Abstract

When potassium dihydrogen phosphate crystals (KH2PO4 or KDP) are illuminated by multi-gigawatt nanosecond pulses, damages may appear in the crystal bulk. One can increase damage resistance through a conditioning that consists in carrying out a laser pre-exposure of the crystal. The present paper addresses the modeling of laser-induced damage and conditioning of KDP crystals. The method is based on heating a distribution of defects, the cooperation of which may lead to a dramatic temperature rise. In a previous investigation [Opt. Express 15, 4557-4576 (2007)], calculations were performed for cases where the heat diffusion was permitted in one and three spatial dimensions, corresponding respectively to planar and point defects. For the sake of completeness, the present study involves the 2D heat diffusion that is associated with linear defects. A comparison to experimental data leads to the conclusion that 1D calculations are the most appropriate for describing the laser-induced damage in KDP. Within this framework, the evolution of the damage density is given as a function of the laser energy density and an in-depth analysis of the results is provided based on simple analytical expressions that can be used for experimental design. Regarding the conditioning, assuming that it is due to a decrease in the defect absorption efficiency, two scenarios associated with various defect natures are proposed and these account for certain of the observed experimental facts. For instance, in order to improve the crystal resistance to damage, one needs to use a conditioning pulse duration shorter than the testing pulse. Also, a conditioning scenario based on the migration of point (atomic-size) defects allows the reproduction of a logarithmic-like evolution of the conditioning gain with respect to the number of laser pre-exposures. Moreover, this study aims at refining the knowledge regarding the precursor defects responsible for the laser-induced damage in KDP crystals. Within the presented modeling, the best candidate permitting the reproduction of major experimental facts is comprised of a collection of one-hundred-nanometer structural defects associated with point defects as for instance cracks and couples of oxygen interstitials and vacancies.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, "Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser," Int. Mater. Rev. 47, 113-152 (2002).
    [CrossRef]
  2. C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004).
    [CrossRef] [PubMed]
  3. J. Swain, S. Stokowski, D. Milam, and F. Rainer, " Improving the bulk laser damage resistance of potassium dihydrogen phosphate crystals by pulsed laser irradiation," Appl. Phys. Lett. 40, 350-352 (1982).
    [CrossRef]
  4. J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
    [CrossRef]
  5. A. K. Burnham, M. Runkel, M. D. Feit, A. M. Rubenchik, R. L. Floyd, T. A. Land, W. J. Siekhaus, and R. A. Hawley-Fedder, "Laser-induced damage in deuterated potassium dihydrogen phosphate," Appl. Opt. 42, 5483-5495 (2003).
    [CrossRef] [PubMed]
  6. R. A. Negres, P. DeMange, and S. G. Demos, "Investigation of laser annealing parameters for optimal laserdamage performance in deuterated potassium dihydrogen phosphate," Opt. Lett. 30, 2766-2768 (2005).
    [CrossRef] [PubMed]
  7. M. Pommies, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J.Y. Natoli, and H. Mathis, "Detection and characterization of absorption heterogeneities in KH2PO4 crystals," Opt. Commun. 267, 154-161 (2006).
    [CrossRef]
  8. J. E. Davis, R. S. Hughes, and H. W. Lee., "Investigation of optically generated transient electronic defects and protonic transport in hydrogen-bonded molecular solids. Isomorphs of potassium dihydrogen phosphate," Chem. Phys. Lett. 207, 540-545 (1993).
    [CrossRef]
  9. C. D. Marshall, S. A. Payne, M. A. Henesian, J. A. Speth, and H. T. Powell, "Ultraviolet-induced transient absorption in potassium dihydrogen phosphate and its influence on frequency conversion," J. Opt. Soc. Am. B 11, 774-785 (1994).
    [CrossRef]
  10. C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electron or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2005).
    [CrossRef]
  11. C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005).
    [CrossRef]
  12. K. Wang, C. Fang, J. Zhang, C. S. Liu, R. I. Boughton, S. Wang, and X. Zhao, "First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals," Phys. Rev. B 72, 184105 (2005).
    [CrossRef]
  13. N. Y. Garces, K. T. Stevens, L. E. Halliburton, S. G. Demos, H. B. Radousky, and N. P. Zaitseva, "Identification of electron and hole traps in KH2PO4 crystals," J. Appl. Phys. 89, 47-52 (2001).
    [CrossRef]
  14. M. M. Chirila, N. Y. Garces, L. E. Halliburton, S. G. Demos, T. A. Land, and H. B. Radousky, "Production and thermal decay of radiation-induced point defects in KDPO crystals," J. Appl. Phys 94, 6456-6462 (2003).
    [CrossRef]
  15. 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]
  16. J. J. De Yoreo and B. W. Woods, "A study of residual stress and the stress-optic effect in mixed crystals of K(DxH1−x)2PO4," J. Appl. Phys. 73, 7780-7789 (1993).
    [CrossRef]
  17. G. Duchateau and A. Dyan, "Coupling statistics and heat transfer to study laser-induced crystal damage by nanosecond pulses," Opt. Express 15, 4557-4576 (2007).
    [CrossRef] [PubMed]
  18. 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]
  19. L. Lamaignére, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J.-C. Poncetta, and H. Bercegol, "An accurate, repeatable, and well characterized measurement of laser damage density of optical materials," Rev. Sci. Instrum. 78, 103105 (2007).
    [CrossRef] [PubMed]
  20. P. DeMange, R. A. Negres, C. W. Carr, H. B. Radousky, and S. G. Demos, "Laser-induced defect reactions governing damage initiation in DKDP crystals," Opt. Express 14, 5313-5328 (2006).
    [CrossRef] [PubMed]
  21. P. Grua, J-P. Morreeuw, and H. Bercegol, "Progress in the understanding of fracture related damage of fused silica," Proc. SPIE 6720, 672003 (2007).
    [CrossRef]
  22. P. DeMange, C. W. Carr, R. A. Negres, H. B. Radousky, and S. G. Demos, "Laser annealing characteristics of multiple bulk defect populations within DKDP crystals," J. Appl. Phys. 104, 103103 (2008).
    [CrossRef]
  23. S. G. Demos, M. Staggs, M. Yan, H. B. Radousky, and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys. 85, 3988-3992 (1999).
    [CrossRef]
  24. S. G. Demos, M. Staggs, J. J. De Yoreo, and H. B. Radousky, "Imaging of laser-induced reactions of individual defect nanoclusters," Opt. Lett. 26, 1975-1977 (2001).
    [CrossRef]
  25. H. S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids (Oxford Science Publications, 1959).
  26. A. Dyan, F. Enguehard, S. Lallich, H. Piombini, and G. Duchateau, "Scaling laws in laser-induced potassium dihydrogen phosphate crystal damage by nanosecond pulses at 3ω," J. Opt. Soc. Am. B 25, 1087-1095 (2008).
    [CrossRef]
  27. J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
    [CrossRef]
  28. M. J. Matthews and M. D. Feit, "Effect of random clustering on surface damage density estimates," Proc. SPIE 6720, 67201J (2007).
    [CrossRef]
  29. By performing calculations considering the liquefaction as phase transition and only considering the volume expansion due to this phase transition, a minimum of 100 times the crack thickness is required to fill it, i.e. a length of a few hundreds of nanometers. Calculations show that with such a length, its value depends on the fluence but not on the pulse duration. since this fact differs from the experimental observations, the liquefaction should be turn down.
  30. T. J. Norman, J. M. Zaug, and C. W. Carr, "High-Pressure Decomposition of DKDP," Chem. Mater. 18, 3074-3077 (2006).
    [CrossRef]
  31. Y. Kobayashi, S. Endo, K. Koto, T. Kikegawa, and O. Shimomura, "Phase transitions and amorphization of KH2PO4 at high pressure," Phys. Rev. B 51, 9302-9305 (1995).
    [CrossRef]
  32. If several ADNS contribute to the determination of d, e.g. n, then d transforms into d/n in our calculations.
  33. The variation of the gain with respect to τcond can be increased by setting the modeling parameters to values differing from the ones used.
  34. S. Xu, X. Yuan, W. Yin, X. Xiang, and X. Zu, "Effect of UV laser conditioning on fused silica in vacuum," Opt. Mater. 31, 1013-1016 (2009).
    [CrossRef]
  35. J. Y. Natoli, B. Bertussi, and M. Commandré, "Effect of multiple laser irradiations on silica at 1064 and 355 nm," Opt. Lett. 30, 1315-1317 (2005).
    [CrossRef] [PubMed]
  36. L. Gallais, J. Y. Natoli, and C. Amra, "Statistical study of single and multiple pulse laser-induced damage in glasses," Opt. Express 10, 1465-1474 (2002).
    [PubMed]
  37. C. W. Carr, H. B. Radousky, and S. G. Demos, "Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms," Phys. Rev. Lett. 91, 127402 (2003).
    [CrossRef] [PubMed]
  38. N. Bloembergen, "Role of cracks, pores, and absorbing inclusions on laser induced damage threshold at surface of transparent dielectrics," Appl. Opt. 12, 661-664 (1973).
    [CrossRef] [PubMed]
  39. F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, "Role of light intensification by cracks in optical breakdown on surfaces," J. Opt. Soc. Am. A 18, 2607-2616 (2001).
    [CrossRef]
  40. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).
  41. The equivalent distance of about 100 nm corresponding to the mean distance between two ADNS with nadns =100 and n = 10000, which represent standard values in our calculations.

2009

S. Xu, X. Yuan, W. Yin, X. Xiang, and X. Zu, "Effect of UV laser conditioning on fused silica in vacuum," Opt. Mater. 31, 1013-1016 (2009).
[CrossRef]

2008

A. Dyan, F. Enguehard, S. Lallich, H. Piombini, and G. Duchateau, "Scaling laws in laser-induced potassium dihydrogen phosphate crystal damage by nanosecond pulses at 3ω," J. Opt. Soc. Am. B 25, 1087-1095 (2008).
[CrossRef]

P. DeMange, C. W. Carr, R. A. Negres, H. B. Radousky, and S. G. Demos, "Laser annealing characteristics of multiple bulk defect populations within DKDP crystals," J. Appl. Phys. 104, 103103 (2008).
[CrossRef]

2007

P. Grua, J-P. Morreeuw, and H. Bercegol, "Progress in the understanding of fracture related damage of fused silica," Proc. SPIE 6720, 672003 (2007).
[CrossRef]

G. Duchateau and A. Dyan, "Coupling statistics and heat transfer to study laser-induced crystal damage by nanosecond pulses," Opt. Express 15, 4557-4576 (2007).
[CrossRef] [PubMed]

L. Lamaignére, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J.-C. Poncetta, and H. Bercegol, "An accurate, repeatable, and well characterized measurement of laser damage density of optical materials," Rev. Sci. Instrum. 78, 103105 (2007).
[CrossRef] [PubMed]

M. J. Matthews and M. D. Feit, "Effect of random clustering on surface damage density estimates," Proc. SPIE 6720, 67201J (2007).
[CrossRef]

2006

T. J. Norman, J. M. Zaug, and C. W. Carr, "High-Pressure Decomposition of DKDP," Chem. Mater. 18, 3074-3077 (2006).
[CrossRef]

P. DeMange, R. A. Negres, C. W. Carr, H. B. Radousky, and S. G. Demos, "Laser-induced defect reactions governing damage initiation in DKDP crystals," Opt. Express 14, 5313-5328 (2006).
[CrossRef] [PubMed]

M. Pommies, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J.Y. Natoli, and H. Mathis, "Detection and characterization of absorption heterogeneities in KH2PO4 crystals," Opt. Commun. 267, 154-161 (2006).
[CrossRef]

2005

R. A. Negres, P. DeMange, and S. G. Demos, "Investigation of laser annealing parameters for optimal laserdamage performance in deuterated potassium dihydrogen phosphate," Opt. Lett. 30, 2766-2768 (2005).
[CrossRef] [PubMed]

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electron or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2005).
[CrossRef]

C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005).
[CrossRef]

K. Wang, C. Fang, J. Zhang, C. S. Liu, R. I. Boughton, S. Wang, and X. Zhao, "First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals," Phys. Rev. B 72, 184105 (2005).
[CrossRef]

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

J. Y. Natoli, B. Bertussi, and M. Commandré, "Effect of multiple laser irradiations on silica at 1064 and 355 nm," Opt. Lett. 30, 1315-1317 (2005).
[CrossRef] [PubMed]

2004

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]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

2003

A. K. Burnham, M. Runkel, M. D. Feit, A. M. Rubenchik, R. L. Floyd, T. A. Land, W. J. Siekhaus, and R. A. Hawley-Fedder, "Laser-induced damage in deuterated potassium dihydrogen phosphate," Appl. Opt. 42, 5483-5495 (2003).
[CrossRef] [PubMed]

M. M. Chirila, N. Y. Garces, L. E. Halliburton, S. G. Demos, T. A. Land, and H. B. Radousky, "Production and thermal decay of radiation-induced point defects in KDPO crystals," J. Appl. Phys 94, 6456-6462 (2003).
[CrossRef]

C. W. Carr, H. B. Radousky, and S. G. Demos, "Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms," Phys. Rev. Lett. 91, 127402 (2003).
[CrossRef] [PubMed]

2002

L. Gallais, J. Y. Natoli, and C. Amra, "Statistical study of single and multiple pulse laser-induced damage in glasses," Opt. Express 10, 1465-1474 (2002).
[PubMed]

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, "Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser," Int. Mater. Rev. 47, 113-152 (2002).
[CrossRef]

2001

1999

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky, and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys. 85, 3988-3992 (1999).
[CrossRef]

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]

Y. Kobayashi, S. Endo, K. Koto, T. Kikegawa, and O. Shimomura, "Phase transitions and amorphization of KH2PO4 at high pressure," Phys. Rev. B 51, 9302-9305 (1995).
[CrossRef]

1994

1993

J. J. De Yoreo and B. W. Woods, "A study of residual stress and the stress-optic effect in mixed crystals of K(DxH1−x)2PO4," J. Appl. Phys. 73, 7780-7789 (1993).
[CrossRef]

J. E. Davis, R. S. Hughes, and H. W. Lee., "Investigation of optically generated transient electronic defects and protonic transport in hydrogen-bonded molecular solids. Isomorphs of potassium dihydrogen phosphate," Chem. Phys. Lett. 207, 540-545 (1993).
[CrossRef]

1982

J. Swain, S. Stokowski, D. Milam, and F. Rainer, " Improving the bulk laser damage resistance of potassium dihydrogen phosphate crystals by pulsed laser irradiation," Appl. Phys. Lett. 40, 350-352 (1982).
[CrossRef]

1973

Adams, J. J.

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

Amra, C.

Bercegol, H.

L. Lamaignére, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J.-C. Poncetta, and H. Bercegol, "An accurate, repeatable, and well characterized measurement of laser damage density of optical materials," Rev. Sci. Instrum. 78, 103105 (2007).
[CrossRef] [PubMed]

P. Grua, J-P. Morreeuw, and H. Bercegol, "Progress in the understanding of fracture related damage of fused silica," Proc. SPIE 6720, 672003 (2007).
[CrossRef]

Bertussi, B.

M. Pommies, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J.Y. Natoli, and H. Mathis, "Detection and characterization of absorption heterogeneities in KH2PO4 crystals," Opt. Commun. 267, 154-161 (2006).
[CrossRef]

J. Y. Natoli, B. Bertussi, and M. Commandré, "Effect of multiple laser irradiations on silica at 1064 and 355 nm," Opt. Lett. 30, 1315-1317 (2005).
[CrossRef] [PubMed]

Bloembergen, N.

Bolourchi, M.

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

Boughton, R. I.

K. Wang, C. Fang, J. Zhang, C. S. Liu, R. I. Boughton, S. Wang, and X. Zhao, "First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals," Phys. Rev. B 72, 184105 (2005).
[CrossRef]

Bouillet, S.

L. Lamaignére, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J.-C. Poncetta, and H. Bercegol, "An accurate, repeatable, and well characterized measurement of laser damage density of optical materials," Rev. Sci. Instrum. 78, 103105 (2007).
[CrossRef] [PubMed]

Bruere, J. R.

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

Burnham, A. K.

Capoulade, J.

M. Pommies, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J.Y. Natoli, and H. Mathis, "Detection and characterization of absorption heterogeneities in KH2PO4 crystals," Opt. Commun. 267, 154-161 (2006).
[CrossRef]

Carr, C. W.

P. DeMange, C. W. Carr, R. A. Negres, H. B. Radousky, and S. G. Demos, "Laser annealing characteristics of multiple bulk defect populations within DKDP crystals," J. Appl. Phys. 104, 103103 (2008).
[CrossRef]

P. DeMange, R. A. Negres, C. W. Carr, H. B. Radousky, and S. G. Demos, "Laser-induced defect reactions governing damage initiation in DKDP crystals," Opt. Express 14, 5313-5328 (2006).
[CrossRef] [PubMed]

T. J. Norman, J. M. Zaug, and C. W. Carr, "High-Pressure Decomposition of DKDP," Chem. Mater. 18, 3074-3077 (2006).
[CrossRef]

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

C. W. Carr, H. B. Radousky, and S. G. Demos, "Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms," Phys. Rev. Lett. 91, 127402 (2003).
[CrossRef] [PubMed]

Chase, L. L.

Chirila, M. M.

M. M. Chirila, N. Y. Garces, L. E. Halliburton, S. G. Demos, T. A. Land, and H. B. Radousky, "Production and thermal decay of radiation-induced point defects in KDPO crystals," J. Appl. Phys 94, 6456-6462 (2003).
[CrossRef]

Commandré, M.

Courchinoux, R.

L. Lamaignére, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J.-C. Poncetta, and H. Bercegol, "An accurate, repeatable, and well characterized measurement of laser damage density of optical materials," Rev. Sci. Instrum. 78, 103105 (2007).
[CrossRef] [PubMed]

Damiani, D.

M. Pommies, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J.Y. Natoli, and H. Mathis, "Detection and characterization of absorption heterogeneities in KH2PO4 crystals," Opt. Commun. 267, 154-161 (2006).
[CrossRef]

Davis, J. E.

J. E. Davis, R. S. Hughes, and H. W. Lee., "Investigation of optically generated transient electronic defects and protonic transport in hydrogen-bonded molecular solids. Isomorphs of potassium dihydrogen phosphate," Chem. Phys. Lett. 207, 540-545 (1993).
[CrossRef]

De Yoreo, J. J.

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, "Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser," Int. Mater. Rev. 47, 113-152 (2002).
[CrossRef]

S. G. Demos, M. Staggs, J. J. De Yoreo, and H. B. Radousky, "Imaging of laser-induced reactions of individual defect nanoclusters," Opt. Lett. 26, 1975-1977 (2001).
[CrossRef]

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky, and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys. 85, 3988-3992 (1999).
[CrossRef]

J. J. De Yoreo and B. W. Woods, "A study of residual stress and the stress-optic effect in mixed crystals of K(DxH1−x)2PO4," J. Appl. Phys. 73, 7780-7789 (1993).
[CrossRef]

DeMange, P.

Demos, S. G.

P. DeMange, C. W. Carr, R. A. Negres, H. B. Radousky, and S. G. Demos, "Laser annealing characteristics of multiple bulk defect populations within DKDP crystals," J. Appl. Phys. 104, 103103 (2008).
[CrossRef]

P. DeMange, R. A. Negres, C. W. Carr, H. B. Radousky, and S. G. Demos, "Laser-induced defect reactions governing damage initiation in DKDP crystals," Opt. Express 14, 5313-5328 (2006).
[CrossRef] [PubMed]

R. A. Negres, P. DeMange, and S. G. Demos, "Investigation of laser annealing parameters for optimal laserdamage performance in deuterated potassium dihydrogen phosphate," Opt. Lett. 30, 2766-2768 (2005).
[CrossRef] [PubMed]

C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electron or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2005).
[CrossRef]

C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005).
[CrossRef]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

M. M. Chirila, N. Y. Garces, L. E. Halliburton, S. G. Demos, T. A. Land, and H. B. Radousky, "Production and thermal decay of radiation-induced point defects in KDPO crystals," J. Appl. Phys 94, 6456-6462 (2003).
[CrossRef]

C. W. Carr, H. B. Radousky, and S. G. Demos, "Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms," Phys. Rev. Lett. 91, 127402 (2003).
[CrossRef] [PubMed]

S. G. Demos, M. Staggs, J. J. De Yoreo, and H. B. Radousky, "Imaging of laser-induced reactions of individual defect nanoclusters," Opt. Lett. 26, 1975-1977 (2001).
[CrossRef]

N. Y. Garces, K. T. Stevens, L. E. Halliburton, S. G. Demos, H. B. Radousky, and N. P. Zaitseva, "Identification of electron and hole traps in KH2PO4 crystals," J. Appl. Phys. 89, 47-52 (2001).
[CrossRef]

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky, and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys. 85, 3988-3992 (1999).
[CrossRef]

Donval, T.

L. Lamaignére, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J.-C. Poncetta, and H. Bercegol, "An accurate, repeatable, and well characterized measurement of laser damage density of optical materials," Rev. Sci. Instrum. 78, 103105 (2007).
[CrossRef] [PubMed]

Duchateau, G.

Dyan, A.

Endo, S.

Y. Kobayashi, S. Endo, K. Koto, T. Kikegawa, and O. Shimomura, "Phase transitions and amorphization of KH2PO4 at high pressure," Phys. Rev. B 51, 9302-9305 (1995).
[CrossRef]

Enguehard, F.

Fang, C.

K. Wang, C. Fang, J. Zhang, C. S. Liu, R. I. Boughton, S. Wang, and X. Zhao, "First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals," Phys. Rev. B 72, 184105 (2005).
[CrossRef]

Feit, M. D.

M. J. Matthews and M. D. Feit, "Effect of random clustering on surface damage density estimates," Proc. SPIE 6720, 67201J (2007).
[CrossRef]

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

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]

A. K. Burnham, M. Runkel, M. D. Feit, A. M. Rubenchik, R. L. Floyd, T. A. Land, W. J. Siekhaus, and R. A. Hawley-Fedder, "Laser-induced damage in deuterated potassium dihydrogen phosphate," Appl. Opt. 42, 5483-5495 (2003).
[CrossRef] [PubMed]

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]

Floyd, R. L.

Gallais, L.

Garces, N. Y.

M. M. Chirila, N. Y. Garces, L. E. Halliburton, S. G. Demos, T. A. Land, and H. B. Radousky, "Production and thermal decay of radiation-induced point defects in KDPO crystals," J. Appl. Phys 94, 6456-6462 (2003).
[CrossRef]

N. Y. Garces, K. T. Stevens, L. E. Halliburton, S. G. Demos, H. B. Radousky, and N. P. Zaitseva, "Identification of electron and hole traps in KH2PO4 crystals," J. Appl. Phys. 89, 47-52 (2001).
[CrossRef]

Génin, F. Y.

Grua, P.

P. Grua, J-P. Morreeuw, and H. Bercegol, "Progress in the understanding of fracture related damage of fused silica," Proc. SPIE 6720, 672003 (2007).
[CrossRef]

Hackel, R. P.

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

Hahn, D. E.

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

Halliburton, L. E.

M. M. Chirila, N. Y. Garces, L. E. Halliburton, S. G. Demos, T. A. Land, and H. B. Radousky, "Production and thermal decay of radiation-induced point defects in KDPO crystals," J. Appl. Phys 94, 6456-6462 (2003).
[CrossRef]

N. Y. Garces, K. T. Stevens, L. E. Halliburton, S. G. Demos, H. B. Radousky, and N. P. Zaitseva, "Identification of electron and hole traps in KH2PO4 crystals," J. Appl. Phys. 89, 47-52 (2001).
[CrossRef]

Hawley-Fedder, R. A.

Henesian, M. A.

Hughes, R. S.

J. E. Davis, R. S. Hughes, and H. W. Lee., "Investigation of optically generated transient electronic defects and protonic transport in hydrogen-bonded molecular solids. Isomorphs of potassium dihydrogen phosphate," Chem. Phys. Lett. 207, 540-545 (1993).
[CrossRef]

Jarboe, J. A.

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

Josse, M.

L. Lamaignére, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J.-C. Poncetta, and H. Bercegol, "An accurate, repeatable, and well characterized measurement of laser damage density of optical materials," Rev. Sci. Instrum. 78, 103105 (2007).
[CrossRef] [PubMed]

Kikegawa, T.

Y. Kobayashi, S. Endo, K. Koto, T. Kikegawa, and O. Shimomura, "Phase transitions and amorphization of KH2PO4 at high pressure," Phys. Rev. B 51, 9302-9305 (1995).
[CrossRef]

Kioussis, N.

C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005).
[CrossRef]

C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electron or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2005).
[CrossRef]

Kobayashi, Y.

Y. Kobayashi, S. Endo, K. Koto, T. Kikegawa, and O. Shimomura, "Phase transitions and amorphization of KH2PO4 at high pressure," Phys. Rev. B 51, 9302-9305 (1995).
[CrossRef]

Koto, K.

Y. Kobayashi, S. Endo, K. Koto, T. Kikegawa, and O. Shimomura, "Phase transitions and amorphization of KH2PO4 at high pressure," Phys. Rev. B 51, 9302-9305 (1995).
[CrossRef]

Lallich, S.

Lamaignére, L.

L. Lamaignére, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J.-C. Poncetta, and H. Bercegol, "An accurate, repeatable, and well characterized measurement of laser damage density of optical materials," Rev. Sci. Instrum. 78, 103105 (2007).
[CrossRef] [PubMed]

Land, T. A.

M. M. Chirila, N. Y. Garces, L. E. Halliburton, S. G. Demos, T. A. Land, and H. B. Radousky, "Production and thermal decay of radiation-induced point defects in KDPO crystals," J. Appl. Phys 94, 6456-6462 (2003).
[CrossRef]

A. K. Burnham, M. Runkel, M. D. Feit, A. M. Rubenchik, R. L. Floyd, T. A. Land, W. J. Siekhaus, and R. A. Hawley-Fedder, "Laser-induced damage in deuterated potassium dihydrogen phosphate," Appl. Opt. 42, 5483-5495 (2003).
[CrossRef] [PubMed]

Lane, L. A.

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

Lee, H. W.

J. E. Davis, R. S. Hughes, and H. W. Lee., "Investigation of optically generated transient electronic defects and protonic transport in hydrogen-bonded molecular solids. Isomorphs of potassium dihydrogen phosphate," Chem. Phys. Lett. 207, 540-545 (1993).
[CrossRef]

Liu, C. S.

C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electron or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2005).
[CrossRef]

C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005).
[CrossRef]

K. Wang, C. Fang, J. Zhang, C. S. Liu, R. I. Boughton, S. Wang, and X. Zhao, "First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals," Phys. Rev. B 72, 184105 (2005).
[CrossRef]

Luthi, R. L.

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

Marshall, C. D.

Mathis, H.

M. Pommies, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J.Y. Natoli, and H. Mathis, "Detection and characterization of absorption heterogeneities in KH2PO4 crystals," Opt. Commun. 267, 154-161 (2006).
[CrossRef]

Matthews, M. J.

M. J. Matthews and M. D. Feit, "Effect of random clustering on surface damage density estimates," Proc. SPIE 6720, 67201J (2007).
[CrossRef]

McElroy, J. N.

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

Milam, D.

J. Swain, S. Stokowski, D. Milam, and F. Rainer, " Improving the bulk laser damage resistance of potassium dihydrogen phosphate crystals by pulsed laser irradiation," Appl. Phys. Lett. 40, 350-352 (1982).
[CrossRef]

Morreeuw, J-P.

P. Grua, J-P. Morreeuw, and H. Bercegol, "Progress in the understanding of fracture related damage of fused silica," Proc. SPIE 6720, 672003 (2007).
[CrossRef]

Natoli, J. Y.

Natoli, J.Y.

M. Pommies, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J.Y. Natoli, and H. Mathis, "Detection and characterization of absorption heterogeneities in KH2PO4 crystals," Opt. Commun. 267, 154-161 (2006).
[CrossRef]

Negres, R. A.

Norman, T. J.

T. J. Norman, J. M. Zaug, and C. W. Carr, "High-Pressure Decomposition of DKDP," Chem. Mater. 18, 3074-3077 (2006).
[CrossRef]

Payne, S. A.

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]

Piombini, H.

A. Dyan, F. Enguehard, S. Lallich, H. Piombini, and G. Duchateau, "Scaling laws in laser-induced potassium dihydrogen phosphate crystal damage by nanosecond pulses at 3ω," J. Opt. Soc. Am. B 25, 1087-1095 (2008).
[CrossRef]

M. Pommies, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J.Y. Natoli, and H. Mathis, "Detection and characterization of absorption heterogeneities in KH2PO4 crystals," Opt. Commun. 267, 154-161 (2006).
[CrossRef]

Pistor, T. V.

Pommies, M.

M. Pommies, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J.Y. Natoli, and H. Mathis, "Detection and characterization of absorption heterogeneities in KH2PO4 crystals," Opt. Commun. 267, 154-161 (2006).
[CrossRef]

Poncetta, J.-C.

L. Lamaignére, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J.-C. Poncetta, and H. Bercegol, "An accurate, repeatable, and well characterized measurement of laser damage density of optical materials," Rev. Sci. Instrum. 78, 103105 (2007).
[CrossRef] [PubMed]

Powell, H. T.

Radousky, H. B.

P. DeMange, C. W. Carr, R. A. Negres, H. B. Radousky, and S. G. Demos, "Laser annealing characteristics of multiple bulk defect populations within DKDP crystals," J. Appl. Phys. 104, 103103 (2008).
[CrossRef]

P. DeMange, R. A. Negres, C. W. Carr, H. B. Radousky, and S. G. Demos, "Laser-induced defect reactions governing damage initiation in DKDP crystals," Opt. Express 14, 5313-5328 (2006).
[CrossRef] [PubMed]

C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electron or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2005).
[CrossRef]

C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005).
[CrossRef]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

M. M. Chirila, N. Y. Garces, L. E. Halliburton, S. G. Demos, T. A. Land, and H. B. Radousky, "Production and thermal decay of radiation-induced point defects in KDPO crystals," J. Appl. Phys 94, 6456-6462 (2003).
[CrossRef]

C. W. Carr, H. B. Radousky, and S. G. Demos, "Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms," Phys. Rev. Lett. 91, 127402 (2003).
[CrossRef] [PubMed]

S. G. Demos, M. Staggs, J. J. De Yoreo, and H. B. Radousky, "Imaging of laser-induced reactions of individual defect nanoclusters," Opt. Lett. 26, 1975-1977 (2001).
[CrossRef]

N. Y. Garces, K. T. Stevens, L. E. Halliburton, S. G. Demos, H. B. Radousky, and N. P. Zaitseva, "Identification of electron and hole traps in KH2PO4 crystals," J. Appl. Phys. 89, 47-52 (2001).
[CrossRef]

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky, and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys. 85, 3988-3992 (1999).
[CrossRef]

Rainer, F.

J. Swain, S. Stokowski, D. Milam, and F. Rainer, " Improving the bulk laser damage resistance of potassium dihydrogen phosphate crystals by pulsed laser irradiation," Appl. Phys. Lett. 40, 350-352 (1982).
[CrossRef]

Rubenchik, A. M.

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

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]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

A. K. Burnham, M. Runkel, M. D. Feit, A. M. Rubenchik, R. L. Floyd, T. A. Land, W. J. Siekhaus, and R. A. Hawley-Fedder, "Laser-induced damage in deuterated potassium dihydrogen phosphate," Appl. Opt. 42, 5483-5495 (2003).
[CrossRef] [PubMed]

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.

Salleo, A.

Sell, W. D.

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

Shimomura, O.

Y. Kobayashi, S. Endo, K. Koto, T. Kikegawa, and O. Shimomura, "Phase transitions and amorphization of KH2PO4 at high pressure," Phys. Rev. B 51, 9302-9305 (1995).
[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]

Siekhaus, W. J.

Spaeth, M. L.

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

Speth, J. A.

Staggs, M.

S. G. Demos, M. Staggs, J. J. De Yoreo, and H. B. Radousky, "Imaging of laser-induced reactions of individual defect nanoclusters," Opt. Lett. 26, 1975-1977 (2001).
[CrossRef]

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky, and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys. 85, 3988-3992 (1999).
[CrossRef]

Stanley, J. R.

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

Stevens, K. T.

N. Y. Garces, K. T. Stevens, L. E. Halliburton, S. G. Demos, H. B. Radousky, and N. P. Zaitseva, "Identification of electron and hole traps in KH2PO4 crystals," J. Appl. Phys. 89, 47-52 (2001).
[CrossRef]

Stokowski, S.

J. Swain, S. Stokowski, D. Milam, and F. Rainer, " Improving the bulk laser damage resistance of potassium dihydrogen phosphate crystals by pulsed laser irradiation," Appl. Phys. Lett. 40, 350-352 (1982).
[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]

Swain, J.

J. Swain, S. Stokowski, D. Milam, and F. Rainer, " Improving the bulk laser damage resistance of potassium dihydrogen phosphate crystals by pulsed laser irradiation," Appl. Phys. Lett. 40, 350-352 (1982).
[CrossRef]

Vickers, J. L.

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

Wang, K.

K. Wang, C. Fang, J. Zhang, C. S. Liu, R. I. Boughton, S. Wang, and X. Zhao, "First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals," Phys. Rev. B 72, 184105 (2005).
[CrossRef]

Wang, S.

K. Wang, C. Fang, J. Zhang, C. S. Liu, R. I. Boughton, S. Wang, and X. Zhao, "First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals," Phys. Rev. B 72, 184105 (2005).
[CrossRef]

Weiland, T. L.

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

Whitman, P. K.

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, "Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser," Int. Mater. Rev. 47, 113-152 (2002).
[CrossRef]

Willard, D. A.

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

Woods, B.W.

J. J. De Yoreo and B. W. Woods, "A study of residual stress and the stress-optic effect in mixed crystals of K(DxH1−x)2PO4," J. Appl. Phys. 73, 7780-7789 (1993).
[CrossRef]

Xiang, X.

S. Xu, X. Yuan, W. Yin, X. Xiang, and X. Zu, "Effect of UV laser conditioning on fused silica in vacuum," Opt. Mater. 31, 1013-1016 (2009).
[CrossRef]

Xu, S.

S. Xu, X. Yuan, W. Yin, X. Xiang, and X. Zu, "Effect of UV laser conditioning on fused silica in vacuum," Opt. Mater. 31, 1013-1016 (2009).
[CrossRef]

Yan, M.

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky, and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys. 85, 3988-3992 (1999).
[CrossRef]

Yin, W.

S. Xu, X. Yuan, W. Yin, X. Xiang, and X. Zu, "Effect of UV laser conditioning on fused silica in vacuum," Opt. Mater. 31, 1013-1016 (2009).
[CrossRef]

Yuan, X.

S. Xu, X. Yuan, W. Yin, X. Xiang, and X. Zu, "Effect of UV laser conditioning on fused silica in vacuum," Opt. Mater. 31, 1013-1016 (2009).
[CrossRef]

Zaitseva, N. P.

N. Y. Garces, K. T. Stevens, L. E. Halliburton, S. G. Demos, H. B. Radousky, and N. P. Zaitseva, "Identification of electron and hole traps in KH2PO4 crystals," J. Appl. Phys. 89, 47-52 (2001).
[CrossRef]

Zaug, J. M.

T. J. Norman, J. M. Zaug, and C. W. Carr, "High-Pressure Decomposition of DKDP," Chem. Mater. 18, 3074-3077 (2006).
[CrossRef]

Zhang, J.

K. Wang, C. Fang, J. Zhang, C. S. Liu, R. I. Boughton, S. Wang, and X. Zhao, "First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals," Phys. Rev. B 72, 184105 (2005).
[CrossRef]

Zhao, X.

K. Wang, C. Fang, J. Zhang, C. S. Liu, R. I. Boughton, S. Wang, and X. Zhao, "First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals," Phys. Rev. B 72, 184105 (2005).
[CrossRef]

Zu, X.

S. Xu, X. Yuan, W. Yin, X. Xiang, and X. Zu, "Effect of UV laser conditioning on fused silica in vacuum," Opt. Mater. 31, 1013-1016 (2009).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. Swain, S. Stokowski, D. Milam, and F. Rainer, " Improving the bulk laser damage resistance of potassium dihydrogen phosphate crystals by pulsed laser irradiation," Appl. Phys. Lett. 40, 350-352 (1982).
[CrossRef]

Chem. Mater.

T. J. Norman, J. M. Zaug, and C. W. Carr, "High-Pressure Decomposition of DKDP," Chem. Mater. 18, 3074-3077 (2006).
[CrossRef]

Chem. Phys. Lett.

J. E. Davis, R. S. Hughes, and H. W. Lee., "Investigation of optically generated transient electronic defects and protonic transport in hydrogen-bonded molecular solids. Isomorphs of potassium dihydrogen phosphate," Chem. Phys. Lett. 207, 540-545 (1993).
[CrossRef]

Int. Mater. Rev.

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, "Developing KH2PO4 and KD2PO4 crystals for the world’s most powerful laser," Int. Mater. Rev. 47, 113-152 (2002).
[CrossRef]

J. Appl. Phys

M. M. Chirila, N. Y. Garces, L. E. Halliburton, S. G. Demos, T. A. Land, and H. B. Radousky, "Production and thermal decay of radiation-induced point defects in KDPO crystals," J. Appl. Phys 94, 6456-6462 (2003).
[CrossRef]

J. Appl. Phys.

P. DeMange, C. W. Carr, R. A. Negres, H. B. Radousky, and S. G. Demos, "Laser annealing characteristics of multiple bulk defect populations within DKDP crystals," J. Appl. Phys. 104, 103103 (2008).
[CrossRef]

S. G. Demos, M. Staggs, M. Yan, H. B. Radousky, and J. J. De Yoreo, "Investigation of optically active defect clusters in KH2PO4 under laser photoexcitation," J. Appl. Phys. 85, 3988-3992 (1999).
[CrossRef]

N. Y. Garces, K. T. Stevens, L. E. Halliburton, S. G. Demos, H. B. Radousky, and N. P. Zaitseva, "Identification of electron and hole traps in KH2PO4 crystals," J. Appl. Phys. 89, 47-52 (2001).
[CrossRef]

J. J. De Yoreo and B. W. Woods, "A study of residual stress and the stress-optic effect in mixed crystals of K(DxH1−x)2PO4," J. Appl. Phys. 73, 7780-7789 (1993).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

M. Pommies, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J.Y. Natoli, and H. Mathis, "Detection and characterization of absorption heterogeneities in KH2PO4 crystals," Opt. Commun. 267, 154-161 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Mater.

S. Xu, X. Yuan, W. Yin, X. Xiang, and X. Zu, "Effect of UV laser conditioning on fused silica in vacuum," Opt. Mater. 31, 1013-1016 (2009).
[CrossRef]

Phys. Rev. B

C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electronic structure calculations of an oxygen vacancy in KH2PO4," Phys. Rev. B 72, 134110 (2005).
[CrossRef]

K. Wang, C. Fang, J. Zhang, C. S. Liu, R. I. Boughton, S. Wang, and X. Zhao, "First-principles study of interstitial oxygen in potassium dihydrogen phosphate crystals," Phys. Rev. B 72, 184105 (2005).
[CrossRef]

Y. Kobayashi, S. Endo, K. Koto, T. Kikegawa, and O. Shimomura, "Phase transitions and amorphization of KH2PO4 at high pressure," Phys. Rev. B 51, 9302-9305 (1995).
[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]

C. S. Liu, N. Kioussis, S. G. Demos, and H. B. Radousky, "Electron or hole-assisted reactions of H defects in hydrogen-bonded KDP," Phys. Rev. Lett. 91, 015505 (2005).
[CrossRef]

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, "Localized dynamics during laserinduced damage in optical materials," Phys. Rev. Lett. 92, 087401 (2004).
[CrossRef] [PubMed]

C. W. Carr, H. B. Radousky, and S. G. Demos, "Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms," Phys. Rev. Lett. 91, 127402 (2003).
[CrossRef] [PubMed]

Proc. SPIE

J. J. Adams, J. R. Bruere, M. Bolourchi, C. W. Carr, M. D. Feit, R. P. Hackel, D. E. Hahn, J. A. Jarboe, L. A. Lane, R. L. Luthi, J. N. McElroy, A. M. Rubenchik, J. R. Stanley, W. D. Sell, J.L. Vickers, T.L. Weiland, and D. A. Willard, "Wavelength and pulselength dependence of laser conditioning and bulk damage in doubler-cut KH2PO4," Proc. SPIE 5991, 59911R-1 (2005).
[CrossRef]

J. J. Adams, T. L. Weiland, J. R. Stanley, W. D. Sell, R. L. Luthi, J. L. Vickers, C. W. Carr, M. D. Feit, A. M. Rubenchik, M. L. Spaeth, and R. P. Hackel, "Pulse length dependence of laser conditioning and bulk damage in KD2PO4," Proc. SPIE 5647, 265 (2005).
[CrossRef]

M. J. Matthews and M. D. Feit, "Effect of random clustering on surface damage density estimates," Proc. SPIE 6720, 67201J (2007).
[CrossRef]

P. Grua, J-P. Morreeuw, and H. Bercegol, "Progress in the understanding of fracture related damage of fused silica," Proc. SPIE 6720, 672003 (2007).
[CrossRef]

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]

Rev. Sci. Instrum.

L. Lamaignére, S. Bouillet, R. Courchinoux, T. Donval, M. Josse, J.-C. Poncetta, and H. Bercegol, "An accurate, repeatable, and well characterized measurement of laser damage density of optical materials," Rev. Sci. Instrum. 78, 103105 (2007).
[CrossRef] [PubMed]

Other

H. S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids (Oxford Science Publications, 1959).

By performing calculations considering the liquefaction as phase transition and only considering the volume expansion due to this phase transition, a minimum of 100 times the crack thickness is required to fill it, i.e. a length of a few hundreds of nanometers. Calculations show that with such a length, its value depends on the fluence but not on the pulse duration. since this fact differs from the experimental observations, the liquefaction should be turn down.

If several ADNS contribute to the determination of d, e.g. n, then d transforms into d/n in our calculations.

The variation of the gain with respect to τcond can be increased by setting the modeling parameters to values differing from the ones used.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

The equivalent distance of about 100 nm corresponding to the mean distance between two ADNS with nadns =100 and n = 10000, which represent standard values in our calculations.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

A 2D temperature field in the ��-plane (see text) for an ADNS distribution not leading to damage (top) and another temperature field implying a damage (bottom). The cluster leading to damage is inside the dashed red circle.

Fig. 2.
Fig. 2.

The damage probability as a function of the laser fluence in the 2D modeling framework. The inset represents the critical laser fluence as a function of the pulse duration for (a) nADNS =5000 and (b) nADNS =2000.

Fig. 3.
Fig. 3.

The damage density as a function of the laser fluence in the 1D modeling framework. (a) The influence of the density of heterogeneities Nh with nADNS =100 and τ=1 ns (b) The influence of nADNS with Nh=106 cm -3 and τ=1 ns (c) The influence of the pulse duration with nADNS =100 and Nh=106 cm -3.

Fig. 4.
Fig. 4.

The damage density as a function of the laser fluence for (a) an unconditioned and a conditioned crystal within the CM1 modeling framework and (b) a conditioned crystal within the CM2 modeling framework.

Fig. 5.
Fig. 5.

The LIDT gain obtained by conditioning with respect to τtest and τcond within (a) CM1 and (b) CM2. For both graphs Fcond =5 J.cm -2. (c) A cut of (a) and (b) for τtest =3 ns.

Fig. 6.
Fig. 6.

The LIDT gain obtained by conditioning with respect to τcond and Fcond within (a) CM1 and (b) CM2. For both graphs τtest =3 ns. (c) Cut of (a) and (b) for τcond =500 ps and 3 ns.

Fig. 7.
Fig. 7.

The conditioning gain as a function of the number of laser pre-exposures. The inset shows the case Fcond =2 J.cm -2 and τcond =3 ns with a logarithmic scale on the horizontal axis.

Tables (1)

Tables Icon

Table 1 A. List of parameters and variables

Equations (40)

Equations on this page are rendered with MathJax. Learn more.

Tt=DΔT+AρCΣi=0nADNS Π (rri)
{Π(rri)=1aifx[xia2;xi+a2]andy[yia2;yi+a2]Π(rri)=0elsewhere
θ2D(r,t)=Aa24λKDP r24Dt du exp (u)u
dEcdt=e2ε0m× vcollc(ω2+vcoll2)×Fτ
x 12 y (nADNS)zlnτ
ρd=ρh(NnADNS1)(nADNSN)f(τ)TcF
Fc=f (τ) Tc ln(nADNSN)ln(ρcNρh)
ρd (F)ρc(Nρhρc)(FFc)Fc
Pm(t)=exp (EakT(t))
g=Fc(ac)Fc(bc)
Tt=DΔT+Eδ(r)F(t)ρC
θ2D(r,s)=TT0=E2πλKDPK0(rsD)
{F(t)=γif0tτF(t)=0elsewhere
θ2D(r,s)=E2πλKDPK0(rsD)1eτss
θ2D(r,s)=ζ (r,s) eτsζ(r,s)
ζ(x,s)=E2πλKDPτK0(rsD)s
θ2D(r,t)=Aa24λKDPr24Dtduexp(u)u
x=ln(Fc1Fc2)ln(τ1τ2)
T2(x=0,t=τ2)=T0+αF2τ212
T1(x=0,t=τ1)=T0+αF1τ112+ncoop4Dτ12Dτ12Dτ1dxθ1D(x,τ1)
T1(x=0,t=τ1)=T0+αF1τ112+βF1n0
x=ln(τ112τ212(α+βn0τ112))ln(τ1τ2)=12ln(α+βn0τ112)ln(τ1τ2)
x 12ln(βn0)lnrlnτ12lnr
P (NnADNS)[nADNS(nADNS1)(nADNSnd1)]N(N1)(Nnd1)
P (NnADNS)(nADNSN)nd
ρd ρh (NnADNS) (nADNSN)f(τ)TcF
Fc=f(τ)Tcln(nADNSN)ln(ρcNρh)
ρd(F)]F=Fc=ρd(Fc)+ρdF]F=Fc(FFc)1!+
2ρdF2]F=Fc (FFc)22! ++nρdFn]F=Fc(FFc)nn! +
nρdFn (f(τ)TcF2ln(nADNSN)) ρd
ρd (F)]F=Fc ρc Σn=0 (f(τ)TcFc2ln(nADNSN)) (FFc)nn!
ρc exp {β(τ)Tc(FFc)Fc2ln(nADNSN)}
ρd (F)ρc(Nρhρc)(FFc)Fc
α=1nani
αNp=1na(1)+na(2)++na(Np)ni
αNp=α(1)+(α(2)1)+(α(3)1)++(α(Np)1)
αNp+1=αNpna(Np+1)ni
αNp+1=αNpβexp(γαNp)
dαdNp=βexp(γα)
dgdNp=βg2exp(γg)

Metrics