelength microstructures induced by the femtosecond vector fields under the irradiation of 100 pulses with its laser fluence of 0.26 J/cm2. (a) Spatial distributions of intensity and polarization of the focused femtosecond radially-polarized vector field with m = 2 and φ0 = 0. (b) SEM image of the microstructure induced by the vector field shown in (a). (c) Magnified image of the central region of the SEM image shown in (b). (d) Spatial distributions of intensity and polarization of the focused femtosecond azimuthally-polarized vector field with m = 2 and φ0 = π/2. (e) SEM image of the microstructure induced by the vector field shown in (d). (f) Magnified image of the central region of the SEM image shown in (e).

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

[ U ρ U φ ] = [ cos ( δ φ ) sin ( δ φ ) ] E ( ρ , φ ; Δ ω ) ,
I ( r , ϕ , z ) = | U ( r , ϕ , z ) | 2 | + E ( r , ϕ ; Δ ω ) h ( r , ϕ , z ; Δ ω ) e j Δ ω t d Δ ω | 2
h ( r , ϕ , z ; Δ ω ) 0 a exp [ j k 0 ρ 2 2 ( 1 f z f 2 ) ] J m ( k 0 ρ r f ) ρ d ρ ,

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