2.1.

Pulsed-Laser Deposition

The deposition of the films investigated in this study was performed with the PLD setup depicted schematically in Fig. 1 and described in more details in Refs. 21, 35, and 40. The targets were fabricated by sintering powders of the materials of interest, which ensures a stoichiometric proportion of the elements, and had a final mass of $\sim 85\%$ of the expected mass for the pure crystalline material of the same volume. Target ablation was achieved using a KrF excimer laser operating at 248 nm, with a pulse duration of $\sim 30$ ns and a repetition rate of 100 Hz, yielding growth rates ranging from 10 (${\mathrm{Lu}}_2{\mathrm{O}}_3$) to $20\mu \mathrm{m}/\mathrm{h}$ (${\mathrm{Sc}}_2{\mathrm{O}}_3$). The motion of the target was configured to obtain an effective bi-directional ablation, which was proven to significantly reduce the number of scattering points in the as-grown films.⁴⁰ A Metricon (Model 2010) prism coupler equipped with a #200-P-2 prism, and a HeNe laser source operating at 633 nm was used to determine the refractive index and thickness of the films investigated.

Fig. 1

Pulsed-laser deposition setup.

To achieve crystalline-film growth, during deposition the rear surface of the substrate was heated by a ${\mathrm{CO}}_2$ laser operating at $10.6\mu \mathrm{m}$. The original Gaussian intensity distribution of the beam was transformed by a ZnSe tetraprism⁴¹ into a nearly-uniform $10\times 10{\mathrm{mm}}^2$ profile, which fits the substrate’s dimensions. The substrate temperature used for the deposition of the samples ranged from 950°C to 1100°C, depending on the material.

The background pressure of the vacuum chamber could be tuned by manually adjusting an oxygen gas in-flow. All sesquioxide films analyzed in this report were deposited at a background pressure of $20(\pm 2) \hspace{0.17em}\mu \mathrm{bar}$.

The deposition parameters of the investigated samples are listed in Table 1. Optimization of the parameters had been conducted previously and the samples for LIDT measurements were selected based on their crystalline properties and surface homogeneity (in terms of the number of scattering points visible under a dark field microscope).

Table 1

Deposition parameters and lattice properties of the sesquioxide films grown on sapphire (Al2O3) or yttrium-aluminum-garnet (YAG) substrates. The measurement of the XRD peaks and lattice constants are detailed in Sec. 3.2. The precision on the position of the (222) XRD peak is limited by the angular resolution of the incident beam, ±0.01  deg. The film lattice constant is calculated for a Cu Kα wavelength of 1.5418  Å and the resolution error is ±0.004  Å.

2.2.

Magnetron Sputtering

MS samples were produced with a Helios coater developed by Bühler Leybold optics.⁴² The layers were deposited by the plasma-assisted reactive magnetron sputtering (PARMS) process. Inside the Helios coater, samples are placed on a rotating plate. At first, the sample passes under a mid-frequency dual magnetron, where a thin substoichiometric layer is deposited from a metallic target. Then the sample passes under a radio frequency plasma source where the thin layer is oxidized. The PARMS process, therefore, produces high-density oxide coatings.⁴³ The speed of rotation and power of magnetron is adjusted to deposit $\sim 0.1$ nm of thin-film in each rotation. Each individual thin-film-layer thickness is controlled by in situ optical monitoring. Optical measurement is performed at each passing of the substrate under the measurement window. This allows the single-layer thickness to be controlled to better than 1 nm accuracy. Both monochromatic and broadband monitoring can be used in this setup.

Typical pressure inside the vacuum chamber during deposition is 50 nbar. An argon and oxygen mix is used as a process gas for magnetron sputtering, while oxygen is used as the source gas in the plasma for thin-film oxidation. Both high- and low-index materials can be coated within one production cycle.

Previous studies have been conducted on films produced by this machine and their LIDT values compared to a large set of samples produced by different methods and manufacturers, exhibiting LIDT in accordance with the state-of-the-art.^3,30,44

3.1.

Samples to Be Tested

The tested samples were monolayers of ${\mathrm{Y}}_2{\mathrm{O}}_3$, ${\mathrm{Sc}}_2{\mathrm{O}}_3$, ${\mathrm{Lu}}_2{\mathrm{O}}_3$, ${\mathrm{HfO}}_2$, ${\mathrm{Nb}}_2{\mathrm{O}}_5$, and ${\mathrm{SiO}}_2$ (See Table 2). The crystalline sesquioxide materials (${\mathrm{Y}}_2{\mathrm{O}}_3$, ${\mathrm{Sc}}_2{\mathrm{O}}_3$, and ${\mathrm{Lu}}_2{\mathrm{O}}_3$) were deposited on a $<0001>$-oriented sapphire substrate. In the case of ${\mathrm{Lu}}_2{\mathrm{O}}_3$ material, one sample was deposited on a $<100>$-oriented yttrium aluminum garnet (YAG) substrate. The amorphous metal oxides (${\mathrm{HfO}}_2$, ${\mathrm{Nb}}_2{\mathrm{O}}_5$, and ${\mathrm{SiO}}_2$) were deposited on fused silica (FS) using the magnetron sputtering process.

Table 2

Tested thin-film materials and their parameters, n means refractive index at 1030 nm wavelength. The Sc2O3, Y2O2, and Lu2O3 sesquioxides were PLD-grown in the Optoelectronics Research Centre (Southampton, United Kingdom). The HfO2, Nb2O5, and SiO2 were MS in the Institut Fresnel (Marseille, France).

3.2.

X-Ray Diffraction

Epitaxial growth of the ${\mathrm{Y}}_2{\mathrm{O}}_3$, ${\mathrm{Lu}}_2{\mathrm{O}}_3$, and ${\mathrm{Sc}}_2{\mathrm{O}}_3$ films on the $<0001>$-cut sapphire was expected to be predominantly in the $<111>$-direction, since the lattice mismatch in this orientation is the smallest with substrate orientation, i.e., 4.9%, 2.9%, and 2.5%, respectively. Similarly, ${\mathrm{Lu}}_2{\mathrm{O}}_3$ $<111>$ has a quasi-perfect lattice match with $<100>$-cut YAG, that facilitates the growth of that orientation.

The out-of-plane x-ray diffraction (XRD) patterns from the samples were recorded by a Rigaku Smartlab, equipped with a Ge(220) 2-bounce monochromator. Two different sets of parameters were selected for the scans. A wide scan with a 2$\mathrm{\Theta }$ value from 20 deg to 80 deg and a step size of 0.02 deg was used to compare the proportion of the different orientations in the film. Since the films were expected to grow preferentially in the $<111>$-direction, the (222) diffraction peak was our main peak of interest. Secondly, an additional high-resolution scan with a step size 0.002 deg was made around this primary peak.

Figure 2 displays the XRD patterns of the films with each peak labeled with the corresponding orientation. The ${\mathrm{Y}}_2{\mathrm{O}}_3$ and ${\mathrm{Sc}}_2{\mathrm{O}}_3$ films grew primarily in the $<111>$-orientation, as demonstrated by the dominance of the (222) peak. The height ratio between the (222)-peak and the peaks corresponding to other orientations is greater than 3000. However, the ${\mathrm{Lu}}_2{\mathrm{O}}_3$ film grown on sapphire exhibits strong polycrystalline characteristics, with several orientations that have a height ratio of $<30$ with the (222) peak. On the contrary, the growth of $<111>$-oriented ${\mathrm{Lu}}_2{\mathrm{O}}_3$ is clearly favored on the YAG substrate: the XRD figure shows also that the (222) peak is 1500 times stronger than the next visible orientation (332) and is nearly perfectly superimposed with the YAG (400) peak at a $2\mathrm{\Theta }$ angle of 29.8 deg. This aspect is highlighted in the high-resolution XRD pattern of that sample in Fig. 3b, with a clear double-peak lying at 29.8 deg.

Fig. 2

Wide XRD scans of the PLD samples: (a) ${\mathrm{Lu}}_2{\mathrm{O}}_3$ film on YAG substrate, (b) ${\mathrm{Lu}}_2{\mathrm{O}}_3$ film on sapphire substrate, (c) ${\mathrm{Y}}_2{\mathrm{O}}_3$ film on sapphire substrate, and (d) ${\mathrm{Sc}}_2{\mathrm{O}}_3$ film on sapphire substrate.

Fig. 3

(222) XRD peaks of the ${\mathrm{Y}}_2{\mathrm{O}}_3$, ${\mathrm{Lu}}_2{\mathrm{O}}_3$, and ${\mathrm{Sc}}_2{\mathrm{O}}_3$ films grown on $<0001>$-sapphire. (b) (222) XRD peak of the ${\mathrm{Lu}}_2{\mathrm{O}}_3$ films grown on $<0001>$-sapphire and $<100>$-YAG.

Figure 3 compares the position of the (222) peak of the different films, which was used to calculate their lattice constants. The results, summarized in Table 1, show that the lattice constant of the as-grown films is close to the value reported for the corresponding bulk materials.^50,51

4.1.

Test Station

The test station used for LIDT tests is described in Ref. 52 detailing the description of test procedures and metrology methods. For the results reported here in this study, the pulses of nearly Gaussian spatial profile and $\sim 500$ fs pulse duration at $\sim 1030$ nm wavelength were incident at a repetition rate of 10 Hz. The maximum achievable pulse energy on a sample was 0.85 mJ. Characterization of the spatial and temporal profiles as well as an energy calibration were carried out before and after the LIDT test campaign. The LIDT tests were performed with samples placed at the focal plane of the lens with 30 cm focal length. The effective beam diameter, as defined by international standards,⁵³ was $84\mu \mathrm{m}$ in a plane perpendicular to the beam propagation. The LIDT tests were performed in an air environment at a room temperature of 25°C and humidity around 27%. A typical spatial beam profile at the focal plane, autocorrelation trace, and spectral distribution are shown in Fig. 4.

Fig. 4

Laser beam characterization: (a) beam profile in the focal plane, (b) autocorrelation trace, and (c) spectral profile of laser at 1 kHz repetition rate. Effective beam diameter is $84\mu \mathrm{m}$. Pulse duration full width at half maximum is 525 fs (${\mathrm{sech}}^2$).

4.2.

LIDT Procedure and Damage Detection

Each sample was irradiated at different spots with unique pulse energies that were changed with a $\sim 1\%$ energy increment in order to get statistical data. The procedure was repeated for different numbers of pulses—from single-shot up to 1000 shots at 10 Hz. The LIDT tests were done at a 45-deg incidence angle with P-polarization. The irradiated sites were analyzed ex situ using a Zeiss Axiotech differential interference contrast microscope with 20× objective magnification. Any observable material modification was evaluated as damage. The damage threshold was determined as the highest fluence that is lower than the lowest fluence causing damage in the experiment. The error bars correspond to the sum of $3\sigma$ variations of effective beam area near focal plane ($\sim 3 \%$), pulse energy ($\sim 0.7 \%$), and a half of pulse energy increment ($\sim 0.5 \%$).

4.3.

Intrinsic LIDT Fluence

Since the optical layers are the scene of interference effects, the distribution of the electric field inside the layer irradiated by the laser is not homogeneous. The electric field distribution is critical for understanding sub-ps LIDT results since the excitation of dielectrics is governed by electronic processes.² To compare LIDT results, accounting for the conditions influencing the electric field distribution, e.g., angle of incidence, polarization, layer thickness, or refractive index, it is necessary to rescale the LIDT results with the electric field intensity (EFI) maximum (${\mathrm{EFI}}_{\max }$) within the given layer. Therefore, the fluence values reported in this study correspond to $F_{\mathrm{int}}$ intrinsic fluence determined using $F_{\exp }$ external fluence and the ${\mathrm{EFI}}_{\max }$ and the relation is given by

Fig. 5

Distribution of the relative EFI inside a ${\mathrm{Sc}}_2{\mathrm{O}}_3$ layer of 1745 nm thickness (refractive index 1.97 at 1030 nm wavelength) deposited on a sapphire substrate (refractive index 1.78 at 1030 nm wavelength). Incident beam was P-polarized at an angle of incidence of $45\mathrm{deg}$. The EFI is normalized to the incident electric field amplitude in air.

5.1.

Deterministic 0 to 1 Transition

To evaluate the uniformity of the tested materials in terms of laser damage, the transition range of the damage probability, as indicated in Fig. 6(a), was calculated for each material and number of shots used, see Fig. 6(b). The 1-on-1 laser damage tests with ${\mathrm{Sc}}_2{\mathrm{O}}_3$, ${\mathrm{Y}}_2{\mathrm{O}}_3$, ${\mathrm{SiO}}_2$, ${\mathrm{HfO}}_2$, and ${\mathrm{Nb}}_2{\mathrm{O}}_5$ show deterministic results, i.e., narrow transition ranges of damage probability from 0 to 1. The transition range of damage probability was only a few percent in fluence, which suggests that the LIDT is limited by intrinsic material properties rather than by defects or impurities caused by the deposition process.⁵⁵ However, in the case of ${\mathrm{Lu}}_2{\mathrm{O}}_3$, we found wider transition ranges that could be a consequence of film imperfections, especially in the case of the film grown on sapphire that could be connected to the polycrystalline nature of this film, see Fig. 7. The larger ranges for the multiple-pulse tests may be due to the stochastic formation of deep and shallow traps in the bandgap, which facilitates electron excitation and material modification.²

Fig. 6

Laser damage results for materials used in GWS: (a) example of the damage probability results in the case of 100-on-1 tests with ${\mathrm{Lu}}_2{\mathrm{O}}_3$ deposited on sapphire; (b) transition ranges for the damage probability expressed in relative fluence, as indicated in Fig. 6(a); and (c) intrinsic LIDT fluence as a function of shot number. The ${\mathrm{Sc}}_2{\mathrm{O}}_3$, ${\mathrm{Lu}}_2{\mathrm{O}}_3$, and ${\mathrm{Y}}_2{\mathrm{O}}_3$ films were fabricated by pulsed-laser deposition, while ${\mathrm{HfO}}_2$, ${\mathrm{Nb}}_2{\mathrm{O}}_5$, and ${\mathrm{SiO}}_2$ by magnetron sputtering. All samples were tested with pulse duration of 500 fs at 1030 nm.

Fig. 7

Laser-induced damage morphologies for the tested crystalline sesquioxide films. Presented spots were irradiated at fluences slightly higher ($\sim 10\%$) than the determined damage thresholds.

5.2.

LIDT—Single Shot

The intrinsic LIDT fluence as a function of shot number for different thin-film materials is shown in Fig. 6(c). Among the tested materials, the ${\mathrm{SiO}}_2$ film shows the highest LIDT while ${\mathrm{Nb}}_2{\mathrm{O}}_5$ shows the lowest. In between, we find the other high-index materials, namely ${\mathrm{HfO}}_2$, ${\mathrm{Sc}}_2{\mathrm{O}}_3$, ${\mathrm{Y}}_2{\mathrm{O}}_3$, and ${\mathrm{Lu}}_2{\mathrm{O}}_3$, that are interesting for high-power applications.

${\mathrm{HfO}}_2$, a widely used high-index material in optical mirrors, showed a single-shot LIDT of $2.3\mathrm{J}/{\mathrm{cm}}^2$, which is higher than the values around $2.0\mathrm{J}/{\mathrm{cm}}^2$ published in the previous works^11,56,57 performed under the conditions close to ones used in this study (1030 nm, 500 fs). The higher LIDT of the tested ${\mathrm{HfO}}_2$ can be explained by the inclusion of ${\mathrm{SiO}}_2$ in the deposited film, which was estimated from the dispersion curve to be around 1% to 2%.⁴⁵ The effect of the ${\mathrm{SiO}}_2$ admixture on the ${\mathrm{HfO}}_2$ damage threshold is in agreement with previous work.³

5.3.

LIDT—Multiple Shots

For all materials, the LIDT is decreasing with an increasing number of shots, see Fig. 6(c). The results show a drop of $>20\%$ of the threshold within the first 100 shots. In contrast, at the transition from 100 to 1000 pulses, we observe only a small decrease. These tendencies were already observed in works performed at similar irradiation conditions with metal oxide coatings.^11,44,58 The gradual decrease is associated with the formation of laser-induced defects, leading to accessible energy levels within the bandgap. The deep or shallow traps can capture electrons from the conduction band even after a sub-threshold irradiation.⁵⁹

In the case of ${\mathrm{Sc}}_2{\mathrm{O}}_3$, the drop in LIDT is more noticeable than for the other sesquioxides and reaches that of ${\mathrm{HfO}}_2$. The larger 1-on-1 LIDT of ${\mathrm{Sc}}_2{\mathrm{O}}_3$ compared to ${\mathrm{HfO}}_2$ was also observed in work with ion-beam sputtered (IBS) films²⁵ which could be related to imperfect damage detection. Going to a higher number of pulses, the ${\mathrm{HfO}}_2$ deposited on FS, ${\mathrm{Y}}_2{\mathrm{O}}_3$ on ${\mathrm{Al}}_2{\mathrm{O}}_3$, ${\mathrm{Sc}}_2{\mathrm{O}}_3$ on ${\mathrm{Al}}_2{\mathrm{O}}_3$, and ${\mathrm{Lu}}_2{\mathrm{O}}_3$ on YAG, samples show very similar LIDT, indicating that any of these materials could be recommended for high-power applications, as far as LIDT is concerned. The 1-on-1 and 100-on-1 LIDT values of ${\mathrm{Y}}_2{\mathrm{O}}_3$, ${\mathrm{Sc}}_2{\mathrm{O}}_3$, and ${\mathrm{HfO}}_2$ materials were determined to be close to each other in the study,¹¹ devoted to electron-beam deposited (EBD) single-layers on FS substrates. The LIDT tests were performed at identical conditions to this work (500 fs, 1030 nm, and 10 Hz).

In the case of ${\mathrm{Lu}}_2{\mathrm{O}}_3$ deposition on an ${\mathrm{Al}}_2{\mathrm{O}}_3$ substrate, we observe significantly lower LIDT values, which could be explained by the polycrystalline and highly textured nature of the film (Fig. 7). The presence of multiple crystal orientations implies the existence of discontinuities in the lattice that may potentially modify the local bandgap of the material. These boundaries between domains of different orientations may initiate the damage.

5.4.

Bandgap

Since the laser-damage initiation in the sub-ps regime is driven by nonlinear ionization, the bandgap represents a critical parameter that correlates with the laser-damage resistance.⁵⁵ The behavior can be explained by taking into account the electron excitation processes playing a dominant role at the beginning of damage formation, i.e., multiphoton and impact ionization.² The intrinsic threshold fluences of tested materials are plotted as a function of their bandgap values in Fig. 8(a). We observe a linear tendency of increasing single-shot LIDT with a larger bandgap value that is in agreement with the studies performed at similar irradiation conditions in Refs. 30 and 60.

Fig. 8

Single-shot intrinsic LIDT fluence as a function of material bandgap (a) and refractive index (b). The bandgap was determined using the Tauc method.

The deviations from the linear tendency in Fig. 8(a) can be explained by the challenges faced to observe the material modifications induced by single-shot irradiation, see Fig. 7. Moreover, some of the sesquioxide crystal films exhibit imperfections that include defect sites. For example, the lower LIDT of ${\mathrm{Lu}}_2{\mathrm{O}}_3$ on sapphire could have been caused by its polycrystalline structure, enabling lower local bandgap values at domain boundaries for different lattice orientations. It should be highlighted that the Tauc method provides a measure of the bandgap at a macroscopic scale, while on the microscopy level there are likely to be numerous defects in the polycrystalline film. Even in the case of the near single-crystal ${\mathrm{Lu}}_2{\mathrm{O}}_3$ on YAG, the error bars on the bandgap would be larger than that determined from the Tauc measurement method used.

In this work, the LIDT (in ${\mathrm{J}/\mathrm{cm}}^2$) tendency on bandgap $E_g$ (in eV) can be well fitted by the following equation

The equation shows a higher slope, i.e., more dynamic dependence on the bandgap than the empirical description in Ref. 30 derived from results for numerous materials deposited by various methods. The differences from the published data could be explained by the limited number of tested samples or the selected method of bandgap determination.

The bandgap values of sesquioxides are very close to each other with a slightly larger bandgap in the case of ${\mathrm{Sc}}_2{\mathrm{O}}_3$, see Fig. 8, whose single-shot LIDT was determined as the highest within the high-index materials. The determined bandgap value for the ${\mathrm{Sc}}_2{\mathrm{O}}_3$ film tested (5.7 eV) is close to the bandgap of ion-beam sputtered ${\mathrm{Sc}}_2{\mathrm{O}}_3$ (5.6 eV).²⁵ However, larger bandgaps have been reported for electron-beam deposition (EBD) of ${\mathrm{Sc}}_2{\mathrm{O}}_3$ (6.5 eV) or ${\mathrm{Y}}_2{\mathrm{O}}_3$ (6.1 eV)¹¹ compared with the samples tested here grown by PLD, i.e., ${\mathrm{Sc}}_2{\mathrm{O}}_3$ (5.7 eV) or ${\mathrm{Y}}_2{\mathrm{O}}_3$ (5.4 eV). It should be noted that care should be taken when comparing bandgaps across publications since the bandgap is not exactly defined and can be determined using different methods.

5.5.

Refractive Index

For the design of multilayer components and GWS in our case, the critical parameter is the refractive index. Thus, in Fig. 8(b), we plot the intrinsic 1-on-1 LIDT of the tested materials as a function of refractive index. The results confirm the trend of increasing refractive index with decreasing intrinsic 1-on-1 LIDT, which was also observed in works^3,30 performed at similar irradiation conditions (500 fs, 1030 nm). Amorphous and single-crystal materials appear to follow the trend, while polycrystalline sesquioxides, such as ${\mathrm{Lu}}_2{\mathrm{O}}_3$ and ${\mathrm{Al}}_2{\mathrm{O}}_3$, seem to be susceptible to a lower LIDT. This could be due to local defects associated with domain boundary interfaces and the highly textured surface. Based on the comparison, ${\mathrm{Sc}}_2{\mathrm{O}}_3$ seems to be the most promising of the sesquioxides, showing both high damage resistance and a high refractive index value. Furthermore, the pulsed-laser deposited ${\mathrm{Sc}}_2{\mathrm{O}}_3$ (1.97) shows a higher refractive index @1030nm than the ion-beam sputtered one (1.93)²⁵ or the EBD ${\mathrm{Sc}}_2{\mathrm{O}}_3$ (1.82).¹¹ The refractive index of the PLD ${\mathrm{Y}}_2{\mathrm{O}}_3$ samples studied here is the same as that of EBD ${\mathrm{Y}}_2{\mathrm{O}}_3$ (1.90).¹¹

5.6.

Deposition Methods

Thanks to the LIDT studies^11,25 performed under identical conditions using the same experimental setup like this work (500 fs, 1030 nm), we can compare the LIDT values of sesquioxides deposited by different fabrication methods as shown in Fig. 9. For both ${\mathrm{Sc}}_2{\mathrm{O}}_3$ and ${\mathrm{Y}}_2{\mathrm{O}}_3$, the laser damage resistance of the PLD samples is comparable to that of EBD layers. The thresholds of both PLD and EBD samples indicate a similar fatigue effect—decrease between the 1-on-1 and 100-on-1 thresholds. In the case of 1-on-1 ${\mathrm{Sc}}_2{\mathrm{O}}_3$ thresholds, the differences between PLD, EBD, and IBS deposition methods can be explained by the difficulty of the detection of material changes. Furthermore, the higher 1-on-1 LIDT of ${\mathrm{Sc}}_2{\mathrm{O}}_3$ layer fabricated by IBS compared with that of the PLD grown layer could be explained by a 1.6% Si fraction of Sc+Si content in the IBS layer.²⁵

Fig. 9

Intrinsic LIDT fluence for (a) ${\mathrm{Sc}}_2{\mathrm{O}}_3$ and (b) ${\mathrm{Y}}_2{\mathrm{O}}_3$. Comparison of deposition methods. The results of EBD and IBS samples are taken from Refs. 11 and 25, respectively. All samples were tested under identical conditions using the same experimental setup with 500 fs pulse duration at 1030 nm wavelength.

5.7.

Sesquioxides in Multilayer Coatings

Lattice-matching constraints strongly limit the potential combinations of materials involving crystalline sesquioxides. Among the materials studied, ${\mathrm{Sc}}_2{\mathrm{O}}_3$ and $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$ have the largest refractive index contrast, i.e., 0.2 at the wavelength of 1030 nm. Despite a lattice mismatch of only 2.5%, the fundamentally different lattice structure of ${\mathrm{Sc}}_2{\mathrm{O}}_3$ and $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$ (space group Ia$\bar{3}$ and R$\overline{3}$c, respectively) can potentially make the fabrication of ${\mathrm{Sc}}_2{\mathrm{O}}_3$/$\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$ multilayer coatings more complex than pairs of cubic sesquioxides. However, for example, the lattice mismatch of a ${\mathrm{Sc}}_2{\mathrm{O}}_3/{\mathrm{Y}}_2{\mathrm{O}}_3$ combination is too large, at 7.6%, for robust thick-multilayer epitaxial growth. Another challenge derives from the lower index contrast between these PLD-grown sesquioxide materials. For instance, a quarter-wave stack of ${\mathrm{HfO}}_2/{\mathrm{SiO}}_2$ needs a minimum of 25 layers to reach 99.9% reflectivity at normal incidence for the wavelength of 1030 nm, while an equivalent ${\mathrm{Sc}}_2{\mathrm{O}}_3/\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$ mirror would require 73 layers. The resulting multilayer stack would have a full-thickness on the order of $20\mu \mathrm{m}$, which is within the scope of PLD crystalline growth.²² Furthermore, owing to the high deposition rates achievable (15 to $20\mu \mathrm{m}/\mathrm{h}$), around 10 times faster than magnetron sputtering, ${10}^{\prime }\mathrm{s}\text{-}\mu \mathrm{m}$ dimensions are entirely feasible within reasonable growth-run times.