Abstract

The role of ablation and incubation processes in the formation of surface nanogratings with femtosecond pulses were investigated by measuring ablation thresholds and depth of nanogrooves at different pulse to pulse spacings. Our observations indicated that the nanograting formation essentially relies on a laser ablation process which can be modeled by a simple set of equations.

© 2011 Optical Society of America

1. Introduction

The incubation process, so-called ”N-on-one” accumulation effect, was discovered in multi-pulse laser-induced damage on the surface of metal and semiconductor with 10 ns Q-switched 1064 nm Nd:YAG laser pulses [1, 2]. The N-pulse fluence threshold FN was found to follow the equation FN = F1NS−1 where S is the incubation factor and N is the overlapping pulse number. This accumulation process was described by thermal stress-strain energy storage [2]. However, for dielectric materials irradiated by ps and sub-ps pulses the incubation effect was described by laser-induced defects and a different equation was proposed FN = F + (F1F)exp[−k(N − 1)] where F is the fluence threshold at infinite number of shots and k is the incubation factor [3, 4]. In this case, the ablation threshold drops dramatically after the first shot and levels off as the overlapping pulse number increases. This incubation effect plays a very important role in femtosecond laser micro- and nano-machining which basically relies on laser ablation [35]. In addition to laser fluence and material ablation threshold, nanograting formation is very sensitive to precise alignment of laser spot as evidenced by a recent report where the transition from smooth modification to well-shaped nanograting was observed by simply scanning the laser spot across the surface of a fused silica sample [7]. In this paper, we report on the surface nanograting formation and its link to the incubation process. In order to avoid the intensity variation which would result from an improper alignment, we carefully align the focal spot on the air-glass interface with a technique based on the third harmonic generation at the vicinity of an interface [8, 9]. We propose and demonstrate that nanograting formation is basically a laser ablation process and study the incubation effect by measuring the nanograting formation thresholds as a function of pulse to pulse spacing.

2. Experiment

A Ti:sapphire chirped-pulse amplification laser system (Spitfire, Spectra-Physics) with a maximum output energy of 2 mJ (1 KHz) at the central wavelength of 800 nm was employed in the experiment. The laser beam was slightly divergent in order to compensate for self-focusing in air and other optical media before reaching the target. The experimental setup is shown in Fig. 1. The laser pulses passing through a neutral density filter and a continuously variable metallic neutral density filter were split in two by a beam splitter (BS). The transmitted part (T = 10%) was directed into a calibrated photodiode which monitored the incident energy for nanograting formation. The reflected part (R = 90%) passing through a half wave plate and an electronic shutter was focused onto the surface of a fused silica block (Corning 7980-UV, surface quality 40–20, wave front λ/4) by a 25X objective (N.A. = 0.5). The pulses were pre-compensated so that they were essentially transform-limited (45 fs) at the fused silica sample which was mounted on a 3D motorized translation stage.

 

Fig. 1 Experimental Setup. The inset shows the third harmonic signal as a function of the translation distance along x-axis. The rising and falling edges correspond to the opening and closing of the electronic shutter. The gradually reduced third harmonic signal indicates the decrease of the laser intensity due to the displacement of the focal spot from the sample surface.

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Based on the fact that the third harmonic signal is critically generated at the interface between a glass surface and air, the sample surface and the x-axis translation stage were precisely aligned perpendicularly to the laser propagation direction by monitoring the retroreflection and the third harmonic signal during the scan. Figure 1 (inset) shows a typical plot of the third harmonic signal from the sample surface as a function of the scanned distance along x-axis. The fast rising and falling edges correspond to the opening and closing of the electronic shutter. The small slope in the third harmonic signal indicates that there is a slight displacement of the focal spot from the sample surface. The decrease of the laser intensity is about 1.7% for a translation distance of 1.5 mm estimated from the linear regression of the third harmonic signal (red line). This decrease is roughly of the order of the RMS of the laser signal whose effect on the nanograting formation can be considered as negligible. After the writing, the sample was etched with 1% HF acid in the ultrasonic bath for about 2 minutes then imaged under a scanning electron microscope (FEI, model Quanta 3D FEG).

3. Ablation threshold for nanograting formation

We assume that the nanogrooves inscription process occurs wherever the pulse fluence is larger than the ablation threshold. Regardless of the mechanism of nanograting formation, the overall extent of the nanograting D is thus related to both incident pulse fluence and ablation threshold (Fth) [10] as schematically shown in Fig. 2(a). Assuming that the laser is a Gaussian beam, the fluence on the surface can be written as:

F(r,z)=F0w02wz2exp(2r2wz2)
where r is the radial distance from the center axis of the beam, z is the axial distance from the beam waist, F0 = F(0, 0) is the peak pulse fluence at the center of the beam at its waist, w0 and wz are respectively the beam waist and the beam radius at a distance z from the beam waist. By replacing F0 by 2Ein/(πw02), F(r, z) by the ablation threshold 2Eth/(πwz2), and substituting D for 2r0, we obtain the threshold energy equation:
Eth=Einexp(D22wz2)
where Eth and Ein are the threshold pulse energy and the incident pulse energy, respectively. In order to study the relation between the overall extent of the nanograting and the pulse energy, the nanogratings were intentionally written with the laser polarization perpendicular to the scan direction. The spatial extent of this type of nanograting is not affected by the local field enhancement [11] and the seeding effect [12], because in this case both of them occur along the scan direction. The inscribed nanogratings are shown in Fig. 2(b) as a function of four pulse energies and for a pulse to pulse spacing d = 10 nm. The overall extent of the nanograting increases with the pulse energy and becomes slightly damaged when the energy is only increased by about 20% with respect to the lowest energy used in the experiment. This lowest energy corresponds to the one that is near the threshold for nanograting formation. The overall extent of the nanograting is plotted in Fig. 3 as a function of the incident pulse energy for pulse to pulse spacings of 5, 10 and 20 nm and fitted according to Eq. (2). The threshold energy Eth is obtained through the extrapolation of the overall extent of the nanogratings to zero value, and the beam radius wz at the surface is also calculated by Eq. (2) [13, 14]. Similar fits were performed for values of d up to 120 nm, allowing to compute the fluence threshold for nanograting formation Fth=2Eth/(πwz2) (Table 1).

 

Fig. 2 (a). Schematic drawing showing the threshold effect of nanograting formation. (b). The SEM pictures for nanograting formation at different pulse energies (90, 100, 110, 120 nJ/pulse) for a given pulse to pulse spacing 10 nm. K: laser propagation direction; S: scan direction; E: electric field

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Fig. 3 The overall extent of the nanogratings as a function of incident pulse energy for three different pulse to pulse spacings (5, 10 and 20 nm). Solid lines were fitted according to Eq. (2).

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Tables Icon

Table 1. Measured Beam Radii, Threshold Energies and the Computed Threshold Fluences for Different Pulse to Pulse Spacings

The good agreement between experimental data and the fit based on Eq. (2) supports our assumption that nanograting formation relies on a laser ablation process. This assumption is further supported by the depth of material removed in the process. Figure 4 shows the cross-section of the nanogratings written with pulse energy 100 nJ at different pulse to pulse spacing. For this experiment the laser polarization is parallel to the scan direction. To produce those pictures, the nanogratings were first filled by platinum deposition (on the right side of each picture) and then etched down by a focused ion beam (FIB) to expose the cross-section of the gratings. Note that the nanogrooves on the right side are completely filled with platinum while those on the left are partially filled due to the diffusion of the platinum during the deposition. The purpose of the deposition of the platinum before etching is to avoid the so-called curtain effect [15] so that the depth of the nanogrooves resulting from the material removal by the laser can be precisely measured. The curtain effect can be seen in the lower half on the left side of the pictures where the nanogrooves are just partially filled with platinum. With the decrease of pulse to pulse spacing (from 100 nm to 20 nm), the pulse overlap is thus increased. This results in an increase of the ablation rate because of the decrease of the ablation threshold and/or the increase of the effective absorption coefficient [10]. An increase of the depth of removed material is thus expected and experimentally observed (from 363 nm to 444 nm), in agreement with an ablation process.

 

Fig. 4 Nanogratings written at pulse energy 100 nJ at different pulse to pulse spacings. K: laser direction; E: electric field; S: scan direction. d: pulse to pulse spacing. (a). d = 100 nm, depth = 363 nm. (b). d = 80 nm, depth = 418 nm. (c). d = 40 nm, depth = 428 nm. (d). d = 20 nm, depth = 444 nm.

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4. Incubation

In previous investigations on incubation in metal, semiconductor and dielectric, the ablation threshold was obtained from the extrapolation of the damage volume represented as a function of the laser fluence at different pulse number per site to zero value. However, in the case of nanograting formation the sample is being scanned at different pulse to pulse spacing per trace. The ablation threshold should thus be represented as a function of the pulse to pulse spacing and obtained through the extrapolation of the overall extent of the nanograting to zero value as plotted in Fig. 3. Although the behavior of pulse overlapping in nanograting formation is different from the stationary focusing case, the essential that the incubation resulting from laser-induced defects should be the same. Therefore, by simply replacing the pulse number N by wz/d which can be considered as the effective pulse number overlapped within the focal spot, the dielectric incubation equation FN = F +(F1F)exp[−k(N – 1)] becomes, in terms of the pulse to pulse spacing d, capable to describe the incubation effect in nanograting formation:

Fd=F0+(FssF0)exp[k(wz/d1)],d<wz
Fd=Fss,dwz
where Fd is the fluence threshold at pulse to pulse spacing d, Fss is the single shot ablation threshold and F0 is the ablation threshold of infinite number of shots when d = 0, k is the so-called incubation factor which is an empirical parameter that indicates the strength of reducing the ablation threshold. The larger k is, the stronger the incubation will be (k = 0 corresponds to no incubation).

As shown in Fig. 5, the nanograting formation ablation threshold drops dramatically for small wz/d corresponding to low effective pulse number, but it rapidly becomes level as the number of overlapping pulses increases. The lower limit of the nanograting formation threshold is probably due to the saturation of the laser-induced defects [4], i.e., the ablation threshold cannot be decreased further by decreasing the pulse to pulse spacing. Through the fit (red curve) according to Eq. ( 3), the single and infinity shot ablation thresholds Fss = 3.89 J/cm2 and F0 = 3.06 J/cm2 are derived together with the value of k (see below). This represents threshold reduction of about 25%. Experimentally we start to observe laser ablation under the SEM at 3.98 ± 0.11 J/cm2 with single shot and no modification at 2.99 ± 0.11 J/cm2 with pulse numbers up to 1000 shots. These two experimental values are close to those (Fss and F0) derived by the fitting, which suggests that the modified dielectric incubation equation is good for nanograting formation. The derived incubation factor k = 0.034 indicates that incubation is weak yet very important in the nanograting formation.

 

Fig. 5 The incubation curve for nanograting formation. The ablation threshold drops dramatically and levels off at low and high effective pulse number (wz/d), respectively.

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According to our experimental observation (section 3 and Fig. 2(b)), the nanograting would be damaged if the incident pulse fluence is about 20% higher than the ablation threshold whose value is influenced by the incubation effect. Therefore, in order to write a good nanograting and avoid damage, the incident pulse fluence should be always kept within the 20% range above the ablation threshold. In other words, the incident pulse fluence should be adjusted in terms of the pulse to pulse spacing based on the modified incubation equation (Eq. (3)).This should be applicable to writing nanograting on the surface of other transparent dielectrics.

5. Conclusion

We have demonstrated that nanograting formation on the surface of fused silica is basically a laser ablation process. The ablation threshold fluence is influenced by the incubation effect which in turn depends on the pulse to pulse spacing. The overall extent of the nanograting follows a logarithmic behavior with pulse fluence and the ablation depth increases with the increase of the effective pulse number within the focal spot. To obtain good gratings without damage, the incident pulse fluence should be carefully selected in terms of the pulse to pulse spacing because of the incubation effect. A modified incubation equation was proposed to describe the role of the incubation process in nanograting formation.

Acknowledgments

This work is supported by the Natural Sciences and Engineering Research Council of Canada, Le Fonds Québécois de la Recherche sur la Nature et les Technologies, Canada Research Chairs, Canada Foundation for Innovation, Canadian Institute for Photonic Innovations, and Ministère du Développement économique, de l’Innovation et de l’Exportation. The authors appreciate Mr. S. Gagnon and Mr. M. Martin for the technical support.

References and links

1. D. K. Sardar, M. F. Becker, and R. M. Walser, “Multipulse laser damage of GaAs surfaces,” J. Appl. Phys. 62, 3688–3693 (1987). [CrossRef]  

2. Y. Jee, M. F. Becker, and R. M. Walser, “Laser-induced damage on single-crystal metal surfaces,” J. Opt. Soc. Am. B 5, 648–659 (1988). [CrossRef]  

3. D. Ashkenasi, M. Lorenz, R. Stoian, and A. Rosenfeld, “Surface damage threshold and structuring of dielectrics using femtosecond laser pulses: the role of incubation,” Appl. Surf. Sci. 150, 101–106 (1999). [CrossRef]  

4. A. Rosenfeld, M. Lorenz, R. Stoian, and D. Ashkenasi, “Ultrashort-laser-pulse damage threshold of transparent materials and the role of incubation,” Appl. Phys. A 69, S373–S376 (1999). [CrossRef]  

5. M. Lenzner, J. Krüger, W. Kautek, and F. Krausz, “Incubation of laser ablation in fused silica with 5-fs pulses,” Appl. Phys. A 69, 465–466 (1999). [CrossRef]  

6. X. Liu, D. Du, and G. Mourou, “Laser ablation and micromachining with ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 1707–1716 (1997). [CrossRef]  

7. F. Liang, Q. Sun, D. Gingras, R. Vallée, and S. L. Chin, “The transition from smooth modification to nanograting in fused silica,” Appl. Phys. Lett. 96, 101903 (2010). [CrossRef]  

8. Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997). [CrossRef]  

9. F. Liang, Q. Sun, R. Vallée, and S. L. Chin, “Multiple refocusing characterization and critical power measurement using third harmonic generation at interface,” Appl. Phys. B 99, 235–239 (2009). [CrossRef]  

10. C. Phipps, Laser Ablation and Its Applications (Springer, 2006).

11. V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett. 96, 057404 (2006). [CrossRef]   [PubMed]  

12. X. Guo, R. Li, Y. Hang, Z. Xu, B. Yu, Y. Dai, B. Lu, and X. Sun, “Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses,” Appl. Phys. A 94, 423–426 (2009). [CrossRef]  

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

14. N. Sanner, O. Utéza, B. Bussiere, G. Coustillier, A. Leray, T. Itina, and M. Sentis, “Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics,” Appl. Phys. A 94, 889–897 (2009). [CrossRef]  

15. L. A. Giannuzzi and F. A. Stevie, Introduction to Focused Ion Beams (Springer Science + Business Media, Inc., 2005). [CrossRef]  

References

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  1. D. K. Sardar, M. F. Becker, and R. M. Walser, “Multipulse laser damage of GaAs surfaces,” J. Appl. Phys. 62, 3688–3693 (1987).
    [Crossref]
  2. Y. Jee, M. F. Becker, and R. M. Walser, “Laser-induced damage on single-crystal metal surfaces,” J. Opt. Soc. Am. B 5, 648–659 (1988).
    [Crossref]
  3. D. Ashkenasi, M. Lorenz, R. Stoian, and A. Rosenfeld, “Surface damage threshold and structuring of dielectrics using femtosecond laser pulses: the role of incubation,” Appl. Surf. Sci. 150, 101–106 (1999).
    [Crossref]
  4. A. Rosenfeld, M. Lorenz, R. Stoian, and D. Ashkenasi, “Ultrashort-laser-pulse damage threshold of transparent materials and the role of incubation,” Appl. Phys. A 69, S373–S376 (1999).
    [Crossref]
  5. M. Lenzner, J. Krüger, W. Kautek, and F. Krausz, “Incubation of laser ablation in fused silica with 5-fs pulses,” Appl. Phys. A 69, 465–466 (1999).
    [Crossref]
  6. X. Liu, D. Du, and G. Mourou, “Laser ablation and micromachining with ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 1707–1716 (1997).
    [Crossref]
  7. F. Liang, Q. Sun, D. Gingras, R. Vallée, and S. L. Chin, “The transition from smooth modification to nanograting in fused silica,” Appl. Phys. Lett. 96, 101903 (2010).
    [Crossref]
  8. Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
    [Crossref]
  9. F. Liang, Q. Sun, R. Vallée, and S. L. Chin, “Multiple refocusing characterization and critical power measurement using third harmonic generation at interface,” Appl. Phys. B 99, 235–239 (2009).
    [Crossref]
  10. C. Phipps, Laser Ablation and Its Applications (Springer, 2006).
  11. V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett. 96, 057404 (2006).
    [Crossref] [PubMed]
  12. X. Guo, R. Li, Y. Hang, Z. Xu, B. Yu, Y. Dai, B. Lu, and X. Sun, “Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses,” Appl. Phys. A 94, 423–426 (2009).
    [Crossref]
  13. J. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7, 196–198 (1982).
    [Crossref] [PubMed]
  14. N. Sanner, O. Utéza, B. Bussiere, G. Coustillier, A. Leray, T. Itina, and M. Sentis, “Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics,” Appl. Phys. A 94, 889–897 (2009).
    [Crossref]
  15. L. A. Giannuzzi and F. A. Stevie, Introduction to Focused Ion Beams (Springer Science + Business Media, Inc., 2005).
    [Crossref]

2010 (1)

F. Liang, Q. Sun, D. Gingras, R. Vallée, and S. L. Chin, “The transition from smooth modification to nanograting in fused silica,” Appl. Phys. Lett. 96, 101903 (2010).
[Crossref]

2009 (3)

N. Sanner, O. Utéza, B. Bussiere, G. Coustillier, A. Leray, T. Itina, and M. Sentis, “Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics,” Appl. Phys. A 94, 889–897 (2009).
[Crossref]

X. Guo, R. Li, Y. Hang, Z. Xu, B. Yu, Y. Dai, B. Lu, and X. Sun, “Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses,” Appl. Phys. A 94, 423–426 (2009).
[Crossref]

F. Liang, Q. Sun, R. Vallée, and S. L. Chin, “Multiple refocusing characterization and critical power measurement using third harmonic generation at interface,” Appl. Phys. B 99, 235–239 (2009).
[Crossref]

2006 (1)

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett. 96, 057404 (2006).
[Crossref] [PubMed]

1999 (3)

M. Lenzner, J. Krüger, W. Kautek, and F. Krausz, “Incubation of laser ablation in fused silica with 5-fs pulses,” Appl. Phys. A 69, 465–466 (1999).
[Crossref]

A. Rosenfeld, M. Lorenz, R. Stoian, and D. Ashkenasi, “Ultrashort-laser-pulse damage threshold of transparent materials and the role of incubation,” Appl. Phys. A 69, S373–S376 (1999).
[Crossref]

D. Ashkenasi, M. Lorenz, R. Stoian, and A. Rosenfeld, “Surface damage threshold and structuring of dielectrics using femtosecond laser pulses: the role of incubation,” Appl. Surf. Sci. 150, 101–106 (1999).
[Crossref]

1997 (2)

X. Liu, D. Du, and G. Mourou, “Laser ablation and micromachining with ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 1707–1716 (1997).
[Crossref]

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[Crossref]

1988 (1)

1987 (1)

D. K. Sardar, M. F. Becker, and R. M. Walser, “Multipulse laser damage of GaAs surfaces,” J. Appl. Phys. 62, 3688–3693 (1987).
[Crossref]

1982 (1)

Ashkenasi, D.

D. Ashkenasi, M. Lorenz, R. Stoian, and A. Rosenfeld, “Surface damage threshold and structuring of dielectrics using femtosecond laser pulses: the role of incubation,” Appl. Surf. Sci. 150, 101–106 (1999).
[Crossref]

A. Rosenfeld, M. Lorenz, R. Stoian, and D. Ashkenasi, “Ultrashort-laser-pulse damage threshold of transparent materials and the role of incubation,” Appl. Phys. A 69, S373–S376 (1999).
[Crossref]

Barad, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[Crossref]

Becker, M. F.

Y. Jee, M. F. Becker, and R. M. Walser, “Laser-induced damage on single-crystal metal surfaces,” J. Opt. Soc. Am. B 5, 648–659 (1988).
[Crossref]

D. K. Sardar, M. F. Becker, and R. M. Walser, “Multipulse laser damage of GaAs surfaces,” J. Appl. Phys. 62, 3688–3693 (1987).
[Crossref]

Bhardwaj, V. R.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett. 96, 057404 (2006).
[Crossref] [PubMed]

Bussiere, B.

N. Sanner, O. Utéza, B. Bussiere, G. Coustillier, A. Leray, T. Itina, and M. Sentis, “Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics,” Appl. Phys. A 94, 889–897 (2009).
[Crossref]

Chin, S. L.

F. Liang, Q. Sun, D. Gingras, R. Vallée, and S. L. Chin, “The transition from smooth modification to nanograting in fused silica,” Appl. Phys. Lett. 96, 101903 (2010).
[Crossref]

F. Liang, Q. Sun, R. Vallée, and S. L. Chin, “Multiple refocusing characterization and critical power measurement using third harmonic generation at interface,” Appl. Phys. B 99, 235–239 (2009).
[Crossref]

Corkum, P. B.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett. 96, 057404 (2006).
[Crossref] [PubMed]

Coustillier, G.

N. Sanner, O. Utéza, B. Bussiere, G. Coustillier, A. Leray, T. Itina, and M. Sentis, “Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics,” Appl. Phys. A 94, 889–897 (2009).
[Crossref]

Dai, Y.

X. Guo, R. Li, Y. Hang, Z. Xu, B. Yu, Y. Dai, B. Lu, and X. Sun, “Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses,” Appl. Phys. A 94, 423–426 (2009).
[Crossref]

Du, D.

X. Liu, D. Du, and G. Mourou, “Laser ablation and micromachining with ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 1707–1716 (1997).
[Crossref]

Eisenberg, H.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[Crossref]

Giannuzzi, L. A.

L. A. Giannuzzi and F. A. Stevie, Introduction to Focused Ion Beams (Springer Science + Business Media, Inc., 2005).
[Crossref]

Gingras, D.

F. Liang, Q. Sun, D. Gingras, R. Vallée, and S. L. Chin, “The transition from smooth modification to nanograting in fused silica,” Appl. Phys. Lett. 96, 101903 (2010).
[Crossref]

Guo, X.

X. Guo, R. Li, Y. Hang, Z. Xu, B. Yu, Y. Dai, B. Lu, and X. Sun, “Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses,” Appl. Phys. A 94, 423–426 (2009).
[Crossref]

Hang, Y.

X. Guo, R. Li, Y. Hang, Z. Xu, B. Yu, Y. Dai, B. Lu, and X. Sun, “Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses,” Appl. Phys. A 94, 423–426 (2009).
[Crossref]

Hnatovsky, C.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett. 96, 057404 (2006).
[Crossref] [PubMed]

Horowitz, M.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[Crossref]

Itina, T.

N. Sanner, O. Utéza, B. Bussiere, G. Coustillier, A. Leray, T. Itina, and M. Sentis, “Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics,” Appl. Phys. A 94, 889–897 (2009).
[Crossref]

Jee, Y.

Kautek, W.

M. Lenzner, J. Krüger, W. Kautek, and F. Krausz, “Incubation of laser ablation in fused silica with 5-fs pulses,” Appl. Phys. A 69, 465–466 (1999).
[Crossref]

Krausz, F.

M. Lenzner, J. Krüger, W. Kautek, and F. Krausz, “Incubation of laser ablation in fused silica with 5-fs pulses,” Appl. Phys. A 69, 465–466 (1999).
[Crossref]

Krüger, J.

M. Lenzner, J. Krüger, W. Kautek, and F. Krausz, “Incubation of laser ablation in fused silica with 5-fs pulses,” Appl. Phys. A 69, 465–466 (1999).
[Crossref]

Lenzner, M.

M. Lenzner, J. Krüger, W. Kautek, and F. Krausz, “Incubation of laser ablation in fused silica with 5-fs pulses,” Appl. Phys. A 69, 465–466 (1999).
[Crossref]

Leray, A.

N. Sanner, O. Utéza, B. Bussiere, G. Coustillier, A. Leray, T. Itina, and M. Sentis, “Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics,” Appl. Phys. A 94, 889–897 (2009).
[Crossref]

Li, R.

X. Guo, R. Li, Y. Hang, Z. Xu, B. Yu, Y. Dai, B. Lu, and X. Sun, “Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses,” Appl. Phys. A 94, 423–426 (2009).
[Crossref]

Liang, F.

F. Liang, Q. Sun, D. Gingras, R. Vallée, and S. L. Chin, “The transition from smooth modification to nanograting in fused silica,” Appl. Phys. Lett. 96, 101903 (2010).
[Crossref]

F. Liang, Q. Sun, R. Vallée, and S. L. Chin, “Multiple refocusing characterization and critical power measurement using third harmonic generation at interface,” Appl. Phys. B 99, 235–239 (2009).
[Crossref]

Liu, J.

Liu, X.

X. Liu, D. Du, and G. Mourou, “Laser ablation and micromachining with ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 1707–1716 (1997).
[Crossref]

Lorenz, M.

A. Rosenfeld, M. Lorenz, R. Stoian, and D. Ashkenasi, “Ultrashort-laser-pulse damage threshold of transparent materials and the role of incubation,” Appl. Phys. A 69, S373–S376 (1999).
[Crossref]

D. Ashkenasi, M. Lorenz, R. Stoian, and A. Rosenfeld, “Surface damage threshold and structuring of dielectrics using femtosecond laser pulses: the role of incubation,” Appl. Surf. Sci. 150, 101–106 (1999).
[Crossref]

Lu, B.

X. Guo, R. Li, Y. Hang, Z. Xu, B. Yu, Y. Dai, B. Lu, and X. Sun, “Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses,” Appl. Phys. A 94, 423–426 (2009).
[Crossref]

Mourou, G.

X. Liu, D. Du, and G. Mourou, “Laser ablation and micromachining with ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 1707–1716 (1997).
[Crossref]

Phipps, C.

C. Phipps, Laser Ablation and Its Applications (Springer, 2006).

Rajeev, P. P.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett. 96, 057404 (2006).
[Crossref] [PubMed]

Rayner, D. M.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett. 96, 057404 (2006).
[Crossref] [PubMed]

Rosenfeld, A.

D. Ashkenasi, M. Lorenz, R. Stoian, and A. Rosenfeld, “Surface damage threshold and structuring of dielectrics using femtosecond laser pulses: the role of incubation,” Appl. Surf. Sci. 150, 101–106 (1999).
[Crossref]

A. Rosenfeld, M. Lorenz, R. Stoian, and D. Ashkenasi, “Ultrashort-laser-pulse damage threshold of transparent materials and the role of incubation,” Appl. Phys. A 69, S373–S376 (1999).
[Crossref]

Sanner, N.

N. Sanner, O. Utéza, B. Bussiere, G. Coustillier, A. Leray, T. Itina, and M. Sentis, “Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics,” Appl. Phys. A 94, 889–897 (2009).
[Crossref]

Sardar, D. K.

D. K. Sardar, M. F. Becker, and R. M. Walser, “Multipulse laser damage of GaAs surfaces,” J. Appl. Phys. 62, 3688–3693 (1987).
[Crossref]

Sentis, M.

N. Sanner, O. Utéza, B. Bussiere, G. Coustillier, A. Leray, T. Itina, and M. Sentis, “Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics,” Appl. Phys. A 94, 889–897 (2009).
[Crossref]

Silberberg, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[Crossref]

Simova, E.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett. 96, 057404 (2006).
[Crossref] [PubMed]

Stevie, F. A.

L. A. Giannuzzi and F. A. Stevie, Introduction to Focused Ion Beams (Springer Science + Business Media, Inc., 2005).
[Crossref]

Stoian, R.

D. Ashkenasi, M. Lorenz, R. Stoian, and A. Rosenfeld, “Surface damage threshold and structuring of dielectrics using femtosecond laser pulses: the role of incubation,” Appl. Surf. Sci. 150, 101–106 (1999).
[Crossref]

A. Rosenfeld, M. Lorenz, R. Stoian, and D. Ashkenasi, “Ultrashort-laser-pulse damage threshold of transparent materials and the role of incubation,” Appl. Phys. A 69, S373–S376 (1999).
[Crossref]

Sun, Q.

F. Liang, Q. Sun, D. Gingras, R. Vallée, and S. L. Chin, “The transition from smooth modification to nanograting in fused silica,” Appl. Phys. Lett. 96, 101903 (2010).
[Crossref]

F. Liang, Q. Sun, R. Vallée, and S. L. Chin, “Multiple refocusing characterization and critical power measurement using third harmonic generation at interface,” Appl. Phys. B 99, 235–239 (2009).
[Crossref]

Sun, X.

X. Guo, R. Li, Y. Hang, Z. Xu, B. Yu, Y. Dai, B. Lu, and X. Sun, “Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses,” Appl. Phys. A 94, 423–426 (2009).
[Crossref]

Taylor, R. S.

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett. 96, 057404 (2006).
[Crossref] [PubMed]

Utéza, O.

N. Sanner, O. Utéza, B. Bussiere, G. Coustillier, A. Leray, T. Itina, and M. Sentis, “Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics,” Appl. Phys. A 94, 889–897 (2009).
[Crossref]

Vallée, R.

F. Liang, Q. Sun, D. Gingras, R. Vallée, and S. L. Chin, “The transition from smooth modification to nanograting in fused silica,” Appl. Phys. Lett. 96, 101903 (2010).
[Crossref]

F. Liang, Q. Sun, R. Vallée, and S. L. Chin, “Multiple refocusing characterization and critical power measurement using third harmonic generation at interface,” Appl. Phys. B 99, 235–239 (2009).
[Crossref]

Walser, R. M.

Y. Jee, M. F. Becker, and R. M. Walser, “Laser-induced damage on single-crystal metal surfaces,” J. Opt. Soc. Am. B 5, 648–659 (1988).
[Crossref]

D. K. Sardar, M. F. Becker, and R. M. Walser, “Multipulse laser damage of GaAs surfaces,” J. Appl. Phys. 62, 3688–3693 (1987).
[Crossref]

Xu, Z.

X. Guo, R. Li, Y. Hang, Z. Xu, B. Yu, Y. Dai, B. Lu, and X. Sun, “Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses,” Appl. Phys. A 94, 423–426 (2009).
[Crossref]

Yu, B.

X. Guo, R. Li, Y. Hang, Z. Xu, B. Yu, Y. Dai, B. Lu, and X. Sun, “Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses,” Appl. Phys. A 94, 423–426 (2009).
[Crossref]

Appl. Phys. A (4)

A. Rosenfeld, M. Lorenz, R. Stoian, and D. Ashkenasi, “Ultrashort-laser-pulse damage threshold of transparent materials and the role of incubation,” Appl. Phys. A 69, S373–S376 (1999).
[Crossref]

M. Lenzner, J. Krüger, W. Kautek, and F. Krausz, “Incubation of laser ablation in fused silica with 5-fs pulses,” Appl. Phys. A 69, 465–466 (1999).
[Crossref]

X. Guo, R. Li, Y. Hang, Z. Xu, B. Yu, Y. Dai, B. Lu, and X. Sun, “Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses,” Appl. Phys. A 94, 423–426 (2009).
[Crossref]

N. Sanner, O. Utéza, B. Bussiere, G. Coustillier, A. Leray, T. Itina, and M. Sentis, “Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics,” Appl. Phys. A 94, 889–897 (2009).
[Crossref]

Appl. Phys. B (1)

F. Liang, Q. Sun, R. Vallée, and S. L. Chin, “Multiple refocusing characterization and critical power measurement using third harmonic generation at interface,” Appl. Phys. B 99, 235–239 (2009).
[Crossref]

Appl. Phys. Lett. (2)

F. Liang, Q. Sun, D. Gingras, R. Vallée, and S. L. Chin, “The transition from smooth modification to nanograting in fused silica,” Appl. Phys. Lett. 96, 101903 (2010).
[Crossref]

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[Crossref]

Appl. Surf. Sci. (1)

D. Ashkenasi, M. Lorenz, R. Stoian, and A. Rosenfeld, “Surface damage threshold and structuring of dielectrics using femtosecond laser pulses: the role of incubation,” Appl. Surf. Sci. 150, 101–106 (1999).
[Crossref]

IEEE J. Quantum Electron. (1)

X. Liu, D. Du, and G. Mourou, “Laser ablation and micromachining with ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 1707–1716 (1997).
[Crossref]

J. Appl. Phys. (1)

D. K. Sardar, M. F. Becker, and R. M. Walser, “Multipulse laser damage of GaAs surfaces,” J. Appl. Phys. 62, 3688–3693 (1987).
[Crossref]

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

Opt. Lett. (1)

Phys. Rev. Lett. (1)

V. R. Bhardwaj, E. Simova, P. P. Rajeev, C. Hnatovsky, R. S. Taylor, D. M. Rayner, and P. B. Corkum, “Optically produced arrays of planar nanostructures inside fused silica,” Phys. Rev. Lett. 96, 057404 (2006).
[Crossref] [PubMed]

Other (2)

L. A. Giannuzzi and F. A. Stevie, Introduction to Focused Ion Beams (Springer Science + Business Media, Inc., 2005).
[Crossref]

C. Phipps, Laser Ablation and Its Applications (Springer, 2006).

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Figures (5)

Fig. 1
Fig. 1 Experimental Setup. The inset shows the third harmonic signal as a function of the translation distance along x-axis. The rising and falling edges correspond to the opening and closing of the electronic shutter. The gradually reduced third harmonic signal indicates the decrease of the laser intensity due to the displacement of the focal spot from the sample surface.
Fig. 2
Fig. 2 (a). Schematic drawing showing the threshold effect of nanograting formation. (b). The SEM pictures for nanograting formation at different pulse energies (90, 100, 110, 120 nJ/pulse) for a given pulse to pulse spacing 10 nm. K: laser propagation direction; S: scan direction; E: electric field
Fig. 3
Fig. 3 The overall extent of the nanogratings as a function of incident pulse energy for three different pulse to pulse spacings (5, 10 and 20 nm). Solid lines were fitted according to Eq. (2).
Fig. 4
Fig. 4 Nanogratings written at pulse energy 100 nJ at different pulse to pulse spacings. K: laser direction; E: electric field; S: scan direction. d: pulse to pulse spacing. (a). d = 100 nm, depth = 363 nm. (b). d = 80 nm, depth = 418 nm. (c). d = 40 nm, depth = 428 nm. (d). d = 20 nm, depth = 444 nm.
Fig. 5
Fig. 5 The incubation curve for nanograting formation. The ablation threshold drops dramatically and levels off at low and high effective pulse number (wz/d), respectively.

Tables (1)

Tables Icon

Table 1 Measured Beam Radii, Threshold Energies and the Computed Threshold Fluences for Different Pulse to Pulse Spacings

Equations (4)

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F ( r , z ) = F 0 w 0 2 w z 2 exp ( 2 r 2 w z 2 )
E th = E in exp ( D 2 2 w z 2 )
F d = F 0 + ( F ss F 0 ) exp [ k ( w z / d 1 ) ] , d < w z
F d = F ss , d w z

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