Birefringent Glass‐Engraved Tilted Pillar Metasurfaces for High Power Laser Applications

Abstract Birefringent materials—which are highly needed in high power laser systems—may be limited in usage due to the laser‐induced damage threshold of traditional birefringent materials. This work reports here on all‐glass metasurfaces, fabricated by angled etching through sacrificial metal nanoparticle (NP) etching masks, for generation of effective birefringence in the formed layer. As a result, a fused silica metasurface, monolithic to the underlying substrate, is demonstrated to exhibit a birefringence of 6.57° under 375 nm illumination. Full‐wave analysis shows a good agreement with the measurement and presents potential paths forward to increasing the effective metasurface birefringence. This is the first demonstration, to the best of knowledge, of an etching technique to obtain the resulting tilted pillar‐like nanofeatures. The anisotropy of the metasurface nanoelements along the two window in‐plane major axes presents different effective paths for the two polarizations and thus generates birefringence in a nonbirefringent material. Additionally, the imparted anisotropy lends itself to manipulation of physical properties of the surface as well, with metasurface feature orientation suppressing water flow along one principal axis and giving rise to water flow steering capabilities.


Introduction
Birefringence, a phenomenon traditionally associated with noncubic crystalline structures [1][2][3] in which light propagates at a different velocity depending on the vibration plane, is the result of optical anisotropy of the index of refraction. Thus, the light propagation may differ between its two polarization components in the ordinary (o) and the extraordinary (e) directions, corresponding to the ordinary refractive index n o and extraordinary refractive index, n e . The difference of these two, |n o -n e |, defines the birefringence of the material. It is not surprising, then, that birefringence duration and beam diameter. Relative to sol-gel layers, potential sources for the decrease of the LIDT with GLAD birefringence is the usage of 31 silica layers, i.e., deposited silica versus bulk fused silica glass, and 31 material interfaces. Furthermore, nanobubbles and voids have been shown to contribute to the LIDT for multilayer dielectric coatings, [22] and a similar mechanism could be factoring in during GLAD processing as the substrate is rotated between the two deposition angles, in turn causing the resultant layers to exhibit a lower LIDT than fused silica.
An alternative approach to this additive fabrication technique, and one we will demonstrate here, is forming a metasurface (MS) by engraving fused silica, i.e., removing material by etching into the substrate. In doing so, the fabricated structure is monolithic to the underlying robust fused silica and there are no added materials or additional interfaces. The end-result of this processing is an anisotropic surface layer, incorporating optical and physical anisotropy (i.e., birefringence and surface energy properties) in a material that does not exhibit bulk anisotropy (i.e., no native birefringence). While there are lithographic techniques to accomplish glass-engraving by carefully etching each metasurface feature individually, [23][24][25] we will focus here on fabrication processes that are compatible with large aperture applications. Two substrate-engraving techniques based on directional dry etch that have demonstrated potential for scaling up to meter-length scale optics apertures while maintaining few tens of nanometers period scale are: (1) ion bombardment or the creation of in situ nucleation sites, [26][27][28] and (2) etching masks to guide the etching process. [29][30][31][32] The result of dry etching in normal incidence are metasurfaces with randomly distributed nanofeatures, yet with a well-controlled and predictive distribution of properties that determine the effective optical properties of the layer from mixing formula rules of the constituents (i.e., glass features and air vacancies). In this work we modify technique (2), since being a mask-based method, it enables the formation and control over the nanoparticle (NP) mask based on prior knowledge, and anisotropy is obtained by tilting the incidence angle of the ion beam with respect to the mask. Moreover, this technique with normal incidence etching through NP masks has previously demonstrated a laser-induced damage onset for 351 nm laser exposure at roughly 30 J cm −2 . [29] Here, we present a method to form tilted nanopillar-based substrate-engraved metasurfaces leading to tailorable effective birefringence applications. These MS layers were generated by angled etching through a sacrificial self-generated NP ensemble functioning as an etching mask. We demonstrate a polarization retardation rotation angle of 6.57°using this method, validated with full-wave simulations predicting 6.69°, and further utilize the model to present potential pathways to further increase the effective birefringence. We will also show that the tilted nanopillars modify the physical surface energy properties to present strong anisotropy, such that water preferentially flows along one principal axis.

Optical Anisotropy: Birefringence
The concept of polarization retardation rotation is depicted in Figure 1a for an example case where a quarter-wave plate is converting the light from a linear polarization to a circular polarization. To accomplish this rotation by using a MS on a nonbirefringent material, the symmetry of the structure on the surface plane must be broken. In this work, fabrication of substrate-engraved birefringent MS was done by angled etching through metal NP etching masks generated atop the substrate, see Figure 1b. Fused silica was used as the underlying substrate material due to its abundant use in optical systems and relatively high laser-damage threshold. The etching masks were generated through solidstate diffusional dewetting (SSD dewetting) of Pt thin films, see Figure 1b step (i) for a depiction, where SSD dewetting is a process by which thin films will self-assemble into ensembles of particles during annealing. In dewetting, which has been investigated previously for gold on fused silica, [33] the ensemble particle center-to-center mean spacing (period) and mean particle size increase with increasing initial metal film thickness; conversely, for a sufficiently thin initial film the resultant particle ensemble has size and period on the nanoscale. In this work, platinum is used rather than gold due to the increased etching selectivity of Pt relative to Au, i.e., Pt enables deeper etching.
To fully exert control over the etching mask, seeded dewetting may be necessary. In conventional SSD dewetting the annealing temperature provides another lever of control, as this temperature permits tunability of the NP size and period. However, the NP size and period remain largely coupled together and cannot be controlled independently. Seeded dewetting can be used to orthogonalize the control over NP size and period, where the initial metal film thickness and dewetting temperature are selected to generate the desired NP size and period of the "seed" NP distribution, and subsequent iterations of thin film deposition/dewetting atop the initial NP ensemble "seed" induces material accumulation at those seeded locations-modifying the size but not the period. [34] These techniques have been demonstrated previously for a fused silica/gold system, and the fabrication process used here to generate platinum etching masks is given in greater detail in Supporting Information.
Following assembly of the Pt etching mask, reactive ion beam etching (RIBE) was used to transfer the mask pattern to the substrate, where RIBE is a process by which etching is obtained by directing a beam of reactive ions toward the substrate, see Figure 1b, step (ii). Benefits of using RIBE include the ease of which angled etching can be completed by rotation of the beam and/or sample, in addition to removing the complications associated with etching thick glass substrates that may plague reactive ion etching, RIE (which requires an electric field to run through the substrate being etched, here insulating glass). For this work, etching was done with the ion beam making an angle of 48°with respect to the substrate normal. Details pertaining to the etch recipe used are given in Supporting Information. Termination of the etch prior to mask material removal results in slanted cylinders, etching to mask depletion results in slanted cones, and etch termination between those two conditions leads to controllable truncated cones. A cross-section depiction of a MS composed of slanted cylinders is depicted in Figure 1b following step (ii). After this etching step, residual Pt masking material was removed by soaking the optic in an aqua regia bath; consequently, the fabricated MS consists of a glass-only structure. If a different substrate material is chosen to be compatible in the infrared (IR) and the MS feature sizes are scaled appropriately, these structures may introduce enhanced IR absorption as was documented elsewhere. [35] Extending the etched cross-section view depicted in Figure 1b to three-dimensional space, see Figure 1c, gives a more insightful visualization of these birefringent surfaces. The structure portrayed in Figure 1c is an idealized case, i.e., an array of identical and periodically repeating MS features. An off-axis viewing angle is shown in Figure 1c on the left, where two orthogonal planes are identified: plane (i) is in the family of planes that includes the feature tilt, referring to Figure 1b for a simplistic view, and plane (ii) represents the family of planes perpendicular to plane (i) in which the features tilt out of the page. Looking more closely at these orthogonal cross-sections, see Figure 1 planes (i) and (ii), it is apparent that light polarized along the two principal axes of the structure (x-z and y-z directions) observes a different metasurface structure and optical effective index, producing effective birefringence. This technology can be married to past antireflective work with vertical etching of similar masks, where it was observed that, similar to uniform films, the observed reflectance is harmonically dependent on the MS layer depth. [36,37] Reflectance is expected to be polarization dependent due to index birefringence, and can be found as a function of incident wavelength in Figure S3 (Supporting Information). Through the described process of dewetting and RIBE, a MS was fabricated with a layer thickness L = 450 ± 20 nm and a mask NP center-to-center spacing (period) of 101 ± 25 nm; the etching mask and resultant structure are displayed as electron micrographs in Figure 2. The etched structure, see Figure 2b, presents viewing plane (i) of the anisotropic structure depicted in Figure 1c. Moreover, every step in this fabrication process is scalable, which is essential for applications requiring large aperture optics. The extinction spectrum of this structure is given in Figure S4 (Supporting Information). Reduction of the etching mask NP spacing, as demonstrated in Figure S1 (Supporting Information), is expected to reduce scattering at the shorter wavelengths.
The MS displayed in Figure 2 was analyzed using an experimental measurement setup shown in Figure 3a consisting of a 375 nm CW laser, two Glan-laser calcite linear polarizers, and a pickoff window. To quantify birefringence, Jones Matrix analysis is used, where, for orthogonal linear polarizers indicated by LP 1 and LP 2 , we have with I 0 being the incident beam intensity, I 1 is the transmitted intensity, ΔΦ is the phase retardation between the fast and slow axis, and is the angle with respect to the horizontal for the birefringent sample's fast axis. During measurements, the birefringent MS is rotated about the optical axis as indicated in the 3D view shown in Figure 3a. It is seen from Equation (1) that, for orthogonally positioned linear polarizers, rotation of the birefringent sample through angle about the optical axis will result in a sinusoidal signal that can be fit to extract the phase retardation ΔΦ. Derivation of Equation (1) is contained in Supporting Information, and this measurement technique was used on commercially available quarter-wave and half-wave plates for validation. Results from birefringence measurements for the MS, shown in Figure 2b, as it is rotated 90°about the optical axis are shown as the black data in Figure 3b. As expected, a sinusoidal signal was recorded; the fitting of this data according to Equation (1) yielded a measured phase retardation ΔΦ = 6.57 ± 0.05°. A reference fused silica slab (planar fused silica, i.e., no etched metasurface) was also measured, and the resultant signal is depicted in Figure 3b by the blue data. No measurable birefringence outside the noise level was observed. Using Equation (1), the expected signal for the cases of ΔΦ = 2.5°and 5°are shown as the red and magenta dashed lines, respectively, to demonstrate the trend with increasing phase retardation. The presence of a birefringent response by the etched structure demonstrates that glass-engraved metasurfaces can be utilized for applications requiring polarization rotation. Furthermore, as structures fabricated through this etching mask approach have been previously demonstrated to exhibit a high laser damage threshold, [29] this opens exciting possibilities of polarization rotation for high energy and high power laser applications. Combining polarized beam splitters and a waveplate provides a commonly used nonabsorbing attenuation element that is key for laser systems. Even more enticing applications may follow when the technology demonstrated here merges with the previously demonstrated ability to pattern the etching mask spatially, [32], i.e., birefringent metaoptics with polarization rotation patterning.
To assist in mapping out the broad MS geometry parameter space, full-wave simulations were performed; these simulations match the measured results. A finite difference time domain (FDTD) simulation of Maxwell Equations (Lumerical FDTD) modeling study was carried out to explain the performance dependence on the structure parameters; the MS feature geometry used in the simulations is presented in Figure 4a while viewing plane (ii) as described in Figure 1c. The features are allowed to vary from cylinders (ΔR/R base = 0) to cones (ΔR/R base = 1), with a height L. The depiction in Figure 4a displays the simulation unit cell, with the expression R base /(Λ/2) representing a one-dimensional view of the area coverage; the true area coverage, or fill factor, will be given by R base /(Λ/2) 2 . As Figure 4a is showing plane (ii), it is important to recall that in in the orthogonal direction of plane (i) these features are tilted with respect to the surface normal. This geometry is then fed in to a FDTD model, see Figure 4b, to predict the birefringence for a fixed feature tilt of 50°with respect to the surface normal, a period Λ = 0.25 , and layer thickness L = 0.5 , where is the wavelength at which operation is intended (here, 375 nm). It is seen, then, that for a given R base /(Λ/2) the birefringence increases as the features become more cylindrical, and for a given feature shape ΔR/R base the birefringence increases with increasing feature area coverage. Or phrased differently, because R base is determined by the etching mask, birefringence increases with increasing etching mask area coverage. For the MS with cylindrical features shown in Figure 2, L = 450 nm and R base /(Λ/2) = 0.53; from these values the simulated phase retardation is 6.69°, which is in good agreement with the measured value of 6.57°.  While this demonstration is a first-of-its-kind, further developing the structure to produce a higher birefringence is key to enabling many applications. Figure 4b gives a roadmap to increasing the birefringence by increasing the mask fill-factor while maintaining a cylindrical feature geometry. As Figure 4 reveals that cylindrical features perform better at a tilting angle of 50°, FDTD calculations were carried out for cylindrical features with a constant MS feature height of 0.5 and R base /(Λ/2) = 0.8, see Figure 5a. The value R base /(Λ/2) = 0.8 was chosen for the practical reason that the corresponding masking fill factor, R base /(Λ/2) [2] = 0.64, has already been demonstrated, refer to Supporting Information here. For the prescribed cylindrical features with layer thickness L = 0.5 shown in Figure 5a, as the period decreases from 0.5 (blue triangles) to 0.1 (black squares), the phase retardation increases from ≈2.5°to ≈12.5°at a tilting angle of 50°from the surface normal. While the cases of Λ = 0.5 and Λ = 0.25 continue to increase with increasing tilt angle, at this time we do not consider cases when > 60°due to the practical implication that, because of undesirable mask material removal during etching, steeper etching angles make it progressively more challenging to increase the layer thickness in the vertical direction.
To investigate the impact of increasing the MS layer thickness, cylindrical features with R base /(Λ/2) = 0.8 and Λ = 0.1 were used in simulations with L = 0.5 (red circles) and L = (black squares) in Figure 5b. It is seen that, as the MS layer thickness increases by a factor of 2, for all tilt angles simulated the phase retardation increases by roughly a factor of two. This finding is intuitive, as each discrete layer should contribute ≈equally to the retardation.
The results from Figure 5 outline the roadmap from a birefringence of 6.6°(as reported here for a MS with period Λ = 0.25 , L = 1.2 , and R base /(Λ/2) = 0.53) to a quarter-wave by decreasing the period and increasing the MS layer thickness for a targeted 1/8 of a wave per optic surface. Notably, as seen in Figure 5b, a period of 0.1 and layer thickness of 2 will yield polarization rotation ΔΦ = 50°. This indicates that an optic processed on both sides will surpass what is necessary to qualify as a quarter-wave plate. If, however, it is technologically challenging to obtain a period of 0.1 , Figure 5b reveals that MS layer thickness can be increased beyond 2 as a means of compensation. This implies the capability of fabrication of a quarter-wave plate that is monolithic to the underlying substrate and compatible with high power and energy lasers.

Structure for Manipulation of Water/Surface Interaction
Anisotropy in the MS structure lends itself to other applications, such as manipulation of the interaction between the etched structure and water. Static water contact angle ( c ) measurements were taken using a 40 μL droplet of water on reference (unetched) fused silica and an anisotropic MS with planes (i) and (ii) facing the camera; images of these are shown in Figure 6a-c, respectively. For the reference fused silica, the contact angle was measured to be 41.2 ± 4.1°, and for the MS planes (i) and (ii) the static contact angles were 54.3 ± 6.1°and 77.6 ± 4.9°, respectively. This emphasizes a MS-introduced anisotropy to the surface of an isotropic material. The MS contact angles, while still considered hydrophilic, represent a shift toward a hydrophobic structure (conventionally accepted to be c > 90°). The fraction of substrate material in contact with the droplet can be determined from the Cassie-Baxter equation, cos MS C = FS is the contact angle of water on the MS, FS C is the contact angle on the underlying fused silica, and FS is the contact area fraction between the water and fused silica MS, projected to the surface plane. [38] From these measurements, the fractional contact area, FS , for the two principal directions was found to be 90% along plane (i), and 69% along plane (ii). Manipulation of the MS period, area coverage, and/or feature tilt are expected to impact the wettability of these structures without any chemical modification to the MS beyond the etching process itself; however, this is a subject for future work.
Another usage for the angled structures fabricated here is to control and redirect the flow of water by modifying the orientation of the MS, i.e., orienting such that plane (i) from Figure 1 is parallel or orthogonal to the direction of gravity. As indicated in the diagrams on the right side of Figure 7, the MS was placed horizontally and a 40 μL water droplet was placed on the surface. The sample was then tilted toward the vertical direction in increments of 5°at a rate ≈2.5°s −1 , held at each incremental steps for 5 s, and the angle tilt was recorded when the droplet had traveled a constant distance l. The MS was allowed to dry, and this procedure was repeated following rotation in the initial horizontal plane by angle MS , see Figure 7a. As the MS is rotated in-plane by 81°relative to the initial orientation MS = 0°(where MS = 0°corresponds to viewing plane (ii) as shown in Figure 1), the tilting angle necessary for the water droplet to travel a constant length increases from tilt = 40°at MS = 0°to tilt = 90°at MS = 81°. This indicates that the effective propagation of water flow is prohibited in one direction and flows freely in the other principal direction, and is also consistent with the fractional coverages determined earlier for plane (i) and plane (ii). A piece of reference fused silica was measured in this way and exhibited a necessary