## Laser-induced damage of KDP crystals by 1ω nanosecond pulses: influence of crystal orientation

Optics Express, Vol. 17, Issue 24, pp. 21652-21665 (2009)

http://dx.doi.org/10.1364/OE.17.021652

Acrobat PDF (708 KB)

### Abstract

We investigate the influence of THG-cut KDP crystal orientation on laser damage at 1064 nm under nanosecond pulses. Since laser damage is now assumed to initiate on precursor defects, this study makes a connection between these nanodefects (throughout a mesoscopic description) and the influence of their orientation on laser damage. Some investigations have already been carried out in various crystals and particularly for KDP, indicating propagation direction and polarization dependences. We performed experiments for two orthogonal positions of the crystal and results clearly indicate that KDP crystal laser damage depends on its orientation. We carried out further investigations on the effect of the polarization orientation, by rotating the crystal around the propagation axis. We then obtained the evolution of the damage probability as a function of the rotation angle. To account for these experimental results, we propose a laser damage model based on ellipsoid-shaped defects. This modeling is a refined implementation of the DMT model (Drude Mie Thermal) [Dyan *et al*., J. Opt. Soc. Am. B 25, 1087-1095 (2008)], by introducing absorption efficiency calculations for an ellipsoidal geometry. Modeling simulations are in good agreement with experimental results.

© 2009 Optical Society of America

## 1. Introduction

^{3}crystal is obtained in two months [1

1. N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, L. M. Carman, and H. R. Spears, “Rapid growth of large-scale (40–55 cm) KDP crystals,” J. Cryst. Growth **180**, 255–262 (
2001). [CrossRef]

2. A. Ciapponi, S. Palmier, F. R. Wagner, J. Y. Natoli, H. Piombini, D. Damiani, and B. Bertussi, “Laser-induced fluorescence as a tool for the study of laser damage precursors in transparent materials,” Proc. SPIE **6998**, 69981E-1 (
2008). [CrossRef]

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

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

8. H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, and T. Sasaki, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. **70**, 195–201 (
2000). [CrossRef]

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

5. S. G. Demos and M. Staggs, “Application of fluorescence microscopy for noninvasive detection of surface contamination and precursors to laser-induced damage,” Appl. Opt. **41**, 1977–1983 (
2002). [CrossRef] [PubMed]

6. 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]

8. H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, and T. Sasaki, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. **70**, 195–201 (
2000). [CrossRef]

6. 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]

*et al.*have evaluated the dependence of damage threshold at 1064 nm. It seems to follow preferential axis direction, consistent with the molecular bonding structure in different direction of the crystal [8

8. H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, and T. Sasaki, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. **70**, 195–201 (
2000). [CrossRef]

*Ω*around the laser beam propagation direction. In section 4, a description of the model is done by proposing a defects ellipsoidal shape consistent with orientation of crystal axis. We seek into Draine framework [14

14. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. B **11**, 1491–1499 (
1994). [CrossRef]

## 2. Experimental set-up and procedure

### 2.1 Facility set-up

15. S. Reyné, M. Loiseau, G. Duchateau, J.-Y. Natoli, and L. Lamaignère, “Towards a better understanding of multi-wavelength effect on KDP crystals,” Proc. SPIE **7361**, 73610Z (
2009). [CrossRef]

*ω*). Laser injection seeding ensures a longitudinal monomode beam and a stable temporal profile. The laser delivers approximately 800 mJ at a nominal repetition rate of 10Hz. The laser beam is P-polarized and its polarization remains the same for the whole study (other configurations with circular or elliptical polarization have not been tested here). The laser beam is focused into the sample by a convex lens which focal length is

*f*=4000 mm. It induces a depth of focus (DOF) higher than the sample thickness, ensuring the beam shape to be constant along the DOF.

*τ*is 6.5 ns, captured by a phototube (with ≈70 ps rise/fall times, 1-σ standard deviation is about 2% of the average value). The beam equivalent surface

_{eq}*S*(i.e. defined as the surface given at 1/e for a Gaussian beam) is determined at the equivalent plane corresponding to the distance d between the focusing lens and the sample. At the focus point, the beam spot is millimetric Gaussian-shaped and diameter (at 1/e) is 700 ±27µm. The energy measurements are sampled by pyroelectric cells and systematically compared with full-beam calorimeter calibrations. Shot-to-shot laser fluence fluctuations (about 7%) are mainly due to fluctuations of

_{eq}*S*. This is the reason why fluence is determined for each shot. Hence the absolute fluence determination is driven by the whole measurement path so as fluence is given with an accuracy of as much as ±15%.

_{eq}## 2.2 Procedure and metrology set-up

*ω*(transmitted) and 2

*ω*(generated by Second Harmonic Generation (SHG)) beams at the exit of the KDP crystal. Secondly, we carried out energy measurements of these beams as a function of the rotation angle

*Ω*. The third one is dedicated to the study of laser damage as a function of

*Ω*.

*ω*

**R**

_{max}mirror (99.9% reflectivity, P-polarized with a P/S extinction ratio of 100:1) to separate 1

*ω*and 2

*ω*beams on two distinct paths. Optical densities (OD) are added to protect and filter (block) the detectors from residual beams. Either the CCD cameras or the pyroelectric cells are used to carry out the appropriate measurements. Spatial profiles are measured through CCD cameras placed in a plane where the beam magnification

*γ*has been determined to 1.01±0.02. The pyroelectric cells are used to measure the energy of each shot. At the end, these two steps give us access to the energetic balance (in J/cm

^{2}, which is easy to understand when compared to damage tests), i.e. the 1

*ω*transmission and the 2

*ω*generation. At the same time, we are able to evaluate the losses induced by the crystal. A scheme of the set-up is given on Fig. 2.

17. L. Lamaignère, T. Donval, M. Loiseau, J. C. Poncetta, G. Razé, C. Meslin, B. Bertussi, and H. Bercegol, “Accurate measurements of laser-induced bulk damage density,” Meas. Sci. Technol. **20**, 095701 (
2009). [CrossRef]

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

18. N. Zaitseva, J. Atherton, R. Rozsa, L. Carman, I. Smolsky, M. Runkel, R. Ryon, and L. James, “Design and benefits of continuous filtration in rapid growth of large KDP and DKDP crystals,” J. Cryst. Growth **197**, 911–920 (
1999). [CrossRef]

*α*=59°. It was produced and polished by Cleveland Crystals, Inc (CCI). The sample is a pristine plate polished on the sides, with dimensions of 100×100×10 mm

^{3}.

## 3. Results

*χ*

^{(n)}(with

*n*the order of the tensor) are likely to happen assuming specific conditions and material properties. These processes may also induce an orientation dependence on LID. So we have to state whether or not the orientation influence on LID is due to the precursor defects. Also, we investigate the crystal inhomogeneity, self-focusing, walk-off and second harmonic generation (SHG) as potential candidates that might influence laser damage. Other effects may occur: either we do not have sufficient knowledge on them or we do not interest in since considered as weak. We report here (i) the main results extracted from preliminary studies entailed to evaluate the contribution of each candidate, and (ii) the results showing the influence of the KDP orientation, i.e. as a function of

*Ω*.

## 3.1 Preliminary studies

*ω*fluence. Tests at 1

*ω*have been performed for two orthogonal positions of the crystal, i.e. (a) the laser polarization along the ordinary axis (blue triangles), (b) the laser polarization along the extraordinary axis (red squares).

^{2}. This implies a factor 1.4–1.5 on the fluence at constant damage density. Many assumptions may be done to explain these observations. Crystal inhomogeneity was sometimes mentioned [18

18. N. Zaitseva, J. Atherton, R. Rozsa, L. Carman, I. Smolsky, M. Runkel, R. Ryon, and L. James, “Design and benefits of continuous filtration in rapid growth of large KDP and DKDP crystals,” J. Cryst. Growth **197**, 911–920 (
1999). [CrossRef]

21. N. Zaitseva, L. Carman, I. Smolsky, R. Torres, and M. Yan, “The effect of impurities and supersaturation on the rapid growth of KDP crystals,” J. Cryst. Growth **204**, 512–524 (
1999). [CrossRef]

17. L. Lamaignère, T. Donval, M. Loiseau, J. C. Poncetta, G. Razé, C. Meslin, B. Bertussi, and H. Bercegol, “Accurate measurements of laser-induced bulk damage density,” Meas. Sci. Technol. **20**, 095701 (
2009). [CrossRef]

^{2}). As for walk-off, KDP crystal exhibit weak anisotropy, inducing a birefringence closer to 20 mrad. This is the reason why comparing the length of the sample with the length on which the energy of each beam is superposed, we can neglect the birefringence issue.

*θ*satisfying the phase-matching condition relation defined by

_{PM}*k*

_{2ω}=2

*k*. It imposes the resolution of the following equation

_{ω}*n*(

_{e}*θ*, 2

_{PM}*ω*)=

*n*(

_{o}*ω*) where

*θ*is solution of the previous equation. According to the characteristics given by CCI and considering

_{PM}*ω*=2

*πc*/

*λ*, the phase-matching condition is ensured for

*θ*≈41°. The optical intensity

_{PM}*I*(

*2ω*,

*l*) for the generated harmonic can be written as [22]:

*Δk*=0. Else, conversion oscillates as

^{2}, etc).

## 3.2 Energy measurements at 1ω and 2ω̣

*ω*and 2

*ω*measurements at the exit of the crystal. Fig. 4(a) shows the evolution of the ratios

*T*

_{1ω}and

*R*

_{2ω}as a function of the rotation angle

*Ω.*

*T*

_{1ω}and

*R*

_{2ω}respectively represent the ratios between (a) 1

*ω*-transmitted energy (

*E*

_{1ω_out}) and 1

*ω*-inlet energy (

*E*

_{1ω_in}), and (b) 2

*ω*-converted energy (

*E*

_{2ω_out}) and 1

*ω*-inlet energy (

*E*

_{1ω_in}). These results are necessary as the initial step to determine if SHG may contribute to damage or not.

*F*

_{1ω}=16.5 J/cm

^{2}. For clarity, Fig. 4(a) does not present the whole measurements obtained with five different fluences

*F*

_{1ω}. We would also indicate that at

*F*

_{1ω}=16.5 J/cm

^{2}, one would expect to observe damage site (according to Fig. 3 for position

*Ω*=0°). But no damage has been observed. It is due to the measurements procedure, previously presented in subsection 2.2, that makes the crystal to get conditioned. This effect is usually studied in crystals to improve their laser damage resistance [13

13. G. Duchateau, “Simple models for laser-induced damage and conditioning of potassium dihydrogen phosphate crystals by nanosecond pulses,” Opt. Express **17**, 10434–10456 (
2009). [CrossRef] [PubMed]

23. 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]

24. P. Demange, C. W. Carr, R. A. Negres, H. B. Radousky, and S. G. Demos, “Multiwavelength investigation of laser-damage performance in potassium dihydrogen phosphate after laser annealing,” Opt. Lett. **30**, 221–223 (
2005). [CrossRef] [PubMed]

*T*

_{1ω}and

*R*

_{2ω}ratios respectively. Fig. 4(a) clearly shows the correlation between the variations of 1

*ω*and 2

*ω*energies. We also notice on the green curve the apparition of four SHG peaks (see arrows), three of them (for

*Ω*=-55°, 45° and 65°) representing less than 5% of 1

*ω*-inlet fluence whereas the fourth (for

*Ω*=-30°) reaching about 20% of 1

*ω*-inlet fluence. This value has led us to wonder whether the 2

*ω*fluence is a key factor in laser damage. This will be discussed in section 3.3. But we do not perform complementary tests to eventually propose an interpretation of the role of a second harmonic when coupled to another during damage tests.

*T*

_{1ω}and

*R*

_{2ω}obtained for five different 1

*ω*-inlet fluences, in order to evaluate the crystal losses (induced by reflection, intrinsic absorption, etc). Losses are estimated to be around 12 to 15 %, which is consistent with losses both induced by reflection (3.5% on each face, i.e. 7%) and absorption (it is commonly found 0.05 cm

^{-1}to 0.07 cm

^{-1}in literature for a KDP crystal). Moreover, the more E

_{1ω_in}is, the more E

_{2ω_out}and the less E

_{1ω_out}are. But in the end, the energetic balance (i.e. the sum of

*T*

_{1ω}and

*R*

_{2ω}) remains nearly constant whatever

*Ω*and

*F*

_{1ω}. Thus, considering Fig. 4(a) and Fig. 4(b), it is possible to evaluate the level of 1

*ω*and 2

*ω*for each position

*Ω*and for each fluence

*F*

_{1ω_in}. For a laser-induced damage fluence

*F*

_{1ω_in}, if now considering the positions

*Ω*=0° and

*Ω*=90° where

*T*

_{1ω}is comparable, one would expect not to observe differences on laser damage probability (or density). And yet, Fig. 3 shows that laser damage is different for these two positions. The analysis of Fig. 3, Fig. 4(a) and Fig. 4(b) suggests that SHG is not responsible for the laser damage orientation dependence at 1

*ω*.

## 3.3 Laser damage probability vs. angle Ω at 1ω

*Ω*. It is worth noting that rotating the crystal is equivalent to turning the beam polarization. We performed this test for two different fluences

*F*

_{1ω}(i.e. at 19 J/cm

^{2}and 24.5 J/cm

^{2}) to investigate a potential effect due to fluence. Note that the choice of these

*F*

_{1ω}test fluences allows scanning damage probabilities in the whole range [0; 1]. Fig. 5 illustrates the damage probability as a function of

*Ω*. Red squares and blue triangles respectively correspond to tests carried out at

*F*

_{1ω}=24.5 J/cm

^{2}and at

*F*

_{1ω}=19 J/cm

^{2}. Curves in dashed points only remind the SHG signal (estimated from Fig. 4(a)) for these fluences.

*Ω*. In the range [-90°, 90°], apart from the points referenced by the black arrows (i.e. the peaks of SHG), we observe that globally laser damage probability increases and decreases in the ranges [-90°, 0°] and [0°, 90°] respectively. If we interest more precisely in the range [0°, 30°], the damage probability decreases progressively while the SHG level remains constant and weak. This confirms that SHG can definitely not explain this behavior. If considering now the points corresponding to the peaks of SHG locations (see black arrows), we notice that the laser damage probability is punctually altered. For these cases only, SHG tends to cooperate as soon as the 2

*ω*level becomes upper than 1 J/cm

^{2}. In particular, for the maximum SHG peak at

*Ω*=-30° (we would also include the point at

*Ω*=-20°), damage probability saturates, meaning that 2

*ω*fluence generated (about 6-7 J/cm

^{2}for

*Ω*=-30° considering

*F*

_{1ω}=24.5 J/cm

^{2}) is sufficient to enhance probability. Indeed, the more the

*F*

_{1ω}is, the more

*F*

_{2ω}is generated, and the more the probability is modified. So probability curves interpretation becomes delicate since damage probability is no more driven by only one wavelength but by two (and their mixing). It sets the glimpse of the coupling efficiency of two wavelengths. We are not able to explain yet the mechanisms due to wavelengths mixing in these punctual cases. But reader can refer to studies dealing with KDP laser damage under multi-wavelength illumination [15

15. S. Reyné, M. Loiseau, G. Duchateau, J.-Y. Natoli, and L. Lamaignère, “Towards a better understanding of multi-wavelength effect on KDP crystals,” Proc. SPIE **7361**, 73610Z (
2009). [CrossRef]

24. P. Demange, C. W. Carr, R. A. Negres, H. B. Radousky, and S. G. Demos, “Multiwavelength investigation of laser-damage performance in potassium dihydrogen phosphate after laser annealing,” Opt. Lett. **30**, 221–223 (
2005). [CrossRef] [PubMed]

25. P. Demange, R. A. Negres, A. M. Rubenchik, H. B. Radousky, M. D. Feit, and S. G. Demos, “The energy coupling efficiency of multiwavelength laser pulses to damage initiating defects in deuterated KH_{2}PO_{4} non linear crystals,” J. Appl. Phys. **103**, 083122 (
2008). [CrossRef]

*F*

_{2ω}≈0.5 J/cm

^{2}), i.e. mainly in the range [0°, 90°], the damage probability follows a monotone decrease with

*Ω*. In this case, we ensure that SHG does not contribute to laser damage, meaning that probability is then not affected by SHG. It is thus necessary to find another explanation (than SHG). This is addressed in the next section which introduces defects geometry dependence and proposes a modeling of the damage probability versus

*Ω*.

## 4. Modeling and comparison to experiments

*et al*. in [14

14. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. B **11**, 1491–1499 (
1994). [CrossRef]

## 4.1 DMT modeling description

*et al*. [11

11. 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 3*ω*,” J. Opt. Soc. Am. B **25**, 1087–1095 (
2008). [CrossRef]

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

*a*. First assuming that a damage site appears as soon as the critical temperature

*T*is reached, and then considering that any defect leads to a damage site, damage density is obtained from Eq. (2):

_{c}*a*-(

*F*),

*a*

_{+}(

*F*)] is the range of defects size activated at a given damage fluence level,

*D*(

_{def}*a*) is the density size distribution of absorbers assumed to be (as expressed in [3

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

*C*and

_{def}*p*are adjusting parameters. This distribution is consistent with the fact that the more numerous the precursors (even small and thus less absorbing), the higher the damage probability. The critical fluence

*F*necessary to reach the critical temperature

_{c}*T*for which a first damage site occurs can be written as [11

_{c}11. 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 3*ω*,” J. Opt. Soc. Am. B **25**, 1087–1095 (
2008). [CrossRef]

*γ*is a factor dependant of material properties,

*T*is the room temperature, τ is the pulse duration and

_{0}*Q*is the absorption efficiency. What is interesting in Eq. (4) is the dependence in

_{abs}*Q*. Equation (4) shows that to deviate

_{abs}*F*from a factor ≈ 1.5 (this value is observed on Fig. 3 between the two extreme positions of the crystal), it is necessary to modify

_{c}*Q*by the same factor. It follows that an orientation dependence can be introduced through

_{abs}*Q*. To do so, we have to deal with an anisotropic geometry instead of a sphere: we then propose an ellipsoidal geometry. Now, the set of equations (i.e. Fourier’s and Maxwell’s equations) has to be solved for this geometry. Concerning Fourier’s equation, to our knowledge, it does not exist a simple analytic solution. So temperature determination remains solved for a sphere. This approximation remains valid as long as the aspect ratio does not deviate too far from unity. This approximation will be checked in the next paragraph. As regards the Maxwell’s equation, it does not exist an analytic solution in the general case. It is then solved numerically by using the discrete dipole approximation. We addressed this issue by the mean of DDScat 7.0 code which enables the calculations of electromagnetic scattering and absorption from targets with various geometries. This is an open-source code, presented by Draine and co-workers [14

_{abs}14. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. B **11**, 1491–1499 (
1994). [CrossRef]

29. B. T. Draine and P. J. Flatau, “User guide for the discrete dipole approximation code DDScat 7.0”, http://arxiv.org/abs/0809.0337.

30. B. T. Draine and P. J. Flatau, “The discrete dipole approximation for periodic targets: theory and tests,” J. Opt. Soc. Am. A **25**, 2693–2703 (
2008). [CrossRef]

*Ω*=0° (

*T*,

_{c}*n*,

_{1}*n*,

_{2}*C*, and

_{def}*p*). The value of each parameter is reported in Table 1 and their choice is explained below. We assume a critical damage density level at 10

^{-2}d/mm

^{3}(it is consistent with experimental results in Fig. 3 that it would be possible to reach with a larger test area). This criterion corresponds to a critical fluence

*F*=11 J/cm

_{c}^{2}and a critical temperature

*T*=6000 K. This latter value agrees qualitatively with experimental results obtained by Carr

_{c}*et al*. [31

31. C. W. Carr, H. B. Radousky, A. M. Rubenchick, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. **92**, 87401 (
2004). [CrossRef]

*n*=0.3 and

_{1}*n*=0.11.

_{2}*C*and

_{def}*p*necessary to define the defects size distribution are chosen to ensure that damage density must fit with experimentally observed probabilities (i.e. P=0.05 to P=1).

*F*

_{1ω}=19 J/cm

^{2}, and remained unchanged for the calculations at

*F*

_{1ω}=24.5 J/cm

^{2}(other experimental fluence used in this study). The only dependence is consequently given by

*Ω*, through the determination of

*Q*for each position. In other words, this model is expected to reproduce the experimental results for any fluence

_{abs}*F*

_{1ω}tested on this crystal.

*a*,

*b*and

*c*are such as

*a*=

*b*≠

*c*conditions. We assume that the defects keep the symmetry of the crystal. So we consider that the defects are isotropic in the (

*a*

*b*) plane due to the multi-layered structure of KDP crystal. The principal axes of the defects match with the crystallographic axes. Assuming this, it is possible to encounter two geometries (either

## 4.2 Numerical results and discussion

*Q*=f(

_{abs}*Ω*), which is re-injected in DMT code to reproduce the curve

*P*

_{|F=cste}=f(

*Ω*), i.e. the evolution of the laser damage probability as a function of

*Ω*. Results are presented on Fig. 7.

*F*

_{1ω}=19 J/cm

^{2}and fluence

*F*

_{1ω}=24.5 J/cm

^{2}. As said in section 3.3, one would note that it is important to dissociate the impact of the SHG on the damage probability from the geometry effect due to the rotation angle

*Ω*. Note that only the branch

*Ω*∈[0, 90°] is modeled since SHG signal remains weak in this range. For a modeling concern, it is thus not mandatory to include SHG as a contributor to laser damage. We do not interest in the range [-90°, 0°] since we consider that results are widely influenced by peaks of SHG (see Fig. 5). So, in the range [0, 90°], we can clearly see that modeling is in good agreement with experimental results for both fluences. Moreover, given the error margins, only the points linked to SHG peaks are out of the model validity. Now considering the two extreme positions (i.e.

*Ω*=0° and

*Ω*=90°)), this modeling reproduces the experimental damage density as function of the fluence on the whole range of the scanned fluences. This approach, with the introduction of an ellipsoidal geometry, enables to reproduce the main experimental trends whereas modeling based on spherical geometry cannot.

*ω*. This study confronts experimental results with modeling for defects sensitive to 1

*ω*only. Henceforth, we are carrying out experimental tests at 2

*ω*and 3

*ω*on orientation effect, to provide an in-depth study. Indeed, multi-parameter studies [32

32. J. Y. Natoli, J. Capoulade, H. Piombini, and B. Bertussi, “Influence of laser beam size and wavelength in the determination of LIDT and associated laser damage precursor densities in KH_{2}PO_{4},” Proc. SPIE **6720**, 672016 (
2007). [CrossRef]

*ω*-defect population and the other gathering 2

*ω*and 3

*ω*defects. Besides, the laser conditioning results agree with this distinction [23

23. 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]

24. P. Demange, C. W. Carr, R. A. Negres, H. B. Radousky, and S. G. Demos, “Multiwavelength investigation of laser-damage performance in potassium dihydrogen phosphate after laser annealing,” Opt. Lett. **30**, 221–223 (
2005). [CrossRef] [PubMed]

*ω*and 3

*ω*or not.

*et al*. have reported in [6

6. 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]

*ω*with R/1 and S/1 procedures, a dependence with the propagation direction has been observed, but not with the polarization. Our results do not contradict those of [6

**42**, 5483–5495 (
2003). [CrossRef] [PubMed]

23. 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]

**30**, 221–223 (
2005). [CrossRef] [PubMed]

*et al*. [12

12. 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]

13. G. Duchateau, “Simple models for laser-induced damage and conditioning of potassium dihydrogen phosphate crystals by nanosecond pulses,” Opt. Express **17**, 10434–10456 (
2009). [CrossRef] [PubMed]

*ω*. This model gives the opportunity to discriminate defects candidates. In Duchateau’s model, heat diffusion is calculated in one, two and three spatial dimensions corresponding to planar, lines and points defects respectively. The best results are obtained for planar defects since they are in good agreement with experimental trends (S-shape damage probability curves, the temporal scaling law characteristic of KDP crystals). Potential defects are growth bands, cracks and dislocations. By comparing our results to those obtained from the model developed in [12

12. 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]

13. G. Duchateau, “Simple models for laser-induced damage and conditioning of potassium dihydrogen phosphate crystals by nanosecond pulses,” Opt. Express **17**, 10434–10456 (
2009). [CrossRef] [PubMed]

12. 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]

**17**, 10434–10456 (
2009). [CrossRef] [PubMed]

*ω*in a pure thermal modeling framework (i.e. without the Mie theory and the Drude model), there is no contradiction between both results. Further, this is an indication that several defects populations (with different geometries) exist in KDP crystal. This conclusion is also in agreement with previous studies [23

**14**, 5313–5328 (
2006). [CrossRef] [PubMed]

**30**, 221–223 (
2005). [CrossRef] [PubMed]

32. J. Y. Natoli, J. Capoulade, H. Piombini, and B. Bertussi, “Influence of laser beam size and wavelength in the determination of LIDT and associated laser damage precursor densities in KH_{2}PO_{4},” Proc. SPIE **6720**, 672016 (
2007). [CrossRef]

*et al*. [8

**70**, 195–201 (
2000). [CrossRef]

*ω*. First, they observed strong anisotropy in the damage thresholds (typically a factor ~2) due to the laser beam propagation directions between the orientation of the incident polarization to

*c*plane and

*a*(

*b*) plane. Secondly, when rotating the crystal around the

*a*(

*b*) propagation direction, they observed a slight variation in LIDT for the extreme positions (i.e. 0° and 90°). These variations are weaker than those we have observed. This may be due to the fact that our sample is not a Z-cut crystal but a THG-cut crystal. And so given the ellipsoid orientation, in Z-cut configuration, the orientation effect is less important. Otherwise, Yoshida

*et al*. tried to link the mechanical characteristics of KDP to the LIDT results. They found that 〈100〉 direction is weaker due to the atomic space of the lattice, more extensible along this direction, which results in mechanical fragility. This proposition is complementary to our interpretation.

## 5. Conclusion

*ω*laser damage density curves as a function of the orientation of KDP crystal. This approach allows giving an explanation for orientation dependence on laser damage whereas modeling based on spherical geometry failed. Besides, several geometries do not qualitatively match. According to the size, the distribution and the shape (i.e. few tens of nanometers, few ppm and elongated shape), we give additional information that allow discriminating the potential defects listed in literature. This study is a promising way to give a reliable model of the physical mechanisms implied in laser damage. By a better description (or knowledge) of defects, solutions would be proposed to perform the crystal growth and to increase the crystal laser-damage resistance.

*ω*and 2

*ω*beams in the bulk. We observed experimentally that the damage probability is altered in the scope of this scenario. The model is no more reliable in this range since we do not take into account wavelength combination. Nevertheless, in literature few studies provide explanations on the mechanisms that occur in the configuration of wavelength mixing. Given the range of 2

*ω*fluences, there is no doubt that a coupling efficiency establishes between the two wavelengths. If taken separately, the level of 2

*ω*fluences can never induce damage sites (or at least not detectable). But once mixed with 1

*ω*fluences, the damage probability is not merely added to the damage probability induced by 1ω, it is noticeably enhanced. A coupling effect between 3

*ω*and 2

*ω*has also been observed by Demange [25

25. P. Demange, R. A. Negres, A. M. Rubenchik, H. B. Radousky, M. D. Feit, and S. G. Demos, “The energy coupling efficiency of multiwavelength laser pulses to damage initiating defects in deuterated KH_{2}PO_{4} non linear crystals,” J. Appl. Phys. **103**, 083122 (
2008). [CrossRef]

*ω*and 3

*ω*. Results at 2

*ω*and 3

*ω*would also be an additional source of information and would give some details as the same as those obtained at 1

*ω*.

## Acknowledgments

## References and links

1. | N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, L. M. Carman, and H. R. Spears, “Rapid growth of large-scale (40–55 cm) KDP crystals,” J. Cryst. Growth |

2. | A. Ciapponi, S. Palmier, F. R. Wagner, J. Y. Natoli, H. Piombini, D. Damiani, and B. Bertussi, “Laser-induced fluorescence as a tool for the study of laser damage precursors in transparent materials,” Proc. SPIE |

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

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

5. | S. G. Demos and M. Staggs, “Application of fluorescence microscopy for noninvasive detection of surface contamination and precursors to laser-induced damage,” Appl. Opt. |

6. | 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. |

7. | F. R. Wagner, A. Hildenbrand, J. Y. Natoli, M. Commandré, F. Théodore, and H. Albrecht, “Laser damage resistance of RbTiOPO |

8. | H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, and T. Sasaki, “Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength,” Appl. Phys. |

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

10. | C. W. Carr, H. B. Radousky, and S. G. Demos, “Wavelength dependence of laser-induced damage: determining the damage initiation mechanisms,” Phys. Rev. Lett. |

11. | 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 3 |

12. | G. Duchateau and A. Dyan, “Coupling statistics and heat transfer to study laser-induced crystal damage by nanosecond pulses,” Opt. Express |

13. | G. Duchateau, “Simple models for laser-induced damage and conditioning of potassium dihydrogen phosphate crystals by nanosecond pulses,” Opt. Express |

14. | B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. B |

15. | S. Reyné, M. Loiseau, G. Duchateau, J.-Y. Natoli, and L. Lamaignère, “Towards a better understanding of multi-wavelength effect on KDP crystals,” Proc. SPIE |

16. | ISO Standard No 11254-1:2000; ISO Standard No 11254-2:2001 |

17. | L. Lamaignère, T. Donval, M. Loiseau, J. C. Poncetta, G. Razé, C. Meslin, B. Bertussi, and H. Bercegol, “Accurate measurements of laser-induced bulk damage density,” Meas. Sci. Technol. |

18. | N. Zaitseva, J. Atherton, R. Rozsa, L. Carman, I. Smolsky, M. Runkel, R. Ryon, and L. James, “Design and benefits of continuous filtration in rapid growth of large KDP and DKDP crystals,” J. Cryst. Growth |

19. | N. P. Zaitseva, I. L. Smolsky, L. Carman, R. Ryon, and Z. U. Rek, “Connection between filtration of solution during growth and defect structure of KDP group crystals,” 1998 SSRL Activity Report, Experimental progress Reports |

20. | S. G. Demos, M. Staggs, and H. B. Radousky, “Bulk defect formations in KH |

21. | N. Zaitseva, L. Carman, I. Smolsky, R. Torres, and M. Yan, “The effect of impurities and supersaturation on the rapid growth of KDP crystals,” J. Cryst. Growth |

22. | N. Bloembergen, |

23. | 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 |

24. | P. Demange, C. W. Carr, R. A. Negres, H. B. Radousky, and S. G. Demos, “Multiwavelength investigation of laser-damage performance in potassium dihydrogen phosphate after laser annealing,” Opt. Lett. |

25. | P. Demange, R. A. Negres, A. M. Rubenchik, H. B. Radousky, M. D. Feit, and S. G. Demos, “The energy coupling efficiency of multiwavelength laser pulses to damage initiating defects in deuterated KH |

26. | R. W. Hopper and D. R. Uhlmann, “Mechanisms of inclusion damage in laser glass,” J. Appl. Phys. |

27. | H. S. Carslaw and J. C. Jaeger, |

28. | H. C. Van de Hulst, |

29. | B. T. Draine and P. J. Flatau, “User guide for the discrete dipole approximation code DDScat 7.0”, http://arxiv.org/abs/0809.0337. |

30. | B. T. Draine and P. J. Flatau, “The discrete dipole approximation for periodic targets: theory and tests,” J. Opt. Soc. Am. A |

31. | C. W. Carr, H. B. Radousky, A. M. Rubenchick, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. |

32. | J. Y. Natoli, J. Capoulade, H. Piombini, and B. Bertussi, “Influence of laser beam size and wavelength in the determination of LIDT and associated laser damage precursor densities in KH |

**OCIS Codes**

(140.3330) Lasers and laser optics : Laser damage

(160.0160) Materials : Materials

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: August 18, 2009

Revised Manuscript: October 2, 2009

Manuscript Accepted: October 2, 2009

Published: November 11, 2009

**Citation**

Stéphane Reyné, Guillaume Duchateau, Jean-Yves Natoli, and Laurent Lamaignère, "Laser-induced damage of KDP crystals by 1ω nanosecond pulses: influence of crystal orientation," Opt. Express **17**, 21652-21665 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-24-21652

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### References

- N. P. Zaitseva, J. J. De Yoreo, M. R. Dehaven, R. L. Vital, L. M. Carman, and H. R. Spears, "Rapid growth of large-scale (40-55 cm) KDP crystals," J. Cryst. Growth 180, 255-262 (2001). [CrossRef]
- A. Ciapponi, S. Palmier, F. R. Wagner, J. Y. Natoli, H. Piombini, D. Damiani, and B. Bertussi, "Laser-induced fluorescence as a tool for the study of laser damage precursors in transparent materials," Proc. SPIE 6998, 69981E-1 (2008). [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 (2004). [CrossRef]
- M. Pommiès, D. Damiani, B. Bertussi, H. Piombini, H. Mathis, J. Capoulade, and J. Y. Natoli, "Detection and characterization of absorption heterogeneities in KH2PO4 crystals," Opt. Commun. 267, 154-161 (2006). [CrossRef]
- S. G. Demos and M. Staggs, "Application of fluorescence microscopy for noninvasive detection of surface contamination and precursors to laser-induced damage," Appl. Opt. 41, 1977-1983 (2002). [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]
- F. R. Wagner, A. Hildenbrand, J. Y. Natoli, M. Commandré, F. Théodore, and H. Albrecht, "Laser damage resistance of RbTiOPO4: evidence of polarization dependent anisotropy," Opt. Express 15, 13849-13857 (2007). [CrossRef] [PubMed]
- H. Yoshida, T. Jitsuno, H. Fujita, M. Nakatsuka, M. Yoshimura, and T. Sasaki, "Investigation of bulk laser damage in KDP crystal as a function of laser irradiation direction, polarization, and wavelength," Appl. Phys. 70, 195-201 (2000). [CrossRef]
- J. B. Trenholme, M. D. Feit, and A. Rubenchik, "Size-selection initiation model extended to include shape and random factors," Proc. SPIE 5991, 59910X (2006). [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]
- 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]
- 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]
- G. Duchateau, "Simple models for laser-induced damage and conditioning of potassium dihydrogen phosphate crystals by nanosecond pulses," Opt. Express 17, 10434-10456 (2009). [CrossRef] [PubMed]
- B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. B 11, 1491-1499 (1994). [CrossRef]
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- ISO Standard No 11254-1:2000; ISO Standard No 11254-2:2001
- L. Lamaignère, T. Donval, M. Loiseau, J. C. Poncetta, G. Razé, C. Meslin, B. Bertussi, and H. Bercegol, "Accurate measurements of laser-induced bulk damage density," Meas. Sci. Technol. 20, 095701 (2009). [CrossRef]
- N. Zaitseva, J. Atherton, R. Rozsa, L. Carman, I. Smolsky, M. Runkel, R. Ryon, and L. James, "Design and benefits of continuous filtration in rapid growth of large KDP and DKDP crystals," J. Cryst. Growth 197, 911-920 (1999). [CrossRef]
- 1. N. P. Zaitseva, I. L. Smolsky, L. Carman, R. Ryon, and Z. U. Rek, "Connection between filtration of solution during growth and defect structure of KDP group crystals," 1998 SSRL Activity Report, Experimental progress Reports 7, 434-437 (1998).
- S. G. Demos, M. Staggs, and H. B. Radousky, "Bulk defect formations in KH2PO4 crystals investigated using fluorescence microscopy," Phys. Rev. B 67, 224102 (2003). [CrossRef]
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- N. Bloembergen, Nonlinear Optics (World Scientific, 4th ed, 1965).
- 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]
- P. Demange, C. W. Carr, R. A. Negres, H. B. Radousky, and S. G. Demos, "Multiwavelength investigation of laser-damage performance in potassium dihydrogen phosphate after laser annealing," Opt. Lett. 30, 221-223 (2005). [CrossRef] [PubMed]
- P. Demange, R. A. Negres, A. M. Rubenchik, H. B. Radousky, M. D. Feit, and S. G. Demos, "The energy coupling efficiency of multiwavelength laser pulses to damage initiating defects in deuterated KH2PO4 non linear crystals," J. Appl. Phys. 103, 083122 (2008). [CrossRef]
- R. W. Hopper and D. R. Uhlmann, "Mechanisms of inclusion damage in laser glass," J. Appl. Phys. 41, 4023-4037 (1970). [CrossRef]
- H. S. Carslaw and J. C. Jaeger, Conduction of heat in solids (Oxford Science Publications, 2nd ed, 1959).
- H. C. Van de Hulst, Light scattering by small particles (Dover publications, Inc., New York, 1981).
- B. T. Draine and P. J. Flatau, "User guide for the discrete dipole approximation code DDScat 7.0," http://arxiv.org/abs/0809.0337.
- B. T. Draine and P. J. Flatau, "The discrete dipole approximation for periodic targets: theory and tests," J. Opt. Soc. Am. A 25, 2693-2703 (2008). [CrossRef]
- C. W. Carr, H. B. Radousky, A. M. Rubenchick, M. D. Feit, and S. G. Demos, "Localized dynamics during laser-induced damage in optical materials," Phys. Rev. Lett. 92, 87401 (2004). [CrossRef]
- J. Y. Natoli, J. Capoulade, H. Piombini, and B. Bertussi, "Influence of laser beam size and wavelength in the determination of LIDT and associated laser damage precursor densities in KH2PO4," Proc. SPIE 6720, 672016 (2007). [CrossRef]

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