Laser-induced Damage Research Articles

Growth, Structural, Spectroscopic and Thermal Analyses of Novel Organic Brucinum-3, 5 –Dihydroxybenzoate Dihydrate Single Crystals for NLO Applications

Along the line of available efficient nonlinear optical (NLO) organic single crystals in the literature, it is worthwhile to bring in a novel organic single crystal of Brucinium-3,5-dihydroxybenzoate dihydrate (B35D) which was successfully grown utilizing the technique of slow evaporation of solution at ambient conditions. As the solubility of B35D was found to be the highest in water-ethanol 1:1 mixed solvent among the conventional solvents, crystallization of B35D was accomplished by making use of the solvent. The required confirmation of the crystal structure of the crystal and its lattice parameter could be achieved by the single-crystal X-ray diffraction analysis such that B35D was found to be crystallized in the monoclinic system with the non-centrosymmetric space group C2. The recording of UV-Vis-NIR transmittance spectrum of the crystal was undertaken between the range of 300 and 900 nm whereby the lower optical cutoff wavelength was identified to be 321 nm. The spectral study of photoluminescence was carried out in the range of 300-600 nm by which the band gap energy was calculated to be about 3.8 eV (at 373 nm) indicating that B35D has a violet fluorescence spectrum. The thermal stability and melting point of the title crystal have been investigated through Thermo gravimetric and differential thermal analysis (TG-DTA) such that the thermal stability of the crystal was found to be 95.6 °C. The Nd: YAG Q-switched laser was employed so as to obtain the laser-induced surface damage threshold of the specimen which was estimated to be 3.1 GW/cm2. The Vickers microhardness test was implemented in order to arrive at the mechanical strength of the crystal. The performed non-linear optical study could reveal that the second-order harmonic generation (SHG) efficiency of B35D crystal is 2.16 times higher than KDP. So that B35D crystals are among the class of NLO materials.

Double alkaline earth metals sulfide SrMgGeS4 with high laser-induced damage threshold and strong second-harmonic generation

The exploration of anti-laser damage wide band gap infrared (IR) nonlinear optical (NLO) materials is urgently needed but challenging due to the contradiction between wide band gap and large NLO coefficient. Herein, by introducing [MQ4] (Q = S, Se) tetrahedral units into the AIIBIICIVD4VI family, three double alkaline earth metals chalcogenides SrMgGeS4, BaMgSiSe4 and SrMgSiSe4 with unprecedented [MgGeS6] or [MgSiSe6] dimers are rationally designed and fabricated. The compounds display an interesting structural change from centrosymmetric (CS) I41/acd (BaMgSiSe4, the first CS compound in this family) to non-centrosymmetric Ama2 (SrMgSiSe4) and Fdd2 (SrMgGeS4). Importantly, SrMgGeS4 shows a wide band gap (3.58 eV), a high laser-induced damage threshold (∼6 × AGS), a moderate birefringence (∼0.11@1064 nm), and a strong second-harmonic generation (SHG) response (∼1.1 × AGS), achieving a good balance between wide band gap (Eg ≥ 3.5 eV) and large SHG response (≥1.0 × AGS) for an excellent IR NLO material. The results enrich the chemical and structural diversity of chalcogenides and give insights into the design of high-performance IR NLO materials.

Study on the laser-induced damage characteristics and structure changes of fluorotellurite glass under femtosecond pulsed laser irradiation

TeO2-ZnF2-BaF2-Ta2O5 fluorotellurite glasses have excellent optical properties and stability which makes them promising candidates for mid-infrared (mid-IR) fiber applications. In this work, the properties and structure of fluorotellurite glasses with gradient change of BaF2 content were compared. Under the irradiation of femtosecond (fs) laser, the potential relationship between fs laser-induced damage characteristics, glass composition and structural property were systematically studied. The fs laser-induced damage threshold (FLIDT) of investigated fluorotellurite glass samples increased from 892.45 mJ/cm2 by more than one-third to 1223.84 mJ/cm2 and the attenuation coefficient of multi-pulse FLIDT increases from 7.69 to 25.29 with the increase of [TeO3] content from 0.312 to 0.565 induced by increasing BaF2 content. Further, structural transformation from TeO4 units to TeO3 units in the glass network triggered by fs laser irradiation is confirmed by Raman spectra measurements. This study provides theoretical guidance for tailoring the fs laser damage threshold through glass microstructural modulation by composition optimization, which is of great importance to improve the output power in mid-IR supercontinuum (SC) spectra and rare earth (RE) doped fiber laser systems.

Eu2MGe2OS6 (M = Mn, Fe, Co): Three Melilite-Type Rare-Earth Oxythiogermanates Exhibiting Balanced Nonlinear-Optical Behaviors.

Metal oxychalcogenides as candidates for novel mid-infrared nonlinear-optical materials have attracted great interest due to the distinctive advantages of oxides and chalcogenides in this field. Herein, the first melilite-type rare-earth (RE) oxythiogermanates Eu2MGe2OS6 [M = Mn (1), Fe (2), Co (3)] are obtained by combining RE metals with localized f electrons, magnetic transition metals with delocalized d electrons, and the highly distorted mixed anionic group [GeOS3] into one structure. They belong to the tetragonal P4̅21m space group, and highly distorted [EuOS7] bicapped trigonal prisms bridge adjacent {[MGe2OS6]4-}∞ layers to build the three-dimensional network. Their optical band gaps are determined as 2.40, 2.11 and 2.14 eV, and they show moderate second-harmonic-generation (SHG) responses (0.3, 0.3 and 0.5 × AGS) and large laser-induced damage thresholds (2.77-8.31 × AGS). Theoretical calculation results indicate that the synergistic effect of [EuOS7] and [MS4] units acts on the SHG effect. This work enriches the crystal chemistry of melilite-structure materials.

A lone spike in blood glucose can enhance the thrombo-inflammatory response in cortical venules

How transient hyperglycemia contributes to cerebro-vascular disease has been a challenge to study under controlled physiological conditions. We use amplified, ultrashort laser-pulses to physically disrupt brain-venule endothelium at targeted locations. This vessel disruption is performed in conjunction with transient hyperglycemia from a single injection of metabolically active D-glucose into healthy mice. The observed real-time responses to laser-induced disruption include rapid serum extravasation, platelet aggregation, and neutrophil recruitment. Thrombo-inflammation is pharmacologically ameliorated by a platelet inhibitor, by a scavenger of reactive oxygen species, and by a nitric oxide donor. As a control, vessel thrombo-inflammation is significantly reduced in mice injected with metabolically inert L-glucose. Venules in mice with diabetes show a similar response to laser-induced disruption and damage is reduced by restoration of normo-glycemia. Our approach provides a controlled method to probe synergies between transient metabolic and physical vascular perturbations and can reveal new aspects of brain pathophysiology.

A study on novel semi-organic material L-phenylalanine mixed with cadmium nitrate single crystals

Slow evaporation solutions turned out to be a good way to get single crystals of semi-organic NLO from an aqueous solution. During this experiment, the ambient temperature was used. Through X-ray diffraction analysis, a single crystal of L-phenylalanine (C9H11NO2) cadmium nitrate (Cd (NO3)2)was characterised. As a result of this construction, the P21 space group has the following cell parameters: a = 12.47 Å, b = 5.43 Å, c = 15.00 Å, α = γ = 90°, β = 107.61°. It was found that a 257 nm cut-off wavelength was found from UV–Vis-NIR spectroscopy. Aside from linear optical characteristics such as the extinction coefficient (K) and reflectance (R), this study examined a number of geometrical features. In addition, the crystal was shown to have a high level of optical transparency. Fluorescence (FL) spectrum analysis has been used in the process of investigating how the luminescence of LPCN behaves. Evidence that functional groups are present may be gleaned from the FT-IR vibrational patterns seen in the LPCN. We used a Vickers microhardness hardness tester to figure out the brittleness index (Bi), as well as the hardness (Hv), Meyer's index (n), yield strength (σy), fracture toughness (Kc), and elastic stiffness constant (C11). The evaluation of the produced crystals' dielectric properties was accomplished by adjusting the frequency. In contrast to KDP and other organic materials, the threshold value for laser-induced damage was found to be much higher. The crystal's surface morphology was analysed using SEM to get a better idea of what it looked like. EDAX analysis of the LPCN crystal was conducted to determine what elements are present in it. The non-linear optical quality of the compound that was discovered with Kurtz powder's second harmonic production in the case of Nd: YAG laser light shows that it is a potential candidate for frequency conversion. The nonlinearity coefficient (β) was measured using the open aperture Z-scan technique (Nd: YAG, 532 nm, 9 ns), and the results showed that it was 0.36 × 10–11m/W. This coefficient is the consequence of a phenomenon known as effective genuine two-photon absorption. The crystal that was created now has a fluency threshold of 3.52 × 1012 W/m2, which makes it a possible candidate for use in optical limiting devices because of its consequent optical limiting behaviour.

From design to realization of high diffraction efficiency Littrow configuration diffraction gratings based on multilayer dielectric mirrors patterned with electron beam lithography

Diffraction efficiency (DE) and laser-induced damage threshold of Chirped pulse amplification (CPA) system diffraction gratings (DGs) are one of the main limiting factors for the anticipated progress of high peak power lasers. Optimization of a high reflectivity dielectric multilayer ZrO2/SiO2 stack mirror with a DG etched in the top SiO2 layer was carried out employing the Rigorous coupled wave analysis method. Two families of solutions possessing DE > 0.99 over the bandwidth of the 1030 nm wavelength ultrashort laser and withstanding different fabrication margins were identified for the Littrow configuration. DGs were produced and verified experimentally. Structures permitting variation in both the depth of the DG and filling factor without loss in DE were obtained for the 690 nm thick SiO2 layer. While the 770 nm thick layer permitted separation of the two parameters requiring either rigorous control of the DG depth or filling factor. DG realization technology was proposed employing electron beam lithography and inductively coupled plasma reactive ion etching. Measurements of the fabricated structures demonstrated 0.91 DE for the first diffraction order over the 60 nm bandwidth and under a 6° mounting error from the Littrow configuration. Spectral angular reflectance DE simulations and respective measurements indicated quantitative agreement. The work provides an integrated overview of high DE periodic structure numerical optimization and manufacturing roadmap which could be applied for the high-peak-power laser CPA system development.

Ca2 Ln(BS3 )(SiS4 ) (Ln = La, Ce, and Gd): Mixed Metal Thioborate-Thiosilicates as Well-Performed Infrared Nonlinear Optical Materials.

The first examples of thioborate-thiosilicates, namely Ca2 Ln(BS3 )(SiS4 ) (Ln = La, Ce, and Gd), are synthesized by rationally designed high-temperature solid-state reactions. They crystalize in the polar space group P63 mc and feature a novel three-dimensionalcrystal structure in which the discrete [BS3 ]3- and [SiS4 ]4- anionic groups are linked by Ca2+ and Ln3+ cations occupying the same atomic site. Remarkably, all three compounds show comprehensive properties required as promising infrared nonlinear optical materials, including phase-matchable strong second harmonic generation (SHG) responses at 2.05µm (1.1-1.2 times that of AgGaS2 ), high laser-induced damage thresholds (7-10 times that of AgGaS2 ), wide light transmission range (0.45-11µm), high thermal stabilities (>800 °C), and large calculated birefringence (0.126-0.149 @1064nm), which justify the material design strategy of combining [BS3 ]3- and [SiS4 ]4- active units. Theoretical calculations suggest that their large SHG effects originate mainly from the synergy effects of the LnS6 , BS3 , and SiS4 groups. This work not only broadens the scope of research on metal chalcogenides but also provides a new synthetic route for mixed anionic thioborates.

The compatibly large nonlinear optical effect and high laser-induced damage threshold in a thiophosphate CsInP2S7 constructed with [P2S7]4- and [InS6]9-

It is challenging to cooperatively improve the nonlinear optical (NLO) efficiency and the laser-induced damage threshold (LIDT). This work reports a novel IR NLO materials CsInP2S7 (CIPS) designed by combination the strategies of alkali metals substitution and microscopic NLO units PS4 introduction based on AgGaS2. CIPS was composed of strongly distorted [InS6]9- octahedra and [P2S7]4- dimers constructed by corner-sharing [PS4]3-, which increase the NLO efficiency and decrease thermal expansion anisotropy simultaneously. Compared with AgGaS2, CIPS exhibited strong phase matchable NLO response ca. 1.1 × AGS@2.1 µm, high LIDT ca. 20.8 × AgGaS2, and IR transparency up to 15.3 µm. Structural analysis and theoretical investigation confirmed that large SHG effect and ultrahigh LIDT of CIPS originated from the synergistic contribution of [InS6]9- octahedra and [P2S7]4- dimers. These results indicate that CIPS is a promising NLO candidate in the mid-IR region, and this study provides a new approach for developing potential NLO-LIDT compatible materials.

Peak-power of 25 W passively Q-switched [formula omitted]2.8 [formula omitted]m Er:YAP bulk laser based on a reflective TaSe2 saturable absorber mirror

Improving the overall performance of saturable absorber mirrors (SAMs) based on Two-dimensional (2D) narrow-band-gap materials is critically important in their applications of mid-infrared pulse laser sources. Herein, a reflective TaSe2 SAM with laser-induced damage threshold of ∼12 MW/cm2 was successfully fabricated, the saturable absorption properties around 2.8 μm were characterized with a modulation depth of 5.3% and a total unsaturated loss of 2.2%. With the as-prepared SAM, high-peak-power passively Q-switched Er:YAP laser operation at ∼2.8 μm was realized. For the condition of the maximum absorbed pump power of 8.0 W, the maximum average output power of 0.7 W was obtained with a pulse width of 264 ns at a repetition rate of 105.5 kHz, which corresponds to a maximum single pulse energy of 6.6 μ J and a peak power of 25.1 W.

Excellent Nonlinear Optical M[M4 Cl][Ga11 S20 ] (M = A/Ba, A = K, Rb) Achieved by Unusual Cationic Substitution Strategy.

The typical chalcopyrite AgGaQ2 (Q = S, Se) are commercial infrared (IR) second-order nonlinear optical (NLO) materials; however, they suffer from unexpected laser-induced damage thresholds (LIDTs) primairy due to their narrow band gaps. Herein, what sets this apart from previously reported chemical substitutions is the utilization of an unusual cationic substitution strategy, represented by [[SZn4 ]S12 + [S4 Zn13 ]S24 + 11ZnS4 ⇒ MS12 + [M4 Cl]S24 + 11GaS4 ], in which the covalent Sx Zny units in the diamond-like sphalerite ZnS are synergistically replaced by cationic Mx Cly units, resulting in two novel salt-inclusion sulfides, M[M4 Cl][Ga11 S20 ] (M = A/Ba, A = K, 1; Rb, 2). As expected, the introduction of mixed cations in the GaS4 anionic frameworks of 1 and 2 leads to wide band gaps (3.04 and 3.01 eV), which exceeds the value of AgGaS2 , facilitating the improvement of high LIDTs (9.4 and 10.3 × AgGaS2 @1.06 µm, respectively). Furthermore, compounds 1 and 2 exhibit moderate second-harmonic generation intensities (0.84 and 0.78 × AgGaS2 @2.9 µm, respectively), mainly originating from the orderly packing tetrahedral GaS4 units. Importantly, this study demonstrates the successful application of the cationic substitution strategy based on diamond-like structures to provide a feasible chemical design insight for constructing high-performance NLO materials.

Ce(IO3)3F and Ce(IO3)2(NO3): Two Mixed-Anion Cerium Iodates with Good Nonlinear Optical and Birefringent Properties.

Two new mixed-anion cerium iodates, namely, Ce(IO3)3F and Ce(IO3)2(NO3), have been rationally designed through the integration of hybrid anionic functional building blocks (FBBs). The structure of Ce(IO3)3F features a novel [Ce(IO3)3F] bilayer, and the material exhibits large birefringence (0.225 @546 nm). The structure of Ce(IO3)2(NO3) features [Ce3(IO3)6]3+ triple layers that are further linked by planar NO3- units. Ce(IO3)2(NO3) shows a moderate SHG response (1 × KDP) and a high laser-induced damage threshold value (22 × AgGaS2). This work demonstrates that the rich coordination geometries of cerium cations facilitate tuning of the structures of related compounds through modulating anionic FBBs.

Chiral Hybrid Germanium(II) Halide with Strong Nonlinear Chiroptical Properties.

Due to the pronounced anisotropic response to circularly polarized light, chiral hybrid organic-inorganic metal halides have been regarded as promising candidates for the application in nonlinear chiroptics, especially for the second-harmonic generation circular dichroism (SHG-CD) effect. However, designing novel lead-free chiral hybrid metal halides with large anisotropy factors and high laser-induced damage thresholds (LDT) of SHG-CD remains challenging. Herein, we develop the first chiral hybrid germanium halide, (R/S-NEA)3 Ge2 I7 ⋅H2 O (R/S-NGI), and systematically investigated its linear and nonlinear chiroptical properties. S-NGI and R-NGI exhibit large anisotropy factors (gSHG-CD ) of 0.45 and 0.48, respectively, along with a high LDT of 38.46 GW/cm2 ; these anisotropy factors were the highest values among the reported lead-free chiral hybrid metal halides. Moreover, the effective second-order nonlinear optical coefficient of S-NGI could reach up to 0.86 pm/V, which was 2.9 times higher than that of commercial Y-cut quartz. Our findings facilitate a new avenue toward lead-free chiral hybrid metal halides, and their implementation in nonlinear chiroptical applications.

Lasers in Medicine: The Changing Role of Therapeutic Laser-Induced Retinal Damage—From de rigeuer to Nevermore

For over five decades, laser-induced retinal damage (LIRD) was thought to be the necessary cost of all therapeutic effects of laser treatment for the most important causes of irreversible visual loss, the chronic progressive retinopathies (CPRs). The development of modern retinal laser therapy with the discovery of “low-intensity/high-density subthreshold micropulse” laser (SDM) showed that the supposed need for LIRD represented a case of confusing association with causation. This revealed that LIRD was unnecessary and detrimental to clinical outcomes, and thus, contraindicated as the most severe complication of retinal laser treatment. SDM allowed for an understanding of the mechanism of retinal laser treatment as a physiologic reset effect, triggered by heat-shock protein (HSP) activation upregulating the unfolded protein response and restoring proteostasis by increasing protein repair by 35% in dysfunctional cells via a thermally sensitive conformational change in the K10 step of HSP activation kinetics. Because HSP activation kinetics are catalytic, even low levels (the “reset” threshold) of HSP activation result in a maximal treatment response. SDM and the study of HSP activation kinetics in the retina show that the therapeutic effects of retinal laser treatment can be fully realized without any degree of LIRD. Besides LIRD, all effects of retinal laser treatment are restorative and therapeutic, without any known adverse treatment effects. Without LIRD, the benefits of retinal laser treatment are infinitely renewable and direct treatment of the fovea is possible. Elimination of LIRD from retinal laser treatment has revolutionized the clinical potential of retinal laser treatment to broaden treatment indications to permit, for the first time, effective early and preventive treatment to reduce visual loss from the most frequent causes of irreversible visual loss worldwide, the CPRs.

Impact of the multilayer dielectric design on the laser-induced damage threshold of pulse compression gratings for petawatt-class lasers.

The peak-power of petawatt-class lasers is limited by laser-induced damage to final optical components, especially on the pulse compression gratings. Multilayer dielectric (MLD) gratings are widely used in compressor systems because they exhibit a high diffraction efficiency and high damage threshold. It is now well established that the etching profile plays a key role in the electric field distribution, which influences the laser damage resistance of MLD gratings. However, less attention has been devoted to the influence of the multilayer design on the laser damage resistance of MLD gratings. In this Letter, we numerically and experimentally evidence the impact of the dielectric stack design on the electric field intensity (EFI) and the laser-induced damage threshold (LIDT). Three different MLD gratings are designed and manufactured to perform laser damage tests. On the basis of the expected EFIs and diffraction efficiencies, the measured LIDTs show how the multilayer design influences the laser resistance of the MLD gratings. This result highlights the impact of the multilayer dielectric design on the electric field distribution and shows how to further improve the laser-induced damage threshold of pulse compression gratings.

First-principles calculation of KH2PO4 anharmonic force constants phonon dispersion curves

The laser-induced damage threshold of potassium dihydrogen phosphate (KDP) crystal is far lower than the theoretical value. The damage mechanism of KDP crystal cannot be clearly determined by various experiments and first-principles density functional theory (DFT) calculation of electronic properties. We attempt to explore the impact of phonons on the damage process by studying lattice dynamics. The phonon dispersion curves of intrinsic KDP crystal with harmonic approximation and anharmonic effect are studied by using the first-principles DFT calculations. With harmonic approximation, there are three large imaginary frequencies in the PE phase, which are the O–H stretching soft modes leading to the FE-PE phase transition. For the large displacement vibration of H atoms in PE phase, the room-temperature phonon dispersion curves with anharmonic effect are calculated. The imaginary frequency caused by three O–H stretching soft modes disappears. Our results have important reference significance for understanding the damage mechanism of KDP crystal.

A Laser Damage Threshold for Microscope Glass Slides

Laser-based light sources have fostered innovative developments in biomedical and biosensor fields. However, laser-induced damage to optical components is a limitation for designing and implementing highly sensitive biosensors, necessitating the development and characterization of suitable optical components. Microscope glass slides are among the most extensively used optical units in this field. This study investigated the laser-induced damage threshold (LIDT) of high-quality microscope glass slides obtained from three different vendors. An S-on-1 protocol following the ISO 21254 series standards was adopted to ensure a meaningful comparative analysis. Multiple laser pulses at a constant fluence (at the three laser wavelengths most widely used in biosensors) were used for LIDT tests. An automated test bench was developed and employed to minimize the influence of human factors on the test results. The fatigue damage mechanism was observed in all the samples. The findings revealed good consistency among LIDT values within and across batches from the same vendor. However, a notable discrepancy was observed when comparing the results of slides obtained from different vendors, with threshold values differing by up to two-fold. This study emphasizes the need to carefully consider the glass material source when selecting microscope glass slides for laser-sensitive applications.

Injection-seeded high-power Yb:YAG thin-disk laser stabilized by the Pound-Drever-Hall method.

We demonstrate an injection-seeded thin-disk Yb:YAG laser at 1030 nm, stabilized by the Pound-Drever-Hall (PDH) method. We modified the PDH scheme to obtain an error signal free from Trojan locking points, which allowed robust re-locking of the laser and reliable long-term operation. The single-frequency pulses have 50 mJ energy (limited to avoid laser-induced damage) with a beam quality of M2 < 1.1 and an adjustable length of 55-110 ns. Heterodyne measurements confirmed a spectral linewidth of 3.7 MHz. The short pulse build-up time (850 ns) makes this laser suitable for laser spectroscopy of muonic hydrogen, pursued by the CREMA collaboration.

α- and β-(C4H5N2O)(IO3)·HIO3: Two SHG Materials Based on Organic-Inorganic Hybrid Iodates.

Organic-inorganic hybrid nonlinear optical (NLO) materials are highly anticipated because of the integration of both merits of the organic and inorganic moieties. Herein, the 2-pyrimidinone cation (C4H5N2O)+ has been incorporated into the iodate system to form two polymorphic organic-inorganic hybrid iodates, namely, α- and β-(C4H5N2O)(IO3)·HIO3. They crystallize in different polar space groups (Ia and Pca21), and their structures feature one-dimensional (1D) chain structures composed of (C4H5N2O)+ cations, IO3- anions, and HIO3 molecules interconnected via hydrogen bonds. α- and β-(C4H5N2O) (IO3)·HIO3 exhibit strong and moderate second-harmonic-generation (SHG) responses of 6.4 and 0.9 × KH2PO4 (KDP), respectively, the same band gaps of 3.65 eV, and high powder laser-induced damage threshold (LIDT) values [51 and 57 × AgGaS2 (AGS)]. The results of theoretical calculations revealed that the large SHG effect of α-(C4H5N2O)(IO3)·HIO3 originated from the IO3 and HIO3 groups. This work indicates that (C4H5N2O)+ is a potential group for designing new NLO materials with brilliant optical performances.

Nonlinear processes and laser damage induced by a temporally modulated nanosecond UV laser beam. Part II: Kerr self-focusing

In this paper, we study the impact of Kerr self-focusing on laser-induced damage of fused silica with temporal modulation. In our experiments, temporal modulations are generated with high bandwidth amplitude modulators between 2 and 10 GHz. Measurement of the spatial profile after propagation is made possible due to a dedicated imaging setup. First results without temporal modulation experimentally and numerically show that the nonlinear gain increases exponentially with intensity. Complementary experiments with temporal modulation at different frequencies show an increase in the nonlinear gain. Eventually, we show that laser-induced damage is enhanced with amplitude modulation, with a dependence on the frequency of the amplitude modulation. Optimization of phase modulation allowed us to mitigate backwards stimulated Brillouin scattering and to focus on the sole impact of Kerr self-focusing on laser-induced damage.