## Defect population variability in deuterated potassium di-hydrogen phosphate crystals |

Optical Materials Express, Vol. 2, Issue 11, pp. 1612-1623 (2012)

http://dx.doi.org/10.1364/OME.2.001612

Acrobat PDF (1752 KB)

### Abstract

Bulk laser damage variability in deuterated potassium dihydrogen phosphate (DKDP) crystals is well known and makes online conditioning of multiple-beam laser systems difficult to optimize. By using an empirical model, called Absorption Distribution Model (ADM), we were able to map the damage variability of the crystals (boule to boule as well as within same boule) in terms of defect population variations. The defect population variation was found to coalesce into two distinct groupings that can be identified by the defect population in the late growth region of the boule. This result allows us to optimize the conditioning protocol for an arbitrary number of beams with crystals of differing damage quality.

© 2012 OSA

## 1. Introduction

1. P. Wegner, J. Auerbach, T. Biesiada Jr, S. Dixit, J. Lawson, J. Menapace, T. Parham, D. Swift, P. Whitman, and W. Williams, “NIF final optics systems: frequency conversion and beam conditioning,” Proc. SPIE **5341**, 180–189 (2004). [CrossRef]

2. 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**(4), 350–352 (1982). [CrossRef]

^{2}beam area. For example, raster scanning all the crystals used in the NIF using a 10-Hz, ~1-mm

^{2}beam with 0.5-mm

^{2}size steps would take roughly 4 years running at 24 hour/day operation. However, this would have the benefit of being able to condition to higher fluences, and it could be done in parallel or before the online laser facility is completed and without impacting the shot schedule of the online laser.

8. M. Yan, R. Torres, M. Runkel, B. Woods, I. Hutcheon, N. Zaitseva, and J. DeYoreo, “Investigation of impurity and laser-induced damage in the growth sectors of rapidly grown KDP crystals,” Proc. SPIE **2966**, 11–16 (1997). [CrossRef]

7. S. G. Demos, M. Staggs, M. Yan, H. B. Radousky, and J. J. De Yoreo, “Investigation of optically active defect clusters in KH_{2}PO_{4} under laser photoexcitation,” J. Appl. Phys. **85**(8), 3988–3992 (1999). [CrossRef]

9. M. Pommiès, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J. Y. Natoli, and H. Mathis, “Detection and characterization of absorption heterogeneities in KH_{2}PO_{4} crystals,” Opt. Commun. **267**(1), 154–161 (2006). [CrossRef]

*on a crystal that has previously been irradiated (and thus conditioned) up to fluence ϕ*

_{OP}*This set of measurements X(ϕ*

_{C}.*ϕ*

_{OP},*), i.e., damage sites as a function of operating fluence and conditioning fluence, can be conveniently represented as a “conditioning map” that would come from precise measurement of the damage density, ρ(ϕ) [12*

_{C}12. C. W. Carr, M. D. Feit, M. C. Nostrand, and J. J. Adams, “Techniques for qualitative and quantitative measurement of aspects of laser-induced damage important for laser beam propagation,” Meas. Sci. Technol. **17**(7), 1958–1962 (2006). [CrossRef]

^{2}) so that damage can be appropriately sampled [12

12. C. W. Carr, M. D. Feit, M. C. Nostrand, and J. J. Adams, “Techniques for qualitative and quantitative measurement of aspects of laser-induced damage important for laser beam propagation,” Meas. Sci. Technol. **17**(7), 1958–1962 (2006). [CrossRef]

^{2}diameter) at a thickness of 10 mm, which corresponds to a MDDD of at most ~2 mm

^{−3}with an error bar on probability value of ± 10%.

14. Z. M. Liao, M. L. Spaeth, K. Manes, J. J. Adams, and C. W. Carr, “Predicting laser-induced bulk damage and conditioning for deuterated potassium dihydrogen phosphate crystals using an absorption distribution model,” Opt. Lett. **35**(15), 2538–2540 (2010). [CrossRef] [PubMed]

## 2. Theory

_{1}+ α

_{2}(c

_{0}+ c

_{1}I + … + c

_{n}I

^{n}) where α

_{1}is the Type 1 linear absorption, α

_{2}is the Type 2 nonlinear absorption, I is the laser intensity, and c

_{n}’s are the coefficients of different orders of intensity-dependent nonlinear absorption. As a result, ADM can extract from each set of R/1 measurements the Type 1 defect absorption parameters (μ

_{1}, σ

_{1}) and from each set of S/1 measurements the Type 2 defect absorption parameters (μ

_{2}, σ

_{2}), a total of 4 parameters for each set of damage probability data (see Fig. 2 ). Note in Fig. 2(a), the damage probability is shown for precursor of maximum size (a

_{max}~500nm); this is because due to size dependence on heat diffusion, maximum size precursors are the first to damage.

_{min}and a

_{max}being the minimum and maximum precursor sizes respectively, and n(a) being the precursor size distribution given by [17,18

18. J. B. Trenholme, M. D. Feit, and A. M. Rubenchik, “Size-selection initiation model extended to include shape and random factors,” Proc. SPIE **5991**, 59910X (2005). [CrossRef]

_{min}and a

_{max}are usually set as 50 and 500 nm respectively, which are consistent with the observed sizes of damage sites and the smallest sizes suitable for absorbing energy in sufficient density [17]. The size-dependent scaling power coefficient, b, is set to be ~3 because this is a typical value for characterizing size variation in optics contamination [18

18. J. B. Trenholme, M. D. Feit, and A. M. Rubenchik, “Size-selection initiation model extended to include shape and random factors,” Proc. SPIE **5991**, 59910X (2005). [CrossRef]

## 3. Data analysis

### 3.1 Precursor defect population variation over all boules

_{1}, σ

_{1}, μ

_{2}, σ

_{2}). Figure 4 shows the histogram of these defect parameters for all samples in the inventory. It is evident from Fig. 4 that there is a range of absorption mean and standard deviation values for all samples in inventory. Type 2 precursors have in general a broader distribution (i.e., larger variance) both in the absorption mean and the absorption standard deviation of any given sample.

14. Z. M. Liao, M. L. Spaeth, K. Manes, J. J. Adams, and C. W. Carr, “Predicting laser-induced bulk damage and conditioning for deuterated potassium dihydrogen phosphate crystals using an absorption distribution model,” Opt. Lett. **35**(15), 2538–2540 (2010). [CrossRef] [PubMed]

### 3.2 Precursor defect population variations over single boule

_{2}) decreases as the boule transitions from FG to LG, which agrees with previous results that show an increasing “purity” [8

8. M. Yan, R. Torres, M. Runkel, B. Woods, I. Hutcheon, N. Zaitseva, and J. DeYoreo, “Investigation of impurity and laser-induced damage in the growth sectors of rapidly grown KDP crystals,” Proc. SPIE **2966**, 11–16 (1997). [CrossRef]

7. S. G. Demos, M. Staggs, M. Yan, H. B. Radousky, and J. J. De Yoreo, “Investigation of optically active defect clusters in KH_{2}PO_{4} under laser photoexcitation,” J. Appl. Phys. **85**(8), 3988–3992 (1999). [CrossRef]

9. M. Pommiès, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J. Y. Natoli, and H. Mathis, “Detection and characterization of absorption heterogeneities in KH_{2}PO_{4} crystals,” Opt. Commun. **267**(1), 154–161 (2006). [CrossRef]

7. S. G. Demos, M. Staggs, M. Yan, H. B. Radousky, and J. J. De Yoreo, “Investigation of optically active defect clusters in KH_{2}PO_{4} under laser photoexcitation,” J. Appl. Phys. **85**(8), 3988–3992 (1999). [CrossRef]

9. M. Pommiès, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J. Y. Natoli, and H. Mathis, “Detection and characterization of absorption heterogeneities in KH_{2}PO_{4} crystals,” Opt. Commun. **267**(1), 154–161 (2006). [CrossRef]

### 3.3 Precursor defect grouping by boule type

_{1}) is plotted vs. Type 2 defect mean absorption (μ

_{2}). In the figure, each boule is represented by an arrow vector whose arrow end represents the value for the LG portion of the boule, and the starting point of the vector represents the FG portion of the boule. The Type 1 mean absorption (μ

_{1}) is extracted using Eqs. (1) and (2) from R/1 damage probability test data and likewise, the Type 2 mean absorption (μ

_{2}) is extracted using S/1 damage probability test data. As a result, the length of the vector denotes the degree of heterogeneity of the boule (from FG to LG), and the direction of the arrow vector indicates the change in the boule “purity” as it grows. What emerges from this graph is a grouping of the boules that shows at least 2 distinct behaviors that we have labeled as Group A and B (see Fig. 6).

- 1. Group A consists of 8 boules that have LG Type 2 mean absorption μ
_{2}(LG) < 19 cm^{−1}. All of these boules have a higher Type 2 absorption mean for FG vs. LG. These boules behave exactly like LL16, which we have presented in Fig. 5(b), where we have seen an increasing “purity” as the boule is grown, which is consistent with previous findings [7_{2}PO_{4}under laser photoexcitation,” J. Appl. Phys.**85**(8), 3988–3992 (1999). [CrossRef]_{2}PO_{4}crystals,” Opt. Commun.**267**(1), 154–161 (2006). [CrossRef] - 2. Group B consists of 6 boules that have LG Type 2 mean absorption μ
_{2}(LG) > 19 cm^{−1}. The primary difference of Group B boules in contrast to Group A boules, is that all boules have a lower Type 2 mean absorption value for FG vs. LG. As a result, Group B boules in general exhibit a decreasing “purity” as the boule is grown. Since these boules in general have a higher Type 2 mean absorption value, these boules also exhibit a poorer damage performance.

### 3.4 Precursor density grouping by boule type

12. C. W. Carr, M. D. Feit, M. C. Nostrand, and J. J. Adams, “Techniques for qualitative and quantitative measurement of aspects of laser-induced damage important for laser beam propagation,” Meas. Sci. Technol. **17**(7), 1958–1962 (2006). [CrossRef]

_{1}. At first glance, there doesn’t seem to be any relationship between the precursor density N and the defect absorption parameters, but when the data was grouped according to the results from Fig. 6, a trend emerges. An exponential dependence emerged in Fig. 7 between the Type 1 mean absorption μ

_{1}and the precursor density N for Boule Type A. The first dependence (blue line) centers around data from Group A boules and other boules (marked with green triangles) that we were not able to classify because of only having damage probability data from the FG growth region (remember it is the LG Type 2 mean absorption μ

_{2}that differentiates group A boules from group B). The four data points from Type B boules in Fig. 7 are closely clustered so that it is impossible to draw any conclusion as to whether or not the dependence of N is constant, linear, or exponential from that data alone. However, in light of the strong exponential dependence of the data from the Type A boules, we argue that the Type B data should follow a similar trend (red dashed line). It is worthwhile to note that the value of N can change from FG to LG in a given boule just as its absorption parameters change within the same boule. As a matter of fact, the four data points from the Type B boules in Fig. 7 come from just two boules. The middle two values (in terms of defect density N) come from samples from the LG portion of same boule and are virtually identical. The other two values come from samples from the FG portion of another boule with N being slightly different. The existence of these dependencies along the same boule groupings using an independent set of measurements (damage density vs. damage probability) underlines the possibility that these groupings do not just provide empirical convenience, but have a fundamental relationship with each other in terms growth conditions. This implies that we can now estimate the precursor density N from just the Type 1 absorption mean, μ

_{1,}using the following fitNote that the Type A boules have a stronger dependence on the Type 1 absorption mean μ

_{1,}than Type B boules; this, however, does not necessary mean that Type A boules will perform better in damage than Type B boules since damage performance is dependent on both absorption distribution and defect density (N). The absorption distribution can have a higher impact with respect to damage threshold, while defect density (N) is in general associated with density of damage sites. Group A boules have better damage performance in that it took higher fluences for damage to start because of the lower absorption values, but there could potentially be more damage at higher fluences.

## 4. Modeling results

^{2}, while the worst boule would need at least three shots to operate safely. This is a simple illustration to demonstrate the potential of calculating optimal conditioning protocols for an arbitrary number of boules. From here, it is a straightforward optimization problem to calculate the optimal conditioning for an arbitrary number of crystals given that the probability damage data on FG and LG parts are available. However, since we are using damage probability to sample the precursors, our sampling is only as good as the sampling resolution of the test (i.e., the number of sites or the area/volume of the testing). For example, most damage probability data is collected using 10 sites per fluence with a small beam volume (~0.75 mm 1/e

^{2}diameter), which corresponds to a dynamic range of 0.5 sites/mm

^{3}to 4 sites/mm

^{3}for a 10-mm-thick part. This implies our calculation is intended for a range of 10

^{3}to 10

^{5}for a volume of ~10

^{4}mm

^{3}, which is consistent with NIF specifications.

## 5. Conclusion

_{2}(LG)). This grouping is also important in determining the relationship between the Type 1 mean absorption and the total defect precursor density. Understanding this grouping can potentially refine growth conditions to produce more damage-resistant boules, as well as help formulate optimal conditioning protocols that can significantly reduce shot time while avoiding damage.

## Acknowledgments

## References and links

1. | P. Wegner, J. Auerbach, T. Biesiada Jr, S. Dixit, J. Lawson, J. Menapace, T. Parham, D. Swift, P. Whitman, and W. Williams, “NIF final optics systems: frequency conversion and beam conditioning,” Proc. SPIE |

2. | 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. |

3. | J. J. Adams, 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 KD |

4. | M. Runkel, K. Neeb, M. Staggs, J. Auerbach, and A. Burnham, “Results of raster scan laser conditioning studies on DKDP triplers using Nd:YAG and excimer lasers,” Proc. SPIE |

5. | M. Runkel and A. K. Burnham, “Difference in bulk damage probability distributions between tripler and z-cuts of KDP and DKDP at 355nm,” Proc. SPIE |

6. | A. K. Burnham, M. Runkel, R. A. Hawley-Fedder, M. L. Carman, R. A. Torres, and P. K. Whitman, “Low-temperature growth of DKDP for improving laser-induced damage resistance at 350nm,” Proc. SPIE |

7. | S. G. Demos, M. Staggs, M. Yan, H. B. Radousky, and J. J. De Yoreo, “Investigation of optically active defect clusters in KH |

8. | M. Yan, R. Torres, M. Runkel, B. Woods, I. Hutcheon, N. Zaitseva, and J. DeYoreo, “Investigation of impurity and laser-induced damage in the growth sectors of rapidly grown KDP crystals,” Proc. SPIE |

9. | M. Pommiès, D. Damiani, B. Bertussi, J. Capoulade, H. Piombini, J. Y. Natoli, and H. Mathis, “Detection and characterization of absorption heterogeneities in KH |

10. | R. A. Negres, N. P. Zaitseva, P. DeMange, and S. G. Demos, “An expedited approach to evaluate the importance of different crystal growth parameters on laser damage performance in KDP and DKDP,” Proc. SPIE |

11. | M. Runkel, M. Yan, J. De Yoreo, and N. Zaitseva, “The effect of impurities and stress on the damage distributions of rapidly grown KDP crystals,” Proc. SPIE |

12. | C. W. Carr, M. D. Feit, M. C. Nostrand, and J. J. Adams, “Techniques for qualitative and quantitative measurement of aspects of laser-induced damage important for laser beam propagation,” Meas. Sci. Technol. |

13. | J. Adams, J. A. Jarboe, M. Feit, and R. P. Hackel, “Comparison between S/1 and R/1 tests and damage density vs. fluence (rho(phi)) results for unconditioned and sub-nanosecond laser-conditioned KD |

14. | Z. M. Liao, M. L. Spaeth, K. Manes, J. J. Adams, and C. W. Carr, “Predicting laser-induced bulk damage and conditioning for deuterated potassium dihydrogen phosphate crystals using an absorption distribution model,” Opt. Lett. |

15. | M. Spaeth, “Absorption distribution model,” LLNL Internal Presentation (2007). |

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

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

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

19. | M. Runkel, M. Yan, J. De Yoreo, and N. Zaitseva, “The effect of impurities and stress on the damage distributions of rapidly grown KDP crystals,” Proc. SPIE |

20. | M. Runkel, J. Bruere, W. Sell, T. Weiland, D. Milam, D. Hahn, and M. Nostrand, “Effects of pulse duration of bulk laser damage in 350-nm raster-scanned DKDP,” Proc. SPIE |

21. | C. W. Carr, J. B. Trenholme, and M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett. |

22. | Z. M. Liao, J. Huebel, J. Trenholme, K. Manes, and C. W. Carr, “Modeling max-of-N fluence distribution using measured shot-to-shot beam contrast,” Appl. Opt. |

**OCIS Codes**

(140.3330) Lasers and laser optics : Laser damage

(140.3390) Lasers and laser optics : Laser materials processing

(190.4400) Nonlinear optics : Nonlinear optics, materials

**ToC Category:**

Nonlinear Optical Materials

**History**

Original Manuscript: July 11, 2012

Revised Manuscript: September 28, 2012

Manuscript Accepted: October 8, 2012

Published: October 15, 2012

**Citation**

Zhi M. Liao, R. Roussell, J. J. Adams, M. Runkel, W. T. Frenk, J. Luken, and C. W. Carr, "Defect population variability in deuterated potassium di-hydrogen phosphate crystals," Opt. Mater. Express **2**, 1612-1623 (2012)

http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-2-11-1612

Sort: Year | Journal | Reset

### References

- P. Wegner, J. Auerbach, T. Biesiada, S. Dixit, J. Lawson, J. Menapace, T. Parham, D. Swift, P. Whitman, and W. Williams, “NIF final optics systems: frequency conversion and beam conditioning,” Proc. SPIE5341, 180–189 (2004). [CrossRef]
- 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(4), 350–352 (1982). [CrossRef]
- J. J. Adams, 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. SPIE5647, 265 (2004).
- M. Runkel, K. Neeb, M. Staggs, J. Auerbach, and A. Burnham, “Results of raster scan laser conditioning studies on DKDP triplers using Nd:YAG and excimer lasers,” Proc. SPIE4679, 348 (2001).
- M. Runkel and A. K. Burnham, “Difference in bulk damage probability distributions between tripler and z-cuts of KDP and DKDP at 355nm,” Proc. SPIE4347, 408 (2000).
- A. K. Burnham, M. Runkel, R. A. Hawley-Fedder, M. L. Carman, R. A. Torres, and P. K. Whitman, “Low-temperature growth of DKDP for improving laser-induced damage resistance at 350nm,” Proc. SPIE4347, 373 (2000).
- 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(8), 3988–3992 (1999). [CrossRef]
- M. Yan, R. Torres, M. Runkel, B. Woods, I. Hutcheon, N. Zaitseva, and J. DeYoreo, “Investigation of impurity and laser-induced damage in the growth sectors of rapidly grown KDP crystals,” Proc. SPIE2966, 11–16 (1997). [CrossRef]
- M. Pommiès, 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(1), 154–161 (2006). [CrossRef]
- R. A. Negres, N. P. Zaitseva, P. DeMange, and S. G. Demos, “An expedited approach to evaluate the importance of different crystal growth parameters on laser damage performance in KDP and DKDP,” Proc. SPIE6403, 64031S (2007).
- M. Runkel, M. Yan, J. De Yoreo, and N. Zaitseva, “The effect of impurities and stress on the damage distributions of rapidly grown KDP crystals,” Proc. SPIE3244, 211 (1997).
- C. W. Carr, M. D. Feit, M. C. Nostrand, and J. J. Adams, “Techniques for qualitative and quantitative measurement of aspects of laser-induced damage important for laser beam propagation,” Meas. Sci. Technol.17(7), 1958–1962 (2006). [CrossRef]
- J. Adams, J. A. Jarboe, M. Feit, and R. P. Hackel, “Comparison between S/1 and R/1 tests and damage density vs. fluence (rho(phi)) results for unconditioned and sub-nanosecond laser-conditioned KD2PO4 crystals,” Proc. SPIE6720, 672014 (2008).
- Z. M. Liao, M. L. Spaeth, K. Manes, J. J. Adams, and C. W. Carr, “Predicting laser-induced bulk damage and conditioning for deuterated potassium dihydrogen phosphate crystals using an absorption distribution model,” Opt. Lett.35(15), 2538–2540 (2010). [CrossRef] [PubMed]
- M. Spaeth, “Absorption distribution model,” LLNL Internal Presentation (2007).
- C. W. Carr, J. D. Bude, and P. DeMange, “Laser-supported solid-state absorption fronts in silica,” Phys. Rev. B82(18), 184304 (2010). [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 (2003).
- J. B. Trenholme, M. D. Feit, and A. M. Rubenchik, “Size-selection initiation model extended to include shape and random factors,” Proc. SPIE5991, 59910X (2005). [CrossRef]
- M. Runkel, M. Yan, J. De Yoreo, and N. Zaitseva, “The effect of impurities and stress on the damage distributions of rapidly grown KDP crystals,” Proc. SPIE3244, 211 (1997).
- M. Runkel, J. Bruere, W. Sell, T. Weiland, D. Milam, D. Hahn, and M. Nostrand, “Effects of pulse duration of bulk laser damage in 350-nm raster-scanned DKDP,” Proc. SPIE4392, 405 (2002).
- C. W. Carr, J. B. Trenholme, and M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett.90(4), 041110 (2007). [CrossRef]
- Z. M. Liao, J. Huebel, J. Trenholme, K. Manes, and C. W. Carr, “Modeling max-of-N fluence distribution using measured shot-to-shot beam contrast,” Appl. Opt.50(20), 3547–3552 (2011). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.