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 Optical Society of America

1.Introduction

Laser-induced periodic surface structures (LIPSSs), also called as ripples, have been intensively studied over nearly 40 years ever since the first discovery by Birnbaum on semiconductor surfaces [1]. A large number of previous reports have confirmed that this could be recognized as a general phenomenon of laser-matter interaction occurring at the low fluence around the ablation threshold, which has been already evidenced on very diverse materials: metals, semiconductors and dielectrics [210]. Generally, the obtained spatial period of the ripples closely depends on the material properties as well as the irradiation conditions such as the laser wavelength, the laser energy, the pulse duration, the pulse number, and the incident angle [2, 3, 1114]. In particular, the ripple period induced by femtosecond lasers can be reduced much less than the laser wavelength [3, 7, 1517]. On the other hand, for the linearly polarized laser incidence, the available ripple orientation can appear either perpendicular or parallel to the laser polarization depending on the incident energy [1821].

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, 23], 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 [2426]. 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]. In addition, the slantwise oriented ripple formation by circularly polarized femtosecond lasers has been also evidenced on other metals and semiconductors [28, 29]. 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 . 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).

 

Fig. 1 A schematic diagram of the experimental setup.

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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 , 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.

 

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.

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When QWP is gradually rotated in a clockwise direction, femtosecond lasers were ready to change into the elliptical polarization states. Then a series of experiments were performed to investigate their influences on the ripple formation processes, and the corresponding results are summarized in Fig. 3 (a) . As shown clearly, when the azimuth angle of QWP is increased monotonously from θ = 0° to 90°, the laser-induced ripples always appear the grating-like distributions but with the orientation slantwise in a clockwise direction. Moreover, during the variation of laser polarization, the obtained ripple period can remain almost unchanged. For instance, at the azimuth angle of θ = 30°, the slantwise angle of ripples orientation is about γ = 34°. In the case of θ = 45°, at which the so-called circular polarization is referred to obtain in many previous reports [23, 2628], the laser-induced surface structures cannot only maintain the period grating-like patterns but also posses a large slantwise orientation angle of about γ = 45°, which is much different from the pervious observations on ceramics [2226]. More interestingly, when the azimuth angle of QWP increased to θ = 60°, the slantwise orientation angle of the ripples surprisingly decreased down to about γ = 34° rather than keeping up to become large. In other words, although the laser-induced ripples were still obliquely oriented clockwise, the slantwise degree of ripples is reduced at this moment. This phenomenon suggests that a maximum angle in the ripple orientation slant should exist for the incidence of elliptically polarized femtosecond lasers. As a matter of fact, at the increased azimuth angle of θ = 90°, the ripple orientation began to turn almost parallel to the reference direction, or the slantwise orientation angle of ripples became zero, γ = 0°.

 

Fig. 3 (a) Evolvement of femtosecond laser-induced ripples on Cu with rotating QWP. At the upper left and right corners of each image the rotation angle of QWP and the obtained laser polarization are indicated, respectively. (b)-(c) Dependences of the slanting ripple orientation on the rotation angle of QWP for two different materials, where the measured data are represented by solid squares and the simulation results are indicated by the red curves.

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On the other hand, as the azimuth angle of QWP continued to increase larger than 90°, the ripple orientation induced by femtosecond lasers was observed to slant again; however, at this time the slantwise orientation became evidently in the counterclockwise direction. Very similar to the above situations, the azimuth angle dependence of the ripple orientation also shows periodic variations. For example, at θ = 120°, 135°, 150° and 180°, the measured slantwise orientation angle of the ripples was approximately γ = −32°, −45°, −30° and 0°, respectively. The maximum slantwise degree appeared at the azimuth angle of θ = 135°. Naturally, if the azimuth angle was further rotated beyond θ = 180°, the above mentioned phenomena would recur, namely, the laser-induced ripple orientation will first periodically slant in a clockwise direction and then in a counterclockwise direction. Anyway, no matter how QWP rotates, the slantwise angle of the ripple orientation was always confined into a range of ± 45°. The measured variation of the ripple orientation vs the QWP azimuth angle for Cu material is shown in Fig. 3(b). Actually, our experiment revealed that this phenomenon can also take place on other metallic materials like W, as shown in Fig. 3 (c). From the obtained results, we can realize some interesting things when comparing the structure formation behaviors on metal surfaces with those on dielectrics especially at the relatively low laser energy incidence: in the former case the material removal is related to the photomechanical effect [30], so that it mainly depends on the major field component of laser ellipse, while in the latter case Coulomb explosion becomes predominant and the material removal in two crossed directions could take place for the elliptical polarization [23]. On the other hand, our observations suggests that ripple formation on metals cannot be simply attributed to the self-organization theory. Moreover, as mentioned by Guo et al [27], the slanting ripple orientation behaviors on metal surfaces can also be used to record both polarization and helicity of the incident lasers.

4. Theoretical analyses

In the following, theoretical analyses are conducted on how the ripple orientation is slanted by the elliptically polarized femtosecond lasers. When the linear polarization of femtosecond lasers pass through QWP, polarization ellipse can be achieved through coupling of the two components due to the birefringence effect, which is described as [31]

Ex2Ax2+Ey2Ay22ExEyAxAycosφ=sin2φ
where ExandEyare the electric fields of two components with amplitudes ofAxandAy, respectively. φis the phase retardation between the two components. Therefore, the angular position of the major axis of the polarization ellipse,α, can be given by the following equation [31]:
1tg2αtgα=Ax2Ay2AxAycosϕ
Normally, for a given QWP, its supplied phase retardation of φ = π/2 is only for a particular wavelength. For the incidence of femtosecond lasers, however, the obtained phase retardation should also be related to the broad laser spectrum because of dispersion properties.

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]. 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
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 . 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.

 

Fig. 4 Calculated polarization ellipticity as a function of the rotation angle of QWP for the incident femtosecond laser with different spectrum widths.

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Figure 5 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.

 

Fig. 5 Sketched evolution of the polarization state for the femtosecond lasers passing through QWP with variable rotation angles.

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According to the physical model of ripple formation [6, 7, 18, 31], 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]  

References

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  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]

2012 (2)

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]

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]

2010 (4)

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]

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]

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).

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]

2009 (2)

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]

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]

2008 (3)

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]

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]

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]

2007 (4)

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]

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]

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

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]

2006 (2)

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

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]

2005 (3)

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]

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]

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]

2004 (1)

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]

2003 (1)

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]

2002 (2)

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]

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]

1992 (1)

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]

1989 (1)

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]

1983 (1)

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]

1982 (1)

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]

1965 (1)

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

Anhut, T.

Audouard, E.

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]

Bai, Y. H.

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

Beraun, J. E.

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]

Birnbaum, M.

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

Bonch-Bruevich, A. M.

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]

Bonse, J.

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).

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]

Borowiec, A.

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]

Bounhalli, M.

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]

Chen, H. X.

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]

Chen, J. K.

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]

Cheng, Y.

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]

Clark, S. E.

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]

Colombier, J.

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]

Costache, F.

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]

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]

Dong, Y.

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]

Emam-Ismail, M.

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]

Emmony, D. C.

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]

Fauchet, P. M.

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]

Faure, N.

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]

Fujita, J.

Garrelie, F.

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]

Grimes, L. E.

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]

Guo, C.

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]

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]

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

Guo, G.

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]

Guo, X.

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]

Guo, Y.

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]

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]

Hashimoto, S.

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]

Haugen, H.

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]

He, X. K.

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]

Henyk, M.

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]

Huang, M.

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]

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]

Hwang, T.

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]

Jia, T. Q.

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]

Keilmann, F.

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

Kinoshita, K.

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]

König, K.

Krüger, J.

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).

Kuroda, H.

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]

Le Harzic, R.

Li, R.

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]

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]

Li, R. X.

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]

Libenson, M. N.

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]

Liu, W.

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]

Ma, H.

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]

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]

Ma, N.

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]

Makin, V. S.

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]

Malzer, S.

Matsuo, S.

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]

Miyaji, G.

Miyazaki, K.

Molian, P.

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]

Munz, M.

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]

Pandelov, S. V.

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]

Pigeon, F.

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]

Preston, J. S.

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]

Qiu, J. R.

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]

Reif, J.

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]

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]

Reynaud, S.

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]

Riemann, I.

Sauer, D.

Schuck, H.

Siegman, A. E.

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]

Sipe, J. E.

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]

Stoian, R.

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]

Sturm, H.

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]

Sun, Y.

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]

Tomita, T.

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]

Trubaev, V. V.

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]

Tzou, D. Y.

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]

van Driel, H. M.

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]

Varlamova, O.

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]

Wang, J.

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]

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

Wang, L. J.

Wang, R.

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).
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[Crossref]

Xu, Z. Z.

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).
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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).
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Xue, L.

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).
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[Crossref]

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]

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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]

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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]

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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).
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Zhao, F. L.

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]

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]

Zhao, Q. Z.

Zhong, J.

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]

Zhong, M.

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).
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Zhu, X.

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).
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[Crossref]

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Figures (5)

Fig. 1
Fig. 1 A schematic diagram of the experimental setup.
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.
Fig. 3
Fig. 3 (a) Evolvement of femtosecond laser-induced ripples on Cu with rotating QWP. At the upper left and right corners of each image the rotation angle of QWP and the obtained laser polarization are indicated, respectively. (b)-(c) Dependences of the slanting ripple orientation on the rotation angle of QWP for two different materials, where the measured data are represented by solid squares and the simulation results are indicated by the red curves.
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.
Fig. 5
Fig. 5 Sketched evolution of the polarization state for the femtosecond lasers passing through QWP with variable rotation angles.

Equations (3)

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E x 2 A x 2 + E y 2 A y 2 2 E x E y A x A y cosφ= sin 2 φ
1t g 2 α tgα = A x 2 A y 2 A x A y cosϕ
cosφ= 0 g(λ)cosφ(λ)dλ 0 g(λ)dλ

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