Abstract

We simulate and calculate numerically the electromagnetic field and energy flux around a surface crack of an Nd-doped phosphate laser glass by using the finite-difference time-domain method. Because of a strong interference between the incident wave and the total internal reflections from the crack and the glass surface, the electric field is redistributed and enhanced. The results show that the electric-field distribution and corresponding energy flux component depend sensitively on the light polarization and crack geometry, such as orientation and depth. The polarization of the incident laser beam relative to the crack surfaces will determine the profile of the electric field around the crack. Under TE wave incidence, the energy flux peak is always inside the glass. But under TM wave incidence, the energy flux peak will be located inside the glass or inside the air gap. For both incident modes, the light intensification factor increases with the crack depth, especially for energy flux along the surface. Because cracks on the polished surfaces are the same as the roots extending down, the probability for much larger intensification occurring is high. The results suggest that the surface laser-damage threshold of Nd-doped phosphate may decrease dramatically with subsurface damage.

© 2010 Optical Society of America

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References

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  1. J. H. Campbell and T. I. Suratwala, “Nd-doped phosphate glasses for high-energy/high-peak-power lasers,” J. Non-Cryst. Solids 263 & 264, 318–341 (2000).
    [CrossRef]
  2. T. I. Suratwala, J. H. Campell, and P. E. Miller, “Phosphate laser glass for NIF: production status, slab section and recent technical advances,” Proc. SPIE 5341, 102–113 (2004).
    [CrossRef]
  3. T. I. Suratwala, P. E. Miller, P. R. Ehrmann, and R. A. Steele, “Polishing slurry induced surface haze on phosphate laser glasses,” J. Non-Cryst. Solids 351, 2091–2101 (2005).
    [CrossRef]
  4. J. H. Campbell, “Damage resistant optical glasses for high power lasers: a continuing glass science and technology challenge,” Glass Sci. Technol. 75, 91–108 (2002).
  5. M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser induced surface damage,” Proc. SPIE 5273, 264–271 (2004).
    [CrossRef]
  6. J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
    [CrossRef]
  7. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [CrossRef]
  8. F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, “Role of light intensification by cracks in optical breakdown on surface,” J. Opt. Soc. Am. A 18, 2607–2616 (2001).
    [CrossRef]
  9. C. J. Stolz, M. D. Feit, and T. V. Pistor, “Laser intensification by spherical inclusions embedded within multilayer coatings,” Appl. Opt. 45, 1594–1601 (2006).
    [CrossRef] [PubMed]
  10. C. J. Stolz, S. Hafeman, and T. V. Pistor, “Laser intensification modeling of coating inclusions irradiated at 351 and 1053nm,” Appl. Opt. 47, C162–C166 (2008).
    [CrossRef] [PubMed]
  11. C. J. Stolz, F. Y. Génin, and T. V. Pistor, “Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45 degrees incidence,” Proc. SPIE 5273, 41–49(2004).
    [CrossRef]
  12. P. P. Hed, D. F. Edwards, and J. B. Davis, “Subsurface damage in optical materials: origin, measurement and removal,” report UCRL-99548 (Lawrence Livermore National Laboratory, 1989), pp. 1–17.
  13. J. Shen, S. Liu, K. Yi, H. He, J. Shao, and Z. Fan, “Subsurface damage in optical substrates,” Optik (Jena) 116, 288–294(2005).
    [CrossRef]
  14. J. A. Randi, J. C. Lambropoulos, and S. D. Jacobs, “Determination of subsurface damage in optical materials using a non-invasive technique,” in Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America, 2002), pp. 61–63.
  15. S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–606 (1986).
    [CrossRef]
  16. B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-Induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251(1995).
    [CrossRef] [PubMed]
  17. J. Lambropoulos, “Subsurface damage in microgrinding optical glasses,” LLE Review: Quarterly Report 73, 45–49 (1997).
  18. J. Hu, J. Yang, W. Chen, and C. Zhou, “Experimental investigation of enhancing the subsurface damage threshold of Nd-doped phosphate glass,” Chin. Opt. Lett. 6, 681–684 (2008).
    [CrossRef]

2008

2006

2005

T. I. Suratwala, P. E. Miller, P. R. Ehrmann, and R. A. Steele, “Polishing slurry induced surface haze on phosphate laser glasses,” J. Non-Cryst. Solids 351, 2091–2101 (2005).
[CrossRef]

J. Shen, S. Liu, K. Yi, H. He, J. Shao, and Z. Fan, “Subsurface damage in optical substrates,” Optik (Jena) 116, 288–294(2005).
[CrossRef]

2004

M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser induced surface damage,” Proc. SPIE 5273, 264–271 (2004).
[CrossRef]

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

T. I. Suratwala, J. H. Campell, and P. E. Miller, “Phosphate laser glass for NIF: production status, slab section and recent technical advances,” Proc. SPIE 5341, 102–113 (2004).
[CrossRef]

C. J. Stolz, F. Y. Génin, and T. V. Pistor, “Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45 degrees incidence,” Proc. SPIE 5273, 41–49(2004).
[CrossRef]

2002

J. H. Campbell, “Damage resistant optical glasses for high power lasers: a continuing glass science and technology challenge,” Glass Sci. Technol. 75, 91–108 (2002).

2001

2000

J. H. Campbell and T. I. Suratwala, “Nd-doped phosphate glasses for high-energy/high-peak-power lasers,” J. Non-Cryst. Solids 263 & 264, 318–341 (2000).
[CrossRef]

1997

J. Lambropoulos, “Subsurface damage in microgrinding optical glasses,” LLE Review: Quarterly Report 73, 45–49 (1997).

1995

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-Induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251(1995).
[CrossRef] [PubMed]

1986

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–606 (1986).
[CrossRef]

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

Borden, M. R.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Campbell, J. H.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

J. H. Campbell, “Damage resistant optical glasses for high power lasers: a continuing glass science and technology challenge,” Glass Sci. Technol. 75, 91–108 (2002).

J. H. Campbell and T. I. Suratwala, “Nd-doped phosphate glasses for high-energy/high-peak-power lasers,” J. Non-Cryst. Solids 263 & 264, 318–341 (2000).
[CrossRef]

Campell, J. H.

T. I. Suratwala, J. H. Campell, and P. E. Miller, “Phosphate laser glass for NIF: production status, slab section and recent technical advances,” Proc. SPIE 5341, 102–113 (2004).
[CrossRef]

Chase, L. L.

Chen, W.

Davis, J. B.

P. P. Hed, D. F. Edwards, and J. B. Davis, “Subsurface damage in optical materials: origin, measurement and removal,” report UCRL-99548 (Lawrence Livermore National Laboratory, 1989), pp. 1–17.

Edwards, D. F.

P. P. Hed, D. F. Edwards, and J. B. Davis, “Subsurface damage in optical materials: origin, measurement and removal,” report UCRL-99548 (Lawrence Livermore National Laboratory, 1989), pp. 1–17.

Ehrmann, P. R.

T. I. Suratwala, P. E. Miller, P. R. Ehrmann, and R. A. Steele, “Polishing slurry induced surface haze on phosphate laser glasses,” J. Non-Cryst. Solids 351, 2091–2101 (2005).
[CrossRef]

Fan, Z.

J. Shen, S. Liu, K. Yi, H. He, J. Shao, and Z. Fan, “Subsurface damage in optical substrates,” Optik (Jena) 116, 288–294(2005).
[CrossRef]

Feit, M. D.

C. J. Stolz, M. D. Feit, and T. V. Pistor, “Laser intensification by spherical inclusions embedded within multilayer coatings,” Appl. Opt. 45, 1594–1601 (2006).
[CrossRef] [PubMed]

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser induced surface damage,” Proc. SPIE 5273, 264–271 (2004).
[CrossRef]

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-Induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251(1995).
[CrossRef] [PubMed]

Génin, F. Y.

C. J. Stolz, F. Y. Génin, and T. V. Pistor, “Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45 degrees incidence,” Proc. SPIE 5273, 41–49(2004).
[CrossRef]

F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, “Role of light intensification by cracks in optical breakdown on surface,” J. Opt. Soc. Am. A 18, 2607–2616 (2001).
[CrossRef]

Hackel, R. P.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Hafeman, S.

Hawley, D.

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–606 (1986).
[CrossRef]

Hawley-Fedder, R. A.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

He, H.

J. Shen, S. Liu, K. Yi, H. He, J. Shao, and Z. Fan, “Subsurface damage in optical substrates,” Optik (Jena) 116, 288–294(2005).
[CrossRef]

Hed, P. P.

P. P. Hed, D. F. Edwards, and J. B. Davis, “Subsurface damage in optical materials: origin, measurement and removal,” report UCRL-99548 (Lawrence Livermore National Laboratory, 1989), pp. 1–17.

Hu, J.

Jacobs, S. D.

J. A. Randi, J. C. Lambropoulos, and S. D. Jacobs, “Determination of subsurface damage in optical materials using a non-invasive technique,” in Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America, 2002), pp. 61–63.

Lambropoulos, J.

J. Lambropoulos, “Subsurface damage in microgrinding optical glasses,” LLE Review: Quarterly Report 73, 45–49 (1997).

Lambropoulos, J. C.

J. A. Randi, J. C. Lambropoulos, and S. D. Jacobs, “Determination of subsurface damage in optical materials using a non-invasive technique,” in Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America, 2002), pp. 61–63.

Liu, S.

J. Shen, S. Liu, K. Yi, H. He, J. Shao, and Z. Fan, “Subsurface damage in optical substrates,” Optik (Jena) 116, 288–294(2005).
[CrossRef]

Menapace, J. A.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Miller, P. E.

T. I. Suratwala, P. E. Miller, P. R. Ehrmann, and R. A. Steele, “Polishing slurry induced surface haze on phosphate laser glasses,” J. Non-Cryst. Solids 351, 2091–2101 (2005).
[CrossRef]

T. I. Suratwala, J. H. Campell, and P. E. Miller, “Phosphate laser glass for NIF: production status, slab section and recent technical advances,” Proc. SPIE 5341, 102–113 (2004).
[CrossRef]

Perry, M. D.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-Induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251(1995).
[CrossRef] [PubMed]

Pistor, T. V.

Randi, J. A.

J. A. Randi, J. C. Lambropoulos, and S. D. Jacobs, “Determination of subsurface damage in optical materials using a non-invasive technique,” in Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America, 2002), pp. 61–63.

Riley, M. O.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Roy, R.

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–606 (1986).
[CrossRef]

Rubenchik, A. M.

M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser induced surface damage,” Proc. SPIE 5273, 264–271 (2004).
[CrossRef]

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-Induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251(1995).
[CrossRef] [PubMed]

Runkel, M.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Salleo, A.

Shao, J.

J. Shen, S. Liu, K. Yi, H. He, J. Shao, and Z. Fan, “Subsurface damage in optical substrates,” Optik (Jena) 116, 288–294(2005).
[CrossRef]

Shen, J.

J. Shen, S. Liu, K. Yi, H. He, J. Shao, and Z. Fan, “Subsurface damage in optical substrates,” Optik (Jena) 116, 288–294(2005).
[CrossRef]

Shore, B. W.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-Induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251(1995).
[CrossRef] [PubMed]

Steele, R. A.

T. I. Suratwala, P. E. Miller, P. R. Ehrmann, and R. A. Steele, “Polishing slurry induced surface haze on phosphate laser glasses,” J. Non-Cryst. Solids 351, 2091–2101 (2005).
[CrossRef]

Stolz, C. J.

C. J. Stolz, S. Hafeman, and T. V. Pistor, “Laser intensification modeling of coating inclusions irradiated at 351 and 1053nm,” Appl. Opt. 47, C162–C166 (2008).
[CrossRef] [PubMed]

C. J. Stolz, M. D. Feit, and T. V. Pistor, “Laser intensification by spherical inclusions embedded within multilayer coatings,” Appl. Opt. 45, 1594–1601 (2006).
[CrossRef] [PubMed]

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

C. J. Stolz, F. Y. Génin, and T. V. Pistor, “Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45 degrees incidence,” Proc. SPIE 5273, 41–49(2004).
[CrossRef]

Stuart, B. C.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-Induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251(1995).
[CrossRef] [PubMed]

Suratwala, T. I.

T. I. Suratwala, P. E. Miller, P. R. Ehrmann, and R. A. Steele, “Polishing slurry induced surface haze on phosphate laser glasses,” J. Non-Cryst. Solids 351, 2091–2101 (2005).
[CrossRef]

T. I. Suratwala, J. H. Campell, and P. E. Miller, “Phosphate laser glass for NIF: production status, slab section and recent technical advances,” Proc. SPIE 5341, 102–113 (2004).
[CrossRef]

J. H. Campbell and T. I. Suratwala, “Nd-doped phosphate glasses for high-energy/high-peak-power lasers,” J. Non-Cryst. Solids 263 & 264, 318–341 (2000).
[CrossRef]

Whitman, P. K.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Yang, J.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

Yi, K.

J. Shen, S. Liu, K. Yi, H. He, J. Shao, and Z. Fan, “Subsurface damage in optical substrates,” Optik (Jena) 116, 288–294(2005).
[CrossRef]

Yu, A. W.

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–606 (1986).
[CrossRef]

Yu, J.

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Zhou, C.

Zhu, S.

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–606 (1986).
[CrossRef]

Am. J. Phys.

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–606 (1986).
[CrossRef]

Appl. Opt.

Chin. Opt. Lett.

Glass Sci. Technol.

J. H. Campbell, “Damage resistant optical glasses for high power lasers: a continuing glass science and technology challenge,” Glass Sci. Technol. 75, 91–108 (2002).

IEEE Trans. Antennas Propag.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

J. Non-Cryst. Solids

J. H. Campbell and T. I. Suratwala, “Nd-doped phosphate glasses for high-energy/high-peak-power lasers,” J. Non-Cryst. Solids 263 & 264, 318–341 (2000).
[CrossRef]

T. I. Suratwala, P. E. Miller, P. R. Ehrmann, and R. A. Steele, “Polishing slurry induced surface haze on phosphate laser glasses,” J. Non-Cryst. Solids 351, 2091–2101 (2005).
[CrossRef]

J. Opt. Soc. Am. A

LLE Review: Quarterly Report

J. Lambropoulos, “Subsurface damage in microgrinding optical glasses,” LLE Review: Quarterly Report 73, 45–49 (1997).

Optik (Jena)

J. Shen, S. Liu, K. Yi, H. He, J. Shao, and Z. Fan, “Subsurface damage in optical substrates,” Optik (Jena) 116, 288–294(2005).
[CrossRef]

Phys. Rev. Lett.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-Induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74, 2248–2251(1995).
[CrossRef] [PubMed]

Proc. SPIE

C. J. Stolz, F. Y. Génin, and T. V. Pistor, “Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45 degrees incidence,” Proc. SPIE 5273, 41–49(2004).
[CrossRef]

T. I. Suratwala, J. H. Campell, and P. E. Miller, “Phosphate laser glass for NIF: production status, slab section and recent technical advances,” Proc. SPIE 5341, 102–113 (2004).
[CrossRef]

M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser induced surface damage,” Proc. SPIE 5273, 264–271 (2004).
[CrossRef]

J. H. Campbell, R. A. Hawley-Fedder, C. J. Stolz, J. A. Menapace, M. R. Borden, P. K. Whitman, J. Yu, M. Runkel, M. O. Riley, M. D. Feit, and R. P. Hackel, “NIF optical materials and fabrication technologies: an overview,” Proc. SPIE 5341, 84–101 (2004).
[CrossRef]

Other

P. P. Hed, D. F. Edwards, and J. B. Davis, “Subsurface damage in optical materials: origin, measurement and removal,” report UCRL-99548 (Lawrence Livermore National Laboratory, 1989), pp. 1–17.

J. A. Randi, J. C. Lambropoulos, and S. D. Jacobs, “Determination of subsurface damage in optical materials using a non-invasive technique,” in Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America, 2002), pp. 61–63.

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Figures (7)

Fig. 1
Fig. 1

Schematic of (a) the lateral crack and (b) its cross section in the simulation domain.

Fig. 2
Fig. 2

Steady-state distribution of the electric-field enhancement around the crack in the simulation domain with crack width W = 0.3 μm , crack angle θ = 36 ° , and crack depth d = 5.0 μm : (a) TE mode and (b) TM mode.

Fig. 3
Fig. 3

Distribution of energy flux enhancement around the crack with crack width w = 0.3 μm , angle θ = 36 ° , and depth d = 5.0 μm : (a) S z of TE, (b) S x of TE, (c) S z of TM, and (d) S x of TM.

Fig. 4
Fig. 4

Distribution of electric-field and energy flux enhancement around the crack with crack width w = 0.3 μm , angle θ = 54 ° , and depth d = 5.0 μm under TM illumination: (a) E x , (b) S z , and (c) S x .

Fig. 5
Fig. 5

Plot of peak electric-field enhancement due to the crack as a function of crack depth for crack angle θ = 36 ° and crack width w = 0.6 μm .

Fig. 6
Fig. 6

Plot of peak energy flux enhancement around the crack as a function of crack depth for crack angle θ = 36 ° and crack width w = 0.6 μm .

Fig. 7
Fig. 7

Plot of peak energy flux enhancement around the crack as a function of crack width for crack angle θ = 36 ° and crack depth d = 5.0 μm .

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