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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 10 — May. 9, 2011
  • pp: 9035–9043
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Evidence of surface plasmon resonance in ultrafast laser-induced ripples

F. Garrelie, J. P. Colombier, F. Pigeon, S. Tonchev, N. Faure, M. Bounhalli, S. Reynaud, and O. Parriaux  »View Author Affiliations


Optics Express, Vol. 19, Issue 10, pp. 9035-9043 (2011)
http://dx.doi.org/10.1364/OE.19.009035


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Abstract

The sensitivity of grating-coupled Surface Plasmon Polaritons (SPPs) on metallic surface has been exploited to investigate the correlation between ripples formation under ultrashort laser exposure and SPPs generation conditions. Systematic examination of coupling of single ultrashort laser pulse on gratings with appropriate periods ranging from 440 nm to 800 nm has been performed. Our approach reveals that a surface plasmon is excited only for an appropriate grating period, the nickel sample exhibits fine ripples pattern, evidencing the plasmonic nature of ripples generation. We propose a systematic investigation supported by a comprehensive study on the obtained modulation of such a coupling efficiency by means of a phenomenological Drude-Lorentz model which captures possible optical properties modification under femtosecond irradiation.

© 2011 Optical Society of America

1. Introduction

In experiments performed on clean surfaces, roughness provides the required momentum to excite surface plasmons, acting as a broadband random grating. In this work, to investigate the mechanism of surface plasmon generation with ultrashort pulse, we propose to provide an experimental evidence that plasmon resonance initiates ripples formation on a grating surface of wave vector kG = 2πNG, where N is an integer which represents the diffraction order and ΛG the period of the grating. A grating acts as a coupler between an incident plane wave and the surface plasmon field. An ultrafast laser beam impinging onto the surface at normal incidence should be coupled into a surface plasmon field for a very well-defined coupling grating period. Gratings diffract light in different orders, one of which being used to couple the free-space wave to the plasmon. The spatial harmonics along x of an incident beam impinging on a grating of period ΛG at a resonant angle θ satisfies the relation:
1ΛLIPPS=sinθλ±NΛG.
(2)
Note that a larger coupling efficiency is obtained by using the first diffraction order. For normal incidence, setting N = 1, and substituting Eq.(2) into Eq.(1), a maximal coupling is obtained for ΛLIPSS = ΛG = λ/η. In this frame, the purpose of this work is to investigate surface plasmon resonance conditions for ultrashort single pulse irradiation, validating this grating equation for a given set of grating periodicities.

The paper is organized as follows. The experimental section is devoted to the details of grating preparation on nickel surface, methodological approach and the irradiation procedure. The following section describes the results obtained by illuminating the different gratings, showing ripples formation for a well-defined period. Experimental evidence is presented that plasmons are definitively involved in the formation of LIPSS. Finally, to explain quantitatively why the coupling resonance period is lower than expected, the formation of LIPSS is discussed in the framework of the conventional surface plasmon theory and in terms of the substantial modifications of the optical properties under ultrashort exposure. A conclusion section summarizes the results.

2. Experimental procedure

2.1. Sample preparation and characterization

Fig. 1 (a) All corrugation gratings of different periods on nickel plates, under natural light illumination. (b) SEM image of the ΛG = 560 nm grating.

2.2. Ultrafast irradiation

The laser system used in the experiment was an amplified Ti:sapphire laser (Thales) with a pulse duration of 150 fs full width at half-maximum (FWHM) at a repetition rate of 1 kHz and a wavelength of 800 nm. The pulse rate used for samples irradiation was adjusted down to single pulse using a Pockels control unit cell. The experiments presented here have all been performed with a single pulse irradiation to avoid all accumulative phenomena which would erase the memory of plasmon resonance. The feedback mechanisms which would also change the initial periodicity by coupling with the incident light are suppressed by performing single pulse irradiation [19

19. Y. Han and S. Qu, “The ripples and nanoparticles on silicon irradiated by femtosecond laser,” Chem. Phys. Lett. 495(4–6), 241–244 (2010). [CrossRef]

, 20

20. 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]

]. The laser beam is focused normally, through an achromatic lens of 50.8 mm focal length, onto the sample that is vertically mounted on an X-Y-Z motorized translation stage. The horizontal polarization is controlled by a plate-polarizer. The dimension of the beam (at 1/e2 intensity) has been determined by the classical linear regression of the impact surface versus the energy logarithm, as expected with the rough assumption of a Gaussian beam [21

21. J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982). [CrossRef] [PubMed]

]. All the samples were placed at the image point of an aperture (diameter 2.8 mm) fixed in the set up. The on-target delivered power was finely controlled by density located in the optical path of the laser beam. Ablation of the samples was conducted in the air. The analysis of the modification of the surfaces under the action of femtosecond light pulses was performed using a scanning electron microscope (FEI, NovaNanoSEM). The topography of surface structures was studied in the Acoustic AC mode of an atomic force microscope AFM (Agilent 5500), which is a resonant mode, equivalent to tapping mode of Veeco’s AFM.

3. Results

Samples with gratings periods in the range 440 to 800 nm have been irradiated with a single shot femtosecond laser beam, either TM or TE polarized as reported on Fig. 2. The small grating depth of 10 nm avoids enhancement of ripples formation resulting from a high roughness. The irradiation of the same sample of nickel without gratings does not lead to ripples formation whatever the polarization of the laser beam, at a laser fluence of 1.42 J/cm2, with a single shot exposure. Fig. 3 shows the SEM images of the samples with initial periods of 710, 760 and 790 nm, irradiated with a TM polarized laser beam at a fluence of 1.42 J/cm2. No fine ripples perpendicular to the polarization are observed for a grating period of 710 nm nor for a grating period of 790 nm, for which we would expect a classical surface plasmon resonance with a femtosecond laser wavelength of 800 nm as discussed in the following section. Interestingly, as reported on the SEM images of the 760 nm period grating, one observes clearly ripples formation for well-defined periods. The period of these fine ripples is close to 760 nm. This is observed only with the TM polarization, which evidences clearly the role of the polarization of the laser beam. This phenomenon gives the experimental evidence of grating assisted surface plasmon laser coupling [10

10. M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano 3(12), 4062–4070 (2009). [CrossRef] [PubMed]

].

Fig. 2 Λ and σ are the grating period and the grating thickness, respectively. The gratings are illuminated under normal incidence. (a) TE polarization : the electric field is parallel to the grooves. (b) TM polarization : the electric field is perpendicular to the grooves.
Fig. 3 SEM images of samples with grating of 710 nm (a), 790 nm (b) and 760 nm (c,d) irradiated with a single pulse TM polarized femtosecond laser beam, at a fluence of 1.42 J/cm2.

In order to go beyond these first qualitative results, a systematic examination of all grating periods has been done. A quantification has been made through the measure of the density of ripples over the surface of the impact, measured as the ratio between the surface covered with ripples and the overall surface of the spot. These results are reported on Fig. 4(a,b) for a fluence of 1.42 J/cm2. For a TE polarization, no ripples are evidenced whatever the period of the gratings on the nickel surface. For TM polarization, a strong increase of the density of ripples is observed for periods of 760 nm, with zero values below 720 nm and above 770 nm. This sharp resonance will be discussed in the following section from theoretical findings on the observed period. These phenomena occur not only for this value of fluence (1.42 J/cm2), but also for a lower laser fluence of 0.97 J/cm2, as reported on Fig. 4(c,d). The same behavior is observed at this lower energy, attesting that in a well-defined energy range and under single laser shot exposure, grating assisted surface plasmon coupling is likely to play a precursor role in ripples formation under ultrashort laser irradiation.

Fig. 4 Role of the TM polarization in well-defined ripples on the irradiated area of the nickel substrate: density of ripples as a function of the period of the grating, with a TM polarization (a,c) and a TE polarization (b,d) and a laser fluence of 1.42 J/cm2 (a,b) and 0.97 J/cm2 (c,d). The density of ripples is measured as the ratio between the surface covered with fine ripples and the overall surface of the spot.

4. Discussion

In its simplest form, a surface plasmon polariton is an electromagnetic excitation that may exist at the interface of two media with dielectric constants of opposite signs, for instance nickel and air. The charge density wave is associated with bound TM-polarized electromagnetic wave at the metal dielectric interface. The amplitude of this field decays evanescently into each medium from the considered interface. This field can interfere with the incident laser beam and then can lead to a modulated energy deposition, forming ripples at the surface. To attempt an explanation of the observed behavior regarding the resonant coupling for 750 nm and 760 nm period gratings, we discuss hereafter the effects of ultrashort irradiation on the optical properties leading to a shift in the expected surface plasmon resonance.

4.1. Calculated plasmon wavelength for nickel

Applying the appropriate boundary conditions to the fields at the dielectric/metal interface results in the familiar expression for the plasmon wave vector kSP=kSP+ikSP=ωc(ɛdɛ˜mɛd+ɛm)1/2. Provided ɛr < −ɛd, a condition satisfied at the air/Ni interface for 800 nm in the Palik’s data set [23

23. E. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

], the plasmon wavelength λSP corresponds to the real part of kSP and can be written:
λSP=2πkSP=λ[(ɛd+ɛ˜mɛdɛ˜m)1/2].
(3)

As the gratings have been designed in terms of aspect ratio to avoid any shift in the resonance period, calculations start from optical properties applicable for smooth and uncontaminated surfaces. The tabulated data from Refs. [22

22. D. E. Gray, American Institute of Physics Handbook, 3rd. ed. (McGraw Hill, 1972).

, 23

23. E. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

] give for λ = 800 nm, ɛr = −13 and ɛi = 21.7, and a calculated surface plasmon wavelength λSP = 792 nm. If a Drude-type absorption dependence is found at low photon energy (λ > 20 μm) for nickel, the interband transitions dominate the spectral optical properties in the infrared range. Consequently, any treatment of the complex dielectric constant close to this region must involve splitting it into two parts, one part corresponding to intraband excitations described by the Drude model, and an interband part corresponding to resonant absorptions based on a Lorentz oscillator model, i.e. ɛ̃m = ɛ̃D + ɛ̃IB.

4.2. Parametric study of the Drude-Lorentz model

From the modeling standpoint, Eq.(3) requires a corrected dielectric function due to nickel excitation and should capture the essence of any ultrashort excitation effect compatible with the observed plasmon resonance shift from 792 nm to 750–760 nm. At a given frequency, the surface plasmon wavelength λSP can be tuned by the dielectric constant which require to evaluate material excitation. At our laser wavelength, the dominant changes of the optical properties is expected to originate from the modification of the electronic states. For nickel, the interband term ɛ̃IB is dominated by transitions from the narrow d bands to the Fermi surface states. Laser energy injection into the electron gas results in a spreading of the electron distribution around the Fermi energy, and thus drastically affects intraband and interband transitions occuring in the electron system.

The frequency-dependent complex dielectric constant ɛ̃m is described by the Drude-Lorentz model as [24

24. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998). [CrossRef]

]:
ɛ˜m=ɛr+iɛi=ɛ˜D+ɛ˜IB=[1f0ωp2ω(ωiγ)]D+[j=1kfjΩp2(ωj2ω2)+iωΓj]IB.
(4)
In the simple Drude model, the key parameters describing the dynamics of free carriers in a material are plasma frequency ωp and the scattering rate γ of the free electrons undergoing intraband transitions. The motion of localized charge carriers is ascribed to the second term, the Lorentz harmonic oscillators, where fj, ωj, and Γj are, respectively, oscillator strength, the center frequency and the scattering rate of the electrons that are excited via interband transition j. To determine the intraband and interband dielectric functions in Ni at 300 K, ɛr and ɛi were calculated with the parametrization data listed by Rakic et al [24

24. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998). [CrossRef]

]. According to these tabulated data, plasma frequencies have been set to ωp=Ωp=ωp0=15.92eV, corresponding to two free electrons per atom.

Fig. 5 Calculated plasmon wavelength in the complex permittivity plane (a). Isowavelength corresponding to λSP = 750 nm is represented by solid green curve and λSP = 760 nm by dashed blue curve. The expected cold value (792 nm) is pointed in black. The set of solutions is plotted as a function of the plasma frequencies used in the Drude-Lorentz model (b).

5. Conclusion

In conclusion, we have demonstrated that laser-induced surface plasmons lead to the generation of fine ripples on a nickel surface undergoing femtosecond laser irradiation. Single pulse TM irradiations have been performed on a large range of grating periods with properly designed groove geometry to determine for which grating spatial frequency the incident beam and the surface plasmon wave vectors are matched. On the basis of this experimental procedure, our results reveal that ripples only appear for a well-defined grating period of 750–760 nm, showing that the coupling with surface plasmons is responsible for the ripples formation. Grating spacing which exhibits ripples differs from the one expected from dielectric constant at λ = 800 nm. A Drude-Lorentz model has been applied with various relative intraband and interband contributions. The dielectric constant of nickel is supposed to undergo a transiently change due to ultrashort excitation. The model shows that nickel surface irradiated by fs laser pulses can lead to a reduction of the surface plasmon wavelength compared to its room-temperature value for particular conditions of plasma frequencies. Therefore, this result is consistent with the data and provides information about the varying electronic density of the sample undergoing ultrashort irradiation.

References and links

1.

M. Birnbaum, “Semiconductor surface damage produced by ruby lasers,” J. Appl. Phys. 36(11), 3688–3689 (1965). [CrossRef]

2.

D. C. Emmony, R. P. Howson, and L. J. Willis, “Laser mirror damage in germanium at 10.6 μm,” Appl. Phys.Lett. 23(11), 598–600 (1973). [CrossRef]

3.

Z. Guosheng, P. M. Fauchet, and A. E. Siegman, “Growth of spontaneous periodic surface structures on solids during laser illumination,” Phys. Rev. B 26(10), 5366–5381 (1982). [CrossRef]

4.

J. E. Sipe, J. F. Young, J. S. Preston, and H. M. van Driel, “Laser-induced periodic surface structure,” Phys. Rev. B 27(2), 1141–1154 (1983). [CrossRef]

5.

A. E. Siegman and P.M. Fauchet, “Stimulated woods anomalies on laser illuminated surfaces,” IEEE J. Quant. Elect. 22(8), 1384–1403 (1986). [CrossRef]

6.

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

7.

E. M. Hsu, T. H. R. Crawford, H. F. Tiedje, and H. K. Haugen, “Periodic xurface xtructures on gallium phosphide after irradiation with 150 fs 7 ns laser pulses at 800 nm,” Appl. Phys. Lett. 91(11), 111102 (2007). [CrossRef]

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 transient dielectrics,” Appl. Surf. Sci. 197–198, 891–895 (2002). [CrossRef]

9.

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]

10.

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano 3(12), 4062–4070 (2009). [CrossRef] [PubMed]

11.

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]

12.

J. Bonse, A. Rosenfeld, and J. Krger, “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(10), 104910 (2009). [CrossRef]

13.

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

14.

A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, 1982).

15.

H. Raether, “Surface plasmons on smooth and rough surfaces and on gratings,” in Springer Tracts in Modern Physics, (Springer, 1988), Vol. 111.

16.

A. Y. Vorobyev and C. Guo, “Femtosecond laser-induced periodic surface structure formation on tungsten,” J. Appl. Phys. 104(6), 063523 (2008). [CrossRef]

17.

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]

18.

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]

19.

Y. Han and S. Qu, “The ripples and nanoparticles on silicon irradiated by femtosecond laser,” Chem. Phys. Lett. 495(4–6), 241–244 (2010). [CrossRef]

20.

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]

21.

J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982). [CrossRef] [PubMed]

22.

D. E. Gray, American Institute of Physics Handbook, 3rd. ed. (McGraw Hill, 1972).

23.

E. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

24.

A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998). [CrossRef]

25.

J. Bonse, A. Rosenfeld, and J. Kruger, “Implications of transient changes of optical and surface properties of solids during femtosecond laser pulse irradiation to the formation of laser-induced periodic surface structures,” Appl. Surf. Sci. (to be published). [CrossRef]

26.

Z. Lin and L. V. Zhigilei, “Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B 77(7), 075133 (2008). [CrossRef]

27.

P. E. Hopkins, J. M. Klopf, and P. M. Norris, “Influence of interband transitions on electron-phonon coupling measurements in Ni films,” Appl. Opt. 46(11), 2076–2083 (2007). [CrossRef] [PubMed]

OCIS Codes
(220.4000) Optical design and fabrication : Microstructure fabrication
(240.6680) Optics at surfaces : Surface plasmons
(320.2250) Ultrafast optics : Femtosecond phenomena

ToC Category:
Optics at Surfaces

History
Original Manuscript: February 7, 2011
Revised Manuscript: March 4, 2011
Manuscript Accepted: March 6, 2011
Published: April 25, 2011

Citation
F. Garrelie, J.-P. Colombier, F. Pigeon, S. Tonchev, N. Faure, M. Bounhalli, S. Reynaud, and O. Parriaux, "Evidence of surface plasmon resonance in ultrafast laser-induced ripples," Opt. Express 19, 9035-9043 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9035


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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. D. C. Emmony, R. P. Howson, and L. J. Willis, “Laser mirror damage in germanium at 10.6 μm,” Appl. Phys. Lett. 23(11), 598–600 (1973). [CrossRef]
  3. Z. Guosheng, P. M. Fauchet, and A. E. Siegman, “Growth of spontaneous periodic surface structures on solids during laser illumination,” Phys. Rev. B 26(10), 5366–5381 (1982). [CrossRef]
  4. J. E. Sipe, J. F. Young, J. S. Preston, and H. M. van Driel, “Laser-induced periodic surface structure,” Phys. Rev. B 27(2), 1141–1154 (1983). [CrossRef]
  5. A. E. Siegman, and P. M. Fauchet, “Stimulated woods anomalies on laser illuminated surfaces,” IEEE J. Quantum Electron. 22(8), 1384–1403 (1986). [CrossRef]
  6. A. Borowiec, and H. K. Haugen, “Subwavelength ripple formation on the surfaces of compound semiconductors irradiated with femtosecond laser pulses,” Appl. Phys. Lett. 82(25), 4462–4464 (2003). [CrossRef]
  7. E. M. Hsu, T. H. R. Crawford, H. F. Tiedje, and H. K. Haugen, “Periodic xurface xtructures on gallium phosphide after irradiation with 150 fs 7 ns laser pulses at 800 nm,” Appl. Phys. Lett. 91(11), 111102 (2007). [CrossRef]
  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 transient dielectrics,” Appl. Surf. Sci. 197–198, 891–895 (2002). [CrossRef]
  9. 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]
  10. M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser,” ACS Nano 3(12), 4062–4070 (2009). [CrossRef] [PubMed]
  11. 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]
  12. J. Bonse, A. Rosenfeld, and J. Krger, “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(10), 104910 (2009). [CrossRef]
  13. M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Mechanisms of ultrafast laser-induced deep-subwavelength gratings on graphite and diamond,” Phys. Rev. B 79(12), 125436 (2009). [CrossRef]
  14. A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, 1982).
  15. H. Raether, “Surface plasmons on smooth and rough surfaces and on gratings,” in Springer Tracts in Modern Physics, (Springer, 1988), Vol. 111.
  16. A. Y. Vorobyev, and C. Guo, “Femtosecond laser-induced periodic surface structure formation on tungsten,” J. Appl. Phys. 104(6), 063523 (2008). [CrossRef]
  17. 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]
  18. 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]
  19. Y. Han, and S. Qu, “The ripples and nanoparticles on silicon irradiated by femtosecond laser,” Chem. Phys. Lett. 495(4–6), 241–244 (2010). [CrossRef]
  20. 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]
  21. J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982). [CrossRef] [PubMed]
  22. D. E. Gray, American Institute of Physics Handbook, 3rd. ed. (McGraw Hill, 1972).
  23. E. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).
  24. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998). [CrossRef]
  25. J. Bonse, A. Rosenfeld, and J. Kruger, “Implications of transient changes of optical and surface properties of solids during femtosecond laser pulse irradiation to the formation of laser-induced periodic surface structures,” Appl. Surf. Sci. (to be published), doi:10.1016/j.apsusc.2010.11.059. [CrossRef]
  26. Z. Lin, and L. V. Zhigilei, “Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B 77(7), 075133 (2008). [CrossRef]
  27. P. E. Hopkins, J. M. Klopf, and P. M. Norris, “Influence of interband transitions on electron-phonon coupling measurements in Ni films,” Appl. Opt. 46(11), 2076–2083 (2007). [CrossRef] [PubMed]

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