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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 1 — Jan. 2, 2012
  • pp: 120–127
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Two-dimensional microstructures induced by femtosecond vector light fields on silicon

Kai Lou, Sheng-Xia Qian, Xi-Lin Wang, Yongnan Li, Bing Gu, Chenghou Tu, and Hui-Tian Wang  »View Author Affiliations


Optics Express, Vol. 20, Issue 1, pp. 120-127 (2012)
http://dx.doi.org/10.1364/OE.20.000120


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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

On the other hand, the interaction of the femtosecond laser with matter produces many novel effects and applications, due to its ultrahigh intensity and ultrashort pulse duration. It is imaginable that based on the combination of ultrastrong and ultrashort advantages of the femtosecond laser and the manipulatable spatial distribution of states of polarization of the vector field, the interaction of femtosecond laser with matter will undoubtedly produces many novel effects and applications. The interaction of the single pulse with matter is only an intensity-dependent process and has no signature on the light polarization whereas, the interaction behavior of multiple pulses with some materials depends not only on the intensity but also the polarization of the light field [10

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]

].

Ultrashort pulse laser-induced periodic structures have been observed inside the various materials or at their surfaces, including insulators [11

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]

], semiconductors [12

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]

] and conductors [13

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]

]. Such a kind of phenomena has been observed in the 150 fs–7 ns regime [14

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]

]. During the past decade, the physical mechanism behind the phenomena of laser-induced periodic structure has gained remarkable attention [14

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]

17

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]

]. The periods of the laser-induced periodic structures for the transparent materials are much shorter than the laser wavelength, which depends on the interference between the incident light field and the electric field of the bulk electron plasma wave [11

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]

]. The laser-induced periodic structures formed at the surface of materials can be classified to two distinct types of low and high spatial frequency, under the illuminating condition of the multiple linearly polarized ultrashort pulses [18

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

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]

].

The silicon as a kind of the most basic and important semiconductor material has been widely applied in mechanical, optical and electronic devices. Miniature structure has become a tendency in producing newfashioned or precise devices. Therefore, the silicon-based micro/nano precise devices have attracted the significant interest. Under the irradiation of tens to thousands of ultrashort laser pulses, the laser-induced periodic structures with the low spatial frequency at the surface of silicon are formed when the laser fluence is above the ablation threshold [20

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

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]

]. The laser-induced periodic structures formed at the surface of silicon has an important feature that ripples of the laser-induced periodic structures are perpendicular to the polarization direction of the incident light field [15

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]

] and a typical period ranging from 620 to 1000 nm [16

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]

]. The most of the researches on the dielectric breakdown are based on the interacting of the materials with the homogenously linearly polarized fields [11

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]

25

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]

], in which the fabricated laser-induced periodic structures exhibit all one-dimensional (1D) structures. The vector light fields have attracted more attention on the interaction of light with the matter, due to their novel properties. The radially and azimuthally polarized light fields, as two representative vector fields, have been applied on laser-drilling [26

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

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

], novel grating structure fabrication [28

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]

] and local field structure [10

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]

]. However, the interaction of the other kinds of vector light fields with the matter is rarely involved so far. Here we focus on two-dimensional (2D) laser-induced microstructures formed by arbitrary designed femtosecond vector laser fields at the surface of silicon.

The experimental schematic is shown in Fig. 1. The laser source is a Ti:sapphire regenerative amplifier system (Coherent In.), which has a fundamental Gaussian mode, a central wavelength of 806 nm, a bandwidth of 32 nm, a pulse duration of 35 fs, and a repetition rate of 1 kHz. A λ/2 wave plate and a broadband polarization beam splitter (PBS) are used to control the intensity of the laser pulses. Another λ/2 wave plate is used to change the polarization direction of the laser pulses incident into a femtosecond vector field generation system (VFGS), which is very similar to the generation system for the continuous-wave arbitrary vector fields [3

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]

]. One should be pointed out that in this femtosecond VFGS, two achromatic λ/4 wave plates with a broadband of 650–1100 nm and two achromatic thin lens with a focal length of 300 mm are used to suppress the pulse broadening effect. Then the generated femtosecond vector field is normally focused on the silicon wafer in air by a focusing system composed of three lenses (L1, L2 and L3 with a focal length of 60 mm) and a spatial filter (A). A polished 10×10×0.45 mm3 p-type single-crystalline Si (100) wafer sample is vertically attached on the XYZ translation stage to prevent the deposition of the laser-induced ejected missiles on the Si surface as much as possible. The irradiated pulse number are controlled by an electromechanical shutter. The morphology of the processed surface is observed by a scanning electron microscopy (Shimadzu Co. SS550).

Fig. 1 Experimental schematic for fabricating the subwavelength microstructures by femtosecond vector fields. M1 and M2: broadband high-reflection mirrors.

By using the technique we presented in Ref. [3

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]

], we generate locally linearly polarized femtosecond vector fields with different integer topological charges m and the same radius a = 5 mm. Even though we resort to the method suppressing the dispersion, the duration of the pulses striking the silicon wafer is measured to be ∼70 fs broader than 35 fs of the Ti:sapphire laser source.

The vector field E with angular midfrequency ω0 is incident on the input plane [with a polar coordinate system (ρ,φ)], which is located at the front focal plane of the focal lens. The silicon wafer is placed at the rear focal plane of the lens. The complex amplitude of the incident femtosecond vector field for the component E(ρ,φ;ω) or E(ρ,φω) of angular frequency ω is expressed in Jones Matrix as
[UρUφ]=[cos(δφ)sin(δφ)]E(ρ,φ;Δω),
(1)
where Δω = ωω0 and δ = +φ0 (where m is the topological charge and φ0 is the initial phase). Based on the Huygens-Fresnel principle, the intensity distribution in the output plane attached to the polar coordinate system (r,ϕ) with a distance z behind the lens is given by [29

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

]
I(r,ϕ,z)=|U(r,ϕ,z)|2|+E(r,ϕ;Δω)h(r,ϕ,z;Δω)ejΔωtdΔω|2
(2)
where U(r,ϕ,z) is the complex amplitude of the field on the (r,ϕ) plane, h(r,ϕ,zω) is the responding amplitude point-spread function. On the basis of the Nyquist sampling theorem, the deterioration of the focused intensity distribution tends to rapid below a critical pulse duration of τ = λ0/2c = π/ω0 (c is the speed of light in vacuum). For the generated femtosecond vector field, 70 fs ≫ τ = 1.34 fs and ω0 ≫ Δω (implying k(ω) ≈ k(ω0) = k0) [30

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]

], when ignoring the spherical and chromatic aberration and apart from an unimportant constant factor, h(r,ϕ,zω) can be written as
h(r,ϕ,z;Δω)0aexp[jk0ρ22(1fzf2)]Jm(k0ρrf)ρdρ,
(3)
where k0 = ω0/c, Jm(·) denotes the Bessel function of the first kind of the mth order.

Here we focus on the locally linearly polarized femtosecond vector fields with the azimuthally varying polarization direction (which implies δ = + φ0). As the left columns shown in Figs. 24 below, the intensity distribution of the focused vector field exhibit the doughnut shape except for m = 0 and the radius increases as the topological charge m enlarges. In particular, the intensity distributions are irrelevant to the initial phase φ0, while the polarizations are dependent of φ0. Under the paraxial condition, despite that the intensity distribution of the focused vector field is completely different from that of the incident vector fields, the spatial polarization distribution in the cross section of the focal plane are the same as that of the incident vector fields. As mentioned above, the vector field with nonzero m is always focused into a doughnut shape instead of a spot, so the size characteristic of the focused vector field incident on the silicon wafer are defined by two parameters R and ΔR. R is the radius of the brightest ring in the doughnut and ΔR is the full width at half-maximum (FWHM) of the doughnut along the radial direction. Thus the average laser fluence F is given by F = ɛ/(2πRΔR), where ɛ is the energy of the focused vector field incident on the silicon wafer. In our experiment, for the focused vector fields with m = ±1 (±2), we have R = 7.08 (9.48) μm and ΔR = 6.80 (6.10) μm, respectively.

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 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 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).

When the focused femtosecond vector field irradiates on the surface of the silicon wafer, the light absorption plays a pivotal role in the formation of the morphology of the material surface [15

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

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]

, 23

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]

]. When the laser fluence is beyond the ablation threshold of material, the microstructure will be formed at the surface, in which the ripples are perpendicular to the polarization direction of the irradiated light. Figures 24 show the laser-induced microstructures irradiated by the femtosecond vector field with the different topological charges m and the initial phases φ0. In all the cases, the number of the irradiated pulses is 100 shots and changing the incident laser energy keeps the average laser fluence at a level of F = 0.26 J/cm2 (for different vector fields) that is slightly higher than the ablation threshold of the silicon at 0.2 J/cm2 [20

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

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]

].

Figure 2 shows the situation when the silicon wafer is irradiated by the femtosecond vector fields with the topological charge m = 1 and the initial phases of φ0 = 0 and φ0 = π/2. Figures 2(a) and 2(d) depict the intensity and polarization distributions of the focused femtosecond radially-polarized (m = 1,φ0 = 0) and azimuthally-polarized (m = 1,φ0 = π/2) fields, respectively. Figures 2(b) and 2(e) are the SEM images of the ripple microstructure at the Si surface, induced by the above two vector fields, which exhibit the equal-interval concentric ring structure and the radial-shaped structure, respectively. The fabricated surface topographies are very similar to the structures reported in Ref. [28

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]

].

Figure 3 furnishes the situation when the silicon wafer is irradiated by the femtosecond vector fields with the topological charge m = −1 and the initial phases of φ0 = 0 and φ0 = π/2. The intensity and polarization distributions are given in Figs. 3(a) and 3(d), for φ0 = 0 and φ0 = π/2, respectively. Figures 3(b) and 3(e) are the corresponding SEM images of the microstructures induced by the above vector fields. One can see that the morphologies of the ripples in the two microstructures seem to be composed of a series of curves x2y2 = C in Fig. 3(b) and xy = C in Fig. 3(e) (where C is a series of discrete constants). In particular, compared Fig. 3(d) with Fig. 3(a), it can be seen that the polarization distribution in Fig. 3(d) is the same as that when Fig. 3(a) is rotated by an angle (n ± 1/4)π, where n is an integer. Correspondingly, the microstructure shown in Fig. 3(e) is the same as that when Fig. 3(b) is rotated by an angle (n ± 1/4)π.

Figure 4 gives the microstructures induced by the femtosecond vector fields with the topological change of m = 2 for the two initial phases of φ0 = 0 and π/2. The intensity and polarization distributions are depicted in Figs. 4(a) and 4(d), for φ0 = 0 and π/2, respectively.The polarization distributions exhibit the electrical-line-like shapes. Compared Fig. 4(d) with Fig. 4(a), the polarization distribution in Fig. 4(d) is the same as that when Fig. 4(a) is rotated by an angle (n + 1/2)π. Correspondingly, as the SEM images shown in Figs. 4(b) and 4(e), if the microstructure [Fig. 4(b)] induced by the femtosecond vector field with φ0 = 0 is rotated by an angle (n+1/2)π, the rotated microstructure is the same as that induced by the vector field with φ0 = π/2.

We should emphasize that in all the situations the ripples induced by the femtosecond vector fields are perpendicular to the locally linearly-polarized directions. In addition, in all the situations there have no obvious topography due to the very lower fluence in the central regions of the microstructure induced by the femtosecond vector fields, in which there are a lot of plume-like nanoparticles, as the magnified SEM image of the central regions shown in Figs. 2(c), 2(f), 3(c), 3(f), 4(c), and 4(f).

We have successfully fabricated 2D complicated microstructures by the femtosecond vector fields. We have measured the interval between the two neighbor ripples in the fabricated microstructures to be within a range of 670–690 nm. The depths of the ablated microstructures have a limited value of 300 nm under the irradiation condition of the 100 pulses. In particular, the interval is independent of both the initial phase and the topological charge of the femtosecond vector field. However, the topological charge and the initial phase could only influence the topography of the microstructures. As a result, the more complicated microstructures can be fabricated provided that the femtosecond vector field with the arbitrary polarization distribution can be generated. The microstructures at the silicon surface, induced by the femtosecond vector fields, are subwavelength. In order to further explore the complicated microstructures formed on the silicon wafer induced by the femtosecond vector light field, we have repeated the experiments on n-type single-crystalline Si (111) wafers and we obtained similar microstructures.

In conclusion, we have experimentally obtained the complicated subwavelength microstructures induced by the femtosecond vector field. The p-type (100) silicon wafer was irradiated by the femtosecond vector field with different topological charges and initial phases, under a repetition rate of 1 kHz and a central wavelength of 806 nm, to fabricate complicated 2D microstructures. In all the situations, the ripples of the microstructures are orientated to be perpendicular to the polarization direction of the femtosecond vector fields and have the interval to be around 670–690 nm smaller than the laser wavelength. The femtosecond vector fields can be applied to fabricate microstructures on the surfaces of the other materials. In particular, the designable spatial structure of polarization of the femtosecond vector light field can manipulate the fabricated microstructure.

Acknowledgments

This work is supported by the National Basic Research Program (973 Program) of China under Grant No. 2012CB921900 and the National Natural Science Foundation of China under Grant No. 10934003.

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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]

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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.

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16.

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17.

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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]

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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]

OCIS Codes
(190.4180) Nonlinear optics : Multiphoton processes
(260.5430) Physical optics : Polarization
(320.2250) Ultrafast optics : Femtosecond phenomena
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Laser Microfabrication

History
Original Manuscript: October 28, 2011
Revised Manuscript: November 23, 2011
Manuscript Accepted: November 23, 2011
Published: December 19, 2011

Citation
Kai Lou, Sheng-Xia Qian, Xi-Lin Wang, Yongnan Li, Bing Gu, Chenghou Tu, and Hui-Tian Wang, "Two-dimensional microstructures induced by femtosecond vector light fields on silicon," Opt. Express 20, 120-127 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-120


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References

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