1. Introduction

Some of the most stringent quality parameters of optical materials are demanded in components of high-power and high-energy lasers and applications involving such lasers. Despite considerable research efforts over the past four decades in non-destructive diagnostics to predict the performance under high power laser load [1], progress is unsatisfactory. The most widely used and successful characterization technique is still laser induced damage (LID) testing to determine the maximum fluence the sample can sustain for a given illumination scenario (wavelength, pulse duration, number of pulses, and repetition rate). The result is a laser induced damage threshold (LIDT) fluence, F_th, above which the material shows permanent damage, mostly associated with the occurrence of a mini-crater.

One must distinguish single and multiple pulse damage thresholds where one or N pulses illuminate the same sample site, respectively. While single pulse (1-on-1) LIDTs are mainly determined by the nascent sample, multi-pulse (N-on-1) LIDTs are controlled by the accumulation and occupation of native and laser induced defects during the pulse train [2–4]. In a typical 1-on-1 measurement the sample is raster-scanned with excitation pulses of different fluence, and for each shot either 1 (damage) or 0 (no damage) is recorded. An individual test that results in damage at a given incident fluence F can only set an upper limit for the LIDT. The actual damage threshold F_th of an individual test is lower, because failure may have occurred at any time during the pulse and at any place within the beam profile. What is reported in the traditional damage test (TDT) is the probability of damage as a function of the incident peak fluence $\tilde{P}(F)$ [5], which represents an average over many sample sites. Depending on the application $\tilde{P}(F)$ is extrapolated to find the lowest fluence at which the damage probability is non-zero (onset fluence) [6], or to obtain a mean damage fluence F_d from, for example, $\tilde{P}(F_d)$ ≈ 0.5. Such LIDT measurement methodologies have been summarized in ISO standards [7] and can be carried out in automated setups [8, 9]. Unrealistically large number of test sites are often required to obtain meaningful LIDTs; note that a typical one-inch-diameter sample provides approximately 250 test sites, assuming a minimum separation of 1.5 mm to avoid contamination due to deposition of ablation debris.

Nanosecond LIDTs of high-quality optical coatings are controlled by statistically distributed defects of largely unknown physical nature [10]. Their existence is well established from traditional studies of the LIDT as a function of excitation spot size [11,12] and from statistical analysis of measured $\tilde{P}(F)$ dependencies [6]. The defect LIDT can be more than ten times smaller than the LIDT associated with the intrinsic material, for example 20 J/cm² versus 600 J/cm² in Sc₂O₃ films [13]. These defects can include small-size material imperfections, for example metal-like particles that are not fully oxidized, nodules, and nano-crystallites with corresponding grain boundaries.

Localized absorbers and micro-crystallites can be identified with photothermal microscopy [14, 15] and third harmonic microscopy [16], respectively; the question whether such defects control pulsed LIDT remains open. This ultimately prevents progress toward optical films exhibiting intrinsic LIDTs and explains why international optical coating competitions produce large spreads in LIDT values (more than a factor of 20) [17]. Attempts have been made to determine LIDTs locally by using pulse trains of increasing fluence [14]. However such techniques probe the property of the sample already affected by the laser and not its nascent state [18].

The relative success of LID tests and the failure of other techniques are a result of the complex and highly nonlinear mechanisms that control performance deterioration in optical components leading to LID, many of them are only triggered and detectable under excitation conditions very close to damage [19]. This motivates the search for characterization methods based on LID.

In this letter we present a pulse LID material characterization technique - Spatio-TEmporally REsolved Optical Laser Induced Damage (STEREO LID) - based on the simultaneous detection of the temporal onset of damage within the excitation pulse envelope and the spatial location of LID initiation within the laser spot. That is, STEREO-LID determines when damage starts during the laser pulse and where this initiation occurs within the beam profile. This method (i) yields the LID fluence F_th and intensity I_th for each damage event, (ii) allows one to measure LIDT locally, for example, of sample spots identified by other diagnostics, (iii) can identify defects that limit the critical incident fluence, and (iv) produces data to retrieve defect density distributions as a function of the critical fluence and intensity at which they initiate damage, $\overline{\rho }(F)$ and $\overline{\rho }(I)$, which can be used for material characterization and to guide coating and deposition improvement for high-power laser applications.

2. Experimental setup and measurement methodology

The experimental setup of a nanosecond STEREO LID measurement is shown in Fig. 1. The seeded Nd:YAG laser (Continuum Powerlite 8000) produces τ_p = 8.5-ns pulses at 1064 nm with a repetition rate of 10 Hz. Single pulses can be selected with an electromechanical shutter. The nearly Gaussian beam is focused onto the sample (thin film on a fused silica substrate) to a beam waist w₀ ≈ 22 µm. The fluence can be adjusted with a half-wave plate and thin film polarizer. The beam is p-polarized with respect to the tilted sample.

 

Fig. 1 Experimental layout of a nanosecond STEREO LID measurement setup. Diodes D1, D2, D3 monitor the transmitted, scattered, and reference pulses. Examples of each are inset. The in-situ microscope (CCD1) images the excited sample site with the incident pulse as illumination source.

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The transmitted and scattered pulses are recorded by InGaAs photodiodes D1 and D2 (time constant 125 ps) and an oscilloscope with 8-GHz bandwidth and 20-GHz sampling rate (Tektronix, TDS6804B). Pulse to pulse energy fluctuations and beam pointing stability are monitored by photodiode D3 and a beam profiler (CCD2) placed at the focus of another lens (focal length 1 m), respectively. The excited sample site is imaged by an in situ microscope with NA ≈ 0.18, 14× magnification and a working distance of ≈ 10 mm. An interference filter centered at 1064 nm (bandwidth 10 nm) ensures that only light scattered from the ns excitation pulse contributes to the image. The sample normal is tilted 30 degrees with respect to the laser axis and 9 degrees with respect to the microscope. This prevents the transmitted laser beam from entering the microscope while providing a suitable field of view of the film and material ablation; other geometries, however, are possible.

Before LID testing, the location of the beam on the sample surface as imaged by the in situ microscope must be established. The sample is illuminated with pulses well below (<0.1×) the LIDT, and the image generated by the weak scattering of the film is correlated with the beam profiler (CCD2) image coordinates. The in situ image is averaged over many pulses and several samples sites (30 µm spacing), and typical uncertainties of the beam center are ≈ 1 µm, below the optical resolution of the microscope (about 5 µm). The in situ image also gives the beam size on the sample surface, which is elliptical due the sample tilt (with respect to laser and microscope axes). These subthreshold pulses are also used to calibrate any optical and electronic timing differences of the three photodiodes.

In an LID test, the sample is excited with a single pulse with peak fluence F₀ large enough to guarantee damage. The recorded beam profile yields the location of the center of the beam spot on the film, (x₀,y₀). The point of damage initiation is identified spatially relative to the beam center coordinates, x_d and y_d, and temporally (t_d) from the in situ microscope and diodes, respectively.

The time of damage initiation, t_d, is provided by monitoring both the transmitted (D1) and scattered (D2) incident pulse. Example data are shown in Fig. 2. The onset of damage is marked by a spike in scatter which coincides with a peak in transmission that is followed by nearly complete attenuation in roughly 1 ns. Both the transmission and scatter signals can be explained by the generation of a dense (absorbing) plasma triggering ablation within 150 ps (temporal resolution Δt of our detection system). The drop in transmission is caused by a combination of scatter, absorption, and diffraction by the expanding ablation plume and/or shockwave. Tests of forward scatter (diffraction) up to 10° from the optical axis with an integrating sphere suggest that absorption and back scattering are most important. Plasma expansion rates of roughly 20 µm/ns [20] and similar shock wave velocities [21] have been observed. This suggests that a beam of 20 µm radius can be affected during the observed 1 ns transmission drop.

 

Fig. 2 Example data from (a) scatter and (b) transmission photodiodes with an line marking the damage initiation time, t_d. The pulse shape from the reference diode is shown in gray.

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The ejection of material and scattering off this plume produces the image in the in situ microscope, see Fig. 3(a). The visible ”streak” represents scattering off of the jet ejected normal to the film. A simple simulation of this process produces the streak shown in Fig. 3(b), which explains the qualitative features of the microscope image, cf. Fig. 3(a). The expansion of the streak image to the left is due partly to the jet extending beyond the depth of field of the imaging system. The scatter signal from the far left of the initiation point stems from interaction of the jet with air and is not visible when the experiment is performed in vacuum.

 

Fig. 3 (a) In situ microscope image of a damage event. The dashed ellipse indicates the beam profile (1/e² contour) at the (tilted) sample; (b) Schematic diagram of image generation in the microscope with simulation results (sim); (c) Ablation crater inspected with a Nomarski microscope showing mini-crater at the point of damage initiation; (d) Location of 159 damage initiation points overlaid upon the beam profile.

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A closer inspection of the jet origin provides the desired spatial coordinates (x_d,y_d) of the LID initiation point. As further evidence of this interpretation, there often appears a mini-crater within the resultant crater [see Fig. 3(c)], whose position correlates with the streak origin in the in situ image. This mini-crater is the result of action on the substrate due to momentum conservation during material ejection. This mini-crater does not appear in high-fluence damage events, which we associate with damage of the intrinsic material.

Figure 3(d) shows a scatter plot of damage initiation sites for 159 tests on a Sc₂O₃ film. These are overlaid on the beam profile to show their statistical distribution centered about the beam’s peak fluence. From the highest fluence events which should be clustered around the center of the beam, we estimate the uncertainty in the position (x_d,y_d) of about 3 µm. It should also be mentioned that there are rare events when we observed multiple jets from within the laser spot. The corresponding Nomarski images then showed several mini-craters at the respective locations of the jet origins. It may be that when damage is initiated at a particular site, the growing plasma prevents initiation at other sites. Note that these rare multiple-initation events must be discarded for measurement of LIDT, because there is no way as of yet to identify the initiation times for the different jets.

The damage fluence F_th is obtained by integrating the intensity at (x_d,y_d) up to time t_d making use of our Gaussian spatial, temporal beam and pulse profiles, respectively

Here τ_p is the pulse duration and $I_0=\sqrt{4\ln 2/\pi }\times (F_0/{\tau }_p)$ is the incident peak intensity. F₀ = 2W₀/(πw_xw_y), where the pulse energy, W₀, is measured by the calibrated reference diode (D3). The damage intensity is simply $I_{th}=I_0{e}^{-2{(x_d/w_x)}^2}{e}^{-2{(y_d/w_y)}^2}{e}^{-4\ln 2t_d^2/{\tau }_p^2}$. Note that in Eq. 1, t_d = 0 is the peak of the pulse. From the uncertainty of the initiation point, Δr, and the time of onset, Δt, we estimate an overall uncertainty for the determination of critical fluence and intensity of about 10–15%. Obviously, the accuracy can be improved by increasing the ratios w₀/Δr and τ_p/Δt.

3. Results and discussion

As mentioned in the introduction STEREO-LID is superior to the TDT in several aspects. The fact that we obtain LIDT fluence and intensity can be used to test the scaling of current ns damage mechanisms, for example to distinguish thermally induced LID processes [22] from those triggered by multi-photon ionization typical for high-quality dielectrics [23].

Unlike TDT the LIDT can be determined by the new technique locally with a single test. As a demonstration we targeted debris particles around an ablation crater, identified by scatter with the in situ microscope, and measured their LIDT. The in situ microscope was able to distinguish between damage initiated at the debris particle and other defects at the edge of the beam profile. The measured LIDTs were just 10% of LIDTs measured when the debris particles were avoided.

STEREO-LID is advantageous in identifying those defects with the lowest damage fluence that will ultimately limit the possible power and pulse energy handling of the optical component.

As a demonstration, a film of Sc₂O₃ was characterized by both TDT and STEREO-LID using the same number of test sites, N = 110. The traditional damage probability $\tilde{P}(F)$ is shown in Fig. 4. Ten tests were performed at each of 11 different incident fluences. The damage probability observed with TDT reaches 100% at about 1.4 kJ/cm². A minimum damage event at 200 J/cm² points to a critical incident fluence near this value. Following the ISO protocol a linear extrapolation of $\tilde{P}(F)$ to $\tilde{P}=0$ suggests a critical fluence of 130 J/cm² from TDT. STEREO-LID provides location, onset time and damage fluence (x_d,j,y_d,j,t_d,j,F_th,j) for each of the 110 test sites j with a peak incident fluence of 1.6 kJ/cm². The measured fluence values F_th,j were grouped into bins with mean fluence F_i and width ΔF_i. The probability that a certain damage fluence F_i is observed is P_i =P(F_i)= n_i/N, where n_i is the number of damage events belonging to bin i. This probability P is plotted in Fig. 4 (squares). The uncertainty of the P(F) values are smaller than the TDT values because they are derived from all 110 tests as opposed to just 10 tests for each TDT data point. Note the tilde to distinguish P(F) from the damage probability $\tilde{P}(F)$, which has a different meaning and behaves very differently. Most notably, the highest probability was measured for the lowest fluence bin. This occurs for two reasons: (1) Because of the Gaussian beam profile, the area of the beam where the local fluence exceeds the defect fluence F_th is largest for small values of F_th; (2) if there are two defects in the beam area, the one with the lower fluence is more likely to fail first and be measured [24]. Therefore, STEREO-LID has a high probability of measuring the fluence of the defects responsible for the damage threshold. In this case, there were many instances of damage events at 25 J/cm², well below the onset predicted by the TDT, which exemplifies the advantages of the new technique if the lowest critical fluence is of interest.

 

Fig. 4 Comparison of TDT and STEREO-LID characterization of a Sc₂O₃ film using 110 sites each. The damage probability $\tilde{P}(F)$ of the TDT is shown in circles up to fluence values of 800 J/cm² (the inset shows complete $\tilde{P}(F)$ curve, the solid line is a guide to the eye.). Linear extrapolation estimates a fluence of 130 J/cm² where the probability of damage is zero. The squares depict P(F) the probability of exciting a defect of fluence F (see text), measured with STEREO-LID.

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STEREO-LID also provides additional information. The dynamic range of STEREO-LID is sufficient to identify a separate cluster of events [see Fig. 4] around 1.3 kJ/cm², which may indicate the intrinsic damage threshold [13]. Also STEREO-LID shows that the events below 600 J/cm² all occur before the peak of the pulse, a detail completely ignored by the TDT.

The damage probability vs. fluence of the TDT has been used to characterize defect density distribution, $\overline{\rho }(F)$, by fitting to model distributions [6, 8]. STEREO-LID data enables the retrieval of defect distribution functions without any a priori assumptions about their shape. For each bin a class of defects with threshold F_i is characterized by an average density, ${\rho }_i=\overline{\rho }(F_i)\Delta F_i$. Assuming that the first defect within the beam to reach its threshold during the pulse will be measured, a set of M transcendental equations (M is the number of bins) relating P_i and ρ_i of the form

Finally, STEREO-LID has the freedom to choose F₀ and the spot size to best characterize a test sample. In the example of Sc₂O₃ a high fluence and small spot size were used to reach the intrinsic damage threshold and reduce the probability of hitting a defect. If only the low fluence defects are of interest, then a lower test fluence can be used with a larger spot size to maintain 100% damage probability.

4. Summary

In summary, we presented a pulsed LIDT measurement technique that produces the damage fluence and intensity in a single shot. This is accomplished by recording the temporal onset and spatial location of damage initiation during a test. The technique can be applied for transmissive and reflective optics. Compared to traditional damage methodologies the new method, dubbed STEREO-LID, yields more information using fewer sample sites. As such it can be used to study the physics of LIDT limiting defects, which can be used to guide research into identifying and mitigating these defects.