Transmittance increase after laser conditioning reveals absorption properties variation in DKDP crystals

doi:10.1364/OE.20.025169

« Show journal navigation

Transmittance increase after laser conditioning reveals absorption properties variation in DKDP crystals

Guohang Hu, Yuanan Zhao, Dawei Li, and Qiling Xiao »View Author Affiliations

Optics Express, Vol. 20, Issue 22, pp. 25169-25180 (2012)
http://dx.doi.org/10.1364/OE.20.025169

View Full Text Article

Acrobat PDF (1095 KB)

Journal Search
Article Lookup

Article Tools

Citations

Alert me when this article is cited
Export Citation/Save

Article Navigation

▸ Article Outline
– Abstract
1. Introduction
2. Experimental setup
3. Results and discussion
4. Conclusion
– References and links

Article Tools
Full Text
Article Info
References
Cited By
Figures
Metrics
Download PDF

Viewing Equations in the
HTML Article

Optimal Viewing Recommendations

Full Text
Article Info
References (27)
Cited By
Figures (12)
Metrics

Abstract

By taking multiple measurements of transmittance before and after laser conditioning in DKDP crystals, we found that the transmittance was increased by 0.05%~0.4% through laser conditioning with maximum fluence 6J/cm², and then decreased by about 0.1% after subsequent higher fluence conditioning. Variation of scattering intensity and absorber density, the two major factors leading to transmittance change, was monitored by on-line and off-line detection systems. The transmittance decrease was attributed to laser damage scattering, and the increase was derived from reduction of absorbers. Moreover, the absorption was reduced further at higher conditioning fluence. Based on the above analysis, the heating process during laser exposure was analyzed in the time domain, and a local rapid-rising and slow-cooling process was confirmed to reduce defect concentration, which can improve laser damage resistance and increase the transmittance.

1. Introduction

KH₂PO₄ (KDP) and KD₂PO₄ (DKDP) crystals are currently the only nonlinear materials suitable as frequency converters and Pockel cells in high-power large-aperture laser systems. These crystals often suffer from laser damage, which adversely affect the quality of downstream beam [1

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH₂PO₄ and KD₂PO₄ crystals for the world's most power laser,” Int. Mater. Rev. 47, 113–152 (2002). [CrossRef]

]. The observed damage thresholds of KDP/DKDP crystals are much lower than the intrinsic thresholds [2

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(12), 127402 (2003). [CrossRef] [PubMed]

]. It is now admitted that this damage is induced by point defects that efficiently absorb laser energy, inducing a fast temperature rise and a subsequent “micro-explosion” [3

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

–5

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

]. In order to ensure a good running of laser system, it is necessary to identify the nature of point defect and to understand the physical mechanism leading to laser damage.

A lot of work has been dedicated to identify the nature of point defect. The point defect may be constituted of metallic impurities, such as Fe, Cr, Si, derived from growth environment. However, several experimental studies based on the correlation between Laser-Induced Damage Threshold (LIDT) and the concentration of impurities seems to show that this kind of defect is not involved in lowering LIDT [6

R. A. Negres, P. DeMange, and S. G. Demos, “Investigation of laser annealing parameters for optimal laser-damage performance in deuterated potassium dihydrogen phosphate,” Opt. Lett. 30(20), 2766–2768 (2005). [CrossRef] [PubMed]

–8

G. Duchateau and A. Dyan, “Coupling statistics and heat transfer to study laser induced crystal damage by nanosecond pulses,” Opt. Express 15(8), 4557–4576 (2007). [CrossRef] [PubMed]

]. K.E. Montgomery and Y. Nishida have demonstrated the correlation between the impurities of crystal growth solution, such as inorganic or organic compounds, or bacteria, and LIDT of KDP [9

K. E. Montgomery and F. P. Milanovich, “High-laser-damage-threshold potassium dihydrogen phosphate crystals,” J. Appl. Phys. 68(8), 3979–3982 (1990). [CrossRef]

, 10

Y. Nishida, A. Yokotani, T. Sasaki, K. Yoshida, T. Yamanaka, and C. Yamanaka, “Improvement of the bulk laser damage threshold of potassium dihydrogen phosphate crystals by re-ducing the organic impurities in growth solution,” Appl. Phys. Lett. 52(6), 420–421 (1988). [CrossRef]

]. B. Dam proved the relationship between dislocation and LIDT of KDP [11

B. Dam, P. Bennema, and W. J. P. van Enckevort, “The mechanism of tapering on KDP-type crystals,” J. Cryst. Growth 74(1), 118–128 (1986). [CrossRef]

]. Recent work based on the electron paramagnetic resonance and resonance Raman scattering experiments provided direct evidence of the [HPO4]ˉ hole center and the hydrogen interstitial H⁰ electron center [12

S. Setzler, K. Stevens, L. Halliburton, M. Yan, N. Zaitseva, and J. DeYoreo, “Hydrogen atoms in KH₂PO₄ crystals,” Phys. Rev. B 57(5), 2643–2646 (1998). [CrossRef]

]. First principle calculation for hydrogen point defects in KDP have found that the band gap for the neutral interstitial H and positive charged H vacancy were greatly reduced to 2.6 and 2.5eV [13

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(1), 015505 (2003). [CrossRef] [PubMed]

, 14

C. S. Liu, Q. Zhang, N. Kioussis, S. Demos, and H. Radousky, “Electronic structure calculations of intrinsic and extrinsic hydrogen point defects in KH₂PO₄,” Phys. Rev. B 68(22), 224107 (2003). [CrossRef]

]. It suggested that thermal point defects played an important role on the lowering LIDT of KDP crystal. The point defects corresponding to hydrogen or oxygen atoms as interstitial atoms or vacancies in the crystalline lattice have attracted more and more attentions in recent years. A simple model based on heat transfer [3

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

, 8

G. Duchateau and A. Dyan, “Coupling statistics and heat transfer to study laser induced crystal damage by nanosecond pulses,” Opt. Express 15(8), 4557–4576 (2007). [CrossRef] [PubMed]

, 15

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(27), 5483–5495 (2003). [CrossRef] [PubMed]

] have demonstrated that the point defect size ranges between roughly 10 nm and 100 nm cannot produce a sufficiently high temperature, only a cluster of point defects can satisfy the defect size requirement.

Although the exact physical mechanism for laser damage has not been identified, experimental studies have demonstrated that the bulk damage thresholds of KDP/DKDP crystals can be increased by 1.5 to 2.5 through laser conditioning [16

J. J. Adams, “Results of sub-nanosecond laser-conditionining of KD₂PO₄ crystals,” Proc. SPIE 6403, 64031M (2007).

, 17

]. Feit suggested that the increase of LIDT was due to the defect decreasing in size during laser exposure [3

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

]. Chirila believed that electronic structure of the defect was altered during laser exposure [18

M. Chirila, N. Garces, L. Halliburton, S. Demos, T. Land, and H. Radousky, “Production and thermal decay of radiation-induced point defects in KD₂PO₄ crystals,” J. Appl. Phys. 94(10), 6456–6462 (2003). [CrossRef]

]. These attempts give a preliminary insight regarding the manner in which the conditioning may work.

Accurate transmittance measurement is important for determining the variation of optical properties and for judgment of availability of optics. In National Ignition Facility, DKDP crystals after laser conditioning should meet the requirement of transmittance reduction less than 0.1% for operation at full fluence [19

M. Runkel, A. K. Burnham, D. Milam, W. Sell, M. Feit, and A. Rubenchik, “The results of pulse scaling experiments on rapid growth DKDP triplers using the optical sciences laser at 351nm,” Proc. SPIE 4347, 359–372 (2000).

]. So the transmittance measurement is an effective and direct tool to prove the success of laser conditioning. High-accuracy spectrophotometers are commonly used for these transmittance measurements.

In this paper, transmittance measurement was applied to detect the variation of optical property after laser conditioning. Multiple measurements and statistical analysis provided the precision of transmittance measurement. Surface defect comparison system and bulk scattering detection system were used to on-line monitor scattering variation during laser conditioning, which is a major factor of transmittance variation. The pinpoint density detection system and fluorescent image system were used to detect the variation of absorber density, which is another major factor of transmittance variation. Laser interaction with optical material and annealing mechanism were applied to understand transmittance improvement during laser conditioning.

2. Experimental setup

2.1. Laser conditioning facility

Laser conditioning was conducted in the facility as seen in Fig. 1 . This facility can be separated into four main parts: the laser source yielding intense laser pulse, the beam delivery system to focus the laser pulse to samples, beam analyzer and damage detector for an accurate metrology of laser damage. The experiments were performed using a tripled Nd:YAG laser that operated at 355nm. The laser had a Gaussian temporal profile with pulse duration of about 8ns. The laser fluence was adjusted using an energy attenuator, which consists of a half waveplate and a polarizer. The beam was focused by focusing optics to the bulk of the sample. The focal length was 5000mm, and the effective area of spot on the sample was 0.25mm², measured by a laser beam analyzer. Bulk damage, produced through the focal range of the focusing optics, was illuminated using a HeNe laser that was collinear with the damage beam. Bulk scattering diagnostics allowed variation of bulk scattering intensity at the exposure site to be recorded in real time [20

R. Sharp III and M. J. Runkel, “Automated damage onset analysis techniques applied to KDP damage and Zeus small area damage test facility,” Proc. SPIE 3902, 361–368 (2000). [CrossRef]

]. Surface exposure site was illuminated by a white light, and Surface detection system provided high resolution images of the sample surfaces immediately before and after laser pulses. The resolution of the surface detection system was 10microns. Defect comparison method was applied to automatically detect surface events in real time [21

J. E. Wolfe and S. E. Schrauth, “Automated laser damage test system with real-time damage event imaging and detection,” Proc. SPIE 6403, 640328 (2007).

Fig. 1 Schematic of laser conditioning experimental bench used for KDP/DKDP crystals

2.2. Transmittance measurement

Transmittance spectra of the samples were measured using a Lambda 1050 double-beam spectrophotometer. Multiple measurements of transmittance at three typical wavelengths, such as 1064nm, 532nm, and 355nm, were tested in this study, because only these three wavelengths propagated through DKDP crystals that were used in frequency converters in large-aperture laser system. The shape of the spectrophotometer beam, irradiating at the front surface of DKDP crystal, was rectangular, of which the length was 11mm and the width was 8mm.

The transmittance homogeneity of a DKDP sample was tested, as shown in Fig. 2 . The difference of transmittance at 355nm among different positions was about 1.8%, and that at 532nm and 1064nm were about 0.7% and 0.6%. It’s seen that this diamond turned DKDP sample did not have a good performance of transmittance homogeneity. So transmittance comparison between before and after laser conditioning should be taken at the same position. In order to fix the position, a mask with a number of rectangular holes was placed at the front of a sample. The dimension of the rectangular hole is as similar as the spectrophotometer beam irradiated at the front surface of the sample. And the dimension of the mask should be as equally as that of the surface of the sample. In this instance, the position, placed for transmittance measured many times at different periods, could be fixed.

Fig. 2 The transmittance homogeneity in a DKDP sample

The repeatability of transmittance measurements was tested many times at different periods, as shown in Fig. 3 . Figure 3(a) displays the variation of transmittance measured fifteen times at the same position in the same time period. The difference between maximum and minimum transmittance is smaller than 0.1% at 532nm and 1064nm, but larger than 0.1% at 355nm. Figure 3(b) displays the variation of transmittance in different periods at the same position. The variation is smaller than 0.1% at 532nm and 1064nm, but larger than 0.1% at 355nm. As seen, the transmittance of 355nm light was not as stable as 532nm and 1064nm light, it’s because light intensity of halogen lamp at 355nm was really weak, not as high as 532nm and 1064nm, and the noise was more prone to disturb the weak light. These results revealed that the repeatability of transmittance measurements at 532nm and 1064nm was excellent; the error was less than 0.07%. Multiple measurements were applied to increase the precision and the confidence in experimental data. So in this study we focused on the 532nm and 1064nm transmittance measurements, 355nm transmittance was ignored due to its relatively low repeatability.

Fig. 3 (a) displays the variation of transmittance measured fifteen times at the same position in the same time period, (b) displays the variation of transmittance in different periods at the same position

2.3. Pinpoint density detection

The density of pinpoint bulk damage sites in DKDP crystals were detected by the system shown in Fig. 4 . A HeNe laser, with a diameter of 3mm, illuminated the bulk sites in DKDP crystals. The illuminated area was 0.3X minified and imaged onto a CCD camera. The image software was applied to account the number of pinpoint sites. The pinpoint density was the number of pinpoint sites divided by the illumination volume in DKDP crystals.

Fig. 4 (a) Schematic of pinpoint density detection system, (b) The image detected by this system

2.4. Fluorescent spot detection

The scheme of fluorescence microscopy is shown in Fig. 5 . The image system used in this investigation was a 2X magnification zoom lens. Fluorescence images of DKDP crystals were detected using a CW argon ion laser operating at 355nm as the photo excitation source, recorded by a CCD camera. Optical filter is used in order to filter out the laser excitation wavelength of 355 nm. The fluorescent spot density was the number of spot sites divided by the imaging region.

Fig. 5 (a) Schematic of fluorescence microscopy, (b) The fluorescent image detected by this microscopy

3. Results and discussion

The DKDP samples used in this study was 70% deuterated, THG-cut from conventional grown DKDP boules. The surface of the crystal was single point diamond turned, and was uncoated. Four 100 × 100 × 10mm³ samples were dedicated to 8ns laser conditioning with above discussed facility. The laser fluence reported in this study was scaled to 3ns by a scaling factor of τ^0.5. Before laser conditioning, the local area used for transmittance comparison was marked by a prepared mask. The transmittance, pinpint density and fluorescent spot density were measured in four positions as the mask marked. Then the sample was raster-scanned with the 8ns conditioning laser. The spatial overlap between two successive shots was 90%. The conditioning fluences for each scanning were 3.5, 6, 7, 8, 9, 10J/cm². The transmittance measurements were performed again at the same positions after 6J/cm² laser conditioning and 10J/cm² conditioning process. Pinpoint density was measured after each scanning. The fluorescent spot were measured after 10J/cm² laser conditioning. The surface and bulk changes were detected by the surface defect comparison system and bulk scattering detection system during laser scanning.

The results of transmittance measurements can be seen in Fig. 6 and Fig. 7 . The 532nm and 1064nm transmittance in the four positions on one DKDP sample revealed that 532nm and 1064nm transmittance was obviously increased after 6J/cm² laser conditioning. And the value of variation was quite different among the four positions. The increase percent of transmittance at position 1 and 2 was about 0.07%, and that at position 3 and 4 was about 0.3%~0.4%. After 10J/cm² laser conditioning process, the transmittance was decreased compared with the transmittance after 6J/cm² conditioning. The decrease percent of transmittance was about 0.1% at the four positions. The same tendency was found in the other three samples after laser conditioning. The increase percent of transmittance after 6J/cm² laser conditioning was about 0.05~0.4%.

Fig. 6 The results of 532nm transmittance measurements at the four different positions

Fig. 7 The results of 1064nm transmittance measurements at the four different positions

The variation of transmittance after laser conditioning was contributed by the absorption and/or scattering variation. The surface change was detected by the surface defect comparison system. After laser conditioning to 6J/cm², this system did not detect any surface damage (bigger than 10um) or surface alteration, such as particle removing or surface smoothing. So it’s believed that the surface scattering would not contribute to the transmittance variation. The bulk scattering variation is detected by the bulk scattering detection system, and this system did not detect any alteration of bulk scattering. The pinpoint density was detected by the pinpoint detection system. The pinpoint density was about 0.002/mm³. As the volume of transmittance measurement was 11 × 8 × 10mm³. The number of pinpoints in this detected area was about 1.8. As the average diameter of pinpoint was 5um, the area ratio of bulk damage sites to the detective area S(damage)/S(detective area) was 0.4 × 10⁻⁶. Assuming that laser irradiated at the damage sites would be all scattered, the bulk pinpoint damage sites decreased the transmittance by about 0.4 × 10⁻⁶. The bulk and surface detection system proved that the scattering variation could not be the reason for the transmittance increase. So it was admitted that the absorption reduction contributed to the transmittance increase.

After 10J/cm² laser conditioning, the transmittance was decreased, and the decrease percent was about 0.1%, compared with the transmittance after 6J/cm² laser conditioning. Figure 8 illustrates the pinpoint density and the percent area covered by surface damage after 10J/cm² laser conditioning. The pinpoint density increased to 0.6/mm³, so the percent area covered by bulk damage sites was about 0.01%. The density of surface damage sites in the detective area was 35/cm². By accumulating the surface area of these damage sites, it’s found that the percent area covered by surface damage was about 0.12%. Assuming that light irradiated at the damage sites would be all scattered, the surface and bulk damage sites would reduce the transmittance by 0.13%. The scattering intensity increased by bulk and surface damage was a little larger than the transmittance difference between after 6J/cm² and 10J/cm² laser conditioning. So it’s concluded that the transmittance decrease after 10J/cm² conditioning was owing to the increase of scattering intensity caused by laser induced damage, and the transmittance could be increased higher if there wasn’t any damage occurred. These results proved that the transmittance increase after 6J/cm² laser conditioning was owing to the absorption reduction, and the absorption would be reduced further after higher fluence conditioning.

Fig. 8 (a) The bulk pinpoint density and (b) the percent area covered by surface damage at the four positions after laser conditioning to 10J/cm²

As we known, laser energy that is absorbed can be dissipated in two ways: (1) lost as heat; (2) re-irradiated as red light (fluorescence). In order to prove the variation of absorption characteristics, heat and fluorescence should be detected before and after laser conditioning. The heat process could lead to laser damage. So the pinpoint density revealed the density of absorber which absorbed laser energy, inducing a fast temperature rise and a micro-explosion. The comparison of pinpoint density before and after laser conditioning is shown in Fig. 9 . The pinpoint density was decreased rapidly after laser conditioning, so the density of absorber was decreased dramatically. The fluorescent spot density revealed the density of absorber, which could absorb laser energy and emit fluorescence. The comparison of fluorescent spot density before and after laser conditioning is shown in Fig. 10 . The number of fluorescent spot in the imaging region dropped from ~10 to ~2 after laser conditioning. These results proved that the absorption characteristics were definitely altered after laser conditioning, which were agreed with the conclusion derived from transmittance measurements.

Fig. 9 Comparison of pinpoint density before and after laser conditioning

Fig. 10 Comparison of fluorescent spot number in the imaging region before and after 10J/cm² laser conditioning in DKDP crystals

Laser interaction with optical material and the annealing mechanism are combined to understand the improvement of absorption characteristics during laser conditioning. Previous works based on heat transfer have demonstrated that the defect size ranges between roughly 10nm and 100nm cannot produce a sufficiently high temperature; only a cluster of point defects can satisfy the defect size requirements. The point defects, such as vacancies and interstitials, are inherently existed because they could decrease the Gibbs free energy. The vacancy concentration in crystals is about the order of 10⁻⁴ [22

J. S. Pan, J. M. Tong, and M. B. Tian, Fundamentals of Materials Science, (Qinghua University Press, 1998).

, 23

J. Q. Chen, M. X. Chen, and J. S. Zhao, Crystal defects, (Zhejiang University Press, 1992).

]. It follows that its density is in an order of 10¹⁶/mm³. The existence of point defects on the other hand increases the randomness of the crystal. So in some parts of area, the point defects stay close together and the concentration in this area is in an order of 10⁻² [24

C. S. Liu, C. J. Hou, N. Kioussis, S. G. Demos, and H. B. Radousky, “Electronic structure calculations of an oxygen vacancy in KH₂PO₄,” Phys. Rev. B 72(13), 134110 (2005). [CrossRef]

], which is quite higher than the average concentration. First principle calculation for hydrogen point defects in KDP has found that the band gap for the neutral interstitial H and positive charged H vacancy are greatly reduced to 2.6 and 2.5eV [13

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(1), 015505 (2003). [CrossRef] [PubMed]

, 14

], which is smaller than photon energy of 355nm laser. Therefore, this defect cluster can be the major factor of inducing laser damage. In this paper, the cluster of point defect is considered as a spherical absorber with a radius of 100nm. The number of point defect in this cluster with concentration of 10⁻² is about the order of 10⁶. The absorption efficiency factor of this cluster is in an order of 10⁻².

When a high-energy laser beam propagates through a DKDP crystal containing the cluster of point defects, some of the beam energy is absorbed by the cluster. This energy heats the cluster directly, and the DKDP crystal around the cluster is heated by thermal conduction from the cluster. After the exposure of laser pulse, the temperature of heated cluster dropped through thermal conduction. Thus it can be seen that the process of laser exposure during conditioning divided into two stages, the heating process and heat dissipation process.

During the heating process, the temperature of the crystal around the cluster will satisfy the heating diffusion equation

\frac{\partial T}{\partial t} = κ \nabla^{2} T

(1)

Where κ = k_m/ρ_mC_m (κ,k_m, ρ_m and C_m are the thermal diffusivity, thermal conductivity, density, and specific heat of DKDP crystals). The boundary conditions are(i)at t = 0, T = T₀ = constant, where T₀ is the room temperature; (ii) at infinity T = T₀, and (iii) the power absorbed by the cluster must equal the power leaving the cluster surface plus the rate of change of heat content of the cluster

I Q_{a b s} π a^{2} = - 4 π a^{2} k_{m} {(\frac{\partial T}{\partial r})}_{r = a} + \frac{4 π}{3} a^{3} ρ_{p} C_{p} {(\frac{\partial T}{\partial t})}_{r = a}

(2)

Where ρ_p and C_p are the density and specific heat of the cluster, I is the laser intensity, a is the radius of the cluster. Q_abs is the absorption efficiency factor and can be calculated from the Mie scattering theory. In Eq. (2) we have assumed that the temperature of the cluster is uniform throughout its volume and have equated the cluster temperature to the temperature at the surface of the cluster.

For the spherically symmetric problem, Eq. (1) can be solved exactly for the given boundary conditions (i)-(iii). The final result for the temperature is given as [4

C. H. Chan, “Effective absorption for thermal blooming due to aerosols,” Appl. Phys. Lett. 26(11), 628–630 (1975). [CrossRef]

T (r, t) = T_{0} + \frac{2 a T_{\infty}}{r \sqrt{π}} \int_{β}^{\infty} {1 - \exp [- \frac{t}{τ_{p}} (1 - \frac{β^{2}}{μ^{2}})]} \exp (- μ^{2}) d μ (t \leq τ)

(3)

And the temperature of the cluster

T (a, t) = T_{0} + T_{\infty} [1 - \exp (- t / τ_{p})] (t \leq τ)

(4)

Where T_∞ = IQ_absa/4k_m is the eventual temperature of the cluster above the ambient temperature, τ_p = a²ρ_pC_p/3k_m is the time to reach it, β = (r-a)(4κt)^1/2 is a dimensionless parameter, and τ is the pulse length. Equation (3) gives the temperature around the cluster at any time (t) and at any distance (r) from the center of the cluster. Figure 11 is an illustration of the temperature variation of the cluster in the time domain during and after laser exposure. As seen, the temperature increases rapidly during the laser exposure time (t≤τ).

Fig. 11 The temperature of defect cluster in the time domain during and after laser exposure

During heat dissipation stage, laser irradiation stopped. Removing the heat source, the boundary condition changed. They are(I)at t = τ, T = T_max, where T_max is the temperature of the cluster at t = τ during heating process; (II) at infinity T = T₀, and (III) the power leaving the surface must equal the rate of change of heat content of the cluster

4 π a^{2} k_{m} {(\frac{\partial T}{\partial r})}_{r = a} = \frac{4 π}{3} a^{3} ρ_{p} C_{p} {(\frac{\partial T}{\partial t})}_{r = a}

(5)

Equation (1) can be solved by putting the heated cluster with temperature T_max into a much larger sphere with diameter of L. The final result for the temperature is given as [25

H. S. Carslaw and J. C. Jeager, Conduction of Heat in Solids, 2nd edition (Clarendon, 1959).

T (r, t) = - \frac{2 L T_{\max}}{π r} \sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{n} \sin \frac{n π r}{a} \exp (- κ n^{2} π^{2} t / L^{2})

(6)

The temperature at the surface of the cluster given by the limit as r→a of (6) is

T (r, t) = - 2 T_{\max} \sum_{n = 1}^{\infty} {(- 1)}^{n} \exp (- κ n^{2} π^{2} t / L^{2}) (t > τ)

(7)

Figure 11 displays the temperature of defect cluster in the time domain during and after laser exposure. The laser beam is characterized as a top hat 8ns pulse with the fluence of 10J/cm². The thermal conductivity of DKDP crystal k_m is 2.0 W·m⁻¹·K⁻¹. The radius of the cluster a is 100nm, the absorption efficiency factor Q_abs is half of 0.05 [26

C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92(8), 087401 (2004). [CrossRef] [PubMed]

, 27

A. Dyan, M. Pommies, G. Duchateau, F. Enguehard, S. Lallich, B. Bertussi, D. Damiani, H. Piombini, and H. Mathis, “Revisited thermal approach to model laser-induced damage and conditioning process in KH₂PO₄ and D_2xKH_{2 (1-x)} PO₄ crystals,” Proc. SPIE 6403, 640307 (2007).

]. The density and specific heat of the cluster ρ_pC_p is 1.88 × 10⁶ J·m⁻³·K⁻¹. As seen, the temperature decreases relative slowly after laser exposure (t>τ). The duration of temperature decreasing is as much as several hundreds times that of temperature increasing. Therefore, the laser conditioning process is a local rapid-rising and slow-cooling process, which is quite like the annealing process.

The formation of point defects, such as interstitials and vacancies, is governed by the principle of minimizing the total Gibbs free energy of DKDP crystals. The thermal equilibrium concentration of point defects increases with the temperature, and it is given by a balance of entropy and enthalpy [22

J. S. Pan, J. M. Tong, and M. B. Tian, Fundamentals of Materials Science, (Qinghua University Press, 1998).

C_{d e f e c t} = \exp (- \frac{Δ G_{d e f e c t}}{R T})

(8)

Δ G_{d e f e c t} = Δ H_{d e f e c t} - T \times Δ S_{d e f e c t}

(9)

where ΔH_defect and ΔS_defect are the formation enthalpy and entropy of a point defect, respectively, T is the lattice temperature and R is the mole gas constant.

As discussed above, during laser conditioning the temperature of cluster increases rapidly and decreases slowly, just like the annealing process. Annealing, in material science, is a treatment wherein a material is altered, causing changes in its properties. It is a process that produces conditions by heating to above the critical temperature, maintaining a suitable temperature, and then cooling. Laser conditioning is just like the local annealing process, as seen in Fig. 11. During laser pulse irradiation with 8ns pulse length, the temperature is increased so rapidly, which doesn’t provide enough time for the point defect to increase their concentration. So the concentration is not increased during the heating process. Then the temperature decreases to the room temperature in several hundreds of nanoseconds. The relatively slow falling process provides enough time and releases heat energy for some vacancy or interstitial point defects to overcome the energy barrier and annealed in this process. When the temperature falling to the room temperature, the laser exposed area changes from the un-equilibrium to equilibrium state, and the defect concentration is reduced dramatically. The reduced equilibrium concentration from the transient maximum temperature to the room temperature can be expressed as following:

Δ C_{d e f e c t} = \exp (- \frac{Δ G_{d e f e c t}}{R T_{1}}) - \exp (- \frac{Δ G_{d e f e c t}}{R T_{2}})

(10)

Where T₁ is the maximum temperature induced by laser conditioning, T₂ is the room temperature. As we known, the annealing effect depends on the maximum annealing temperature and the rising/falling speed rate. During laser conditioning, the rising/falling speed rate is mainly determined by DKDP characteristics, which are fixed value. So the maximum probable defect reduction, which represents the conditioning effect, is determined by the maximum temperature during laser conditioning. Therefore, Eq. (10) could stand for the maximum probable defect reduction. Figure 12 illustrates the maximum reduced defect concentration Vs the maximum temperature induced by laser exposure. As seen, accompanied with increasing temperature, the maximum probable defect reduction is increased. The temperature depends on laser energy during conditioning process. So increasing laser energy can reduce more defects, and then increase the conditioning efficiency. Too high or too low temperature cannot provide an efficient conditioning process. Too high temperature would lead to functional laser damage, which makes the crystal unusable. Too low temperature cannot reduce the defect effectively, as seen in Fig. 12. All of these are quite agreed with the experimental results.

Fig. 12 The maximum probable reduction of defect concentration Vs. the maximum temperature induced during laser exposure (ΔH_defect is set at 200kJ/mol, ΔS_defect is 19.27 × 10⁻³kJ/mol·K).

As shown in Fig. 12, the 4500K temperature would reduce the defect concentration by 8.0 × 10⁻³. As discussed above, the point defects are assumed to absorb all of the photon energy of 355nm laser irradiated on them. So the defect reduction decreases the absorption by 8.0 × 10⁻³. This will increase the transmittance by 8.0 × 10⁻³, which is on the order of the transmittance increase discovered in the above experimental results. As the increase of laser conditioning energy, more defects can be reduced and transmittance increases higher.

4. Conclusion

By taking multiple measurements of transmittance at 355nm, 532nm, 1064nm before and after laser conditioning in DKDP crystals, we found that the transmittance is increased by about 0.05~0.4% after 6J/cm² laser conditioning, and then decreased by about 0.1% after 10J/cm² laser conditioning. The transmittance decrease was attributed to laser damage scattering, and the increase was derived from the absorption reduction. Moreover, the absorption was reduced further at higher conditioning fluence. The heating process during laser exposure was analyzed in the time domain, and the local rapid-rising and slow-cooling process led to decrease the defect concentration, which can improve the laser damage resistance and increase the transmittance.

References and links

1.	J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH₂PO₄ and KD₂PO₄ crystals for the world's most power laser,” Int. Mater. Rev. 47, 113–152 (2002). [CrossRef]
2.	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(12), 127402 (2003). [CrossRef] [PubMed]
3.	M. D. Feit and A. M. Rubenchik, “Implications of nanoabsorber initiators for damage probability curves, pulselength scaling and laser conditioning,” Proc. SPIE 5273, 74–82 (2004). [CrossRef]
4.	C. H. Chan, “Effective absorption for thermal blooming due to aerosols,” Appl. Phys. Lett. 26(11), 628–630 (1975). [CrossRef]
5.	G. Duchateau, “Simple models for laser-induced damage and conditioning of potassium dihydrogen phosphate crystals by nanosecond pulses,” Opt. Express 17(13), 10434–10456 (2009). [CrossRef] [PubMed]
6.	R. A. Negres, P. DeMange, and S. G. Demos, “Investigation of laser annealing parameters for optimal laser-damage performance in deuterated potassium dihydrogen phosphate,” Opt. Lett. 30(20), 2766–2768 (2005). [CrossRef] [PubMed]
7.	C. Marshall, S. Payne, M. Henesian, J. Speth, and H. Powell, “Ultraviolet-induced transient absorption in potassium dihydrogen phosphate and its influence on frequency conversion,” J. Opt. Soc. Am. B 11(5), 774–785 (1994). [CrossRef]
8.	G. Duchateau and A. Dyan, “Coupling statistics and heat transfer to study laser induced crystal damage by nanosecond pulses,” Opt. Express 15(8), 4557–4576 (2007). [CrossRef] [PubMed]
9.	K. E. Montgomery and F. P. Milanovich, “High-laser-damage-threshold potassium dihydrogen phosphate crystals,” J. Appl. Phys. 68(8), 3979–3982 (1990). [CrossRef]
10.	Y. Nishida, A. Yokotani, T. Sasaki, K. Yoshida, T. Yamanaka, and C. Yamanaka, “Improvement of the bulk laser damage threshold of potassium dihydrogen phosphate crystals by re-ducing the organic impurities in growth solution,” Appl. Phys. Lett. 52(6), 420–421 (1988). [CrossRef]
11.	B. Dam, P. Bennema, and W. J. P. van Enckevort, “The mechanism of tapering on KDP-type crystals,” J. Cryst. Growth 74(1), 118–128 (1986). [CrossRef]
12.	S. Setzler, K. Stevens, L. Halliburton, M. Yan, N. Zaitseva, and J. DeYoreo, “Hydrogen atoms in KH₂PO₄ crystals,” Phys. Rev. B 57(5), 2643–2646 (1998). [CrossRef]
13.	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(1), 015505 (2003). [CrossRef] [PubMed]
14.	C. S. Liu, Q. Zhang, N. Kioussis, S. Demos, and H. Radousky, “Electronic structure calculations of intrinsic and extrinsic hydrogen point defects in KH₂PO₄,” Phys. Rev. B 68(22), 224107 (2003). [CrossRef]
15.	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(27), 5483–5495 (2003). [CrossRef] [PubMed]
16.	J. J. Adams, “Results of sub-nanosecond laser-conditionining of KD₂PO₄ crystals,” Proc. SPIE 6403, 64031M (2007).
17.	R. A. Negres, P. DeMange, and S. G. Demos, “Investigation of laser annealing parameters for optimal laser-damage performance in deuterated potassium dihydrogen phosphate,” Opt. Lett. 30(20), 2766–2768 (2005). [CrossRef] [PubMed]
18.	M. Chirila, N. Garces, L. Halliburton, S. Demos, T. Land, and H. Radousky, “Production and thermal decay of radiation-induced point defects in KD₂PO₄ crystals,” J. Appl. Phys. 94(10), 6456–6462 (2003). [CrossRef]
19.	M. Runkel, A. K. Burnham, D. Milam, W. Sell, M. Feit, and A. Rubenchik, “The results of pulse scaling experiments on rapid growth DKDP triplers using the optical sciences laser at 351nm,” Proc. SPIE 4347, 359–372 (2000).
20.	R. Sharp III and M. J. Runkel, “Automated damage onset analysis techniques applied to KDP damage and Zeus small area damage test facility,” Proc. SPIE 3902, 361–368 (2000). [CrossRef]
21.	J. E. Wolfe and S. E. Schrauth, “Automated laser damage test system with real-time damage event imaging and detection,” Proc. SPIE 6403, 640328 (2007).
22.	J. S. Pan, J. M. Tong, and M. B. Tian, Fundamentals of Materials Science, (Qinghua University Press, 1998).
23.	J. Q. Chen, M. X. Chen, and J. S. Zhao, Crystal defects, (Zhejiang University Press, 1992).
24.	C. S. Liu, C. J. Hou, N. Kioussis, S. G. Demos, and H. B. Radousky, “Electronic structure calculations of an oxygen vacancy in KH₂PO₄,” Phys. Rev. B 72(13), 134110 (2005). [CrossRef]
25.	H. S. Carslaw and J. C. Jeager, Conduction of Heat in Solids, 2nd edition (Clarendon, 1959).
26.	C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett. 92(8), 087401 (2004). [CrossRef] [PubMed]
27.	A. Dyan, M. Pommies, G. Duchateau, F. Enguehard, S. Lallich, B. Bertussi, D. Damiani, H. Piombini, and H. Mathis, “Revisited thermal approach to model laser-induced damage and conditioning process in KH₂PO₄ and D_2xKH_{2 (1-x)} PO₄ crystals,” Proc. SPIE 6403, 640307 (2007).

OCIS Codes
(140.3440) Lasers and laser optics : Laser-induced breakdown
(160.3380) Materials : Laser materials
(350.1820) Other areas of optics : Damage

ToC Category:
Materials

History
Original Manuscript: September 4, 2012
Revised Manuscript: October 12, 2012
Manuscript Accepted: October 13, 2012
Published: October 19, 2012

Citation
Guohang Hu, Yuanan Zhao, Dawei Li, and Qiling Xiao, "Transmittance increase after laser conditioning reveals absorption properties variation in DKDP crystals," Opt. Express 20, 25169-25180 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-22-25169

Sort: Author | Year | Journal | Reset

References

J. J. De Yoreo, A. K. Burnham, and P. K. Whitman, “Developing KH2PO4 and KD2PO4 crystals for the world's most power laser,” Int. Mater. Rev.47, 113–152 (2002). [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(12), 127402 (2003). [CrossRef] [PubMed]
M. D. Feit and A. M. Rubenchik, “Implications of nanoabsorber initiators for damage probability curves, pulselength scaling and laser conditioning,” Proc. SPIE5273, 74–82 (2004). [CrossRef]
C. H. Chan, “Effective absorption for thermal blooming due to aerosols,” Appl. Phys. Lett.26(11), 628–630 (1975). [CrossRef]
G. Duchateau, “Simple models for laser-induced damage and conditioning of potassium dihydrogen phosphate crystals by nanosecond pulses,” Opt. Express17(13), 10434–10456 (2009). [CrossRef] [PubMed]
R. A. Negres, P. DeMange, and S. G. Demos, “Investigation of laser annealing parameters for optimal laser-damage performance in deuterated potassium dihydrogen phosphate,” Opt. Lett.30(20), 2766–2768 (2005). [CrossRef] [PubMed]
C. Marshall, S. Payne, M. Henesian, J. Speth, and H. Powell, “Ultraviolet-induced transient absorption in potassium dihydrogen phosphate and its influence on frequency conversion,” J. Opt. Soc. Am. B11(5), 774–785 (1994). [CrossRef]
G. Duchateau and A. Dyan, “Coupling statistics and heat transfer to study laser induced crystal damage by nanosecond pulses,” Opt. Express15(8), 4557–4576 (2007). [CrossRef] [PubMed]
K. E. Montgomery and F. P. Milanovich, “High-laser-damage-threshold potassium dihydrogen phosphate crystals,” J. Appl. Phys.68(8), 3979–3982 (1990). [CrossRef]
Y. Nishida, A. Yokotani, T. Sasaki, K. Yoshida, T. Yamanaka, and C. Yamanaka, “Improvement of the bulk laser damage threshold of potassium dihydrogen phosphate crystals by re-ducing the organic impurities in growth solution,” Appl. Phys. Lett.52(6), 420–421 (1988). [CrossRef]
B. Dam, P. Bennema, and W. J. P. van Enckevort, “The mechanism of tapering on KDP-type crystals,” J. Cryst. Growth74(1), 118–128 (1986). [CrossRef]
S. Setzler, K. Stevens, L. Halliburton, M. Yan, N. Zaitseva, and J. DeYoreo, “Hydrogen atoms in KH2PO4 crystals,” Phys. Rev. B57(5), 2643–2646 (1998). [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(1), 015505 (2003). [CrossRef] [PubMed]
C. S. Liu, Q. Zhang, N. Kioussis, S. Demos, and H. Radousky, “Electronic structure calculations of intrinsic and extrinsic hydrogen point defects in KH2PO4,” Phys. Rev. B68(22), 224107 (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(27), 5483–5495 (2003). [CrossRef] [PubMed]
J. J. Adams, “Results of sub-nanosecond laser-conditionining of KD2PO4 crystals,” Proc. SPIE6403, 64031M (2007).
R. A. Negres, P. DeMange, and S. G. Demos, “Investigation of laser annealing parameters for optimal laser-damage performance in deuterated potassium dihydrogen phosphate,” Opt. Lett.30(20), 2766–2768 (2005). [CrossRef] [PubMed]
M. Chirila, N. Garces, L. Halliburton, S. Demos, T. Land, and H. Radousky, “Production and thermal decay of radiation-induced point defects in KD2PO4 crystals,” J. Appl. Phys.94(10), 6456–6462 (2003). [CrossRef]
M. Runkel, A. K. Burnham, D. Milam, W. Sell, M. Feit, and A. Rubenchik, “The results of pulse scaling experiments on rapid growth DKDP triplers using the optical sciences laser at 351nm,” Proc. SPIE4347, 359–372 (2000).
R. Sharp and M. J. Runkel, “Automated damage onset analysis techniques applied to KDP damage and Zeus small area damage test facility,” Proc. SPIE3902, 361–368 (2000). [CrossRef]
J. E. Wolfe and S. E. Schrauth, “Automated laser damage test system with real-time damage event imaging and detection,” Proc. SPIE6403, 640328 (2007).
J. S. Pan, J. M. Tong, and M. B. Tian, Fundamentals of Materials Science, (Qinghua University Press, 1998).
J. Q. Chen, M. X. Chen, and J. S. Zhao, Crystal defects, (Zhejiang University Press, 1992).
C. S. Liu, C. J. Hou, N. Kioussis, S. G. Demos, and H. B. Radousky, “Electronic structure calculations of an oxygen vacancy in KH2PO4,” Phys. Rev. B72(13), 134110 (2005). [CrossRef]
H. S. Carslaw and J. C. Jeager, Conduction of Heat in Solids, 2nd edition (Clarendon, 1959).
C. W. Carr, H. B. Radousky, A. M. Rubenchik, M. D. Feit, and S. G. Demos, “Localized dynamics during laser-induced damage in optical materials,” Phys. Rev. Lett.92(8), 087401 (2004). [CrossRef] [PubMed]
A. Dyan, M. Pommies, G. Duchateau, F. Enguehard, S. Lallich, B. Bertussi, D. Damiani, H. Piombini, and H. Mathis, “Revisited thermal approach to model laser-induced damage and conditioning process in KH2PO4 and D2xKH2 (1-x) PO4 crystals,” Proc. SPIE6403, 640307 (2007).

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.

Click here to see a list of articles that cite this paper