1. Introduction

Laser-induced damage of optical components at relatively low laser energy densities remains a key limitation on the performance characteristics of optical systems [1–6]. The formation of damage sites is due to the presence of defect structures (damage precursors) that interact with the laser light. This problem represents a major challenge in the use of optical materials for various applications from miniaturized optoelectronic devices to UV lithography and laser systems for inertial confinement fusion. A complete eradication of the problem is limited by the difficulty in identifying the exact structure of the precursors, primarily for two reasons. First, the concentration of these precursors in the material can be extremely small and often below the detection limit of existing chemical analysis tools. Second, several types of defects exist in every batch of material and it is difficult to determine the one type responsible for damage. It is therefore imperative to develop new methods to investigate the nature and reveal the fingerprint properties of the precursors, understand the parameters that govern their interaction with laser pulses, and develop models to optimize and predict the performance of the materials.

A typical example of an optical material in which localized laser-induced damage is observed at relatively low fluences is the nonlinear material KH₂PO₄ and its analog KD_xH_{2- x}PO₄ (also referred to as KDP and DKDP, respectively) [7]. Exposure of the bulk of these materials to nanosecond laser pulses leads to micron-sized damage sites at fluences of more than an order of magnitude below the intrinsic breakdown threshold. A key behavior of the damage precursors in KDP and DKDP [8] (as well as in other systems [9–12]) is that the overall damage performance is improved with exposure to sub-damage laser fluences, a phenomenon often referred to as laser conditioning. It is believed that the precursors in KDP/DKDP are clusters of intrinsic defects or impurity nanoparticles incorporated during the growth process [7, 13–17]. Nonetheless, the mechanisms by which these precursors interact with the laser light are unknown.

In this work, we investigate the interaction of damage precursors in DKDP with laser pulses of variable fluence and frequency in order to probe the conditioning and damage initiation processes. Our approach takes advantage of the change to the damage characteristics of the material following pre-exposure to laser pulses by measuring the ensuing density of damage sites (pinpoints per mm³ or PPD). The results suggest that there are two types of precursors, each leading to damage initiation over a different frequency range. Moreover, depending on the pre-exposure frequency and fluence, there are different mechanisms leading to conditioning of the same population of precursors. These results also reveal the laser parameters necessary for optimizing the effectiveness of conditioning. This information is directly applicable to the development of methods to enhance the performance of KDP and DKDP optics currently under manufacturing for utilization in the new generation of large-aperture laser systems [18, 19]. In addition, the results provide insight into the fundamental mechanisms of laser light interaction with defects in large bandgap materials.

2. Experimental setup and procedure

The experimental system used to perform this work has been described in detail elsewhere [20]. The damage testing laser used is an injection-seeded pulsed-Nd:YAG laser (Infinity, Coherent) providing single longitudinal mode operation. The injection seeding provides good beam quality in both the temporal and spatial dimensions. In brief, the fundamental at 1064 nm (1ω), second (2ω), and third (3ω) harmonics of a pulsed-Nd:YAG laser (pulse durations at FWHM of 3.3, 2.6, and 2.5 ns, respectively) were aligned to co-propagate and focused by a 200-mm focal length cylindrical lens to the bulk of the crystal samples. The averages and standard deviations of the beams at focus had 1/e² heights of 3565 ± 80.1, 2520.8 ± 61.3, and 2891.2 ± 68.4 µm and widths of 95.7 ± 2.9, 64.8 ± 1.6, and 41.4 ± 1.1 µm for 1ω, 2ω, and 3ω, respectively. A 632.8-nm beam from a HeNe laser was focused by a 250-mm focal length cylindrical lens through the back of the crystal to illuminate the tested volume and any resulting damage pinpoints.

Images of each volume were captured orthogonally to the direction of laser propagation prior to and after damage testing. The width of this imaged volume was 5800 µm (well within the Raleigh range of the focused pulsed beam) along the direction of beam propagation. The height of the imaged volume (along the elongated dimension of the focused beam) was on the order of a few mm. However, the PPD was measured over the full width of the image and 338 µm in height, representing the region of the crystal exposed only to peak laser fluence to within 5% along those dimensions. Within the third (depth) dimension of the imaged volume, the 1/e² widths of each pulsed beam at focus were used (95.7, 64.8, and 41.4 µm for 1ω, 2ω, and 3ω, respectively) in order to calculate the PPD. It should be noted that the measured PPD is an underestimation of the PPD resulting from peak laser fluence due to the gaussian profile of the beam in this (depth) dimension [21].

To provide the most accurate measurements, the energy of each pulse during the damage testing experiments was monitored in order to maintain an error to within 5%. The variations in the beam dimensions from pulse to pulse accounted for a maximum fluctuation of 10% (standard deviation of 2%). This fluctuation was determined from fifty recorded measurements by the beam profiling instrumentation. As a result, the fluence values quoted in this work have an estimated variation of as much as 15%.

Previous studies in KDP and DKDP samples have demonstrated different damage characteristics even within the same crystal boule [7, 8, 22]. For this reason, results shown in this work were all obtained from samples originating from regions of the same crystal boule that exhibit nearly identical damage characteristics. The DKDP samples were conventionally grown and the KDP samples were grown using the fast growth method. All samples were plates cut from crystal boules to dimensions of 1×5×5 cm³ and polished on all sides. All of the tested DKDP and KDP samples produced identical qualitative behaviors but varying levels of damage with testing at the same laser fluences.

3. Experimental results and preliminary analysis

Several different experiments were performed in this work, each aiming to reveal a different aspect of the dependence of damage initiation and conditioning on the laser parameters. For clarity, each specific set of experiments is presented in a separate section along with a preliminary discussion which introduces the rationale for undertaking each set.

3.1. The dependence of conditioning effectiveness on the laser frequency

In the first set of experiments, we investigated the dependence of laser conditioning on the laser pre-exposure and damage testing frequency. To achieve this, we performed experiments at the nine damage testing and pre-exposure combinations of the three laser harmonics. The experimental protocol for all frequency combinations was to pre-expose pristine (previously unexposed) material to ten pulses of the same fluence and then damage test with a single pulse. The fluence of the ten pre-exposure pulses was varied from site to site while the fluence of the damage testing pulse was fixed. Thus, each data set represents the PPD resulting from damage testing at a fixed fluence as a function of the pre-exposure fluence. This allowed for quantification of the change in the damage characteristics of the material by monitoring the density of precursors that initiate damage at the test fluence prior to and after pre-exposure.

Figure 1 shows results for damage testing at 1ω [Fig. 1(a)], 2ω [Fig. 1(b)], and 3ω [Fig. 1(c)]. Each figure contains six data sets (each set forming a PPD vs fluence profile) that can be separated into two groups of three sets. For both groups, each data set corresponds to pre-exposure frequencies at 1ω, 2ω, or 3ω. The first group is comprised of the unfilled data points, depicting the PPD measured after pre-exposure only as a function of the pre-exposure fluence. The second group is comprised of the filled data points, depicting the total measured PPD from both pre-exposure and damage testing. The data points are color coded so that the red, green, and blue indicate laser exposure at 1ω, 2ω, and 3ω, respectively. The color of the outline (circle) of the data point indicates the pre-exposure frequency while the fill color indicates the damage testing frequency. We will refer to these data sets as PE(i) and DT(i,j) to describe the first and second groups, respectively, where i=1ω, 2ω or 3ω refers to the pre-exposure and j (=1ω, 2ω or 3ω) to the damage testing frequencies. The DT(i,j) profiles in each figure start from a maximum PPD corresponding to testing of the pristine material. The damage testing fluences were kept the same between each data set at 46 J/cm² for 1ω, 31 J/cm² for 2ω, and 26 J/cm² for 3ω. In order to improve clarity, DT(i,j) data points that demonstrated no decrease in the PPD following pre-exposure were replaced with horizontal arrows to represent unchanged PPD (within experimental error). The PE(i) profiles represent the PPD profiles of the pristine material over the range of fluences used for pre-exposure. The group of three PE(i) profiles was essentially the same in all Figs. 1(a), 1(b), and 1(c) over the range of fluences used for pre-exposure but was included in each figure for more accurate depiction of the material behavior. Each data point represents the average of four measurements. The standard error is shown for selected data points at different PPD ranges in each experiment.

 

Fig. 1. The PPD in bulk DKDP resulting from testing at a) 46 J/cm² at 1ω, b) 31 J/cm² at 2ω, and c) 26 J/cm² at 3ω following pre-exposure at 1ω, 2ω, and 3ω (filled data points, representing the PPD from both damage testing and pre-exposure [DT(i,j)]). The PPD from pre-exposure only at each frequency (PE(i)) is also shown (unfilled data points). Lines are drawn in for each data set as a guide to the eye.

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Figure 1(a) shows that damage testing of the pristine material at 46 J/cm² at 1ω produces ~380 pinpoints per mm³ (pp/mm³). Following pre-exposure at 3ω, the results indicate that the total PPD after damage testing rapidly decreases with increase in pre-exposure fluence starting from ~1 J/cm². At ~6 J/cm², the PPD decreases to almost 0 pp/mm³. Pre-exposure at 2ω shows a change in performance only after the pre-exposure fluence reached ~6 J/cm2, clearly demonstrating the presence of a threshold fluence for conditioning. The DT(2ω,1ω) profile meets the PE(2ω) profile at ~14 J/cm², indicating that above this pre-exposure fluence there are no additional pinpoints from damage testing. Similarly, pre-exposure at 1ω shows that a threshold pre-exposure fluence exists for conditioning, located at ~10 J/cm². Further increase in pre-exposure fluence provides a linear decrease to the total PPD with the DT(1ω,1ω) profile intersecting the PE(1ω) profile at ~40 J/cm².

Figure 1(b) shows the three DT(i,2ω) profiles resulting from damage testing at 31 J/cm² at 2ω along with the three corresponding PE(i) profiles at each frequency. Damage testing of the pristine material provides ~420 pp/mm³. With pre-exposure at 3ω, the total PPD after damage testing appears to decrease linearly with increase in pre-exposure fluence starting from the lowest tested pre-exposure fluence (~1 J/cm²). The DT(3ω,2ω) profile then converges with the PE(3ω) profile at a pre-exposure fluence of ~15 J/cm². Pre-exposure at 2ω also results in a linear decrease in the total PPD. However, the DT(2ω,2ω) profile converges with the PE(2ω) profile at a much higher pre-exposure fluence of ~27 J/cm². Damage testing following preexposure at 1ω up to ~40 J/cm² (well above the damage threshold fluence of the material at 1ω) does not show any improvement to the damage performance suggesting that pre-exposure at 1ω does not provide conditioning for 2ω.

Figure 1(c) shows that damage testing of the pristine material at ~26 J/cm² at 3ω provides ~1250 pp/mm³. Pre-exposure at 3ω demonstrates the presence of a threshold fluence for conditioning at ~7 J/cm². This threshold appears ~1 J/cm² below the damage threshold fluence and the total PPD then rapidly decreases with increasing pre-exposure fluence. Pre-exposure at 2ω shows a similar behavior but the pre-exposure threshold fluence for conditioning occurs at a much higher fluence of ~20 J/cm². Unlike with pre-exposure at 3ω, this threshold takes place ~10 J/cm² above the damage threshold fluence of the material at 2ω. As with damage testing at 2ω [shown in Fig. 1(b)], pre-exposure at 1ω up to ~39 J/cm² provides no conditioning for 3ω.

The results in Fig. 1 show two different behaviors. For damage testing at 1ω and 3ω, a “threshold” fluence for conditioning is observed. For damage testing at 2ω, a linear decrease with pre-exposure fluence is observed. These behaviors can be attributed either to different laser-defect interaction processes and/or to the presence of different types of precursors responsible for damage initiation at each frequency (1ω, 2ω, and 3ω).

3.2. The number of discrete precursor populations responsible for damage initiation

To address whether different precursor populations are involved in damage initiation at the different frequencies, the following set of experiments was executed. First, we found the fluences at each frequency that led to about the same PPD. Using these predetermined fluences, pristine sites were first damage tested at one frequency and subsequently tested again at another frequency. The PPD resulting from testing at each frequency separately was compared to the total PPD resulting from exposure to both frequencies. Assuming that each frequency produces the same PPD, N, a total PPD of 2N indicates two completely different precursor populations at each frequency. The experiments were repeated using several different fluences at each frequency.

To realize this concept, we also need to consider that the first pulse may condition the material and thus influence the PPD resulting from exposure to the second pulse. From ramp-conditioning experiments performed in the sample used in the present work (discussed in Ref. [23]), we determined that fluencies smaller than ~20 J/cm² at 2ω did not result in conditioning for 3ω. On the other hand, even a single pulse at 3ω provides conditioning for 2ω. Thus, we used a 2ω pulse followed by a 3ω pulse to test the overlap of the 2ω and 3ω precursor populations. Similarly, we determined that pre-exposure with fluences less than ~40 J/cm² at 1ω did not provide conditioning for 2ω and 3ω. Consequently, we used 1ω pulses followed by 2ω pulses to test the overlap of the 1ω and 2ω precursors.

The results of the damage overlapping experiments have been detailed elsewhere [24] but due to their importance for the analysis of the current work, they will be briefly summarized here. Damage testing at 3ω over sites previously damage tested at 2ω showed that the average total PPD was the same within experimental error as the average PPD from each pulse separately. This indicates that the precursors at 2ω and 3ω are largely the same. However, damage testing at 2ω over sites previously tested at 1ω demonstrated the opposite behavior. Namely, the 2ω pulse resulted in an additional PPD density within experimental error to that measured in the pristine material. This suggests that there is a large non-overlap in the precursors at 1ω with those at 2ω and 3ω.

Figures 1(b) and 1(c) demonstrate that exposure below 7 J/cm² at 3ω leads to no improvement for damage testing at 3ω but a significant improvement for damage testing at 2ω. Since the precursors at these two frequencies are the same, these results indicate different laser-defect interaction pathways at 2ω and 3ω. If we consider the process of conditioning as a laser-induced modification of the original precursor population (call them D₀ precursors), conditioning arising from different interaction pathways is leading to more that one type of modification of the D₀ precursors. The two distinctly different conditioning behaviors observed indicate the formation of two types of derivative defect structures that depends on the pre-exposure frequency and fluence. Pre-exposure to lower fluence pulses at 2ω or 3ω leads to the generation of the first type of derivative defect structures (call them D₁). The electronic structure or other characteristic property of the D₁ provides for enhanced damage resistance at 2ω but not at 3ω. Pre-exposure at ~7 J/cm² and higher at 3ω and ~20 J/cm² at 2ω promotes the modification of the D₀ precursors into a second type of derivative defect structures, D₂. The electronic structure of the D₂ provides enhanced damage resistance at both 3ω and 2ω.

3.3. The dependence of conditioning effectiveness on the number of pre-exposure pulses

To gain more insight into the mechanisms of the laser-induced modifications of the original precursor population leading to D₁ and D₂ species, we performed experiments in which the PPD resulting from damage testing was measured as a function of the number of pre-exposure pulses (from 1 to 1024 in multiples of 2), with fixed damage testing and pre-exposure fluences at 3ω and 2ω. In these experiments, the damage onset fluence was used for pre-exposure while the fluence that provides the same PPD (~450 pp/mm³) in the pristine material were chosen for damage testing. This corresponded to pre-exposure fluences of 13 J/cm² for 2ω and 10 J/cm² for 3ω and damage testing fluences of 35 J/cm² for 2ω and 17 J/cm² for 3ω.

Figure 2 shows results for the normalized total PPD (from ~450 ppt/mm³ in pristine material) resulting from damage testing and pre-exposure at 2ω (shown as green circles) and damage testing and pre-exposure at 3ω (shown as blue circles) as a function of the number of pre-exposure pulses. Each data point represents the average of four measurements. The experimental results for damage testing at 2ω show that a 50% reduction in the PPD is achieved with pre-exposure to 32 pulses at 2ω while reduction to about 20% requires exposure to more than 1024 pulses. On the other hand, damage testing at 3ω shows over 50% reduction in the PPD with pre-exposure to just one pulse at 3ω while reduction to about 20% was observed with pre-exposure to only 32 pulses. These results demonstrate that conditioning at 2ω is gradual with increase in the number of pre-exposure pulses while, in contrast, conditioning at 3ω is substantial with only a few pre-exposure pulses.

 

Fig. 2. Normalized PPD following damage testing and pre-exposure at fixed fluences at both 2ω (green) and 3ω (blue) as a function of the number of pre-exposure pulses.

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Fluctuations in the pulse energy with pre-exposure to large number of pulses requires special consideration in this experiment. As discussed in section 2, the energy of each pulse in this work was monitored in order to maintain an error to within 5%. In this experiment, measurements using pre-exposure up to 16 pulses were thrown out when fluctuations greater than 5% were observed. However, when using pre-exposure to 32 pulses and greater, fluctuations greater than 5% were often unavoidable and therefore could not be feasibly monitored using the same method. Specifically, a maximum fluctuation of ~12% was measured within a set of 1000 pulses, accounting for an additional error of 7% in the fluence between measurements using 16 and 1024 pre-exposure pulses. It is difficult to accurately assess the effects of conditioning resulting from these energy fluctuations. However, the primary features relating to conditioning as a function of number of pre-exposure pulses observed in Fig. 2 are also present in the early parts of the profile (1-16 pre-exposure pulses). Therefore, we believe that the observed behaviors are not related to these fluence fluctuations.

3.4. Conditioning effectiveness on different parts of the precursor population

Another important aspect of the interaction of the precursors with laser pulses is the conditioning effectiveness of different parts of the precursor population that initiate damage at different fluences. To explore this aspect, we measured the PPD profiles (damage density) as a function of the testing fluence for damage testing at 2ω and 3ω in both pristine material and conditioned material. The conditioning in this case was performed using pre-exposure to ten pulses at fixed fluences (7 J/cm² at 3ω, 9 J/cm² and 13 J/cm² at 2ω). Figure 3(a) shows typical results. The plot is on semi-log scale to better depict the damage performance over the entire range of PPDs. Solid lines represent best fits using 6^th-order polynomial functions. In fitting each data set, the first three data points were removed in order to obtain a better coefficient of determination (R²) fit to the data set in the fluence direction.

 

Fig. 3. (a) PPD versus damage testing fluence at 2ω (green) and 3ω (blue) in pristine (unfilled circles) and pre-exposed material (filled circles). Lines represent best fits to each PPD profile. (b) The derivatives of the best fits to the profiles shown in (a) illustrating the density of precursors as a function of the fluence that they initiate damage (within a Δfluence=0.5 J/cm²).

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These results for damage testing at 3ω in the pristine material show that the damage onset is at ~5 J/cm². With pre-exposure at 7 J/cm² at 3ω, the fluence of damage onset is shifted higher, to ~8 J/cm². However, an overlap of the two PPD profiles is observed for testing at fluences above ~17 J/cm². This indicates that pre-exposure at 7 J/cm² improved the damage characteristics of only a fraction of the precursor population, i.e., those most susceptible to damage.

Damage testing at 2ω in the pristine material shows that the damage onset is at ~10 J/cm². Upon pre-exposure to 9 J/cm² and 13 J/cm² at 2ω, the fluence of damage onset shifts to ~15 J/cm² and ~18 J/cm², respectively. For these pre-exposure fluences, a significant shift of the damage profiles is observed which, in this case, do not appear to converge with that of the pristine material.

The improvement to the damage performance for all testing fluences at 2ω indicates that pre-exposure at 2ω involves a modification of the entire tested precursor population to result in conditioning. Moreover, the PPD profile shifts even more with pre-exposure to a higher fluence, indicating further improvement to the damage performance. On the other hand, pre-exposure at 3ω leads to conditioning of only a portion of the precursor population.

These behaviors are better depicted in Fig. 3(b) where the derivatives of the best fits to the profiles shown in Fig. 3(a) are plotted. These new profiles depict the density of precursors as a function of the fluence that they initiate damage. This is discussed in more detail in the Discussion section.

3.5. Laser conditioning in crystals with different damage characteristics

The differences in the damage performance between crystals obtained from different boules are manifested as differences in the damage threshold and PPDs under identical damage testing conditions [7, 8, 22]. This indicates that the distribution of the precursor population in crystals can be significantly different. In light of this, it is important to understand how the conditioning threshold is affected by the changing distribution of the precursor population. To address this issue, we measured the DT(3ω,3ω) profiles (as discussed in section 3.1) in various samples cut from multiple crystal boules that exhibit different damage characteristics. Figure 4 shows typical experimental results for four of the samples tested. In all cases, the experimental results reproduced the presence of a threshold fluence for conditioning. However, the threshold fluence for conditioning was found to be different between samples. The damage threshold fluence of the pristine material was always found to be 1–3 J/cm² above the conditioning threshold in each sample, as previously observed in the experimental results shown in Fig. 1(c).

 

Fig. 4. PPD from damage testing at fixed fluence at 3ω following pre-exposure at 3ω as a function of the pre-exposure fluence, for four samples cut from different KDP and DKDP crystal boules. The testing fluences were varied between samples.

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3.6. Laser conditioning as observed under different damage testing fluences

The results of the previous section show that the conditioning threshold fluence varies in different crystals (closely followed by the damage initiation threshold fluence). This indicates that different parts of the defect population have a different conditioning threshold. This behavior has important implications in understanding how to best condition the crystals. In developing optimal conditioning protocols, a distribution of defects associated with a specific crystal must be modified via laser exposure to provide maximum enhancement to the damage performance. It is therefore important to verify that the conditioning threshold varies within the same distribution of defects. This was accomplished by measuring the DT(3ω,3ω) profile for different testing fluences in the same sample.

Figure 5 shows the PPD resulting from damage testing and pre-exposure at 3ω as a function of the pre-exposure fluence in the same sample for two different damage testing fluences (20 J/cm² and 15 J/cm²). The results show that the conditioning threshold starts at ~6.5 J/cm² for damage testing at both fluences and that the portion of the defect population that initiates damage at 15 J/cm² has been mostly conditioned (some defects form damage sites during pre-exposure) with pre-exposure fluences at 10 J/cm². The PPD profile obtained with damage testing at 20–21 J/cm² shows that further pre-exposure up to ~13 J/cm² further reduces the observed PPD indicating that an additional population of defects condition at a higher fluence.

 

Fig. 5. PPD from damage testing at fixed fluence at 3ω following pre-exposure at 3ω as a function of the pre-exposure fluence, in a single DKDP sample. Two different fluences were used for testing.

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4. Discussion

The experiments performed in this work reveal several important characteristics of the damage precursor populations and the damage initiation and conditioning processes. The results presented in section 3.2 showed that there are two precursor populations: a first giving rise to damage at 2ω and 3ω and a second giving rise to damage at 1ω. In this section, we will discuss the behaviors of each precursor population separately for clarity.

4.1. The behavior of damage precursors at 1ω

Previous work has shown that thermal annealing improves the damage performance for operation at 1ω but not at 3ω [25]. This is in support of our findings that there is a different precursor population at 1ω. Furthermore, the results shown in Figs. 1(a) and 1(b) indicate a distinctly different conditioning behavior under 2ω pre-exposure of the precursors initiating damage at 1ω compared to those at 2ω. Specifically, for 1ω testing, a threshold fluence for conditioning of ~6 J/cm² is observed while the same material exhibits a threshold fluence for conditioning lower than 1 J/cm² when tested at 2ω. These results provide additional supportive evidence that the precursor population at 1ω is different from the precursor population at 2ω and 3ω.

The improvement to the damage performance at 1ω as a function of the pre-exposure fluence (shown in Fig. 1(a)) demonstrated the presence of a threshold fluence for conditioning. The presence of conditioning of the 1ω precursors at all pre-exposure frequencies indicates that these precursors absorb light at 1ω, 2ω, and 3ω. Assuming that damage initiation is due to heating of the precursor to reach a critical temperature, as described by Feit et al. in the linearly absorbing nanoparticle model [26], the conditioning threshold may also be associated with the precursors reaching a lower characteristic temperature. The results in Fig. 1(a) also demonstrate that the ratio of pre-exposure fluences at 3ω, 2ω, and 1ω to provide the same level of conditioning remains about the same (~1/2.7/8). Within the linearly absorbing particle model, these ratios can be related to the ratios of the absorptivities of the particle at each frequency.

Within the same model, the ratio of the damage thresholds of the pristine material also relates to the ratio of the absorptivities. Using the ratio of absorptivities (~1/2.7/8) extrapolated from the conditioning profiles and taking into account that the damage threshold at 1ω is about 22 J/cm², the damage threshold at 2ω would be expected to be about 7.5 J/cm² and at 3ω less than 3 J/cm². These estimated damage thresholds at 2ω and 3ω are much lower than the measured damage thresholds of the material at 2ω and 3ω while the difference in beam size (as discussed in the Experimental Setup section) of the different laser frequencies cannot account for this variation. Most important, the experiment described in section 3.2 showed a non-overlap of the populations damaging at 1ω with the population damaging at 2ω and 3ω. This indicates that the actual threshold fluence of the 1ω precursors required to initiate damage under exposure to 2ω or 3ω pulses must be much higher than the threshold fluence to initiate damage at the 2ω and 3ω precursors (damage threshold of the material at these frequencies). At the tested fluences used in the experiments to probe the overlap of the populations, any measurable PPD associated with the initiation of 1ω precursors is masked by the experimental error of the measurement. Therefore, the threshold fluence to initiate damage at the 1ω precursors with 2ω and 3ω irradiation is clearly outside the range of values predicted from the ratio of fluences required to provide same conditioning. This is a strong indication that the conditioning and damage initiation processes for the 1ω population involve different mechanisms.

4.2. The behavior of damage precursors at 2ω and 3ω

Damage initiation at both 2ω and 3ω was demonstrated to arise from the same precursor population based on the results of section 3.2. In addition, these experiments were performed using multiple pairs of fluences to test this concept at various PPDs in order to probe different portions of the precursor population. In all cases, the results demonstrated no additional damage events (within experimental error) from the second (3ω) pulse. This indicates that the precursors initiate damage in the same order as a function of laser fluence at both 2ω and 3ω.

The improvement to the damage performance at 2ω and 3ω as a function of the pre-exposure fluence [shown in Figs. 1(b) and 1(c), respectively] demonstrated two different damage behaviors arising from the same precursor population. This suggests that there are two different laser-induced defect reaction pathways leading to conditioning. The pathway that prevails depends on the pre-exposure fluence and frequency. As discussed in section 3.2, conditioning can be considered to involve the modification of the original (D₀) precursors to two different derivative defect structures (D₁ and D₂). As demonstrated by the results shown in Fig. 1(c), the modification to D₂ (manifested by an increase to the damage resistance of the material under testing at 3ω) took place with pre-exposure above the conditioning threshold for 3ω testing. On the other hand, modification to D₁ (manifested by increase to the damage resistance at 2ω but not at 3ω) was observed for all utilized pre-exposure fluences in the experimental results shown in Fig. 1(b). This prompted the need to explore the possibility of achieving conditioning via cw exposure. To test this concept, a 351-nm cw-Argon laser beam at ~1 W was used to pre-expose the material for one hour using the same focusing optics. Subsequently, the material was damage tested at 2ω and no improvement to the damage performance (no conditioning) was observed. This indicates that a threshold for conditioning for 2ω via the modification of the D₀ precursors to D₁ exists but that the minimum energy density required is below 1 J/cm².

The improvement to the damage performance as a function of the number of pre-exposure pulses (shown in Fig. 2) provides additional information on the way the original D₀ precursors are modified to D₁ and D₂ defect structures. Specifically, the experiments for pre-exposure and testing at 2ω probe the modification to D₁ while the corresponding experiments using 3ω pulses probe the modification to D₂. The results suggest a more efficient conversion to D₂ compared to D₁ from pre-exposure to a single pulse. For example, damage testing at 3ω after pre-exposure to a single pulse at 3ω provided the same percentage decrease in PPD as observed for damage testing at 2ω after pre-exposure to over 100 pulses at 2ω. This behavior was tested for various pre-exposure fluences and similar results were obtained. The improvement under pre-exposure to 3ω pulses above the conditioning threshold for 3ω damage reaches nearly optimal improvement with a very few number of pulses with the most improvement coming with the first pulse. On the other hand, the improvement under 2ω pre-exposure is always gradual and higher number of pre-exposure pulses always offers better performance.

The PPD profiles for damage testing at 2ω and 3ω measured in pristine and in preexposed material [shown in Fig. 3(a)] demonstrated that only a portion of the precursor population is conditioned (i.e., those most susceptible to damage) for pre-exposure and testing at 3ω. On the other hand, the entire precursor population is conditioned for pre-exposure and testing at 2ω. Figure 3(b) better highlights the processes involved in this case. Specifically, Fig. 3(b) shows the density of precursors as a function of their damage testing threshold fluence [derivative of the curve fits to the PPD profiles shown in Fig. 3(a)]. The profiles obtained for damage testing at 3ω in the pristine and pre-exposed material are different and intersect at about 13 J/cm². Below this fluence, the density of precursors giving rise to damage in the pristine material is greater than the density of precursors giving rise to damage in the pre-exposed material. The light gray shaded region can be interpreted as the D₀ precursors that have been conditioned (modified to D₂). Above 13 J/cm², the density of precursors giving rise to damage in the pristine material is lower than the density of precursors giving rise to damage in the pre-exposed material until about 21 J/cm². The light blue shaded region between the profiles can be interpreted as the conditioned population that is now exhibiting a higher damage threshold (or the D₀ population from the gray area that has been converted to D₂). This indicates that the conditioned population of precursors is not annihilated (as suggested elsewhere) but has attained a higher damage threshold.

The results shown in Fig. 5 for the DT(3ω,3ω) profiles of the same crystal at different testing fluences provide additional evidence that pre-exposure at a fixed fluence at 3ω conditions only a portion of the precursor population but has no effect on the remaining precursors, as also indicated by the results shown in Fig. 3. Moreover, the order with which the precursors initiate damage with increasing testing fluence is largely the same as the order with which the precursors are conditioned with increasing pre-exposure fluence.

Figures 3(a) and 3(b) demonstrate that for the case of 2ω damage testing, the modification to D₁ takes place for the entire population of the D₀ precursors. In addition, the density of precursors profiles from testing at 2ω following pre-exposure at different 2ω fluences [shown in Fig. 3(b)] demonstrate increased conditioning of the entire precursor population with the higher pre-exposure fluence. This suggests an incremental modification of the D₀ precursors with pre-exposure to higher fluences.

The origin of the differences to the damage threshold of each precursor is due to one or more yet unknown structural properties such as size, density, or shape. In particular, the size of each precursor can affect its absorptivity as discussed in Ref. [24]. Also, a change in density affects the density of defect states [27, 28] and, as a result, the fluence needed to achieve the density of conduction band electrons required to initiate damage [16]. The effect of the shape of an absorbing defect in the damage initiation fluence has been discussed in Ref. [29]. As a result, a sample that exhibits improved damage characteristics (such as higher damage threshold) may be the result of an absence of the most damage susceptible precursors of, for example, a certain size range otherwise present in the precursor distribution in the lower damage performance samples. The experiments to measure the DT (3ω,3ω) profiles in several samples exhibiting different damage thresholds (shown in Fig. 4) demonstrated the presence of different threshold fluences for conditioning. This suggests that each damage precursor has a threshold for both conditioning and damage initiation with the threshold of the precursors most susceptible to damage determining what is defined as a “damage (or conditioning) threshold” of a specific crystal. In addition, the observation of the same qualitative damage and conditioning behaviors in all crystals tested that exhibit different damage performance characteristics as shown in Fig. 4 further supports that the precursors are of the same type in all samples.

An important observation of the results shown in Fig. 4 is that the threshold fluence for damage was also measured to be different, occurring just above the threshold fluence for conditioning (about 1–3 J/cm²) in each sample. The relationship between damage and conditioning thresholds for 3ω may suggest that the same structural properties that govern the ability of each precursor to initiate damage also governs its ability to condition (modify to D₂). However, the results in Fig. 1(c) strongly suggest a difference between the damage initiation and conditioning mechanisms. Specifically, the PE (3ω) profile in Fig. 1(c) shows that the damage threshold fluence at 3ω of the pristine material is just above the conditioning threshold fluence. On the other hand, the PE (2ω) profile shows that the damage threshold (at 2ω) is well below the conditioning threshold for damage testing at 3ω. These observations indicate that the conditioning mechanism is different from the damage initiation mechanism and that the onset fluence (threshold) of each mechanism is governed by the laser parameters. It is therefore only incidental that the conditioning and damage thresholds using the 3ω, 2.5- ns pulses are separated by 1–3 J/cm². This is supported by recent publication results on the pulse-length dependence of conditioning using 3ω pulses [30] which indicate that the separation between damage and conditioning thresholds depends on the pulse-length.

The presence of a threshold pre-exposure fluence to achieve an improvement to the damage characteristics at 3ω suggests that a nonlinear absorption mechanism is the catalyst for the modification to the D₂ precursors. This assignment is further supported by the dependence of conditioning on the number of pre-exposure pulses which indicates that this precursor modification takes place with much fewer pulses than the modification to D1 and, thus, depends more significantly on the energy density of the pre-exposure. In contrast, there is a low threshold for modification of D₀ precursors to D₁ (leading to improvement of the damage performance at 2ω) while the results of Fig. 2 clearly show that the conditioning effectiveness strongly depends on the total number of pre-exposure pulses (cumulative pre-exposure energy). The low fluence threshold for modification to D₁ precursors indicates that a minimum energy absorbed per unit time is required. However, the continuous improvement to the damage performance at 2ω with greater number of pre-exposure pulses suggests that this modification is gradual and there exist intermediary forms of D₁ precursors (such as a mix between D₀ and D₁ defects within defect clusters).

Previous results on the wavelength dependence of the damage threshold [16], in addition to the present conditioning results, provide strong evidence in support of a defect-assisted nonlinear absorption mechanism. This plays a key role in both damage initiation and conditioning of the 2ω and 3ω precursor population (D₀ precursors) and can be understood in the context of defect states within the bandgap. These nonlinear mechanisms may be promoted by the presence of defect states within the bandgap. Density functional theory (DFT) calculations have shown that both hydrogen and oxygen lattice defects provide states in the bandgap [27, 28] allowing for enhanced absorption. A sufficiently dense cluster of such individual point defects can provide the necessary ingredients to initiate localized damage. These DFT calculations have also demonstrated mechanisms that can be associated with the conditioning processes [27, 28]. The experimental results presented in this work revealed the salient behaviors of the damage initiation and conditioning processes but also highlighted their complex nature. For the development of analytical models to describe the underlying fundamental mechanisms, these results are complimenting previous work regarding the damage characteristics as a function of laser wavelength and pulse-length. Furthermore, we plan to carry out pump-and-probe experiments to reveal the temporal evolution of these processes as well as experiments under simultaneous exposure to multiple wavelengths to probe the electronic structure of the precursors.

4.3. The development of conditioning protocols

Laser conditioning is currently considered as a viable method to improve the damage characteristics of KDP and DKDP optical components for harmonic generation and polarization control. Laser conditioning has been investigated and used for more than two decades but, to the best of our knowledge, this work is the first comprehensive study that combines the damage dependence on laser parameters (wavelength, number of pulses, and fluence), with each treated as an independent parameter. This work reveals important aspects of conditioning that can be directly applied to the design and optimization of conditioning protocols. Such protocols need to take into account a number of parameters such as a) pre-exposure maximum fluence and wavelength to minimize the risk of damaging the material during conditioning, b) number of pre-exposure pulses that ultimately determines the time to scan a large-aperture optic using small pre-exposure laser beams, and c) the fluence that the optic must withstand during operation.

This work raises the issue that a different protocol may need to be considered for each operational frequency or set of frequencies (present during frequency conversion). This is due to the fact that a) two precursor populations are present (those initiating damage at 1ω and those at 2ω and 3ω) and b) there are two conditioning pathways for the 2ω and 3ω precursors (one providing conditioning for 2ω only and one providing conditioning for both 2ω and 3ω).

For operation at 1ω, Fig. 1(a) suggests that conditioning (of the precursors initiating damage at 1ω) may be attained by pre-exposure to 1ω, 2ω, or 3ω at fluences well below the damage threshold of the material. Therefore, laser conditioning for operation at 1ω is a relatively safe procedure. There is a number of different ways that conditioning can be performed using a variety of laser systems. Consequently, 1ω conditioning can be performed in a facility that has been designed for optimized conditioning at 2ω or 3ω with only modification of the pre-exposure laser fluence and number of pulses. In addition, material that has been conditioned for operation at 2ω and 3ω will also exhibit enhanced damage performance for operation at 1ω since the 1ω precursors will be affected by the pre-exposure to laser irradiation designed to minimize damage due to the 2ω and 3ω precursors.

For operation at 3ω, only pre-exposure at 3ω using fluences above the conditioning threshold (which is located just below the damage threshold for 2.5-ns pulses) of the material results in improvement to the damage performance as shown in Fig. 1(c) and Fig. 4. This process has been assigned to the modification of the original precursors D₀ to D₂. Figure 2 shows that this modification is very efficient and takes place with pre-exposure to only a few pulses. For practical purposes this also implies that the time to scan a large-aperture optic can be expedited. However, the need to utilize pre-exposure fluences very close to the damage threshold of the material represents a significant risk. In addition, Fig. 4 demonstrates that the conditioning and damage thresholds vary within the same precursor population. Consequently, the most efficient and safe way to condition the material is to use the ramped-pre- exposure fluence method as discussed in Ref. [31]. This method uses incremental pre-exposure fluence steps up to a maximum pre-exposure fluence. The results presented here indicate that this method is effective because it conditions first the lower damage threshold precursors which then are able to withstand a higher pre-exposure fluence to achieve conditioning of the largest possible precursor population (and thus the maximum damage threshold).

For operation at 2ω, there two different approaches that can be used, each method having specific benefits and limitations. In the first approach, the material can be conditioned for operation at 3ω (modification of D₀ precursors to D₂). This will also provide conditioning at 2ω with the benefits of expedited scanning but the drawback of exposing the material to near damage threshold fluences, as discussed above. The second method is based on the pre-exposure of the material that leads to modification of the D₀ precursors to D₁. Figure 1(b) suggests that pre-exposure at both 2ω and 3ω will provide conditioning using fluences well below the damage threshold of the material. However, Fig. 2 demonstrates that optimizing damage performance may require pre-exposure to multiple pulses. This extended pre-exposure can lead to impractical long scanning times for conditioning large-aperture optics, and thus may not be suitable for practical purposes.

5. Conclusion

This work has revealed the “fingerprint” behaviors of the damage precursors in KDP/DKDP crystals. In the short term, this work helps understand the damage behavior of the material at each operational frequency and provides the basis to optimize performance via laser conditioning. In addition, recognizing the fingerprint properties of the precursors in DKDP (or in any optical material) is essential for their exact identification. This may be achieved by various methods such as a) eliminating possible precursor candidates that exhibit different behavior under laser excitation, b) correlating the strength of spectroscopic signatures of defects in various crystals prior to and after different conditioning protocols, or c) figuring out a method to produce materials with sufficient number of these precursors to be detectable with existing chemical analysis tools.