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The transient changes in the optical properties of bulk DKDP material arising from its exposure to high temperatures and pressures associated with localized laser energy deposition are investigated. Two methods for initiation of laser-induced breakdown are used, intrinsic, involving relatively large energy deposition brought about by focusing of the laser beam to high intensities, and extrinsic, arising from more localized deposition due to the presence of pre-existing absorbing damage initiating defects. Each method leads to a very different volume of material being affected, which provides for different material thermal relaxation times to help better understand the processes involved.
© 2012 Optical Society of America
1. Introduction
The process of laser-induced breakdown in the bulk of solid state materials such as transparent dielectrics, commonly used as optical materials, leads to a large increase in their localized temperature and pressure with a subsequent relaxation that is accompanied by irreversible material modifications (commonly referred to as “laser damage”) [1–9]. The amount of total energy deposited depends mostly on the laser pulse duration but also on the intensity [7, 10–14]. The initial phase of the buildup of an electronic excitation leads to the transformation of the material into a strong absorber which is responsible for the subsequent energy transfer of the laser energy into the affected region of the material [13–15]. The volume of affected material includes various modifications such as formation of a void and densification via material transport, and mechanical damage (such as cracks), and is proportional to the total energy deposited [16–20]. Laser-induced breakdown with nanosecond pulses is associated with transient material temperatures on the order of 1 eV and pressures on the order of 10 GPa [17]. The response of the material to these conditions takes place in a much longer time scale and is associated with the dissipation of the absorbed energy mainly via heat diffusion [7]. The cooling of the material is gradual and its dynamics depends on the size of the initial energy deposition volume [21]. This leads to transient material phases that are associated with high temperatures and pressures [1–6,11,13]. Understanding the electronic and optical properties of these transient phases is of importance for the fundamental understanding of material response under extreme conditions but also for the optimization of current or near future laser applications. For example, cumulative effects may arise during laser micro-machining of transparent materials or laser-induced damage in large aperture optical materials and the maximum repetition rate of the laser may be limited by the relaxation times of some of these transient material phases.
In a recent report we provided for the first time a detailed investigation into the sequence of relaxation processes governing the response of fused silica following laser-induced breakdown in the bulk of the material [7]. These results showed a two-component transient absorption exhibiting lifetimes on the order of about 150 ns and 150 μs, respectively. The first component was associated with crack formation and was localized at or very near the crack surfaces. The second component was localized in the central region of modified material overlapping with the initial focal region of the pump laser beam. It was hypothesized that this second transient absorption mechanism is related to the material at higher temperatures which lead to enhanced transient absorptivity and subsequent decay as the thermal energy is diffused into the surrounding cold material. This hypothesis suggests that the temporal characteristics of this transient absorption are directly related to the diffusion of the thermal energy and can be tested by changing the volume of initial energy deposition. In this case, the subsequent local temperature profiles are expected to change due to the different rate of temperature decay as a function of the size of the initial heated volume. In this work, we employ an experimental method to test the above hypothesis using DKDP as the material of choice. This choice stems from the fact that we can achieve very different energy deposition volumes in this material via different laser-induced breakdown (damage) methods. Specifically, pre-existing damage precursors in the bulk of DKDP cause localized energy deposition within volumes on the order of 1–10 μm3 (extrinsic or spontaneous damage) [11, 14]. We note that extrinsic bulk damage does not occur in fused silica material currently available from major optics vendors. In addition, we can also create much larger energy deposition volumes in DKDP, on the order of 100–1000 μm3, via focusing the laser beam into the bulk material, similar to the experiments performed in fused silica (intrinsic damage) [7]. The large difference in the volume of modified material produced by each damage testing method leads to a very different dynamics of temperature relaxation of the directly affected material. This in turn allows for separating out different mechanisms of generation of the transient absorption.
2. Experimental details
Laser-induced breakdown in the bulk of the material is initiated by a pump pulse, either spontaneously due to localized absorption by pre-existing defects at relatively low fluences (∼9 J/cm2) or intrinsically by dielectric breakdown caused by focusing the laser beam into the material at relatively high fluences (∼1200 J/cm2), leading to final damage sites on the order of 5 μm and 200 μm in diameter, respectively. The dynamics of the transient absorption of the modified DKDP bulk material following localized energy deposition is experimentally measured using two distinctly different methods. In the first method, referred to as “pump-probe damage testing”, we transiently expose the modified region of the material to a second (probe) pulse that follows the pump pulse in order to facilitate additional energy deposition arising (at least in part) from the pump-induced transient absorption. This procedure leads to“re-initiation” of the damage event due to the probe pulse and subsequent additional energy deposition leading to formation of damage sites with increased dimensions (probe-induced growth of the damage site). Hence, this pump-probe damage technique is different from the classical definition of pump-probe experiments in which a delayed, weak probe pulse monitors (without altering) the optical or other transient properties induced by the preceding pump pulse. We postulate that the final size of the damage site is directly related to the amount of energy deposition by the probe pulse which in turn is proportional to the strength of the transient absorption. Hence, the dependence of the size of the final damage sites on the delay between the pump and probe pulses provides direct information on the rise and decay of the transient absorption within the modified region of the material. The second method, referred to as “time-resolved imaging”, is based on capturing transient images of the damage sites using a time-resolved shadowgraphy microscope system to monitor the change in the amount of transmitted light through the affected region as a function of time delay from the damage initiating pump pulse.
The pump-probe damage technique is integrated within a damage testing system that allows detection and imaging of damage events in the bulk of optical materials with very high spatial resolution (presented in detail elsewhere [22, 23]). We have expanded this system to include an additional (probe) laser. This pump and probe configuration employs two independent, nanosecond Q-switched Nd:YAG laser systems (injection-seeded to ensure single longitudinal mode operation) that are synchronized using an electronic pulse delay generator. This feature enabled flexible time delays between pump and probe pulses which can be varied from nanoseconds to microseconds, and even milliseconds. A single pulse at either 355-nm or 532-nm from the pump laser (near-Gaussian temporal profile, ∼3-ns full-width at half maximum of intensity or FWHM) was used to induce breakdown in the bulk material at a fixed fluence above the damage threshold (with 10% shot-to-shot variation). A pulse from the probe laser at 355-nm (∼7-ns FWHM) is aligned to spatially overlap the pump beam path inside the sample. Figure 1 illustrates the pump and probe beam paths within the sample and the arrangement used for the detection of bulk damage events in (a) collinear and (b) non-collinear geometries, respectively. The collinear, one-color (355-nm) pump-probe scheme was employed to study the dynamics of transient absorption in the material following spontaneous (small size) bulk damage in DKDP. The non-collinear geometry, two-color 532-nm pump and 355-nm probe, enabled characterization of intrinsic (large size) bulk damage in DKDP, similar to that used in the previous studies performed in fused silica [7]. A He-Ne laser beam is focused through the back of the sample to illuminate the tested volume. A CCD camera coupled to a microscope equipped with a long-working-distance objective lens is used to record high-resolution light-scattering images (2 μm per pixel) in order to monitor in situ changes in the overall size of bulk damage sites (induced by the pump pulse) with adequate spatial resolution.
Fig. 1 Pump-probe damage testing apparatus in (a) collinear and (b) non-collinear geometries, respectively. Pump and probe pulses are 3-ns and 7-ns in duration, respectively.
For the case of spontaneous damage in DKDP [see Fig. 1(a)], the co-propagating pump (3-ns FWHM) and probe (7-ns FWHM) beams at 355-nm were focused using a 200-mm focal length cylindrical lens within the bulk of the material, i.e., slit beams at the focal region. The pump peak fluence at the sample location was fixed at ∼9 J/cm2 with near-Gaussian spatial beam profile (with radius of 60 μm, defined as the half-width at 1/e2 of maximum intensity, or HW1/e2M, and height of 2.2 mm) and resulted in a damage pinpoint density of 400 mm−3 [22]. The probe fluence was varied from 0 up to 17 J/cm2 (HW1/e2M of 110 μm and height of 2.4 mm) to minimize the amount of spontaneous damage due to the probe beam alone. The individual damage sites created separately by either the pump (at 3-ns, 9 J/cm2) and or the probe (at 7-ns, between 11 and 17 J/cm2) pulses were measured to be ∼5 μm and ∼10 μm in diameter, respectively. It should be noted here that the relative damage densities and sizes at the above pump and probe fluences are in good agreement with the pulse scaling laws at 355-nm for bulk damage in DKDP, i.e. ∼ t0.35 and ∼ t0.9, respectively, where t is the Gaussian, laser pulse duration [24, 25]. This experimental arrangement (collinear geometry) was chosen in order to maximize the number of damage sites generated by the pump that are intercepted by the probe beam.
Initiation of intrinsic bulk damage in DKDP requires two orders of magnitude higher laser intensities (and corresponding fluences), in excess of 200 GW/cm2 at 532-nm (3-ns pulses). To satisfy this requirement and prevent surface damage on the samples (1-cm thick), we employed a ×10 long-working distance microscope objective to achieve a tightly focused pump beam in the bulk, as illustrated in Fig. 1(b). Thus, the pump intensity at 532-nm (3-ns) was fixed at ∼400 GW/cm2 (estimated based on the measured focal spot radius of 6 μm inside the sample) to ensure shot-to-shot deterministic damage within the bulk. Under these conditions, typical damage sites induced by the focused pump pulse at 532-nm in DKDP consisted of one large site of ∼200 μm in diameter. The non-collinear geometry in Fig. 1(b) allows for independent control of the probe beam size in the interaction region (i.e., by using separate focusing elements) which was kept at ∼1.5× the size of the damage sites created by the pump pulse. The probe fluence at 355-nm (7-ns) was varied between 0 and ∼28 J/cm2. In this set of experiments, a measurable probe-induced growth of the damage sites was observed for probe fluences above ∼12 J/cm2.
For all pump-probe damage testing experiments the overall size of individual damage sites was quantified in terms of a rectangular area encompassing the sites as observed from He-Ne light scattering images. He-Ne illumination was routinely employed to monitor the overall spatial distribution and sizes of the damage sites formed in the interaction region after each laser exposure (as in Fig. 2, for spontaneous damage). In addition, the morphology of larger individual sites, i.e. cracks and core region, was adequately resolved using white-light illumination (to avoid artifacts arising from illumination with coherent light) with 1 μm spatial resolution (not shown here). We have confirmed that, for the damage sites created in our pump-probe experiments (setup in Fig. 1), the perceived sizes are very similar upon comparing images of the same damage region using either illumination method.
Fig. 2 Typical light-scattering image of spontaneous bulk damage sites in DKDP near the focal region (located on the right hand side) of the spatially overlapping pump and probe pulses at 25 ns delay. The arrows indicate typical damage sites from pump only.
The time-resolved microscopy system used to map the pump-induced bulk material modifications with high spatial and temporal resolution is illustrated in Fig. 3 and has been described in detail elsewhere [7, 26]. Two separate but externally synchronized pulsed lasers provide the pump and probe pulses at adjustable delay times. A single pump pulse at 355-nm (3-ns) was focused in the DKDP bulk material using a 5-cm focal length lens (estimated focal spot radius of 10 μm inside the sample) to induce intrinsic (deterministic) damage. The estimated peak pump irradiance was ∼200 GW/cm2. We note however that single-pulse irradiation at 355-nm often lead to significant spontaneous bulk damage manifested as multiple, small in size sites throughout the focal region. This effect was negligible for the case of 532-nm pump in Fig. 1(b) due to i) higher DKDP bulk damage threshold [27] and ii) tighter focal spot achieved at 532-nm compared to that at 355-nm. This choice of focusing optics allowed the study of both intrinsic and spontaneous damage at 355-nm. However, efforts were made to minimize the latter effect (which otherwise dominates) by pre-exposure of the bulk material to sub-threshold fluences using a ramp-up fluence sequence prior to irradiation at the desired fluence [28], a process known as laser conditioning leading to an increased threshold for spontaneous damage. A probe pulse at 532-nm, 180-ps pulse duration was used to back-illuminate the pump focal volume and its surroundings at low fluence. We emphasize that the use of a sub-ns probe pulse in the present work (system upgrade from the 4.5-ns probe laser described in [7]) enables high dynamic image spatial resolution on the order of ∼1 μm, thus matching the static image spatial resolution of the microscope system. The former parameter is determined by the product between the speed of the observed transient events and the pulse duration of the imaging probe pulse and was discussed in [7, 26]. The images were captured using a CCD detector with pixel size of 4.4×4.4 μm2. For each damage event, the temporal shapes and relative time delay of pump and probe pulses were recorded with 0.5-ns resolution.
Fig. 3 Time-resolved microscopic imaging apparatus in trans-illumination geometry. Pump and probe pulses are 3-ns and 180-ps in duration, respectively.
The material investigated in this study was a z-cut, rapidly grown DKDP (70% deuteration level) [29]. Samples were cut to 5×5×1 cm3 plates with optical inspection quality finish on four sides to allow imaging of damage sites in a direction orthogonal to the pump beam propagation direction (as in Fig. 1).
3. Results
The pump-probe damage testing configurations shown in Fig. 1 were used to measure the size of the damage sites observed in the region of spatial overlap between the pump and probe pulses versus the probe time delay and energy. For the case of spontaneous damage in DKDP, the difference in the local intensities of the pump and probe beams as they co-propagate through the crystal is translated into a distribution of final sizes for damage sites created in the interaction region (focal region). This effect is best illustrated in the light-scattering image shown in Fig. 2. Specifically, the right hand side of the image shows the final damage sites at locations where the probe beam at maximum fluence (at the focal region) interacted at 25 ns delay with modified material resulting from localized damage initiation induced by the pump beam at peak fluence. On the other hand, the damage sites shown on the left hand side of the image (indicated by arrows) were marginally affected in the presence of the lower fluence probe beam (out of focus). Throughout this work we have used the largest observed damage sites as representative of maximum interaction effects, i.e., spatial overlap of pump and probe pulses at peak intensities.
Figures 4(a)–(b) summarize the results of pump and probe damage testing in DKDP for spontaneous and intrinsic bulk damage, respectively. The data points represent the average values of the largest damage sites at five testing locations for each probe fluence and delay combination. The error bars were derived from the standard deviation of the measurement. Specifically, in the left panels of Figs. 4(a)–(b) we report the measured cross-sectional area of damage sites versus probe time delay and two different probe fluences. The time delay was varied from 1 ns up to 500 ns. For comparison, the average size of damage sites from pump only is also shown in the left panels (see solid lines at constant values, 0.25×10−4 mm2 and 0.028 mm2, respectively).
Fig. 4 Final size (damage cross-section area) of DKDP bulk damage sites observed in the region of spatial overlap between pump and probe pulses versus probe time delay (left panel, semi-log scale) and peak fluence at 25 ns and 80 ns fixed delays (right panel) for (a) spontaneous and (b) intrinsic damage, respectively.
The results demonstrate that the size of the damage sites following exposure to the combined pump (responsible for damage initiation) and probe (responsible for growth of the initiated sites) pulses can be significantly larger than that of damage sites induced by the pump pulse alone, for both spontaneous and intrinsic damage. This suggests that the initial energy deposition modifies the surrounding material which becomes the cause for additional absorption by the probe pulse. Furthermore, the amount of energy absorbed from the probe pulse (and deposited into the material) exhibits a peak at time delays of ∼20 ns and ∼50 ns, for spontaneous and intrinsic damage, respectively.
We hypothesize that the absorptivity of the material is directly related to its temperature and therefore, the value of the absorptivity should be maximum at the center of the damage site and continuously decreasing with distance away from the center of the site. When the probe pulse arrives, the amount of material that re-initiates the laser damage process (leading to growth) would be the volume with increased absorptivity (temperature) above a certain threshold value (Tth). This growth threshold value of the material temperature would be a function of the probe pulse fluence. Therefore, the dependence of the size of the final damage sites on probe fluence could provide information on this process. These results are shown in the right panels of Figs. 4(a)–(b) for fixed time delays near the peak of the absorption profiles (25 ns and 80 ns) for spontaneous and intrinsic bulk damage, respectively. The solid lines represent exponential fits, i.e., ∼exp(ϕ), to guide the qualitative comparison of the damage cross-section area vs. probe fluence data sets. It can be seen from Figs. 4(a)–(b) that the size of DKDP bulk damage sites increases nonlinearly with probe fluence above ∼10 J/cm2 for both cases.
The time-resolved imaging configuration in Fig. 3 was used as an alternative direct method to monitor the transient changes in the material. Specifically, this method monitors the changes in transmission of the illumination probe through the damage region due to changes in the material’s complex index of refraction. Figure 5 shows typical images capturing transient material modifications associated with intrinsic bulk damage in DKDP at various probe time delays between 8 ns and 100 μs. The time resolved imaging experiments suggest that the final physical dimensions of the damage sites (including the core region and cracks) are established within about 25 ns delay with respect to the pump pulse. This assertion was done by comparing the overall site dimensions from the transient and final images acquired for each breakdown event (not shown here). This is similar to the observations from intrinsic damage in the bulk of fused silica [7]. For this reason and in accordance to the previous work [7], all images were processed via pixel-by-pixel division of the final and transient images to factor out any features related to the spatially non-uniform (near Gaussian) illumination source and enhance the visibility of transient effects. As a result, the bright features in the ratio images indicate a transient reduction in the probe beam transmission through the affected volume. Such images captured at various delay times are shown in Fig. 5 for the case of intrinsic bulk damage in DKDP demonstrating the presence of a transient loss of transmission.
Fig. 5 Typical ratio images (final divided by transient) of intrinsic bulk damage sites in DKDP for pump and probe time delays between 8 ns and 100 μs. For comparison, all images have the same spatial scale and contrast.
Although only one transient image can be captured from each damage event, the use of intrinsic breakdown initiated by a focused beam enables the study of the entire timeline by capturing images of different but similarly evolving events. We note that imaging of the formation of spontaneous bulk damage sites in DKDP is much more challenging due to i) the smaller affected volumes, i.e., only ∼1–10 μm3, comparable with the image spatial resolution on the order of ∼ 1μm and ii) non-deterministic damage location which ultimately limits our ability to capture in-focus events. Also, when imaging intrinsic bulk damage, due to the ∼30° angle between the direction of propagation of the pump beam with respect to the image plane, not all of the pump-induced modified region can be maintained in focus by the imaging system with a depth of focus of ∼50 μm. Therefore, we chose to keep in focus the main, largest damage site (deterministic damage, as opposed to spontaneous bulk damage occurring throughout the focal region) containing a core region surrounded by cracks. The images shown in Fig. 5 suggest that cracks exhibit transient absorption up to about 100 ns delay. This may suggest the presence of absorption due to transient defects formed on and/or near the crack surface immediately after its formation [30]. In addition, the ratio images highlight the core region of the damage site as a bright feature indicating that it may also be associated with a transient absorption which exhibits a much longer lifetime, up to about 1 μs delays. A very similar effect has been observed following intrinsic damage in bulk fused silica [7] where the cracks and the core regions also exhibited a transient absorption with distinct lifetimes. However, the relaxation times in fused silica are very different from those observed in DKDP (this work). For both materials, we hypothesize that the host material properties in this damage core region are in a transient state, i.e. a liquid phase at high temperatures, giving rise to a transient absorption. In addition, short-lived absorbing defects forming near the crack interfaces cause the observed loss of transmission near the cracks. As these two temperature-induced processes are different in the two materials, the resulting transient absorption components should exhibit distinct lifetimes.
4. Model of transient absorption relaxation
The cooling rate of the core region is expected to be inversely proportional to its size (from heat diffusion considerations) and consequently the lifetime of the transient absorption of the core region should increase with its size. This characteristic difference in the profiles shown in Figs. 4(a)–(b) may suggest that the amount of energy deposited by the probe pulse depends on the volume of initial energy deposition. To further explore this concept, we developed a simple model to describe this temperature activated transient absorption and relaxation process. Let us assume that following initial laser damage caused by the pump pulse, a region of radius a with peak temperature T0 (on the order of 1 eV) is formed. During the delay time td between the pump and probe pulses, heat is conducted into the colder material thus expanding the heated region while reducing the peak temperature. For a given probe laser fluence (Φ), a sufficient amount of laser energy to re-initiate the damage process is deposited within the volume of the material where the temperature is greater than some threshold temperature Tth(Φ). The radius (r) of this volume with temperature (T) above Tth(Φ) is a function of delay since the initially formed (by the pump pulse) region of high temperature will at first expand in size because of heat diffusion and later decrease in size because of cooling. To be specific, let us assume an initial Gaussian temperature distribution with peak temperature T0 and 1/e radius a. In a uniform medium with temperature independent properties, the temperature at delay time td is given by:
where r is distance from the damage center and D is the thermal diffusivity. From Eq. 1, we find that the cross sectional area A(td, Tth) corresponding to the volume with temperature of at least Tth is given by: with the characteristic diffusion timeThe three profiles of the cross sectional area A normalized to the initial cross sectional area (πa2) at td =0 as a function of the delay (td) shown in Fig. 6(a) were obtained for several choices for the ratio of threshold to initial temperature Tth/T0 of 1/10, 1/25 and 1/50 (corresponding to temperatures of about 1000, 400 and 200 K above material background temperature). The results show that the cross sectional area corresponding to each Tth first grows and then decreases with time. The smallest threshold temperature corresponds to the longest lasting and largest absorbing area.
Fig. 6 Model of transient absorption from Eqs. (1)–(3) describing the cross sectional area, A, corresponding to an affected volume (pump-induced) with temperature above a growth threshold Tth: (a) normalized area vs. delay corresponding to different ratios Tth/T0, (b) area vs. delay corresponding to Tth = T0/50 and different initial relative radii, a, of energy deposition volume.
Assuming a Tth=T0/50 (corresponding to about the melting temperature of the material) the cross sectional area of the volume with T > Tth is shown in Fig. 6(b) where the curves correspond to initial relative radii of 1,3,9 and 27. These results demonstrate that the maximum volume where temperature is above Tth depends strongly on the initial size of the hot volume created by the pump pulse. Consequently, if the final size of the damage site reached after the second pulse depends on the size of the sufficiently absorbing region when the second pulse arrives, the size of the damage site from the combined pump and probe pulses will reach its peak when the volume profile depicted in Fig. 6(b) is at its maximum (peak) position. This predicted behavior follows our experimental observations, at least qualitatively.
5. Discussion
The model presented above incorporates our main hypothesis regarding the rise and decay of the transient absorption. We have assumed that this transient absorption is responsible for the behaviors captured by the time-resolved imaging experimental results (such as those shown in Fig. 5) and the pump-probe damage testing results presented in Fig. 4(b). The aim of this model is to help better interpret the underlying mechanisms and kinetics of the transient absorption following bulk damage in DKDP. Specifically, the main peak of the transient absorption in the 10–100 ns range of delays observed in Fig. 4(b) can be correlated with the presence of transient absorption manifested in the ratio images in Fig. 5 for the same range of delays, originating both in the crack and core regions. Furthermore, the longer lived transient absorption associated with the core region up to about 1 μs delays observed in the time resolved images is also in agreement with the slower decay of transient absorption observed in Fig. 4(b)in the 100 ns to 1 μs range.
The temporal profile of the transient absorption as a function of the initial volume of energy deposition during the damage event (intrinsic vs. spontaneous) is qualitatively reproduced by the model as depicted in Fig. 6(b). The model predicts that, depending on the size of the initial volume of energy deposition, the maximum cross sectional area of the volume with temperature above the threshold for damage re-initiation reaches its peak position at longer delays. This is in agreement with the experimental observations in Fig. 4, (a) vs. (b), corresponding to increasing initial breakdown volume. In addition, the results shown in the right panels of Fig. 4 indicate that the size of DKDP bulk damage sites grows nonlinearly with probe fluence at fixed delay time. This is also qualitatively predicted by the model as exemplified in Fig. 6(a) which indicates that with decreasing threshold temperature (which is associated with increased probe laser fluence) the volume of material with temperature above threshold rapidly increases giving rise to larger final damage site after exposure to the combined pump-and-probe damage pulses.
The intrinsic bulk damage sites created in DKDP are significantly larger than those observed in fused silica under similar pump-probe excitation conditions (see [7]). The final damage sites in both materials are typically surrounded by a network of cracks. The fracture toughness in DKDP is only about 0.2 MPa·m1/2 [31], about 1/4 that of fused silica. As a result, much smaller stress can initiate cracks in DKDP and growth will continue up to a length where the local stress is sufficiently low. In comparison to fused silica the damage sites are larger for DKDP, with larger fractures at comparable probe fluence. We recall that DKDP melts and undergoes phase transitions starting at temperatures of only 200 °C and that these transitions involve significant volume changes [9, 18]. On the other hand, fused silica has no low temperature phase transitions. Therefore, the transient stresses present during the early part of the damage site formation process will have a much longer impact toward the creation of a network of cracks with extended spatial dimensions in DKDP compared to fused silica.
The model presented here is intended to qualitatively account for the effect of re-initiation of the damage process by the probe pulse due to the transient change in space and time of the temperature-induced absorptivity in the modified material following laser induced damage by the preceding pump pulse. A detailed and complete description of the experimental observations would require both the capability to model and understanding of all the intermediate processes involved. These include the transient changes in the material such as the spatial distribution of temperature and localized absorptivity arising from material modification and heat diffusion following damage by the pump pulse. The ultimate changes would need to be related to the re-initiation process by the probe pulse and to the amount of total energy deposited in the site. Finally, the final size of the damage site would be directly related to the total amount of energy deposited as well as the dynamics of the energy deposition (spatial distribution of damage re-initiated region, combined shockwave generation and propagation, transient stress fields formed, crack generation and propagation, etc.). Since the aforementioned intermediate processes are not well understood, the model was limited to description of only one parameter (temperature) to provide a qualitative account of the overall process and relate to the experimental observations.
6. Conclusion
This work provides new insight into the localized dynamics of the material electronic structure transformation including transient absorption in response to localized laser energy deposition. We have shown that the response of the material is largely independent of the excitation process and is characteristic of the transient material properties. This provides the basis for future studies to better understand and control the energy deposition of laser power in materials and the behavior of optical materials for high power laser systems. It also helps better understand the damage process in optical materials as a function of the laser parameters. For practical applications of laser-induced material modifications (laser ablation, micro-machining, etc.), the pulse duration, and less often the pulse shape and wavelength are considered as the only parameters for optimization of the process. However, it must be realized that the optical properties of the material very quickly change after the initiation of the breakdown, thus the leading part of a pulse interacts with a material that has completely different optical properties (such as absorption coefficient) than those of material interacting with the trailing part of the pulse. This fundamental mechanism can be utilized to enhance efficiency of the material processing application and achieve better control on the energy deposition process and resulting material modification.
Acknowledgments
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
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