## Investigation of laser-induced damage by various initiators on the subsurface of fused silica |

Optics Express, Vol. 20, Issue 20, pp. 22095-22101 (2012)

http://dx.doi.org/10.1364/OE.20.022095

Acrobat PDF (796 KB)

### Abstract

We develop a model that describes the effect of size distribution of nanoabsorbers on the subsurface of fused silica on laser-damage probability. Using Mie theory and heat equation, we obtain the correlation between the critical fluence and particle radius. Considering a power law distribution of nanoabsorbers, the curves of laser-damage probability are calculated based on experimental results of contents of contaminations and a fit parameter of size distribution of nanoabsorbers. This paper presents the influence of various potential candidates, jointly, on laser-induced damage.

© 2012 OSA

## 1. Introduction

_{2}) and potassium dihydrogen phosphate (KDP), remains today a key limitation for large aperture, high-power laser systems. It is inevitable that the nano-absobing particles and nano-defects originated from polishing and grinding processes are formed on the subsurface of fused silica [1

1. M. R. Kozlowski, J. Carr, I. D. Hutcheon, R. A. Torres, L. M. Sheehan, D. W. Camp, and M. Yan, “Depth profiling of polishing-induced contamination on fused silica surface,” Proc. SPIE **3244**, 365–375 (1998). [CrossRef]

2. J. Neauport, L. Lamaignere, H. Bercegol, F. Pilon, and J. C. Birolleau, “Polishing-induced contamination of fused silica optics and laser induced damage density at 351 nm,” Opt. Express **13**(25), 10163–10171 (2005). [CrossRef] [PubMed]

^{11}W/cm

^{2}) [3

3. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter **53**(4), 1749–1761 (1996). [CrossRef] [PubMed]

5. P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. **35**(16), 2702–2704 (2010). [CrossRef] [PubMed]

1. M. R. Kozlowski, J. Carr, I. D. Hutcheon, R. A. Torres, L. M. Sheehan, D. W. Camp, and M. Yan, “Depth profiling of polishing-induced contamination on fused silica surface,” Proc. SPIE **3244**, 365–375 (1998). [CrossRef]

2. J. Neauport, L. Lamaignere, H. Bercegol, F. Pilon, and J. C. Birolleau, “Polishing-induced contamination of fused silica optics and laser induced damage density at 351 nm,” Opt. Express **13**(25), 10163–10171 (2005). [CrossRef] [PubMed]

6. S. Papernov, A. W. Schmid, R. Krishnan, and L. Tsybeskov, “Using colloidal gold nanoparticles for studies of laser interaction with defects in thin films,” Proc. SPIE **4347**, 146–154 (2001). [CrossRef]

10. J. Y. Natoli, L. Gallais, B. Bertussi, A. During, M. Commandre, J. L. Rullier, F. Bonneau, and P. Combis, “Localized pulsed laser interaction with submicronic gold particles embedded in silica: a method for investigating laser damage initiation,” Opt. Express **11**(7), 824–829 (2003). [CrossRef] [PubMed]

6. S. Papernov, A. W. Schmid, R. Krishnan, and L. Tsybeskov, “Using colloidal gold nanoparticles for studies of laser interaction with defects in thin films,” Proc. SPIE **4347**, 146–154 (2001). [CrossRef]

7. F. Bonneau, P. Combis, J. L. Rullier, J. Vierne, M. Pellin, M. Savina, M. Broyer, E. Cottancin, J. Tuaillon, M. Pellarin, L. Gallais, J. Y. Natoli, M. Perra, H. Bercegol, L. Lamaignere, M. Loiseau, and J. T. Donohue, “Study of UV laser interaction with gold nanoparticles embedded in silica,” J. Appl. Phys. **75**(8), 803–815 (2002). [CrossRef]

8. S. Papernov and A. W. Schmid, “Correlations between embedded single gold nanoparticles in SiO_{2} thin film and nanoscale crater formation induced by pulsed-laser radiation,” J. Appl. Phys. **92**(10), 5720–5728 (2002). [CrossRef]

11. R. Hopper and D. Uhlmann, “Mechanism of inclusion damage in laser glass,” J. Appl. Phys. **41**(10), 4023–4037 (1970). [CrossRef]

12. M. D. Feit and A. M. Rubenchik, “Implications of nanoabsorber initiators for damage probability curves, pulselength scaling and laser conditioning,” Proc. SPIE **5273**, 74–82 (2004). [CrossRef]

## 2. Model

### 2.1. Threshold equation

*Q*absorbed by the particle is

*Q*=

*π a*

^{2}

*αI*, where,

*α*is the absorptivity,

*I*the intensity and

*a*the particle radius. The absorptivity

*α*is calculated with Mie theory [14]. The details of the model for calculation are exposed in Ref [15

15. X. Gao, G. Y. Feng, J. H. Han, N. J. Chen, C. Tang, and S. H. Zhou, “Investigation of laser-induced damage by nanoabsorbers at the surface of fused silica,” Appl. Opt. **51**(13), 2463–2468 (2012). [CrossRef] [PubMed]

_{2}, Fe, Zr) embedded in fused silica. The particles of few 100 nm can be detectable by classical optical techniques, so we pay our attention to only the left parts of the absorptivity curves. We can see from Fig. 1 that the absorptivity of Cu and Fe particles is larger than the others (Al, CeO

_{2}, and Zr), when the particles radius is less than 160 nm.

*I*=

*I*

_{0}exp[-4(

*t*

^{2}/

*τ*

^{2})]. The temperature evolution in the spherical particle can be obtained by solving the equation of heat conduction where,

*T*is finite as

_{i}*r*→ 0 and

*T*→ 0 as

_{s}*r*→ ∞. The boundary condition iswhere,

*T*,

*C*, and

*D*present the temperature, thermal conductivity and thermal diffusivity, respectively. The suffixes

*i*and

*s*denote nanoparticle and surrounding matrix. Damage is assumed to take place when the temperature of the surrounding matrix reaches a critical value

*T*(2200 K) [16

_{c}16. C. W. Carr, J. D. Bude, and P. DeMange, “Laser-supported solid-state absorption fronts in silica,” Phys. Rev. B **82**(18), 184304 (2010). [CrossRef]

^{2}, during pulse duration of 7 ns and numerically calculate the solution. Figure 2 illustrates the evolution of temperature at various particle-silica interfaces with particle radius of 5 nm.

*F*required to reach the critical temperature

_{c}*T*

_{c}_{.}Subsequently,

*F*can be plotted as a function of the particle radius by iterating above calculation for different particle radius.

_{c}_{2}, and Zr), when the particles radius is less than 160 nm.

### 2.2. Laser-damage probability

15. X. Gao, G. Y. Feng, J. H. Han, N. J. Chen, C. Tang, and S. H. Zhou, “Investigation of laser-induced damage by nanoabsorbers at the surface of fused silica,” Appl. Opt. **51**(13), 2463–2468 (2012). [CrossRef] [PubMed]

17. J. Y. Natoli, L. Gallais, H. Akhouayri, and C. Amra, “Laser-induced damage of materials in bulk, thin-film, and liquid forms,” Appl. Opt. **41**(16), 3156–3166 (2002). [CrossRef] [PubMed]

20. L. Gallais, J. Capoulade, J. Y. Natoli, and M. Commandré, “Investigation of nanodefect properties in optical coatings by coupling measured and simulated laser damage statistics,” J. Appl. Phys. **104**(5), 053120 (2008). [CrossRef]

15. X. Gao, G. Y. Feng, J. H. Han, N. J. Chen, C. Tang, and S. H. Zhou, “Investigation of laser-induced damage by nanoabsorbers at the surface of fused silica,” Appl. Opt. **51**(13), 2463–2468 (2012). [CrossRef] [PubMed]

19. J. B. Trenholme, M. D. Feit, and A. M. Rubenchik, “Size-selection initiation model extended to include shape and random factors,” Proc. SPIE **5991**, 325–336 (2005). [CrossRef]

20. L. Gallais, J. Capoulade, J. Y. Natoli, and M. Commandré, “Investigation of nanodefect properties in optical coatings by coupling measured and simulated laser damage statistics,” J. Appl. Phys. **104**(5), 053120 (2008). [CrossRef]

*n*(

*a*) of particles (per area, per size) to have a power law form as a function of size

*a*with exponent

*γ*.

*a*is the particle radius with the range of

*a*

_{min}≤

*a*≤

*a*

_{max}. Then the number density

*n*(

*a*) is given by [19

19. J. B. Trenholme, M. D. Feit, and A. M. Rubenchik, “Size-selection initiation model extended to include shape and random factors,” Proc. SPIE **5991**, 325–336 (2005). [CrossRef]

*N*is the total density of per area. The suffix

*k*presents different types of particles. We can see in subsection 2.1 that particles of few nanometers cannot initiate damage under our experimental condition, so we insert the lower size limit

*a*

_{min}from the results of calculation. The upper size limit

*a*

_{max}is just a convenience in numerical computations, since it has very small effect on the results of the model. Thereby, the total volume

*V*of particles (per area) can be expressed asIf

_{k}*γ*= 4, the solution can be written asIf

*γ*≠4, the solution can be written asUsing the relations Eqs. (6) or (7), the Eq. (4) can be written aswhere,

*V*can also be expressed as

_{k}*V*/

_{k}= m_{k}*ρ*.

_{k}*m*is the total mass of particles (per area) and

_{k}*ρ*is mass density of the particles. With the knowledge of the critical fluence as mentioned in subsection 2.1 and the defect size distribution, we can obtain the density of damaging defects as a function of critical fluence,

_{k}*g*(

*F*)where,

_{c,k}*g*(

*F*) gives the number of defects per unit area that damage at fluence between

_{c,k}*F*and

_{c,k}*F*+

_{c,k}*dF*. Thus, the number of defects

_{c,k}*N*(

*F*) located under the laser spot area

*S*(

_{Fc,k}*F*) which can induce damage at the fluence

*F*can be expressed aswhere,

*S*(

_{Fc,k}*F*) can be written as

*S*(

_{Fc,k}*F*) = (

*πω*

_{0}

^{2}/2) ln(

*F/F*) and

_{c,k}*ω*

_{0}is the spot radius. The damage probability

*P*(

*F*) is the probability of defect receiving more fluence than its critical fluence, which can be expressed as [20

20. L. Gallais, J. Capoulade, J. Y. Natoli, and M. Commandré, “Investigation of nanodefect properties in optical coatings by coupling measured and simulated laser damage statistics,” J. Appl. Phys. **104**(5), 053120 (2008). [CrossRef]

*m*is given, the curves of damage probability can be calculated as a function of fluence by choosing a fit parameter

_{k}*γ*.

## 3. Experiment

**51**(13), 2463–2468 (2012). [CrossRef] [PubMed]

*F*. By counting the number of damage regions at each fluence

*F*, we can plot the probability curve

*P*(

*F*). As mentioned in subsection 2.2, laser-damage probability has a correlation with the spot radius

*ω*

_{0}, so two different kinds of spot radii (155 μm and 360 μm at 1/

*e*

^{2}) have been applied to check the validity of our model.

2. J. Neauport, L. Lamaignere, H. Bercegol, F. Pilon, and J. C. Birolleau, “Polishing-induced contamination of fused silica optics and laser induced damage density at 351 nm,” Opt. Express **13**(25), 10163–10171 (2005). [CrossRef] [PubMed]

_{2}, Fe, Zr) on the subsurface (3~5 μm) of our samples.

*m*(per area) have a homogeneous distribution on the subsurface of fused silica. Thereby,

_{k}*m*can be obtained according to the measured results in Table 2. Considering our experimental condition, the lower size limit

_{k}*a*min for various particles can be obtained by calculating the critical fluence as a function of particle radius as mentioned in subsection 2.1 with fluence ranging from 0 J/cm2 to 25 J/cm2. From the result of the calculation, the values of

*a*

_{min}for Cu and Fe particles are lower than others (Al, CeO

_{2}, and Zr). The particle sizes most susceptible to create damage are chosen as the upper size limit

*a*

_{max}for various particles as seen in Fig. 3

_{.}The values of

*a*

_{max}are set to 30 nm for convenience in numerical computations, since they have very small effect on the results of the model. The theoretical laser-damage probability can be calculated with different spot sizes by choosing a fit parameter

*γ*. We now apply the calculated damage probability to fit the experimental data with 155 µm and 360 µm spot radii. By estimating the average dissolved depth is 4 µm, the error for the calculated damage probability is about 0.04. Figure 5 shows the experimental curves of laser-damage probability measured on the surface of fused silica and theoretical curves calculated with the parameter

*γ*= 34.

*γ*= 34. The calculated damage threshold with spot size dependence can be obtained with good agreement to the experimental result. The interesting point is that the model can describe observed spot size dependence since with the same parameter

*γ*= 34 the data can be fit with the two different spot sizes. Conversely, once the parameter

*γ*is obtained by fitting the experimental data, the defect distribution for various particles embedded in the subsurface of fused silica can be identified.

## 4. Conclusion

*e*

^{2}), when the parameter

*γ*= 34 is considered in our simulation. Consequently, the size distribution

*γ*of nanoabsorbers on the surface of optical materials can be obtained according to the method. Of course the result must be taken with caution since different assumptions have been made for the calculations, but it is noteworthy that the curves of laser-damage probability obtained with different spot sizes have been explained with same size distribution. This model is of interest for the study of polishing process since it improves the knowledge on the properties of metallic or dielectric nanoabsorbers on the subsurface of fused silica.

## Acknowledgments

## References and links

1. | M. R. Kozlowski, J. Carr, I. D. Hutcheon, R. A. Torres, L. M. Sheehan, D. W. Camp, and M. Yan, “Depth profiling of polishing-induced contamination on fused silica surface,” Proc. SPIE |

2. | J. Neauport, L. Lamaignere, H. Bercegol, F. Pilon, and J. C. Birolleau, “Polishing-induced contamination of fused silica optics and laser induced damage density at 351 nm,” Opt. Express |

3. | B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter |

4. | T. A. Laurence, J. D. Bude, N. Shen, T. Feldman, P. E. Miller, W. A. Steele, and T. Suratwala, “Metallic-like photoluminescence and absorption in fused silica surface flaws,” Appl. Phys. Lett. |

5. | P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett. |

6. | S. Papernov, A. W. Schmid, R. Krishnan, and L. Tsybeskov, “Using colloidal gold nanoparticles for studies of laser interaction with defects in thin films,” Proc. SPIE |

7. | F. Bonneau, P. Combis, J. L. Rullier, J. Vierne, M. Pellin, M. Savina, M. Broyer, E. Cottancin, J. Tuaillon, M. Pellarin, L. Gallais, J. Y. Natoli, M. Perra, H. Bercegol, L. Lamaignere, M. Loiseau, and J. T. Donohue, “Study of UV laser interaction with gold nanoparticles embedded in silica,” J. Appl. Phys. |

8. | S. Papernov and A. W. Schmid, “Correlations between embedded single gold nanoparticles in SiO |

9. | P. Jonnard, G. Dufour, J. L. Rullier, J. P. Morreeuw, and J. Donohue, “Surface density enhancement of gold in silica film under laser irradiation at 355 nm,” Appl. Phys. Lett. |

10. | J. Y. Natoli, L. Gallais, B. Bertussi, A. During, M. Commandre, J. L. Rullier, F. Bonneau, and P. Combis, “Localized pulsed laser interaction with submicronic gold particles embedded in silica: a method for investigating laser damage initiation,” Opt. Express |

11. | R. Hopper and D. Uhlmann, “Mechanism of inclusion damage in laser glass,” J. Appl. Phys. |

12. | M. D. Feit and A. M. Rubenchik, “Implications of nanoabsorber initiators for damage probability curves, pulselength scaling and laser conditioning,” Proc. SPIE |

13. | M. J. Weber, |

14. | H. C. Hulst, |

15. | X. Gao, G. Y. Feng, J. H. Han, N. J. Chen, C. Tang, and S. H. Zhou, “Investigation of laser-induced damage by nanoabsorbers at the surface of fused silica,” Appl. Opt. |

16. | C. W. Carr, J. D. Bude, and P. DeMange, “Laser-supported solid-state absorption fronts in silica,” Phys. Rev. B |

17. | J. Y. Natoli, L. Gallais, H. Akhouayri, and C. Amra, “Laser-induced damage of materials in bulk, thin-film, and liquid forms,” Appl. Opt. |

18. | H. Krol, L. Gallais, C. Grezes-Besset, J. Y. Natoli, and M. Commandre, “Investigation of nanoprecursors threshold distribution in laser-damage testing,” Opt. Commun. |

19. | J. B. Trenholme, M. D. Feit, and A. M. Rubenchik, “Size-selection initiation model extended to include shape and random factors,” Proc. SPIE |

20. | L. Gallais, J. Capoulade, J. Y. Natoli, and M. Commandré, “Investigation of nanodefect properties in optical coatings by coupling measured and simulated laser damage statistics,” J. Appl. Phys. |

**OCIS Codes**

(140.3440) Lasers and laser optics : Laser-induced breakdown

(310.3840) Thin films : Materials and process characterization

(320.4240) Ultrafast optics : Nanosecond phenomena

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: June 29, 2012

Revised Manuscript: September 2, 2012

Manuscript Accepted: September 7, 2012

Published: September 12, 2012

**Citation**

Xiang Gao, Guoying Feng, Jinghua Han, and Lingling Zhai, "Investigation of laser-induced damage by various initiators on the subsurface of fused silica," Opt. Express **20**, 22095-22101 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-20-22095

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### References

- M. R. Kozlowski, J. Carr, I. D. Hutcheon, R. A. Torres, L. M. Sheehan, D. W. Camp, and M. Yan, “Depth profiling of polishing-induced contamination on fused silica surface,” Proc. SPIE3244, 365–375 (1998). [CrossRef]
- J. Neauport, L. Lamaignere, H. Bercegol, F. Pilon, and J. C. Birolleau, “Polishing-induced contamination of fused silica optics and laser induced damage density at 351 nm,” Opt. Express13(25), 10163–10171 (2005). [CrossRef] [PubMed]
- B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter53(4), 1749–1761 (1996). [CrossRef] [PubMed]
- T. A. Laurence, J. D. Bude, N. Shen, T. Feldman, P. E. Miller, W. A. Steele, and T. Suratwala, “Metallic-like photoluminescence and absorption in fused silica surface flaws,” Appl. Phys. Lett.94(15), 151114 (2009). [CrossRef]
- P. E. Miller, J. D. Bude, T. I. Suratwala, N. Shen, T. A. Laurence, W. A. Steele, J. Menapace, M. D. Feit, and L. L. Wong, “Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces,” Opt. Lett.35(16), 2702–2704 (2010). [CrossRef] [PubMed]
- S. Papernov, A. W. Schmid, R. Krishnan, and L. Tsybeskov, “Using colloidal gold nanoparticles for studies of laser interaction with defects in thin films,” Proc. SPIE4347, 146–154 (2001). [CrossRef]
- F. Bonneau, P. Combis, J. L. Rullier, J. Vierne, M. Pellin, M. Savina, M. Broyer, E. Cottancin, J. Tuaillon, M. Pellarin, L. Gallais, J. Y. Natoli, M. Perra, H. Bercegol, L. Lamaignere, M. Loiseau, and J. T. Donohue, “Study of UV laser interaction with gold nanoparticles embedded in silica,” J. Appl. Phys.75(8), 803–815 (2002). [CrossRef]
- S. Papernov and A. W. Schmid, “Correlations between embedded single gold nanoparticles in SiO2 thin film and nanoscale crater formation induced by pulsed-laser radiation,” J. Appl. Phys.92(10), 5720–5728 (2002). [CrossRef]
- P. Jonnard, G. Dufour, J. L. Rullier, J. P. Morreeuw, and J. Donohue, “Surface density enhancement of gold in silica film under laser irradiation at 355 nm,” Appl. Phys. Lett.85(4), 591–593 (2004). [CrossRef]
- J. Y. Natoli, L. Gallais, B. Bertussi, A. During, M. Commandre, J. L. Rullier, F. Bonneau, and P. Combis, “Localized pulsed laser interaction with submicronic gold particles embedded in silica: a method for investigating laser damage initiation,” Opt. Express11(7), 824–829 (2003). [CrossRef] [PubMed]
- R. Hopper and D. Uhlmann, “Mechanism of inclusion damage in laser glass,” J. Appl. Phys.41(10), 4023–4037 (1970). [CrossRef]
- M. D. Feit and A. M. Rubenchik, “Implications of nanoabsorber initiators for damage probability curves, pulselength scaling and laser conditioning,” Proc. SPIE5273, 74–82 (2004). [CrossRef]
- M. J. Weber, Handbook of Optical Materials (CRC, 2002).
- H. C. Hulst, Light Scattering by Small Particles (Wiley, 1957).
- X. Gao, G. Y. Feng, J. H. Han, N. J. Chen, C. Tang, and S. H. Zhou, “Investigation of laser-induced damage by nanoabsorbers at the surface of fused silica,” Appl. Opt.51(13), 2463–2468 (2012). [CrossRef] [PubMed]
- C. W. Carr, J. D. Bude, and P. DeMange, “Laser-supported solid-state absorption fronts in silica,” Phys. Rev. B82(18), 184304 (2010). [CrossRef]
- J. Y. Natoli, L. Gallais, H. Akhouayri, and C. Amra, “Laser-induced damage of materials in bulk, thin-film, and liquid forms,” Appl. Opt.41(16), 3156–3166 (2002). [CrossRef] [PubMed]
- H. Krol, L. Gallais, C. Grezes-Besset, J. Y. Natoli, and M. Commandre, “Investigation of nanoprecursors threshold distribution in laser-damage testing,” Opt. Commun.256(1–3), 184–189 (2005). [CrossRef]
- J. B. Trenholme, M. D. Feit, and A. M. Rubenchik, “Size-selection initiation model extended to include shape and random factors,” Proc. SPIE5991, 325–336 (2005). [CrossRef]
- L. Gallais, J. Capoulade, J. Y. Natoli, and M. Commandré, “Investigation of nanodefect properties in optical coatings by coupling measured and simulated laser damage statistics,” J. Appl. Phys.104(5), 053120 (2008). [CrossRef]

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