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Abstract
Three-dimensional printing enables the fabrication of silica glass optics with complex structures. However, shrinkage remains a significant obstacle to high-precision 3D printing of glass optics. Here we 3D-printed Dammann gratings (DGs) with low lateral shrinkage (<4%) using a two-photon polymerization (2PP) technique. The process consists of two steps: patterning two-photon polymerizable glass slurry with a 515 nm femtosecond laser to form desired structures and debinding/sintering the structures into transparent and dense silica glass. The sintered structures exhibited distinct shrinkage rates in the lateral against longitudinal directions. As the aspect ratio of the structures increased, the lateral shrinkage decreased, while the longitudinal shrinkage increased. Specifically, the structure with an aspect ratio of approximately 60 achieved a minimal lateral shrinkage of 1.1%, the corresponding longitudinal shrinkage was 61.7%. The printed DGs with a surface roughness below 20 nm demonstrated good beam-shaping performance. The presented technique opens up possibilities for rapid prototyping of silica diffractive optical elements.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Silica glass is a highly valuable and extensively employed material in optical systems, owing to its remarkable properties such as exceptional optical transparency, as well as its robust thermal, chemical, and mechanical stability [1,2]. In recent years, the three-dimensional (3D) printing of silica glass has gained increasing interest due to its flexibility in creating components with complex structures that are challenging to manufacture using conventional technologies such as grinding, polishing, or wet chemical etching [3]. Direct printing by fused deposition modeling (FDM) enables the production of large-scale transparent components, but it is not suitable for producing high-resolution glass components [4,5]. Indirect 3D printing technologies such as stereolithography (SL) [6–8], direct ink writing (DIW) [9,10], and two-photon polymerization (2PP) [11–13] use glass precursors like nanocomposites or sol-gel mixtures to fabricate glass structures. The printed precursors can be transformed into transparent and dense glass through a subsequent heat treatment. These technologies have the capability to produce glass components with good optical performance and high resolution. Among these technologies, 2PP stands out with the highest processing resolution, allowing for the fabrication of micro-structures with micrometer-level precision, minimal peak-to-valley deviation, and low surface roughness [14]. However, these indirect 3D printing technologies using glass precursors suffer from the large shrinkage caused by the burnout of organics and consolidation of the remaining inorganic groups. This shrinkage is generally isotropic and falls within the range of approximately 20% to 60%, depending on the proportion of inorganic groups present in the precursors [14–16]. This inevitable shrinkage poses a significant challenge to the successful 3D printing of inorganic glass diffractive optical elements (DOEs) like Dammann gratings (DGs). DGs are important elements employed for generating structured illumination in the far field solely through a binary surface relief profile [17–19]. The shrinkage can lead to alterations in the relative positions of phase transition points within DGs, which significantly affects its beam splitting performance.
In this paper, we present a 2PP process for 3D printing of Dammann gratings with minimal lateral shrinkage. A glass slurry consisting of SiO2 nanoparticles and two-photon curable resins was developed for the 515 nm 2PP system. The structured glass slurry was subsequently converted into silica glass through a heat treatment process. The printed structures exhibited different shrinkage in the lateral and longitudinal directions. A minimal lateral shrinkage of 1.1% was achieved in structures with an aspect ratio of approximately 60, while the corresponding longitudinal shrinkage reached 61.7%. The low lateral shrinkage ensured the accuracy of the fabricated binary-phase structures, while the large longitudinal shrinkage contributed to a significantly smoother surface after sintering. The printed DGs showed relatively nice beam-shaping performance, and the surface roughness was measured to be below 20 nm.
2. Methods
2.1 Materials
The glass slurry developed for 515 nm 2PP was a mixture of 22wt% hydroxyl-ethyl-methacrylate (HEMA, Aladdin, Shanghai, China), 33wt% trimethylolpropane ethoxylate triacrylate (Aladdin, Shanghai, China) and 45wt % amorphous silica nanoparticles (Aerosil OX50, Evonik, Germany), blended with 0.2 phr bis-(2,4,6-trimethylbenzoyl) phenylphosphine oxide (Irgacure 819, Aladdin, Shanghai, China) as a photo-initiator and 2 phr hydroquinone (Aladdin, Shanghai, China) as an inhibitor.
In the preparation process, HEMA and trimethylolpropane ethoxylate triacrylate were mixed in proportion. Subsequently, silica nanoparticles were slowly added into the mixture by a mechanical stirrer. Next, the photo-initiator and inhibitor were added to the slurry. The homogenized slurry was found to contain a significant number of air bubbles, which were subsequently removed through ultrasonic degassing.
2.2 2PP direct laser writing
The diffractive micro-optics elements were fabricated using a laboratory developed 2PP laser system presented in Fig. 1(a). The main components of the 2PP setup included a femtosecond laser source, high-precision translation stages, and a scanning galvanometer. The laser source operated at a wavelength of 515 nm, with a repetition rate of 1 kHz and a pulse duration of 400 fs. The scanning galvanometer was employed to precisely control the laser beam position in the horizontal XY plane as it scans along the designated path according to the design. In the Z direction, the focal spot position was regulated by the translation stages. The travel range and positioning precision of the translation stages were 25 mm and 0.1 $\mu m$, respectively. A 20${\times} $ objective with a numerical aperture (NA) of 0.42 was utilized to focus the 515 nm femtosecond laser beam inside the glass slurry, resulting in 2PP and solidification occurring at the focal point, as shown in Fig. 1(b). The glass slurry was spin-coated onto a silica glass substrate (25 × 25 mm2 and a thickness of 2 mm) at a speed of 7000 rpm to achieve a thin and flat liquid layer. This can help reduce errors caused by refraction due to uneven liquid surfaces during processing and facilitate the removal of uncured resin during development. Following the printing process, the samples were immersed in methanol for 10 minutes to remove the uncured glass slurry. The resulting green component remained on the substrate throughout the entirety of the subsequent heat treatment process.
Fig. 1. (a) Schematic diagram of the 2PP 3D printing system. (b) 2PP process of the glass slurry, which is consisting of SiO2 nanoparticles and photocurable resins. (c) Schematic diagram of the heat treatment process. The organic binder was removed by debinding at 600$\circ\mathrm{C}$, and the resulting porous structure was subsequently densified into silica glass by sintering at 1250$\circ\mathrm{C}$.
2.3 Heat treatment
The heat treatment process is schematically shown in Fig. 1(c). The debinding process was performed in a Muffle furnace in an air atmosphere, with a heating rate of 0.5$\circ\mathrm{C}/min$ and a maximum temperature of 600$\circ\mathrm{C}$. After debinding, the resulting porous part was transferred into a Tube furnace, and sintered at 1250$\circ\mathrm{C}$ at a pressure below 5 Pa with a heating rate of 3$\circ\mathrm{C}/min$.
3. Results and discussion
3.1 Shrinkage of the printed structure
During the debinding process, the organic binder in the printed structure was removed by thermal deformation, resulting in porous “brown part”. The “brown part” can be densified into transparent silica glass through high temperature vacuum sintering. After sintering, the structure inevitably undergoes shrinkage due to the burnout of organics and the consolidation of the remaining particles. The shrinkage of the sintered parts is usually isotropic and falls within the range of 20% to 60%, depending on the loading of inorganic particles [6,11,14,16]. However, in our experiment the sintered structures demonstrated non-isotropic shrinkage, marked by a significant difference between the lateral and longitudinal shrinkage rates.
Figure 2 displays scanning electron microscopy (SEM) images and surface profiles of fabricated rectangular structures with diverse widths and heights. The measurements of these surface profiles were conducted through laser confocal microscopy. Laser confocal microscopy is capable of measuring the three-dimensional morphological features of micro-structures through optical sectioning. This process involves capturing images from different focal planes within a sample, which are then used to reconstruct a detailed three-dimensional representation of the sample's morphology. Surface profiles of the printed structures, both before and after sintering, were extracted utilizing dedicated analysis software. To facilitate a quantitative comparison, Table 1 presents the average height and width of the printed structures before and after sintering. Since the sidewalls of the printed structure have a slight inclination, the full-width at half-maximum (FWHM) is utilized to represent the width of the structures for comparison. Structures 1 to 4 demonstrate similar heights ranging from 3.4µm to 5.0µm, accompanied by increasing widths ranging from 21.0µm to 200.2µm. As the structure's width expands, the lateral shrinkage diminishes from 18.6% to 1.1%, while the longitudinal shrinkage escalates from 56.0% to 61.7%. Moreover, for structures 2, 5, and 6, which possess a consistent width of approximately 50µm and increasing heights ranging from 4.3µm to 25.7µm, an increase in height leads to a rise in the lateral shrinkage from 7.4% to 22.1%, while the longitudinal shrinkage decreases from 60.5% to 37.7%. In summary, the aspect ratio of the printed structure plays a pivotal role in determining its lateral and longitudinal shrinkage. As the aspect ratio increases, the lateral shrinkage decreases, whereas the longitudinal shrinkage increases, as shown in Fig. 3. A minimal lateral shrinkage of 1.1% is achieved in structure 4, which exhibits an aspect ratio of 58.8. Isotropic shrinkage is not expected unless we print structures with a specific aspect ratio that ensures equivalent horizontal and vertical shrinkage rates.
Fig. 2. SEM images of fabricated rectangular structures with different geometric dimensions, the profiles of the structures along the red dashed lines were measured using laser confocal microscopy before and after thermal treatment. (a) Structures with different widths. (b) Structures with different heights.
Table 1. Evaluation of shrinkage in structures with various geometric dimensions
We believe that the disparity in lateral and longitudinal shrinkage can be attributed to the bonding strength between the SiO2 nanoparticles and the glass substrate in the sintering process. Figure 4 shows the microstructures of the printed structures sintered at different temperature, which can help us understand the consolidation process. After debinding at 600°C, the organic binder in the printed structure was removed, resulting in a loose interconnected network formed by SiO2 particles. The sample sintered at 1150°C shows the initial neck formation between particles caused by surface diffusion [20]. As the sintering temperature increases, the nanoparticle network is smoothed (at 1200°C), and the pores are removed to form a dense glass (at 1250°C). The sintering mechanism of amorphous nanoparticles is reported to be viscous flow with interparticle van der Waals interactions acting as additional driving force [21–23]. In this work, the structures are printed on a silica glass substrate, and left on the substrate throughout the heat treatment. The presence of bonding between the nanoparticles and the substrate restricts the viscous flow of nanoparticles in close proximity to the substrate, thereby resulting in minimal lateral shrinkage. Meanwhile, the remained voids between these nanoparticles are filled by the overlying nanoparticles through a viscous flow process during densification, leading to significant longitudinal shrinkage. However, as the height of the structures increases, the force exerted by the substrate on the nanoparticles diminishes, leading to an increase in the lateral shrinkage rate and a decrease in the longitudinal shrinkage rate.
We believe that the low lateral shrinkage in our study can be attributed to two primary factors: (1) The utilization of a nanoparticle-based glass slurry in our 2PP process, and (2) The retention of the fabricated structures on a silica glass substrate throughout the heat treatment phase. In particular, the low lateral shrinkage effect is only significant when the aspect ratio of the micro-structure exceeds 20, as exemplified by structures 3 and 4. Simultaneously, it is worth noting that these structures exhibit substantial longitudinal shrinkage, reaching up to 60%. To counteract this longitudinal shrinkage, it is essential to elevate the height of the printed structures. In addition, increasing the solid loading in glass slurry can reduce both lateral and longitudinal shrinkage. However, an excessive solid loading can lead to increased slurry viscosity, thereby impacting the successful completion of the printing process.
3.2 Fabrication and characterization of DGs
These shrinkage properties of the printed structures make the 2PP process well-suited for the fabrication of binary optics, such as DGs. In DGs, structures usually possess a large aspect ratio (>20), with widths ranging in the order of tens of micrometers and heights spanning the range of hundreds of nanometers. When utilizing the 2PP process to fabricate DG structures, the low lateral shrinkage results in minimal errors in phase transition points for the printed DGs. Additionally, the significant longitudinal shrinkage would contribute to a smoother surface after sintering.
Herein, we designed and fabricated 2D DGs with odd orders and conducted a performance characterization. The DGs in our experiments were designed to split an incident beam into an N × N spot array (order O = N) with uniform power intensity. Using the simulated annealing algorithm [19], DGs with an odd number order of O = 7, with transition points located at (0.23191, 0.42520, 0.52571), were obtained. Figure 5(a) illustrates a unit of the DGs, where the light gray blocks represent phase zero, and the blue color indicates a phase shift of π across the transition points. The local phase on a DG is determined by the corresponding structural height. To achieve a phase of π, the height of each phase block can be calculated by
where $\lambda $ represents the wavelength of the incident light, and n is the refractive index of glass. In our experiment, we utilized a collimated laser with a wavelength of 650 nm as the incident beam. The refractive index of the silica glass at this particular wavelength is 1.456. Consequently, the theoretical height of the phase block corresponding to a phase shift of π is calculated to be 712.7 nm. The width of the phase blocks is interconnected with both the diffraction order (O-number) and the grating period. The grating period has been set at 200 µm, ensuring that each of the phase blocks maintains an aspect ratio exceeding 25. This deliberate choice guarantees a lateral shrinkage rate of less than 5%.Minimal lateral shrinkage is crucial in the fabrication of DGs. For a single flat structure, the shrinkage can be easily addressed by understanding the shrinkage rate and then appropriately designing the structure, as shown in Fig. 5(b). However, for 2D DGs, which consist of individual rectangular structures with diagonal connections, the shrinkage cannot be easily addressed by adjusting the structures’ dimensions. As shown in Fig. 5(c), if we enlarge the dimensions of the entire DG, significant lateral shrinkage would result in changes in the relative positions of the phase blocks. Figure 5(d) illustrates experimental results of three rectangular structures exhibiting a lateral shrinkage of 25.6%. This lateral shrinkage causes significant changes in the relative positions of phase blocks within DGs, thereby substantially impacting the beam-splitting performance [24]. The shrinkage is also uncompensatable through modifications in the dimensions of individual structures, as enlarging each block would lead to sections overlapping with each other, as shown in Fig. 5(e). This work offers a simple method to achieve minimal lateral shrinkage, making it suitable for binary optics fabrication.
Fig. 5. (a) A unit of the designed DG at order O = 7, with transition points marked. The light gray regions represent phase zero, while the blue color indicates a phase shift of π across the transition points. (b) The shrinkage of a single flat structure can be easily addressed by adjusting the dimensions. (c) Enlarging the dimensions of the entire DG would result in changes in the relative positions of the phase blocks. (d) An example of 3 rectangular structures with lateral shrinkage of 25.6%. (e) Enlarging each individual block would lead to sections overlapping with each other.
Printing was performed using the following parameters: laser power 20%, hatching distance 1 µm, and scan speed 1000 µm/s. Prior to printing the phase blocks of the DGs, a base layer with a thickness of approximately 2 µm was printed using the same parameters. This base layer is designed to compensate for errors in accurately identifying the position of the interface between the substrate and glass slurry, as well as any substrate tilt. Once the base layer was completed, the z-axis of the translation stage was moved downward by 1.8 µm to initiate the printing of the DGs.
The fabricated DG at order O = 7 is shown in Fig. 6(a). The substrate dimensions are 700 µm ${\times} $ 700 µm, and the DG dimensions are 600 µm 600 µm. Figure 6(b) presents a comparison of the surface roughness in a 20 µm × 20 µm region before and after sintering. The surface roughness, characterized by an atomic force microscope (AFM), is reduced from Rq = 52.6 nm to Rq = 19.9 nm after sintering, which is significantly smaller than the wavelength of the red laser.
Fig. 6. (a) The SEM image of the printed and sintered DG. (b) Surface roughness of a 20 µm × 20 µm region before and after sintering. (c)-(e) Surface profiles of 2 phase blocks with different sizes before and after sintering were captured using a laser confocal microscope to analyze the shrinkage. Phase block 1 exhibited a lateral shrinkage of 3.3% and a longitudinal shrinkage of 64.4%, while phase block 2 showed a lateral shrinkage of 2.2% and a longitudinal shrinkage of 59.0%. (f) The laser spot arrays generated from the DG on CCD.
The shrinkage during the sintering process was analyzed by capturing surface profiles of phase blocks using a laser confocal microscope. Figure 6(c) illustrates phase block 1 and phase block 2, representing the smallest and largest phase blocks in the DG, respectively. A comparison of their surface profiles before and after sintering is depicted in Fig. 6(d) and Fig. 6(e), correspondingly. The phase block 1 exhibits a lateral shrinkage of 3.3% (width decreases from 21.2 µm to 20.5 µm), while the longitudinal shrinkage is 64.4% (average height decreases from 2.28 µm to 0.81 µm). Similarly, the measured phase block 2 demonstrate a lateral shrinkage of 2.2% (width decreases from 94.4 µm to 92.3 µm), and a longitudinal shrinkage of 59.0% (average height decreases from 1.76 µm to 0.72 µm). Since both phase block 1 and phase block 2 are printed on the same base layer, they exhibited similar shrinkage rates. Figure 6(f) shows the DG generated 7 ${\times} $ 7 laser spot arrays record using a CCD. The presence of a prominent central bright spot arises from the laser beam size surpassing that of the grating and is further affected by height errors in the grating structure. We measured the relative intensity of each spot (relative to the total incident laser intensity) to determine diffraction efficiency. The diffraction efficiency was calculated to be 23.46%, which is lower than the theoretical value of 61.82%. This divergence in diffraction efficiency can be attributed primarily to the presence of height errors within the phase blocks [24]. In this study, a 20× objective with a NA of 0.42 was employed. The adoption of a higher NA objective lens has the potential to achieve enhanced processing accuracy.
4. Conclusion
In summary, we have developed a glass slurry consisting of SiO2 nanoparticles and photocurable resins for use in 515 nm 2PP process, and demonstrated the 3D printing of silica glass DGs for the first time. The printed structures can be transformed into transparent and dense silica glass through debinding at 600°C and sintering at 1250°C. The sintered structures exhibit different shrinkage rates in the lateral and longitudinal directions. As the aspect ratio of the structures increases, the lateral shrinkage decreases while the longitudinal shrinkage increases. We achieved a minimal lateral shrinkage of 1.1% in structures with an aspect ratio of approximately 60. Additionally, the relatively large longitudinal shrinkage of over 60% contributes to a much smoother surface after sintering. These shrinkage properties make our 2PP process well-suited for the fabrication of binary optics, such as DGs. We designed and printed DGs with odd-order of O = 7, which exhibit lateral shrinkage of less than 4% and smooth surface with Rq =19.9 nm. By using the printed DGs, the incident red laser successfully forms a 7 × 7 laser spot array. The developed glass slurry, which exhibits minimal lateral shrinkage, in conjunction with 2PP 3D printing, introduces a novel approach for producing binary DOEs. Furthermore, our approach can also be applied to the fabrication of multilevel or continuous surface profile structures, enabling the realization of complex optical functions.
Funding
National Natural Science Foundation of China (62105308, 62175221).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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