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Abstract
Modern two-photon lithography (TPL) technologies provide convenient methods for 3D printing sub-micron featured structures in photopolymers. TPL is a valuable tool for rapid prototyping of micro-optics, photonic metamaterials, and nanostructures. The ability to tune the optical properties of the resin materials used for TPL greatly expands the capabilities of 3D printing these types of components. Here we couple a sol-gel method of synthesizing and functionalizing titanium dioxide (TiO2) nanoparticles to modify off-the-shelf commercial resins designed for TPL to tune the refractive index of the 3D printable resin. The range of refractive indices expands up to 1.66 at 633 nm which is higher than commercially available, unmodified resins at that wavelength.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Two photon lithography (TPL) is a valuable tool for rapid prototyping of micro-optics and metamaterials thanks to additive manufacturing. Commercial systems are available with voxel resolution under 200 nm. Such technology has been used to produce micro-optics for applications including: microscopy, [1,2] endoscopy, [3,4] metamaterials, [5,6] and sensors [7,8]. The nature of 3D printing allows for a wide range of lens profiles, from spherical to free-form optics, that can be difficult to obtain using traditional micro-lens fabrication techniques involving 2D lithography and resist reflow [9,10]. These techniques are useful for mass production of lens arrays but have limited capabilities for fabricating specific surface profiles. Fabricating structures using TPL is significantly slower, but mass production can be achieved by using the TPL printed structure as a master for nano-imprint lithography.
Commercially available resins for TPL are difficult to find with a refractive index greater than 1.62 with most falling somewhere between 1.45 and 1.55. [11] Commercial examples of these include: IP-S, IP-Dip, and IP-n162 from the IP line of resins from Nanoscribe GmbH [12]. Work has been done to increase refractive index by doping resins with nanoparticles like TiO2 or ZnO, but these modified materials have only demonstrated refractive index increases of up to about 0.1.
When synthesizing nanocomposites, it is important to have a uniform distribution of nanoparticles within the polymer matrix. If nanoparticles agglomerate within the polymer, the resulting composite will scatter light and the material will become less transparent. Further, in order to achieve a good dispersion of nanoparticles, particularly for higher doping concentrations, it is often necessary to functionalize the nanoparticles to improve miscibility.
Here we report the first instance where glycidyl methacrylate (GLYME) functionalized titanium oxide (GLYME-TiO2) nanoparticles are used as a dopant in a commercially available acrylate based resin, IP-Dip, to increase the effective material index of refraction. There are various doping agents that can be used to generate optical grade high refractive index polymers, refer to Macdonald et al. (2014) [13]. Of general interest is the use of organo-metal oxides such as functionalized titania and zirconia. Prior work in the functionalization of titania has featured en-capping with catechols [14–16], acryalte groups [17–19], poly-vinyl alcohol, [20,21] etc.; where, the capping agent is chosen such that it decreases particle agglomeration and increases loading concentration in a target polymer matrix. However, to our knowledge optical grade composites derived from commercially available acrylate based resins have only previously been demonstrated by Weber et al. (2020) via the use of proprietary capping agents. [22] We report a straightforward and simple synthesis route for the growth and functionalization of $\sim$5 nm GLYME-TiO2 based on thin-film work presented by Himmelhuber et al. (2011) [23]. We demonstrate that by varying the doping concentration, the refractive index of an IP-Dip nanocomposite can be tuned from 1.54 to 1.66 at 633 nm.
2. Theory
TPL operates on the principle of two-photon absorption (TPA) which is a third order nonlinear optical phenomenon. A photosensitive material is exposed to photons with lower energy than required for excitation and thus polymerization can only occur if two photons are simultaneously absorbed. Absorption probability for TPA is proportional to the intensity of the light squared and thus requires high intensity to achieve significant polymerization. By tightly confining the exposure light to a small volume using a microscope objective, polymerization can be localized to a small voxel at the focus.
The requirements for a resin to be compatible with TPA are that it must be transparent at the illumination wavelength in order to be able to be focused through the material, and it must be photopolymerizable at half the wavelength of the illumination field.
A composite material consisting of two separate materials with different refractive indices will have an effective refractive index somewhere between the two materials. A linear change in refractive index based on the volume concentrations of the two materials can serve as a first order approximation of the effective refractive index. More sophisticated approximations like the Lorentz-Lorenz equation [13], see Eq. (1), can be used to estimate the effective refractive index, $n_{eff}$, as:
3. Methods
3.1 Resin preparation
Synthesis and functionalization of nanoparticles was done following the method by Himmelhuber et al. [23] This method is a very straightforward room temperature sol-gel synthesis. First, 1.59 mL (0.36 M) Titanium tetrachloride (TiCl4) was added drop-wise into 15 mL ethanol under magnetic stirring. The resulting reaction is highly volatile and was reacted inside a fume hood. After the solution cooled to room temperature (3-5 minutes) an excess of 0.325 mL (1.2 M) of water was added and the solution was cooled for another 3-5 minutes. Following the water, an epoxide was added. In this case, we used a combination of GLYME and propylene oxide (PO). The ratio of the two epoxides can be used to tune the refractive index of the nanocomposite dopant as described in literature. [23] While the highest index is obtained using only PO, we found that miscibility of the nanocomposite in resin was significantly better with including some GLYME, likely due to compatibility with the commercial resins used. We found that a 95/5 molar ratio of PO/GLYME provides reliable miscibility. The total molarity of epoxide in ethanol was kept as 1.3M (1.25 mL (1.235 M) PO and 0.130 mL (0.065 M) GLYME).
After synthesis, the solution was aged by resting at room temperature for 5-7 days before processing. To dope a commercial resin with the high index nanocomposite, the ethanol, excess water, and reaction byproducts were removed by evaporation. During evaporation at 150$^{\circ }$C, the solution viscosity increases dramatically. An acrylate or methacrylate resin designed for 2PP is added towards the end of the evaporation process. Here we opted to dope a commercially available acryalte based resin, IP-Dip, from Nanoscribe GmbH.
If the solution became overly viscous, a small amount of propylene glycol methyl ether acetate (PGMEA) was added to maintain a viscosity suitable for the TPL process. The precise viscosity is not critical, but should be low enough to allow for a microscope objective to maneuver while submersed without dragging material and high enough to remain in a drop formation when deposited onto a glass substrate. If using a direct immersion configuration for printing, the height of the printable structure may be limited if the viscosity is too low and the resin flows away from the objective as it moves away from the substrate. A viscosity between 2000 and 14000 mPas (at 20$^{\circ }$C) is acceptable for printing.
3.2 Resin testing and characterization
The size distribution of the GLYME- functionalized TiO$_2$ was measured using a Malvern Zetasizer Nano ZS. The Zetasizer is a commercially available optical instrument that estimates size of dilute particles by correlating scattered light patterns to a particle radius; this technique is referred to as dynamic light scattering (DLS) or Photon Correlation Spectroscopy (PCS). Briefly, the diffusion of small spherical particles dispersed in a liquid can be characterized by the Stokes-Einstein equation:
where, $k_B$ is Boltzmann’s constant, $T$ is the absolute temperature $\eta$ is the dynamic viscosity, and $r$ is the radius of the spherical particle. The synthesized GLYME-TiO$_2$ was dispersed into ethanol. The dispersant had a know refractive index of 1.360 with a viscosity of 1.2000 cP; while the dispersed material was assumed to have a mean index of 2.7 at the instrument operating wavelength of ($\lambda _0 = 532 nm$). The sample was kept at a constant temperature of 20$^{\circ }$C by the instrument, measurement duration was $\sim$90s depending on the convergence of the correlation function.3D printing using 2PP was tested using a Nanoscribe Professional GT lithography system. The exposure wavelength was 780 nm. While testing new materials, the system was used in an oil immersion configuration in which resin is applied to a microscope cover slide and the microscope objective is immersed in an index matching oil on the opposite side of the slide. Exposure is done through the cover slip as opposed to immersing the objective directly in the resin as is done with the dip-in laser lithography (DiLL) configuration.
Illumination dosage testing was done by adjusting the scanning speed and the laser power. For a 20x microscope objective, a suitable dosage of 0.375 mJ/mm was found to reliably polymerize the resin and could be developed following standard developing procedure for IP resins. Developing consisted of a soaking the sample for 15-30 minutes in PGMEA followed by rinsing in an isopropyl alcohol (IPA) bath for one minute to remove any remaining PGMEA. The sample was then dried using an air blowing bulb.
The refractive index of the 2PP resin was measured using a Meticon 2010 prism coupler with five wavelengths. The sample was prepared by printing a 5mm x 5mm x 10um thin film with the Nanoscribe printer. Due to the limited field of view of the Nanoscribe, the film was printed by stitching 300um x 300um sections. This way of printing results in double exposure where the stitching windows overlap and the boundaries can cause scattering and losses during prism coupling, but nonetheless, clear modes were discernable by the instrument. To compare 2PP and one photon polymerization (OPP), a second thin film was fabricated using a spin coater and UV flood exposure. The resin was diluted with ethanol to achieve thin films for spin coating.
The surface quality of the 3D printed thin films was determined by measuring surface profiles using white light interferometry (WLI) and calculating the RMS deviation from an ideal planar surface. This was done using a Profilm3D interferometer from Filmetrics with vertical resolution down to 1 nm using a combination of WLI and phase shifting interferometry (PSI).
3.3 Micro-optic design and fabrication
To demonstrate the application of such material for 3D printing micro-optics, a micro-lens was designed and printed. The design is a convex-plano lens in which the planar side is on the coverslip substrate as shown in Fig. 1.
Fig. 1. Micro-lens to be printed on a 170 um microscope coverslip designed in Zemax using custom resin based on measured dispersion.
Since 3D printing allows for freedom of surface shape, the convex surface is a rotationally symmetric asphere with the surface sag described by Eq. (2):
where $C$ is the surface curvature, $k$ is the conic constant, $\alpha _1$ and $\alpha _2$ are polynomial expansion coefficients. The curvature, conic constant, and aspheric coefficients were optimized using OpticStudio Zemax optical design software to minimize the spot size. The optimized values are presented in Table 1.
Table 1. Optimized parameters for micro-lens surface
The micro-lens was designed using the measured refractive index and dispersion of the custom resin. Optimization was done for a single wavelength of 633 nm. The focal length was measured using a collimated helium-neon laser beam and a CCD camera array with a microscope objective as shown in Fig. 2.
Fig. 2. Focal length of micro-lenses measured using collimated light from a helium-neon laser with camera mounted on translation stage.
The camera was initially focused on the glass coverslip surface and images were taken of the focusing beam as the camera was translated away from the coverslip. The relative beam width was determined by taking cross sections of the beam in the images at each z distance and finding the full width half max (FWHM) value. The beam waist and spot size were determined by fitting the FWHM values to the expression for a Gaussian beam width. Surface profiles for the lenses were measured using the Filmetric Profilm3D interferometer.
4. Results and discussion
The sol-gel solution consisted of the organic capped TiO2 nanoparticles and any remaining GLYME and propylene glycol from the reaction. The solution acquired a light amber hue after evaporating the ethanol and concentrating the solution due to the organic capping and host epoxides. The diameters of the nanoparticles were measured to be 5.19 $\pm$ 1.54 nm in diameter with a polydispersity index (PDI) of 0.226 using a Malvern Zetasizer Nano ZS. Under the dilute sizing conditions the functionalized nanoparticles appeared highly transparent and did not show visible scattering. Moreover, sizing data demonstrated little to no agglomeration with a narrow size distribution $\pm$ 1.54 nm and low PDI.
Evaporation of excess ethanol, water, and reaction byproducts resulted in an increased concentration of GLYME-TiO2. While commercially available nano TiO2 have a distinct white, milky color, functionalized titania particles appear to have functional group dependent coloration; where previously it has been shown that olate groups appear to yellow in color while catechols appear red. [14,16]. Here we note that adding the nanoparticles solution to an acrylate based TPL photoresin resulted in a resin with a reddish hue with no noticeable scattering. The ability to 3D print using TPL and develop the object, was tested on complex structures presented in Fig. 3.
Fig. 3. (a)-(d) SEM images of structures printed in the composite resin ($f = 0.52$, $n = 1.66$ at 633 nm) and (e) a 4 um thick thin film deposited by spin coating the resin shown and measured transmission spectrum.
GLYME itself can be photopolymerized with the addition of a photoinitiator, and the same is true for the GLYME functionalized TiO2 nanocomposite. This has been demonstrated in the past but has limited usefulness due to only being able to create very thin films (<200 nm) for traditional 2D photolithography using one-photon polymerization. [23] This material has never been applied to TPL for 3D printing. While it may be possible to apply TPL directly to this material by itself, we found poor printing performance and were unable to reliably develop the samples without also dissolving the structure. However, by using this composite as a dopant for the commercially available IP resins, a much more reliable printing material was achieved. Adding the IP resin does dilute the original nanocomposite and lowers the maximum achievable refractive index. Figure 4 shows indices for doped and undoped IP-Dip measured using a prism coupler system for five wavelengths and the data was fit to Cauchy’s equation:
where A-D are the Cauchy coefficients. The refractive index predicted by the Lorentz-Lorenz shown in Fig. 4 was calculated using the measured values for IP-Dip ($n = 1.54$ at 633 nm) and the nanocomposite solution ($n = 1.80$ at 633 nm).Fig. 4. Refractive index for IP-Dip with various doping concentrations (left) and the dependence of the refractive index at 633 nm on the doping concentration (right).
The nanocomposite solution consists of the epoxides (PO and GLYME) and the TiO2 nanoparticles. The volume fraction of TiO2 within this composite (using a 95/5 ratio of PO/GLYME) was 38.54 vol%. The effective refractive index of the epoxide-TiO2 nanocomposite was found using Eq. (1) using this volume fraction and $n = 2.7$ for TiO2 and $n = 1.45$ for the epoxide solution. The predicted value was 1.7965 which agreed well with the prism coupler measurements of this material of $n = 1.80$.
When combined with the IP-Dip resin, the total volume percent of TiO2 was 20.04 vol% for $f = 0.52$. Since the same epoxide-TiO2 nanocomposite was used for all of the experiments, values of the doping concentration reported are the concentration of the epoxide-TiO2 nanocomposite to IP-Dip.
The refractive index of the undoped IP-Dip was increased by 0.13 up to 1.66 at 633 nm by adding the nanocomposite dopant. The increase in refractive index based on the volume fraction of the dopant is in good agreement with Eq. (1) with an RMS error of 0.0077. Doping concentrations greater than $f = 0.52$ were unreliable due to either agglomeration of nanoparticles and loss of transparency and/or due to poor printing performance.
WLI measurements of the thin films printed with TPL were used to determine the surface roughness of printed features. Figure 5 is an example of the surface topography for a film printed using the $f = 0.52$ resin. The RMS surface roughness based on 20 measurements was found to be (15.8 ±0.5) nm.
Fig. 5. Surface profile for a thin film printed using a doped resin ($f = 0.52$) measured using white light interferometry.
The focal length of the micro-lens from Fig. 1 has an expected back focal distance (BFD) of 810 um according to the ray tracing model. This model was designed for an operating wavelength of 633 nm which was the same as the laser used for testing. The refractive index of the material used for the design was based on the measured 2PP refractive index in Fig. 4 for $f = 0.52$. The measured beam width as a function of distance from the coverslip is presented in Fig. 6.
Fig. 6. Measured focal length for micro-lens (a) and ray tracing tolerance of refractive index at design wavelength (b).
The measured BFD at the beam waist was 800.1 um. This corresponds to a deviation of 1.2% from the expected value from ray tracing. Assuming the surface profile of the printed lens is ideal and matches the design, the refractive index of the lens can be determined by relating the BFD and the refractive index using the ray tracing model as illustrated in Fig. 6(b). This method predicts the refractive index of this resin to be 1.668 at 633 nm. From the prism coupler measurements, this value was measured to be 1.6602. The difference between the refractive index as determined by the two methods is 0.0078, corresponding to 0.47% of either refractive index. This error can also be attributed to the surface profile of the micro-lens which was not ideal. A cross section of the microlens measured using WLI is shown in Fig. 7.
The RMS surface error between WLI measurements and the designed profile described by Eq. (3) was determined for seven samples and found to be (31.1 ±5.3) nm. This corresponds to approximately $\frac {\lambda }{20}$ at 633 nm. Due to the printing resolution and the vertical stitching distance of the printer, the fabricated lens has a stepped profile as evident in Fig. 3(d),7.
5. Conclusion
Here we have demonstrated the use of a sol-gel synthesized TiO2 nanocomposite as a dopant for TPL photoresins to raise and tune the refractive index in 3D printed components. The refractive index of the IP-Dip resin was increased by 0.13 from 1.53 to 1.66 at 633 nm by doping with 52 vol% of the nanocomposite consisting of TiO2, glycidyl methacrylate, and propylene glycol. Even higher indices are achievable by starting with a higher index base resin. The index of the nanocomposite can be increased by reducing the volume of the epoxides used, provided the molarity of the epoxides remains high enough to mediate nanoparticle growth. Tuning the proportions of the PO and GLYME while maintaining the overall epoxide molarity can also raise the index of the nanocomposite but may affect the miscibility of the nanoparticles with the TPL resin. This non-miscibility could increase scattering of the material, and lead to poor performance during 3D printing.
The resulting resins are promising for several applications in optics and photonics. Higher refractive indices can lead to thinner optical elements or higher index contrast for better confinement in photonic applications.
Funding
Office of Naval Research (N00014-14-1-0505).
Acknowledgments
The authors would like to thank Jude Larbi Kwesi Coompson and Hao Xin for access to 3D printing and Roland Himmelhuber for guidance on nanoparticle synthesis. The authors also acknowledge the support from the Department of the Navy under grant #N68335-21-C-0114.
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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