2.1.

Materials

Hafnia (${\mathrm{HfO}}_2$) and silica (${\mathrm{SiO}}_2$) single layers were selected for these tests as they are common materials used in multilayer dielectric optical components employed in short-pulse laser systems as high- and low-refractive-index materials, respectively. They have been deposited by electron-beam evaporation with ion assistance deposition on BK7 substrates. The layer thicknesses are 149.9 and 194.3 nm, respectively, with refractive indices of 1.930 and 1.448 determined at 1053 nm via ellipsometry. Multiple samples from the same deposition batch were fabricated and sent individually to the five testing facilities. This means that each test was carried out on a single sample, which should be nominally identical to all other samples in the batch. However, this equivalence assumption has not been verified by means of cross measurements. Therefore sample-to-sample repeatability will also be taken into account in the final comparison.

2.2.

Experimental Conditions

The experimental conditions have been selected to be as close as possible between the different setups.

The four testing configurations ($0°\text{-}{\mathrm{P}}_{\mathrm{pol}}$, $45°\text{-}{\mathrm{P}}_{\mathrm{pol}}$, $0°\text{-}{\mathrm{S}}_{\mathrm{pol}}$, and $45°\text{-}{\mathrm{S}}_{\mathrm{pol}}$) were implemented on the basis of the ISO 1-on-1 procedure on each setup.¹⁴ Because damage in the sub-picosecond regime is deterministic, there is no need to perform a detailed statistical analysis by reproducing the measurement on a large number of spots per fluence. Finally, each laboratory had selected itself the number of sites and the fluence interval to minimize the sharp transition from 0% to 100% damage probability. The reported experimental LIDT (${\mathrm{LIDT}}_{\exp }$) is defined as the mean between the lowest fluence where damage is detected and the highest fluence where no damage occurs. The uncertainty of the measurement is set to be the mean absolute deviation between these two fluences. Therefore, the uncertainty of the measurement can be reduced by testing additional fluences around the damage-threshold fluence: to this end the fluence steps are decreased near the threshold.

The spatial profile of the laser-beam intensity was nearly Gaussian for all lasers used in this study. The equivalent areas are in the range ($0.4\times {10}^{-4}$ to $3.5\times {10}^{-4}\mathrm{c}{\mathrm{m}}^2$), which corresponds to beam diameters in the range (70 to $210\mu \mathrm{m}$). The in situ damage detection was done either (a) analyzing the variation of the scattered light from the focal spot (damage is recorded when the scattered light increases, based on Schlieren imaging, see Fig. 1 of Ref. 15) or (b) direct imaging using a long-working distance microscope. However, these in situ detection approaches were used only for guidance during the 1-on-1 procedure and not as a damage threshold determination. The final determination was a precise observation with a differential-interferential–contrast (DIC) microscope, as recommended by the ISO standard. A damage site is defined as a modification, e.g., pits or discoloration, on the sample seen by means of the DIC. The results reported in this paper obtained from different facilities are presented anonymously in the form Lab A, B, C, D, and E (for laboratory A, B, C, D, and E).

2.3.

Experimental Laser-Induced Damage Threshold

The experimental results of LIDTs obtained by the five laboratories on the two single layers and for the four configurations are given in Table 1. They are expressed in energy density (fluence in $\mathrm{J}{\mathrm{cm}}^{-2}$), and reported based on the beam normal, that is to say that the beam area on the layers is not corrected for the AOI. The LIDTs are raw, as-measured data without taking into account the electric-field intensity (EFI) inside the single layer, which is different for each configuration. For illustration purposes, Fig. 1 shows two representative damage sites on ${\mathrm{HfO}}_2$ irradiated at 10% and 20% above damage threshold, respectively, with the former being a light discoloration and the latter is a pit.

Table 1

LIDTexp measured by the five laboratories (labeled as Lab A, Lab B, Lab C, Lab D, and Lab E) on the two dielectric single layers (SiO2 and HfO2). All values represent beam normal fluences in J cm−2. Results are also reported by lab C and lab E in a vacuum environment. “NLT Max Fluence” means that fluences necessary to perform the test cannot be reached (limit at 5  J cm−2). “—” means that the test was not realized.

Fig. 1

Post-mortem observation by means of a Nomarski microscope for two irradiations on ${\mathrm{HfO}}_2$ at 10% and 20% above ${\mathrm{LIDT}}_{\exp }$.

3.1.

Electric Field Intensity

We base our discussion on the first-order assumption that each dielectric material is characterized by its own damage threshold. It is a property that is specific to it and other properties such as the melting temperature, the conductivity, and the permittivity. A material is thus characterized by its intrinsic LIDT (${\mathrm{LIDT}}_{\mathrm{int}}$), a property of the material independent of experimental conditions such as the AOI and the state of polarization of the beam. These last two parameters act on the maximum value of the EFI and on its position within the material (see Fig. 2). Thus intrinsic threshold and experimental threshold for a given layer are related by the EFI via the relationship:

Fig. 2

Electric field calculations in (a) ${\mathrm{SiO}}_2$ and (b) ${\mathrm{HfO}}_2$ single layers at 0° of AOI, P or S polarizations. The EFI is maximum at the top of the ${\mathrm{SiO}}_2$ layer (at the air interface and its value is 69.9%) and maximum at the bottom of the ${\mathrm{HfO}}_2$ layer (at the substrate interface and its value is 54.6%).

This implies that independent of the experimental conditions (AOI and polarization states), the ${\mathrm{LIDT}}_{\mathrm{int}}$ must be the same despite different ${\mathrm{LIDT}}_{\exp }$. This property is beneficial and more essential to the damage metrology because it makes it possible:

Values of the refractive index and thickness were used to calculate numerically the EFI distribution within each single layer using OptiLayer software.¹⁶ Samples are modeled as a single layer deposited on a semi-infinite BK7 substrate and a superstrate with a refractive index of 1 (air or vacuum). Samples are illuminated at normal incidence or 45°AOI, from the incident medium with a linearly polarized plane wave (horizontally or vertically) at the wavelength $\lambda =1053\mathrm{nm}$. The distribution of the square of the time-averaged electric field ${|E|}^2$ is calculated and normalized by the incident electric field ${|E_{\mathrm{inc}}|}^2$. The maximum enhancement of the EFI in the layer, ${|E|}^2/{|E_{\mathrm{inc}}|}^2$ denoted by ${\mathrm{EFI}}_{\max }$ is estimated and given in Table 2 for the four configurations and the two single layers.

Table 2

Calculated EFImax in SiO2 and HfO2 single layers at 0° and 45° in P and S polarizations.

EFI calculations have also been made at the wavelength $\lambda =1030\mathrm{nm}$. Deviations between the EFIs at 1053 and 1030 nm are about 0.03% and 0.17% for ${\mathrm{SiO}}_2$ and ${\mathrm{HfO}}_2$ single layers, respectively. More the uncertainty in this factor using some nominal variances for the refractive index, the layer thickness, and the AOI were precisely discussed in Ref. 17. The uncertainties have been estimated about few %.

3.2.

Intrinsic Laser-Induced Damage Threshold

The ${\mathrm{LIDT}}_{\mathrm{int}}$ for the two single layers was estimated from Eq. (1) using the ${\mathrm{LIDT}}_{\exp }$ values provided in Table 1 and calculated ${\mathrm{EFI}}_{\max }$ given in Table 2. Results are given in Tables 3 and 4 for ${\mathrm{SiO}}_2$ and ${\mathrm{HfO}}_2$ single layers, respectively. For a meaningful comparison, only results obtained in air environment are reported. The last three columns of the tables indicate the average fluences measured on each installation as well as the standard deviation on the measurement. The standard deviation is a qualitative indicator of the repeatability of the measurement. The last line corresponds to the average of the measurements made on each installation.

Table 3

LIDTint of SiO2 single layer estimated by means of relation (1) from experimental data of Table 2 and EFImax of Table 3. Thresholds are given in terms of energy density (fluence) in J cm−2.

Table 4

LIDTint of HfO2 single layer estimated by means of relation (1) from experimental data of Table 2 and EFImax of Table 3. Thresholds are given in terms of energy density (fluence) in J cm−2.

To better visualize the distribution of the LIDT values obtained from measurements in the five different facilities, the results are also presented in the form of a histogram (Fig. 3). To quantify this distribution, the ratio between standard deviation and mean ($\sigma /\text{mean}$) is used to estimate the deviation of the measurement. A number of behaviors can be readily appreciated.

Fig. 3

Histogram of intrinsic LIDTs on each laboratory for ${\mathrm{SiO}}_2$ and ${\mathrm{HfO}}_2$ single layers. The last two bars correspond to the averages of the different installations. Vertical lines are error bars.

3.3.

Characteristics of the Laser Pulses

The tests were carried out at a pulse duration ($\tau$) of 800 fs to achieve nominally identical conditions at the five laboratories regarding this parameter. The small deviations in this value were corrected using the temporal scaling law reported by Mero et al.,⁸ in the form of $F_{th}\sim {\tau }^{\kappa }$ with an exponent $\kappa$ of about 0.30 and 0.33 for ${\mathrm{HfO}}_2$ and ${\mathrm{SiO}}_2$, respectively. $F_{th}$ stands for LIDT.

The pulse durations in all cases were estimated from the autocorrelation trace, but that estimation strongly depends on the assumption made on the shape of the temporal pulse (Gaussian, hyperbolic secant, and Lorentzian). The uncertainty on this measurement has also to be considered. On the other hand, the exact intensity profile must also be considered. Recently, Olle et al.¹³ have reported experimentally and numerically large LIDT differences due to small differences in relatively similar intensity profiles (see Fig. 15 of Ref. 13). Ideally, exact temporal profiles have to be determined by means of specific apparatus such as frequency-resolved optical gating,¹⁸ SPIRITED,¹⁹ or other equivalent diagnostics. Finally, LIDT errors due to the pulse duration are certainly at least of the order of 5% but can also reach 30% for different intensity profiles. For this, we refer to Sec. 3 of Olle’s article¹³ dealing with the influence of temporal shape on the temporal scaling law.

Numerical ${\mathrm{LIDT}}_{\mathrm{int}}$ estimations based on the model described in Ref. 13 and based on the resolution of the multiple rate equation were also performed for three different temporal profiles acquired during this campaign at Lab B, by means of SPIRITED diagnostic. Small differences appear on their shapes and their full-width half maximum (FWHM) pulse durations are close (FWHM: 782 – 801 – 810 fs), see Fig. 4. Table 5 gives the ${\mathrm{LIDT}}_{\mathrm{int}}$ numerical estimations for ${\mathrm{SiO}}_2$ and ${\mathrm{HfO}}_2$. Deviations between maximum and minimum values are about 9% and 5% for ${\mathrm{SiO}}_2$ and ${\mathrm{HfO}}_2$, respectively. These deviations are part of the repeatability of the measurement on the same setup.

Fig. 4

Three different temporal profiles measured during the campaign at Lab B by means of SPIRITED diagnostic, for the same laser fluence.

Fig. 5

Laser beam sizes and spatial for the five facilities.

Table 5

Numerical LIDTs (J cm−2) of SiO2 and HfO2 single layers estimated from numerical model for the three temporal profiles given in Fig. 4. Relation (1) can be applied to estimate the intrinsic LIDT.

Another parameter that may have a significant impact is the temporal contrast. Prepulses and/or postpulses can have a double effect. First, it is established that the ablation efficiency in dielectrics depends on the delay between the pre-/post-pulses and the main pulse.²⁰ The first pulse promote electrons into the conduction band while the second pulse induces the ablation of the dielectric. The analogy with laser damage mechanisms is obvious. These pre- and post-pulses must be minimal and sufficiently spaced in time from the main pulse to avoid any pre- or post-excitation effect. In addition, these pulses are taken into account in the energy balance (the measurement of the pulse energy is integrated on a pyroelectric detector or on a photoelectric cell), biasing the true value of the intensity/energy involved in the process and damage mechanisms by the main pulse. The impact of this parameter is currently not known. Therefore, it may be important to include in the diagnostics the capability to measure the full intensity profile (for that purpose see Fig. 4 of Ref. 13).

The determination of beam fluence has been the gold standard in damage testing for decades. Its accuracy is intimately linked to a precise and rigorous determination of the equivalent beam area (Fig. 5). However, it can be challenging to ensure that the measurement is correct to better than 5%,¹⁵ and the measure can strongly diverge via seemingly minor effects. Here, we detail a few missteps to be aware of when managing short pulses and small beams.

Self-focusing is known to be an important parameter for the design of short-pulse laser-damage setups, which is why it is recommended to carry out tests under a vacuum environment to circumvent this issue (with the difficulties inherent in measurements in a vacuum chamber). For tests in an air environment, it is necessary to estimate the B-integral through the focal volume prior to the test surface. In the setups, B-integral is due to the self-focusing in the air after the last focusing lens. For a Gaussian beam with a wavelength $\lambda$ and waist radius $\omega$, the Rayleigh distance $Z_R$ is defined as

The intensity $I$ at the focal spot is given by the relation:

The intensity $I$ is assumed to be constant within the Raleigh distance $Z_R$, then combination of Eqs. (3)–(5) gives

During all of the tests, samples were tested up to $6\mathrm{J}{\mathrm{cm}}^{-2}$ in the beam normal at 800 fs. It has been established that the nonlinear refractive index of air was $n_2=3.{10}^{-19}\mathrm{c}{\mathrm{m}}^2/\mathrm{W}$;²¹ it follows that Eq. (6), with an energy of 2 mJ, which corresponds to the maximum energy delivered during these tests, gives a $B$-integral value of $\mathrm{B}\sim 0.85$. This value is below the self-focusing limit, which can be taken as $B\sim 2\mathrm{rad}$.²² Thus, beam propagation should not be subject to self-focusing.

This issue was also verified experimentally by changing the AOI from 0° to 45° and verifying that the ${\mathrm{LIDT}}_{\mathrm{int}}$ estimated from the ${\mathrm{LIDT}}_{\exp }$ remains constant. This is based on the following testing hypothesis: given that the test fluence increases when the AOI is increased, if the self-focusing effect is negligible one should find the same intrinsic LIDT for any AOI and corresponding fluence. The EFI was calculated at each AOI; it must be specified that the uncertainty on its determination increases with the AOI. Results are given in Table 6. Increasing the AOI means an increase of the experimental fluence (from 3.77 to $5.57\mathrm{J}{\mathrm{cm}}^{-2}$ in the reported case for experiments carried out by Lab B). And yet, it is observed that the intrinsic LIDT is quite constant within experimental error, without the error in determining the EFI being taken into account. The mean value and the standard deviation are 2.06 and $0.02\mathrm{J}{\mathrm{cm}}^{-2}$, respectively, which is a variation of $<1\%$. It can be concluded that

Table 6

LIDTint of HfO2 single layer estimated from LIDTexp tested in air environment and S-polarization between 0° and 45° AOI during the campaign at Lab B. EFI was determined at each angle, the uncertainty (not reported here) on its estimation increases with the AOI.17

The question of the impact of the environment for testing is a difficult question. Specifically, can one extrapolate results from thresholds measured in the air to expected thresholds in vacuum? This is a complex question to which an element of an answer is brought indirectly in this paragraph. To explore this question, EFI values were estimated for the layers in vacuum. We start from the principle that the vacuum can be approximated by a dry air environment, in particular with regards to the refractive index of the dielectric layers. The estimation of the refractive index not being possible with our means in vacuum, measurements with a spectrophotometer in dry air were carried out to estimate the refractive index of the layers, and therefore determine the value of the EFI. Refractive indices, and consequently EFIs, were found to be little different regardless of the environment. Damage thresholds were subsequently measured in ambient air (45% relative humidity) and in dry air (4% relative humidity) on one ${\mathrm{HfO}}_2$ single layer and one ${\mathrm{SiO}}_2$ single layer. ${\mathrm{LIDTs}}_{\exp }$ were also measured to be approximately the same. Finally, intrinsic LIDT values are quite similar (see Table 7), with differences of $<3\%$. These results suggest that “intrinsically,” environment should have a negligible effect on the damage thresholds of these samples. A key aspect of this determination is the relatively slow change in EFI versus layer thickness for a single layer, such as those tested in this study, versus the very rapid change in EFI for some multilayer coating designs.²³ The EFI becomes much more complex when these materials are integrated in multilayer coating designs, requiring additional investigation beyond the scope of this work.

Table 7

LIDTexp of HfO2 end SiO2 single layers measured in ambient and dry air, at 0° AOI during the campaign at Lab B. LIDTint were estimated with EFI calculated from refractive indices measured in ambient and air environments.

Despite this analysis, a significant difference was nevertheless obtained experimentally between tests carried out in air and in vacuum. Table 1 reports higher ${\mathrm{LIDT}}_{\exp }$ in vacuum than in air, these results were obtained by both Lab C and Lab E. For ${\mathrm{HfO}}_2$ coating, ${\mathrm{LIDT}}_{\mathrm{int}}$ are 1.42 and $1.34\mathrm{J}{\mathrm{cm}}^{-2}$ in air and 1.63 and $1.52\mathrm{J}{\mathrm{cm}}^{-2}$ in vacuum, from laboratories C and E, respectively. This means a difference of around 13% for the two labs.

Thus, considering the analysis of the impact of all of these different contributors (they are summarized in Table 8 with the assumption that they are not correlated), it is appropriate to consider that differences around 20% between tests carried out on different facilities can be reasonably obtained.

Table 8

Synthesis of error margins (standard uncertainty at 1σ) for identified contributors (error budget). A quadratic summation provides an accuracy around 19% for the determination of fluences.