1. Introduction

In a recent paper [1] we described the Sandia Z- Backlighter lasers and the Large Optics Coating Operation that provides high laser-induced damage threshold (LIDT) hafnia/silica optical thin-film coatings for these lasers at their operating wavelengths of 1054 and $527\mathrm{nm}$, which we refer to by 1w and 2w, respectively. That paper focused on the design and production of high LIDT antireflection (AR) and high-reflection (HR) coatings using electron-beam deposition with and without ion assistance and on ways of reducing surface roughness of HR coatings in the case of ion-assisted deposition. This paper deals just with AR coatings, featuring comparisons of design and LIDT for a variety of these coatings tailored for use at 1w or dual 2w/1w wavelengths, for angles of incidence (AOIs) ranging from $0°$ to $45°$, and for S and/or P polarization (Spol and/or Ppol) for the nonnormal AOIs. All the AR coatings of this study consist of two hafnia/silica thin-film layer pairs (four layers total) produced by electron-beam deposition on fused silica or BK7 substrates with the coating chamber at $200°\mathrm{C}$ and without ion assistance. The hafnia/silica/hafnia/silica layer sequences start at the substrate and progress to the incident medium, which is air or vacuum in the Z-Backlighter beam trains.

The LIDT tests of this paper used laser pulses at 532 and $1064\mathrm{nm}$, which are, respectively, close enough to the 2w and 1w wavelengths of 527 and $1054\mathrm{nm}$ that we can reliably assume the LIDTs measured at 532 or $1064\mathrm{nm}$ differ insignificantly from what they would be had they been correspondingly measured at $527\mathrm{nm}$ (2w) or $1054\mathrm{nm}$ (1w). Accordingly, we refer to LIDTs measured at $532\mathrm{nm}$ as 2w LIDTs or LIDTs at 2w, and to those measured at $1064\mathrm{nm}$ as 1w LIDTs or LIDTs at 1w. The LIDT measurements were done by Spica Technologies, Inc. (www.spicatech.com) following a protocol from the National Ignition Facility (NIF) of Lawrence Livermore National Laboratory [2]. We have explained the specifics of this protocol previously [1] and refer to it as the NIF–MEL protocol. All the AR coating LIDTs we report here are of the same damage threshold type as their counterparts of our earlier report [1]; that is, they are damage thresholds due to accumulation of nonpropagating damage sites in contrast with those due to development of one or more propagating damage sites. The earlier paper [1] contains an explanation and discussion of these two LIDT types.

We first present results for debris shields, a key category of Z-Backlighter AR-coated optics. They are $32.5\mathrm{cm}\times 32.5\mathrm{cm}\times 1\mathrm{cm}$ fused silica substrates with each side coated by an AR coating, which we designate as 2w_1w AR, designed for normal or near-normal AOIs and excellent AR ($<0.5\%$ reflectivity) at 2w and nominal AR ($\sim 1\%$ to 2% reflectivity) at 1w. We report 2w and 1w LIDTs of three debris shield coatings, arbitrarily selected from many coating runs between 2005 and 2008, to test how consistent our coating process is over time with respect to LIDT. The LIDTs show good consistency, but those at 2w are not as high as we would like. We analyze LIDT behavior in terms of the 2w and 1w optical electric field (E-field) intensities within the coating. This analysis provides an explanation for these lower 2w LIDTs based on intensity maxima exhibited by the 2w E-fields.

We next turn to AR at nonnormal AOIs, and report LIDTs at use conditions of 1w, $45°$ and $32°$ AOI Spol and Ppol AR coatings. These results show that the LIDT of AR coatings tends to increase with AOI except for an anomalously low LIDT for the $45°$ AOI, Ppol case. An analysis of the E-fields for these AR coatings shows that Ppol E-field intensity discontinuities at the optical media interfaces explain the LIDT results. Finally, we present LIDTs of Side 1 and Side 2 AR coatings for a 2w diagnostic beam splitter and interpret the LIDT results again in terms of the Spol and Ppol E-field behaviors within the coating layers. The paper ends with our conclusions.

2. LIDTs of Three Debris Shield 2w_1w AR Coatings Arbitrarily Selected over a Three Year Period

Figure 1 shows 2w and 1w LIDTs at normal incidence of three debris shield 2w_1w AR coatings that we arbitrarily selected from many debris shield product coating runs conducted between December 2005 and June 2008. These LIDTs are adequate for most Z-Backlighter laser fluences, especially the 1w LIDTs that range between 18 and $25\mathrm{J}/{\mathrm{cm}}^2$, similar to those we previously reported [1]. However, $>10\mathrm{J}/{\mathrm{cm}}^2$ at 2w would be more to our liking [1]. Overall, these results confirm that our debris shield coating process provides, over time, 2w_1w AR coatings with LIDTs consistently in the ranges of $6–9\mathrm{J}/{\mathrm{cm}}^2$ at 2w and $18–25\mathrm{J}/{\mathrm{cm}}^2$ at 1w.

Our interest in improving the 2w LIDTs of the 2w_1w AR coatings beyond $10\mathrm{J}/{\mathrm{cm}}^2$ led us to examine E-field behaviors within the coating resulting from the AR process of interference of forward and backward propagating components of light. We calculated the E-field intensities using the OptiLayer thin film software (www.optilayer.com). Figure 2 shows the results. The 2w E-field intensity is a little more than 90% of its incident amount at the boundary between the coating and the incident medium with two pronounced intensity peaks within the coating, one peak a bit higher and the other a bit lower than 90% of the incident intensity. These intensity peaks, even though they are in silica layers which are more robust than hafnia layers against laser damage, could nevertheless explain the moderately low 2w LIDTs ($<10\mathrm{J}/{\mathrm{cm}}^2$) of our 2w_1w AR debris shield coatings. The 1w E-field intensity, on the other hand, is at or very near 100% of its incident amount at the coating/incident medium interface but then re mains low, at $<80\%$ of the incident intensity, within the coating. This is consistent with the high ($\sim 20\mathrm{J}/{\mathrm{cm}}^2$ and higher) 1w LIDTs of Fig. 1, and similar to the LIDTs and E-field behavior of our 1w $0°$ AOI AR coatings [1, 3]. These results motivate us to look for alternative 2w_1w AR coating designs for which both 1w and 2w E-field intensities remain low without pronounced peaks within the coating. Such coating designs should maintain high 1w LIDTs, such as those of Fig. 1, but also provide 2w LIDTs exceeding those of Fig. 1, perhaps at values $>10\mathrm{J}/{\mathrm{cm}}^2$.

3. LIDTs of 1w $\mathsf{45}°$ and $\mathsf{32}°$ AOI Spol and Ppol AR Coatings at Their Use Conditions

Figure 3 displays 1w LIDTs at the use AOIs and polarizations of 1w AR coatings for $45°$ and $32°$ AOIs and Spol and Ppol. The difference between the $45°$ AOI Spol and Ppol AR coating designs is that the former optimizes the Spol AR without regard for the Ppol AR, whereas the latter does just the opposite. On the other hand, the 1w $32°$ AOI Spol and Ppol AR coating design is optimal for both Spol and Ppol AR. We would normally expect these coatings to exhibit higher LIDTs than their $0°$ AOI counterparts due to the fact that a given fluence in the cross section of the laser beam projects over a larger coated surface area as the AOI increases, with a corresponding decrease by a factor of $\mathrm{cos(AOI)}$ in the fluence at the coated surface. Indeed, all but one of the LIDTs of Fig. 3 might be explained simply by this “projected fluence” assumption, with the exception being the 1w $45°$ AOI Ppol AR coating for which the LIDT, at $\sim 14\mathrm{J}/{\mathrm{cm}}^2$, is anomalously low. Other than this exception, the LIDTs of Fig. 3 (which range between 34 and $47\mathrm{J}/{\mathrm{cm}}^2$) are larger than their $0°$ AOI counterparts (both those of Fig. 1 and those we reported in our recent paper [1], which range between 18 and $27\mathrm{J}/{\mathrm{cm}}^2$), and the $45°$ AOI Spol LIDT is higher than the $32°$ AOI LIDTs. These trends are consistent with higher projected laser fluence at a lower AOI. It is, however, this exception, the anomalously low 1w $45°$ AOI Ppol LIDT, that leads us to look beyond projected fluence alone in order to understand the LIDTs for these $45°$ and $32°$ AOI AR coatings.

We considered E-field behaviors to gain better insight into the LIDTs of Fig. 3, especially the low LIDT of the 1w $45°$ Ppol AR coating. For these nonnormal AOIs, we must consider both the Spol and the Ppol optical E-fields. Spol intensities are continuous at the media interfaces because Spol fields, being normal to the plane of incidence, are tangential to the interfaces and satisfy the boundary condition of continuity of E-fields tangential to an interface [4]. Ppol intensities are, however, discontinuous at the interfaces because Ppol fields, being in the plane of incidence, have components tangential as well as normal to the interfaces. The tangential Ppol fields, like Spol fields, are continuous across interfaces, but not the normal Ppol fields. They satisfy boundary conditions of discontinuity across media interfaces [4]. The Spol and Ppol intensities for the $45°$ and $32°$ AOI AR coatings of Fig. 3 bear this out, as shown in Fig. 4.

We first note from Fig. 4 that both the Spol and the Ppol intensities for these nonnormal AOI 1w coating designs are modest ($\sim 60\%$ of the incident intensity or lower) and without peaks throughout most of each coating. This is similar to the 1w E-field intensities of Fig. 2 and also to the 1w E-field intensities for our normal AOI 1w AR coating [3]. These modest intensities without peaks are favorable to the high LIDTs that characterize our normal AOI AR coatings [1, 3], and they add to the projection of laser intensity over a larger area as another factor contributing to the high LIDTs of the nonnormal AOI coatings of Fig. 3.

Next we address the differences between the Spol and the Ppol LIDTs of Fig. 3. The Ppol LIDTs are less than those for Spol. This correlates with the Ppol intensity jumps of Fig. 4, especially the largest such jumps which, for all three coatings, are at the coating/incident medium interfaces, where the largest field intensities also occur. The most dramatic case is for the 1w $45°$ AOI Ppol AR coating, with an in tensity jump of $\sim 40\%$ (from $\sim 100\%$ to $\sim 60\%$ of the incident intensity). This very large intensity jump correlates with this coating’s anomalously low LIDT (see Fig. 3). For the 1w $32°$ AOI Spol and Ppol AR coating, a smaller yet significant intensity jump of $\sim 20\%$ occurs (from $\sim 100\%$ to $\sim 80\%$ of the incident intensity), and the LIDT is less for Ppol than for Spol by a small amount (34 versus $37\mathrm{J}/{\mathrm{cm}}^2$).

A way to think about the Ppol intensity jumps is that, as light propagates from one medium to the next, the Ppol field transfers energy to the next medium at the molecular level by interacting with electrons along directions both tangential and normal to the interface, with the latter interactions increasing as the normal Ppol component increases with AOI. This combination of tangential and normal Ppol field interactions can enhance the transfer of optical energy into the next medium as compared to Spol field interactions, which are solely tangential. This, in turn, can make Ppol fields more likely than Spol fields to cause laser damage. Ppol fields may not always be more effective than Spol fields in causing laser damage, but we believe they are at larger nonnormal AOIs for which larger Ppol intensity jumps occur.

Ppol intensity jumps depend on AOI, index of refraction mismatch between media, and coating design. AOI and indices of refraction of substrates and coating layers are often fixed by performance and material requirements. So coating design plays a key role in mitigating negative impact of Ppol intensity jumps on LIDTs. Ppol intensities vary according to the forward-propagating and backpropagating Ppol components as specified by the coating design. The best nonnormal AOI AR coating designs for high LIDTs will be those that not only provide moderate field intensities without peaks within the coating but also minimize Ppol intensity jumps, especially at coating/incident medium interfaces and for large AOIs.

4. Side 1 and Side 2 AR Coatings for a 2w Diagnostic Beam Splitter

We turn now to Side 1 and Side 2 AR coatings of a 2w diagnostic beam splitter designed for a 2w/1w ($527\mathrm{nm}/1054\mathrm{nm}$) dual wavelength high-intensity laser beam at $22.5°$ AOI. Our coating designs for this beam splitter were to meet AR performances at the $22.5°$ AOI as follows: for Side 1, 0.5%–1.0% reflectivity at 2w and $\sim 0.15\%$ or less reflectivity at 1w; for Side 2, $\sim 0.15\%$ or less reflectivity at 2w and 0.5%–1.5% reflectivity at 1w. A $22.5°$ AOI is actually in the category of near-normal incidence because its “projected fluence” factor, $\cos (22.5°)\sim 0.924=92.4\%$, is very large. In other words, a laser beam at $22.5°$ AOI projects $\sim 92.4\%$ of the full fluence in its beam cross section onto the optic surface, and this is substantially the same as the full fluence the optic surface would receive at normal incidence. So, we expect for these $22.5°$ AOI AR coatings that projected fluence has considerably less of an influence on LIDT than we did for the $45°$ and $32°$ AOI AR coatings of the previous section, for which there are much lower projected fluences, corresponding to factors $\cos (45°)\sim 0.707$ and $\cos (32°)\sim 0.848$.

Figure 5 displays the 2w and 1w, Spol and Ppol LIDTs of the Side 1 and Side 2 AR coatings that we deposited on this beam splitter. The 2w Spol and Ppol LIDTs are all very close in value at levels $>10\mathrm{J}/{\mathrm{cm}}^2$ not only in the beam cross section but also as projected on the coating itself at the $22.5°$ AOI. Such 2w LIDTs in excess of $10\mathrm{J}/{\mathrm{cm}}^2$ are adequate to protect against laser damage in the Z-Backlighter laser beam trains [1], in contrast to those of Fig. 1 for the 2w_1w AR debris shield coatings at normal incidence which, at $<10\mathrm{J}/{\mathrm{cm}}^2$, are only marginally adequate.

We again look to E-field intensities within the coatings in order to assess these LIDT results. For the Side 1 coating at 2w, both the Spol and the Ppol intensities, shown in Fig. 6, behave somewhat like the 2w E-field intensities of Fig. 2 for the 2w_1w AR debris shield coating, with two peaks, but overall are more moderate by $\sim 10\%$ (peaks at $\sim 80\%$ versus $\sim 90\%$). Figure 6 also shows that the Side 2 coating’s 2w E-field intensities are generally lower than those of the Side 1 coating and much lower than those of the 2w_1w AR coating (Fig. 2), except at the interface of the coating and incident medium, where they are $\sim 10\%$ higher. We attribute the higher 2w LIDTs of the Side 1 and Side 2 coatings ($>10\mathrm{J}/{\mathrm{cm}}^2$, even as projected onto the coating surface; Fig. 5) compared to those of the 2w_1w AR coating at $0°$ AOI ($<10\mathrm{J}/{\mathrm{cm}}^2$; Fig. 1) to the generally lower E-field intensities of the former two coatings compared to those of the latter coating. From Fig. 5, we note that the differences between the 2w Spol and the Ppol LIDTs of the Side 1 and Side 2 coatings are very slight. This is consistent with the E-fields of Fig. 6, which exhibit small Spol/Ppol differences and slight Ppol intensity jumps at the media interfaces for each coating. We expect this for the $22.5°$ AOI because of its large “projected fluence” factor of $\sim 0.924$ (see above), which is the same factor that determines the Ppol component tangential to a media interface [4]. Thus, at $22.5°$ AOI most of the Ppol field is tangential to the media interface and behaves like the Spol field, whereas the component of the Ppol field normal to the media interface, which is the component responsible for Ppol intensity jumps, is very small.

Overall, the 2w E-field intensities of each beam splitter AR coating behave both in ways that favor a high LIDT and in ways that do not. For the Side 1 coating, the two intensity peaks, though moderate (at $\sim 80\%$ of the incident intensity), do not favor a high LIDT, whereas the moderate intensity (80%–90% of the incident intensity) at the incident medium interface does. For the Side 2 coating, the very low intensities within the coating favor a high LIDT, whereas the larger intensity (90%–100% of the incident intensity) at the incident medium interface does not. These E-field intensity behaviors weigh one against the other in subtle ways to account for the slight differences between the 2w LIDTs of Fig. 5, and for the LIDTs being slightly larger for Ppol than for Spol. In any case, there is room for improvement in these AR coating designs to enhance 2w E-field behaviors that do favor higher LIDTs and suppress those that do not.

The beam splitter’s 1w Spol and Ppol LIDTs of Fig. 5 are all $>38\mathrm{J}/{\mathrm{cm}}^2$ and similar to those of the 1w $45°$ and $32°$ AOI coatings of Fig. 3 (except for the 1w $45°$ AOI Ppol case) in that they are larger than their $0°$ AOI counterparts, both those of Fig. 1 and those we reported previously [1]. But, as we mentioned above, these LIDTs at $22.5°$ AOI are due more to the coatings’ 1w E-field intensity behaviors and less to the projection of the laser beam over a larger area. Figure 7 shows these 1w E-field intensity behaviors, which are indeed at moderate levels ($<60\%$ of the incident intensity) for both Spol and Ppol throughout most of each coating. The 1w Ppol and Spol LIDTs are the same for the Side 1 coating, whereas the former exceeds the latter for the Side 2 coating. This LIDT behavior does not particularly correlate with the Side 1 and Side 2 E-field intensities of Fig. 7, except that they both exhibit similar, very moderate Spol and Ppol levels and small Ppol intensity jumps at media interfaces. So, the LIDT behavior must reflect subtle balances of these similar intensity features. This differs from the 1w LIDTs of the AR coatings of Fig. 3 for the larger $45°$ and $32°$ AOIs, for which the Ppol intensity jumps at the media interfaces are large and correlate with lower Ppol LIDTs compared to Spol LIDTs. Finally, we note that the 1w Ppol and Spol LIDTs for the Side 2 coating exceed those of the Side 1 coating. This could correlate with the lower E-field intensities for the Side 2 coating at the incident medium interface ($\sim 80\%$ to $\sim 90\%$ of the incident intensity) versus higher corresponding intensities for the Side 1 coating ($\sim 90\%$ to $\sim 100\%$ of the incident intensity).

5. Conclusions

We have presented design and LIDT comparisons of hafnia/silica AR coatings for dual 2w/1w and 1w wavelengths and AOIs ranging from $0°$ to $45°$. Starting with the $0°$ AOI 2w_1w AR debris shield coating, we reported LIDTs at 2w and 1w of the same debris shield coatings from three runs arbitrarily selected over a three year period and found the 1w LIDTs were high, at $\sim 20\mathrm{J}/{\mathrm{cm}}^2$ or higher, while the 2w LIDTs, at $<10\mathrm{J}/{\mathrm{cm}}^2$, were lower than we prefer. We analyzed these LIDTs in terms of the calculated 2w and 1w optical E-field intensities within the coating during the antireflection process, showing that higher intensities and two intensity peaks for 2w, but not for 1w, correlate with the lower 2w LIDTs and higher 1w LIDTs for this coating. We then turned to 1w AR coatings for nonnormal AOIs of $45°$ and $32°$, addressing Spol and Ppol differences and finding higher LIDTs for Spol ($>35\mathrm{J}/{\mathrm{cm}}^2$) than for Ppol ($>30\mathrm{J}/{\mathrm{cm}}^2$ for $32°$ AOI and $\sim 15\mathrm{J}/{\mathrm{cm}}^2$ for $45°$ AOI). Looking again at E-field intensities within the coatings, we found that the Ppol intensity discontinuities, as governed by E-field boundary conditions at media interfaces for the Ppol E-field component normal to the interface, are particularly large at the coating/ incident medium interface for these relatively large AOIs. We showed that the lower Ppol LIDTs correlate with these large Ppol intensity jumps, pointing out that this effect increases as the AOI for AR performance increases. And we noted that the LIDTs do not exhibit this effect for Spol E-fields because, being tangential to media interfaces, they exhibit boundary conditions of continuity between media. Finally, we featured Side 1 and Side 2 AR coatings of a 2w diagnostic beam splitter for use at $22.5°$ AOI, with coating design goals of nominal 2w AR and very low 1w AR for Side 1 and vice versa for Side 2. The 2w Spol and Ppol LIDTs in this case are $>10\mathrm{J}/{\mathrm{cm}}^2$, whereas their 1w counterparts are $>35\mathrm{J}/{\mathrm{cm}}^2$, which we found to be consistent with the moderate behavior of the 1w and 2w Spol and Ppol E-fields within each coating.

An important result of this study is our identification of correlations between LIDTs and E-field intensity behaviors for AR coatings, including Spol and Ppol behaviors at nonnormal AOIs. In particular, we have shown that enhanced laser damage (lower LIDT) of AR coatings is associated with Ppol intensity jumps, especially at coating/incident medium boundaries and for larger AOIs. And we have also shown that E-field intensity peaks within AR coatings do work against achievement of higher LIDTs for such coatings. These results add to studies of the relationship between E-field intensity behaviors and LIDTs for HR coatings [1, 5]. They also provide new insight for interpreting and understanding well-known mechanisms in laser damage associated with defects, microstructural imperfections, and contaminates including nanoscale particulates at or near interfaces between substrates and coatings, between coating layers, and between coatings and incident media [5, 6, 7]. With regard to this latter context, in the E-field behaviors we report here (Figs. 2, 4, 6, 7) there are some intensity maxima at interfaces, especially at the interfaces of the coatings and in cident media; and the Ppol intensity jumps occur, according to E-field boundary conditions, just at interfaces and, for our nonnormal AOI AR coatings, are largest at the coating/incident medium interfaces. Such intensity maxima and Ppol intensity discontinuities at media interfaces create favorable conditions for initiation of laser damage by defects and imperfections at or near these interfaces. In general, AR coating designs for enhancing LIDTs should be ones for which E-field intensities are moderate without peaks within the coating, and for which Ppol intensity jumps, especially at the coating/incident medium interface and for larger AOIs, are as small as possible. We emphasize that the E-field/LIDT trends we have presented here, while they hold promise for understanding and guiding the development of high LIDT AR coating designs, are not conclusive in this regard. We plan in future work to explore AR coating designs that incorporate the E-field behav iors we have found here to be favorable to high LIDTs, and to do this in ways that are practical and balanced against other design constraints, and in this way to see if such a coating design approach does indeed lead to improved LIDTs.

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

 

Fig. 1 LIDTs at 2w ($532\mathrm{nm}$) and 1w ($1064\mathrm{nm}$) and $0°$ AOI of three debris shield 2w_1w AR coatings arbitrarily selected from coating runs between 2005 and 2008.

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Fig. 2 Calculated E-field intensities at 2w ($527\mathrm{nm}$) and 1w ($1054\mathrm{nm}$) for the 2w_1w AR debris shield coating at $0°$ AOI. Shaded areas denote substrate (left) and incident medium (right). Vertical dashed lines mark the boundaries of the coating layers.

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Fig. 3 LIDTs at 1w ($1064\mathrm{nm}$) and use AOIs and polarizations of 1w AR coatings on BK7 and fused silica for $45°$ and $32°$ AOIs and Spol and Ppol as indicated.

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Fig. 4 Calculated Spol and Ppol E-field intensities at 1w ($1054\mathrm{nm}$) for the three nonnormal AOI AR coatings of Fig. 3 at their use AOIs, as indicated. Left and right shaded areas and dashed vertical lines identify optical media, as described in Fig. 2.

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Fig. 5 LIDTs at 2w ($532\mathrm{nm}$) and 1w ($1064\mathrm{nm}$) of the 2w diagnostic beam splitter Side 1 and Side 2 AR coatings at their $22.5°$ use AOI for Spol and Ppol, as indicated.

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Fig. 6 Calculated Spol and Ppol E-field intensities at 2w ($527\mathrm{nm}$) within the 2w diagnostic beam splitter Side 1 and Side 2 AR coatings at their design AOI of $22.5°$. Left and right shaded areas and dashed vertical lines identify optical media, as described in Fig. 2.

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Fig. 7 Calculated Spol and Ppol E-field intensities at 1w ($1054\mathrm{nm}$) within the 2w diagnostic beam splitter Side 1 and Side 2 AR coatings at their design AOI of $22.5°$. Left and right shaded areas and dashed vertical lines identify optical media, as described in Fig. 2.

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