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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 23 — Nov. 5, 2012
  • pp: 25826–25833
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Control of periodic ripples growth on metals by femtosecond laser ellipticity

Yanfu Tang, Jianjun Yang, Bo Zhao, Mingwei Wang, and Xiaonong Zhu  »View Author Affiliations


Optics Express, Vol. 20, Issue 23, pp. 25826-25833 (2012)
http://dx.doi.org/10.1364/OE.20.025826


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Abstract

Formation of the periodic ripples on metallic surfaces is investigated comprehensively using variable ellipticities of femtosecond lasers. Compared with the linearly polarized incidence, the well defined grating-like ripple structures rather than the uniform arrays of nanoparticle can always be obtained for the elliptical polarization lasers. The ripple orientation is slanted clockwise or anticlockwise depending on the laser helicity but always display a maximum angle of 45°. Theoretical analyses indicate that no circular polarization is achieved for femtosecond lasers passing through quarter waveplate, and the induced ripple orientation is determined by the major axis of the polarization ellipse. The simulation results agree well with the experimental observations.

© 2012 OSA

1.Introduction

Recently, many researchers have attempted to investigate the formation of surface structures with different polarization of femtosecond lasers. For example, Varlamova et al. studied the influence of variable laser polarizations of incidence on ceramics like CaF2 and MgF2through multi-shot irradiation method [22

22. J. Reif, O. Varlamova, and F. Costache, “Femtosecond laser induced nanostructure formation: self-organization control parameters,” Appl. Phys., A Mater. Sci. Process. 92(4), 1019–1024 (2008). [CrossRef]

, 23

23. Y. Dong and P. Molian, “Coulomb explosion-induced formation of highly oriented nanoparticles on thin films of 3C–SiC by the femtosecond pulsed laser,” Appl. Phys. Lett. 84(1), 10–12 (2004). [CrossRef]

], and found that different ripple orientations could be created with elliptically polarized femtosecond lasers, but for circular polarization, arrays of spherical nanoparticles began to appear on the material surfaces. They argued that in the latter case no distinguished field direction could be imposed. Furthermore, such a phenomenon of nano-dots formation by the circularly polarized lasers was also reported on other ceramic materials (such as SiC, ZnSe and ZnO) owing to Coulomb explosion process [24

24. J. Zhong, G. Guo, J. Yang, N. Ma, G. Ye, X. Guo, R. Li, and H. Ma, “Femtosecond pulse laser-induced self-organized nanostructures on the surface of ZnO crystal,” Chin. Phys. B 17(4), 1223–1226 (2008). [CrossRef]

26

26. Q. Z. Zhao, S. Malzer, and L. J. Wang, “Formation of subwavelength periodic structures on tungsten induced by ultrashort laser pulses,” Opt. Lett. 32(13), 1932–1934 (2007). [CrossRef] [PubMed]

]. However, in contrast to the aforementioned observations, Zhao et al. recently pointed out that the regular ripple structures could still be produced on the metal surface even under the irradiation of circularly polarized femtosecond lasers, but the ripple orientation seemed to slant by 45° with respect to the linear polarization case [27

27. J. Wang and C. Guo, “Permanent recording of light helicity on optically inactive metal surfaces,” Opt. Lett. 31(24), 3641–3643 (2006). [CrossRef] [PubMed]

]. In addition, the slantwise oriented ripple formation by circularly polarized femtosecond lasers has been also evidenced on other metals and semiconductors [28

28. J. Yang, R. Wang, W. Liu, Y. Sun, and X. Zhu, “Investigation of microstructuring CuInGaSe2 thin films with ultrashort laser pulses,” J. Phys. D 42(21), 215305 (2009). [CrossRef]

, 29

29. M. Emam-Ismail, “Retardation calculation for achromatic and apochromatic quarter and half wave plates of gypsum based birefringent crystal,” Opt. Commun. 283(22), 4536–4540 (2010). [CrossRef]

]. In spite of these observations, until present no convincing relevant explanations have been achieved, but which it is very important and interesting to understand the ripple formation physics.

In this paper we present new insights into the ripple formation on metallic materials such as W and Cu by irradiating variable elliptical polarization of 800 nm femtosecond lasers. Firstly we demonstrate evolvement properties of the ripple orientation with varying laser ellipticities in experiment, and the regular rippling structures are shown to grow on the metal surfaces irrespective to the rotation of quarter waveplate (QWP). Theoretical analyses reveal that circular polarization state cannot be obtained through QWP for the incident broad bandwidth of femtosecond lasers, and the ripple orientation is eventually defined by the interference between the major axis of polarization ellipse and excited surface plasmon polaritons.

2. Experimental descriptions

A Ti: sapphire femtosecond laser amplifier system (Spectra Physics HP-Spitfire 50) based on the chirped-pulse-amplification technique was employed as a light source in our experiments, which delivers the linearly polarized pulse trains at the repetition rate of 1 kHz, centered at the wavelength of 800 nm with the pulse time duration of 50 fs. The linear polarization direction of the lasers was checked using a Glan prism. A quartz material based zero-order QWP was inserted into the beam path to transfer the laser polarization into variable elliptical states. Upon rotation of QWP, its azimuth angle θ between the optical axis and the original laser polarization was varied, resulting in different laser polarization ellipticities. The samples were two different metallic plates (Cu, W) with optical polished surfaces, which were mounted on a motorized x-y-z translation stage (New Port UTM100 PPE1) with a resolution of 1 μm. The laser beam was normally focused through a microscopic objective (4 × , N.A = 0.1), and the estimated laser spot size on the sample surfaces was about 60 μm (Gaussian beam diameter at 1/e2). Under the fixed irradiation of femtosecond lasers, the line scribing method was performed at a sample moving speed of 0.2 mm/s parallel to the original laser polarization direction. A schematic diagram of our experimental setup is shown in Fig. 1
Fig. 1 A schematic diagram of the experimental setup.
. Laser energy was adjusted by a neutral-density filter and measured before the objective. All experiments were carried out in ambient air in a Class 1000 clean room. After irradiation, the samples were cleaned ultrasonically with acetone. The morphological evolvement of the laser-exposed surfaces was examined by means of scanning electronic microscope (SEM, Hitachi S-4800).

3. Results and discussion

First, at the azimuth angle of θ = 0°, i.e., the slow axis of QWP is aligned with the original linear polarization of femtosecond lasers, experiments revealed that the periodic ripples were formed on the sample surfaces, accompanying the structure orientation perpendicular to the laser polarization direction. In this case, a typical result obtained on copper surface at the laser fluence of about F = 1.4 J/cm2 is shown in Fig. 2
Fig. 2 SEM image of the periodic ripples formed on Cu surface with linearly polarized femtosecond lasers. The bi-directional arrows represent both the sample translation and the laser polarization directions.
, where the zoom picture indicates that the induced ripple structures consist of an array of groove patterns with the period of Λ≈600 nm. As can be seen, such subwavelength ripples are spatially arranged perpendicular to the direction of an incidence electric field. Moreover, a mass of nanoparticles at hundred-nanometer scale were also produced to cover up the groove ridges. For the sake of convenient study, this kind of ripple alignment direction can be marked as a reference, which is applied throughout the paper.

4. Theoretical analyses

In our experiment, the quartz material based QWP has a thickness of d = 28 μm, and its wavelength dependent phase retardation can be calculated by φ(λ)=2πdλ(Δ0+Δ1λ+Δ2λ2) (with Δ0 = 0.011945, Δ1 = −0.008214 and Δ2 = 0.005714) [32

32. A. M. Bonch-Bruevich, M. N. Libenson, V. S. Makin, and V. V. Trubaev, “Surface electromagnetic waves in optics,” Opt. Eng. 31(4), 718–730 (1992). [CrossRef]

]. If g(λ) represents the spectral distribution function of the incident femtosecond lasers, the following equation can be obtained:
cosφ=0g(λ)cosφ(λ)dλ0g(λ)dλ
(3)
This form can be considered as average phase retardation for the wide spectral femtosecond lasers. When the experimentally measured bandwidth (full-width half-magnitude) of 30 nm for femtosecond lasers was adopted, we can getcosφ=0.8, which indicates that the phase retardation of φ = π/2 cannot be taken for femtosecond lasers. Moreover, if the elliptical degree ε is introduced (where ε = 0 corresponds to linear polarization and ε = 1 corresponds to circular polarization), we can obtain relationship between the polarization ellipticity and the azimuth angle of QWP, as shown in Fig. 4
Fig. 4 Calculated polarization ellipticity as a function of the rotation angle of QWP for the incident femtosecond laser with different spectrum widths.
. Clearly, we can find that the obtained polarization ellipticity of femtosecond lasers is less than unity even at the angle of θ = 45°, or circularly polarized femtosecond lasers are in fact never achieved through rotating QWP. The broader the femtosecond laser spectrum, the induced polarization ellipticity becomes the smaller.

Figure 5
Fig. 5 Sketched evolution of the polarization state for the femtosecond lasers passing through QWP with variable rotation angles.
sketches evolvement of available polarization for femtosecond lasers when the optic axis of QWP is gradually rotated. If the field amplitude of incident linearly polarized lasers is denoted by A, the two field components in QWP will have amplitudes ofAx=Acosθ andAx=Asinθ, respectively, Within a range θ(0o,45o), Ax>Ayis fulfilled. According to Eq. (2), the major axis of the polarization ellipse (determined by both θ and φ) will move clockwise away from the original linear polarization direction. When the two amplitudes become equalAx=Ay atθ=45o, the angular position of the major axis becomesα=45o. In the case of θ(45o,90o), sinceAx<Ayis obtained, the angular value of αwill be reduced, which implies that the major axis of the polarization ellipse moves back towards the original linear polarization. Atθ=90o, the linear polarization of femtosecond lasers can be generated owing to no birefringence. On the other hand, when QWP rotation goes into a new range of θ(90o,180o), the major axis of the polarization ellipse can also display the waggling movement behaviors, but at this time their angular positions appear to be mirror symmetric to the above phenomena, which is due to the larger azimuth angle θ and the reverse-ordered alternative increment of two field amplitudes. This result physically indicates that the elliptical laser polarization undergoes transitions between the left and the right helicities, so that the observed slantwise orientation of ripples turns from the clockwise to the counterclockwise directions.

According to the physical model of ripple formation [6

6. J. Bonse, M. Munz, and H. Sturm, “Structure formation on the surface of indium phosphide irradiated by femtosecond laser pulses,” J. Appl. Phys. 97(1), 013538 (2005). [CrossRef]

, 7

7. G. Miyaji and K. Miyazaki, “Origin of periodicity in nanostructuring on thin film surfaces ablated with femtosecond laser pulses,” Opt. Express 16(20), 16265–16271 (2008). [CrossRef] [PubMed]

, 18

18. J. Wang and C. Guo, “Formation of extraordinarily uniform periodic structures on metals induced by femtosecond laser pulses,” J. Appl. Phys. 100(2), 023511 (2006). [CrossRef]

, 31

31. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge, 1999).

], the ripple orientation results from the optical interference between the incident light and surface plasmon excitation. For the elliptically polarized femtosecond laser irradiation, the effective wave vector of the incident laser is determined by the major axis of the polarization ellipse; thus, the direction of ripple arrangement will be perpendicular to the major axis of the laser ellipse, and of course the ripple orientation is deemed to change in phase. Based on the above discussion, we can simulate variations of the ripple orientation as a function of the rotation angle of QWP, as shown by the solid curves in Figs. 3(b)-(c). Undoubtedly, our simulation results are in consistent with the experimental data, which can confirm the validity of our theory.

5. Conclusions

We have performed a detailed study of how femtosecond lasers passing through QWP affect the ripple formation especially on metal surfaces. Experimental results have revealed that the grating-like ripple structures can always appear on metals no matter whatever rotation angle of QWP. Slantwise orientation of the ripples associated with the maximum angle of ± 45° has been evidenced to oscillate in either clockwise or anticlockwise direction depending on the laser helicity property. Theoretical analyses suggested that dispersion properties of QWP substantially lead to no generation of circular polarization for femtosecond laser incidence. The obtained polarization ellipticity is reduced with increasing femtosecond laser bandwidth. The major axis of the polarization ellipse, being as an effective wave vector of the laser, has been confirmed to be responsible for the ripple alignment. This investigation will be helpful to control the nanostructures formation on metals.

Acknowledgments

The authors would like to thank C. Liang and H. Wang for assisting in SEM inspections. This work was supported by the National Natural Science Foundation of China (Grant No.10874092), by the Tianjin Natural Science Foundation (Grant Nos. 10JCZDGX35100, 12JCZDJC20200), and by the Open Fund of the State Key Laboratory of High Field Laser Physics (Shanghai Institute of Optics and Fine Mechanics).

References and links

1.

M. Birnbaum, “Semiconductor Surface Damage Produced by Ruby Lasers,” J. Appl. Phys. 36(11), 3688–3689 (1965). [CrossRef]

2.

T. Hwang and C. Guo, “Angular effects of nanostructure-covered femtosecond laser induced periodic surface structures on metals,” J. Appl. Phys. 108(7), 073523 (2010). [CrossRef]

3.

Y. Yang, J. Yang, L. Xue, and Y. Guo, “Surface patterning on periodicity of femtosecond laser-induced ripples,” Appl. Phys. Lett. 97(14), 141101 (2010). [CrossRef]

4.

A. J. Huis in’t Veld, and J. van de Veer, “Initiation of femtosecond laser machined ripples in steel observed by scanning helium ion microscopy (SHIM),” in Proceeding on Laser Precision Microfabrication (LPM), Japan (2009).

5.

J. Colombier, F. Garrelie, N. Faure, S. Reynaud, M. Bounhalli, E. Audouard, R. Stoian, and F. Pigeon, “Effects of electron-phonon coupling and electron diffusion on ripples growth on ultrafast-laser-irradiated metals,” J. Appl. Phys. 111(2), 024902 (2012). [CrossRef]

6.

J. Bonse, M. Munz, and H. Sturm, “Structure formation on the surface of indium phosphide irradiated by femtosecond laser pulses,” J. Appl. Phys. 97(1), 013538 (2005). [CrossRef]

7.

G. Miyaji and K. Miyazaki, “Origin of periodicity in nanostructuring on thin film surfaces ablated with femtosecond laser pulses,” Opt. Express 16(20), 16265–16271 (2008). [CrossRef] [PubMed]

8.

J. Reif, F. Costache, M. Henyk, and S. V. Pandelov, “Ripples revisited: non-classical morphology at the bottom of femtosecond laser ablation craters in transparent dielectrics,” Appl. Surf. Sci. 197-198, 891–895 (2002). [CrossRef]

9.

A. Borowiec and H. Haugen, “Subwavelength ripple formation on the surfaces of compound semiconductors irradiated with femtosecond laser pulses,” Appl. Phys. Lett. 82(25), 4462–4464 (2003). [CrossRef]

10.

T. Q. Jia, H. X. Chen, M. Huang, F. L. Zhao, J. R. Qiu, R. X. Li, Z. Z. Xu, X. K. He, J. Zhang, and H. Kuroda, “Formation of nanogratings on the surface of a ZnSe crystal irradiated by femtosecond laser pulses,” Phys. Rev. B 72(12), 125429 (2005). [CrossRef]

11.

J. Bonse and J. Krüger, J. “Pulse number dependence of laser-induced periodic surface structures for femtosecond laser irradiation of silicon,” Appl. Phys. (Berl.) 108, 034903 (2010).

12.

T. Tomita, K. Kinoshita, S. Matsuo, and S. Hashimoto, “Effect of surface roughening on femtosecond laser-induced ripple structures,” Appl. Phys. Lett. 90(15), 153115 (2007). [CrossRef]

13.

L. Xue, J. Yang, Y. Yang, Y. Wang, and X. Zhu, “Creation of periodic subwavelength ripples on tungsten surface by ultrashort laser pulses,” Appl. Phys. A (to be published). http://www.springerlink.com/content/h521l75956w57186/.

14.

P. M. Fauchet and A. E. Siegman, “Surface ripples on silicon and gallium arsenide under picosecond laser illumination,” Appl. Phys. Lett. 40(9), 824–826 (1982). [CrossRef]

15.

G. Miyaji, K. Miyazaki, K. Zhang, T. Yoshifuji, and J. Fujita, “Mechanism of femtosecond-laser-induced periodic nanostructure formation on crystalline silicon surface immersed in water,” Opt. Express 20(14), 14848–14856 (2012). [CrossRef] [PubMed]

16.

R. Le Harzic, H. Schuck, D. Sauer, T. Anhut, I. Riemann, and K. König, “Sub-100 nm nanostructuring of silicon by ultrashort laser pulses,” Opt. Express 13(17), 6651–6656 (2005). [CrossRef] [PubMed]

17.

M. Huang, F. L. Zhao, Y. Cheng, N. S. Xu, and Z. Z. Xu, “Mechanisms of ultrafast laser-induced deep-subwavelength gratings on graphite and diamond,” Phys. Rev. B 79(12), 125436 (2009). [CrossRef]

18.

J. Wang and C. Guo, “Formation of extraordinarily uniform periodic structures on metals induced by femtosecond laser pulses,” J. Appl. Phys. 100(2), 023511 (2006). [CrossRef]

19.

J. F. Young, J. S. Preston, H. M. van Driel, and J. E. Sipe, “Laser-induced periodic surface structure. II. Experiments on Ge, Si, Al, and brass,” Phys. Rev. B 27(2), 1155–1172 (1983). [CrossRef]

20.

S. E. Clark and D. C. Emmony, “Ultraviolet-laser-induced periodic surface structures,” Phys. Rev. B Condens. Matter 40(4), 2031–2041 (1989). [CrossRef] [PubMed]

21.

F. Keilmann and Y. H. Bai, “Periodic surface structures frozen into CO2 laser-melted quartz,” Appl. Surf. Sci. 253, 7932–7936 (2007).

22.

J. Reif, O. Varlamova, and F. Costache, “Femtosecond laser induced nanostructure formation: self-organization control parameters,” Appl. Phys., A Mater. Sci. Process. 92(4), 1019–1024 (2008). [CrossRef]

23.

Y. Dong and P. Molian, “Coulomb explosion-induced formation of highly oriented nanoparticles on thin films of 3C–SiC by the femtosecond pulsed laser,” Appl. Phys. Lett. 84(1), 10–12 (2004). [CrossRef]

24.

J. Zhong, G. Guo, J. Yang, N. Ma, G. Ye, X. Guo, R. Li, and H. Ma, “Femtosecond pulse laser-induced self-organized nanostructures on the surface of ZnO crystal,” Chin. Phys. B 17(4), 1223–1226 (2008). [CrossRef]

25.

H. Ma, Y. Guo, M. Zhong, and R. Li, “Femtosecond pulse laser-induced self-organized nanogratings on the surface of a ZnSe crystal,” Appl. Phys., A Mater. Sci. Process. 89(3), 707–709 (2007). [CrossRef]

26.

Q. Z. Zhao, S. Malzer, and L. J. Wang, “Formation of subwavelength periodic structures on tungsten induced by ultrashort laser pulses,” Opt. Lett. 32(13), 1932–1934 (2007). [CrossRef] [PubMed]

27.

J. Wang and C. Guo, “Permanent recording of light helicity on optically inactive metal surfaces,” Opt. Lett. 31(24), 3641–3643 (2006). [CrossRef] [PubMed]

28.

J. Yang, R. Wang, W. Liu, Y. Sun, and X. Zhu, “Investigation of microstructuring CuInGaSe2 thin films with ultrashort laser pulses,” J. Phys. D 42(21), 215305 (2009). [CrossRef]

29.

M. Emam-Ismail, “Retardation calculation for achromatic and apochromatic quarter and half wave plates of gypsum based birefringent crystal,” Opt. Commun. 283(22), 4536–4540 (2010). [CrossRef]

30.

J. K. Chen, J. E. Beraun, L. E. Grimes, and D. Y. Tzou, “Modeling of femtosecond laser-induced non-equilibrium deformation in metal films,” Int. J. Solids Struct. 39(12), 3199–3216 (2002). [CrossRef]

31.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge, 1999).

32.

A. M. Bonch-Bruevich, M. N. Libenson, V. S. Makin, and V. V. Trubaev, “Surface electromagnetic waves in optics,” Opt. Eng. 31(4), 718–730 (1992). [CrossRef]

OCIS Codes
(140.3390) Lasers and laser optics : Laser materials processing
(220.4000) Optical design and fabrication : Microstructure fabrication
(260.5430) Physical optics : Polarization
(320.2250) Ultrafast optics : Femtosecond phenomena

ToC Category:
Laser Microfabrication

History
Original Manuscript: September 4, 2012
Revised Manuscript: October 18, 2012
Manuscript Accepted: October 24, 2012
Published: November 1, 2012

Citation
Yanfu Tang, Jianjun Yang, Bo Zhao, Mingwei Wang, and Xiaonong Zhu, "Control of periodic ripples growth on metals by femtosecond laser ellipticity," Opt. Express 20, 25826-25833 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-23-25826


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References

  1. M. Birnbaum, “Semiconductor Surface Damage Produced by Ruby Lasers,” J. Appl. Phys.36(11), 3688–3689 (1965). [CrossRef]
  2. T. Hwang and C. Guo, “Angular effects of nanostructure-covered femtosecond laser induced periodic surface structures on metals,” J. Appl. Phys.108(7), 073523 (2010). [CrossRef]
  3. Y. Yang, J. Yang, L. Xue, and Y. Guo, “Surface patterning on periodicity of femtosecond laser-induced ripples,” Appl. Phys. Lett.97(14), 141101 (2010). [CrossRef]
  4. A. J. Huis in’t Veld, and J. van de Veer, “Initiation of femtosecond laser machined ripples in steel observed by scanning helium ion microscopy (SHIM),” in Proceeding on Laser Precision Microfabrication (LPM), Japan (2009).
  5. J. Colombier, F. Garrelie, N. Faure, S. Reynaud, M. Bounhalli, E. Audouard, R. Stoian, and F. Pigeon, “Effects of electron-phonon coupling and electron diffusion on ripples growth on ultrafast-laser-irradiated metals,” J. Appl. Phys.111(2), 024902 (2012). [CrossRef]
  6. J. Bonse, M. Munz, and H. Sturm, “Structure formation on the surface of indium phosphide irradiated by femtosecond laser pulses,” J. Appl. Phys.97(1), 013538 (2005). [CrossRef]
  7. G. Miyaji and K. Miyazaki, “Origin of periodicity in nanostructuring on thin film surfaces ablated with femtosecond laser pulses,” Opt. Express16(20), 16265–16271 (2008). [CrossRef] [PubMed]
  8. J. Reif, F. Costache, M. Henyk, and S. V. Pandelov, “Ripples revisited: non-classical morphology at the bottom of femtosecond laser ablation craters in transparent dielectrics,” Appl. Surf. Sci.197-198, 891–895 (2002). [CrossRef]
  9. A. Borowiec and H. Haugen, “Subwavelength ripple formation on the surfaces of compound semiconductors irradiated with femtosecond laser pulses,” Appl. Phys. Lett.82(25), 4462–4464 (2003). [CrossRef]
  10. T. Q. Jia, H. X. Chen, M. Huang, F. L. Zhao, J. R. Qiu, R. X. Li, Z. Z. Xu, X. K. He, J. Zhang, and H. Kuroda, “Formation of nanogratings on the surface of a ZnSe crystal irradiated by femtosecond laser pulses,” Phys. Rev. B72(12), 125429 (2005). [CrossRef]
  11. J. Bonse and J. Krüger, J. “Pulse number dependence of laser-induced periodic surface structures for femtosecond laser irradiation of silicon,” Appl. Phys. (Berl.)108, 034903 (2010).
  12. T. Tomita, K. Kinoshita, S. Matsuo, and S. Hashimoto, “Effect of surface roughening on femtosecond laser-induced ripple structures,” Appl. Phys. Lett.90(15), 153115 (2007). [CrossRef]
  13. L. Xue, J. Yang, Y. Yang, Y. Wang, and X. Zhu, “Creation of periodic subwavelength ripples on tungsten surface by ultrashort laser pulses,” Appl. Phys. A (to be published). http://www.springerlink.com/content/h521l75956w57186/ .
  14. P. M. Fauchet and A. E. Siegman, “Surface ripples on silicon and gallium arsenide under picosecond laser illumination,” Appl. Phys. Lett.40(9), 824–826 (1982). [CrossRef]
  15. G. Miyaji, K. Miyazaki, K. Zhang, T. Yoshifuji, and J. Fujita, “Mechanism of femtosecond-laser-induced periodic nanostructure formation on crystalline silicon surface immersed in water,” Opt. Express20(14), 14848–14856 (2012). [CrossRef] [PubMed]
  16. R. Le Harzic, H. Schuck, D. Sauer, T. Anhut, I. Riemann, and K. König, “Sub-100 nm nanostructuring of silicon by ultrashort laser pulses,” Opt. Express13(17), 6651–6656 (2005). [CrossRef] [PubMed]
  17. M. Huang, F. L. Zhao, Y. Cheng, N. S. Xu, and Z. Z. Xu, “Mechanisms of ultrafast laser-induced deep-subwavelength gratings on graphite and diamond,” Phys. Rev. B79(12), 125436 (2009). [CrossRef]
  18. J. Wang and C. Guo, “Formation of extraordinarily uniform periodic structures on metals induced by femtosecond laser pulses,” J. Appl. Phys.100(2), 023511 (2006). [CrossRef]
  19. J. F. Young, J. S. Preston, H. M. van Driel, and J. E. Sipe, “Laser-induced periodic surface structure. II. Experiments on Ge, Si, Al, and brass,” Phys. Rev. B27(2), 1155–1172 (1983). [CrossRef]
  20. S. E. Clark and D. C. Emmony, “Ultraviolet-laser-induced periodic surface structures,” Phys. Rev. B Condens. Matter40(4), 2031–2041 (1989). [CrossRef] [PubMed]
  21. F. Keilmann and Y. H. Bai, “Periodic surface structures frozen into CO2 laser-melted quartz,” Appl. Surf. Sci.253, 7932–7936 (2007).
  22. J. Reif, O. Varlamova, and F. Costache, “Femtosecond laser induced nanostructure formation: self-organization control parameters,” Appl. Phys., A Mater. Sci. Process.92(4), 1019–1024 (2008). [CrossRef]
  23. Y. Dong and P. Molian, “Coulomb explosion-induced formation of highly oriented nanoparticles on thin films of 3C–SiC by the femtosecond pulsed laser,” Appl. Phys. Lett.84(1), 10–12 (2004). [CrossRef]
  24. J. Zhong, G. Guo, J. Yang, N. Ma, G. Ye, X. Guo, R. Li, and H. Ma, “Femtosecond pulse laser-induced self-organized nanostructures on the surface of ZnO crystal,” Chin. Phys. B17(4), 1223–1226 (2008). [CrossRef]
  25. H. Ma, Y. Guo, M. Zhong, and R. Li, “Femtosecond pulse laser-induced self-organized nanogratings on the surface of a ZnSe crystal,” Appl. Phys., A Mater. Sci. Process.89(3), 707–709 (2007). [CrossRef]
  26. Q. Z. Zhao, S. Malzer, and L. J. Wang, “Formation of subwavelength periodic structures on tungsten induced by ultrashort laser pulses,” Opt. Lett.32(13), 1932–1934 (2007). [CrossRef] [PubMed]
  27. J. Wang and C. Guo, “Permanent recording of light helicity on optically inactive metal surfaces,” Opt. Lett.31(24), 3641–3643 (2006). [CrossRef] [PubMed]
  28. J. Yang, R. Wang, W. Liu, Y. Sun, and X. Zhu, “Investigation of microstructuring CuInGaSe2 thin films with ultrashort laser pulses,” J. Phys. D42(21), 215305 (2009). [CrossRef]
  29. M. Emam-Ismail, “Retardation calculation for achromatic and apochromatic quarter and half wave plates of gypsum based birefringent crystal,” Opt. Commun.283(22), 4536–4540 (2010). [CrossRef]
  30. J. K. Chen, J. E. Beraun, L. E. Grimes, and D. Y. Tzou, “Modeling of femtosecond laser-induced non-equilibrium deformation in metal films,” Int. J. Solids Struct.39(12), 3199–3216 (2002). [CrossRef]
  31. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge, 1999).
  32. A. M. Bonch-Bruevich, M. N. Libenson, V. S. Makin, and V. V. Trubaev, “Surface electromagnetic waves in optics,” Opt. Eng.31(4), 718–730 (1992). [CrossRef]

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