1. Introduction

Multiphoton polymerization (MPP) is a powerful tool allowing the fabrication of complex shape 3D microstructures with the feature sizes beyond sub-diffraction limited resolution [1]. Due to a tightly focused femtosecond laser beam in the volume of transparent photopolymer, the cross-linking reactions happen only at a tiny focal spot, which is known as a volumetric pixel - voxel. By spatially moving the laser focus in a layer-by-layer fashion, well-defined complex shape 3D structures could be fabricated. Subsequently, in the negative-tone photopolymer case, the laser unexposed areas are simply washed-out with a developer leaving only solidified structures. This technique could be widely applied in a vast range of the applications, for instance, fabrication of the micro-optics [2], metamaterial elements [3], scaffolds for tissue engineering [4], microfluidic devices [5], etc.

However, apart from the resolution beyond the diffraction limit and versatility of technology capabilities, the major drawback of MPP technology is its relatively low throughput using high numerical aperture objectives. In additive manufacturing, the common principle is to hatch 3D object into multiple separate lines on each of the plane and stack up into layers. The voxel spacing parameters have to be selected more carefully that each individual voxel overlaps onto the previous one. Usually, larger voxels are selected for bulky less precision required structures, while critical tiny features need to be done with smaller voxels. Under tight focusing conditions, the typical layer-by-layer processing method of the mm-size structure fabrication with high resolution features would require an unreasonable and impractical laser processing time. Nonetheless, there are multiple ways to increase the writing speed and shorten the process. For instance, the processing speed could be improved by using alternation of different numerical aperture objectives [6], shaped laser beams (e.g. Bessel [7] or ring-Airy [8]), multiple laser beam focus by diffractive optical elements [9] or spatial light modulator [9,10], advanced holographic light shaping [11], interference-lithography [12], voxel control by spatiotemporal focusing [13], scanning with synchronized linear stages and galvo-scanner mirrors [14]. Throughput could also be improved by different scanning approaches, as fabrication of the superficial layer (shell) of the structure and subsequent ultraviolet exposure [15], or applying adaptive stitching algorithms [16].

In this work, we present our results on implementing the dynamic voxel control for a traditional MPP system by using a motorized beam expander. In contrast with feature size change by incrementally increasing the laser exposure, this method hugely extends the dynamic range of fabrication window for a single high numerical aperture (NA) objective. We demonstrate that by changing the focusing conditions, the resolution of feature size could be easily tuned and realized for continuous single fabrication of 3D structures. Furthermore, this potential technique gives the ability to optimize the fabrication process and have on-demand feature size control without sacrificing precision.

2. Laser experimental setup

The experiments were performed with a commercial laser system (Laser Nanofactory, Femtika Ltd.) with an Yb-based femtosecond laser (Carbide, Light Conversion Ltd.), which was operated at a frequency-doubled wavelength of 515 nm, $\sim$250 fs pulse duration and at a 1 MHz repetition rate. The principal experimental setup is displayed in Fig. 1. The initial beam waist diameter was 1.1 mm ($1/e^2$). The laser beam was directed to the entrance aperture of an integrated motorized telescope. Then, the expanded beam was delivered to the high NA microscope objective, which focused the light into the volume of photosensitive resin. The fabrication process was realized by moving XYZ linear motion stages, and the average laser power was varied by an acousto-optical modulator (AOM). The fabrication speed was kept 100 µm/s for all the structures.

 

Fig. 1. Schematics of direct laser writing optical setup with a motorized telescope (1-8x expansion ratio) and high NA objective. M1-M4 – reflective mirrors; L1-L5 – lenses.

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To change the beam diameter, we used a motorized beam expander (MEX18, Optogama Ltd.), which had a possibility to enlarge the beam between 1- to 8-fold. It consisted of 3 lenses, the last element was fixed, while the first two lenses were driven by two independent motors along the optical axis. The used motorized telescope had high pointing stability of <0.2 mrad and a response time of <50 ms from sent command to the stage/motor motion. The position of the lenses are achievable within 0.2 s and then are corrected and stabilized. Practically, any operation took less 1 s, including the movement and stabilization process over the entire dynamic beam expansion range. Moreover, the motorized beam expander had the ability to regulate/compensate laser beam divergence. In principle, by changing the position of the lenses, the divergence angle could be adjusted. Therefore, the same setup could work as a dynamic laser focus along the optical z axis, which could be applied for 3D micro-processing.

For the experiments, we used a hybrid inorganic/organic photosensitive polymer SZ2080 [17], which was additionally photo-sensitized with 1$\%$wt of Irgacure 369 photoinitiator. The negative tone SZ2080 liquid polymer was drop-casted on a standard glass coverslip and then prebaked on a hot-plate with short temperature ramps at 40$^{\circ }$C, 70$^{\circ }$C, and kept at 90$^{\circ }$C for 1 h. During the prebake procedure, the solvent was evaporated and the polymer turned into a soft gel. Afterwards, the sample was used for the laser fabrication step. The laser irradiated samples were immersed into a 4-methyl-2-pentanone developer bath for 30 min to wash out the laser non-scanned, not polymerized areas. Later, the samples were submerged into isopropanol and dried in ambient air. For inspection with a scanning electron microscope (SEM), the samples were coated with a thin gold layer via sputter-coating.

3. Results and discussion

Typically, the laser beam is expanded to completely fill the input objective aperture in order to obtain ultimate feature size resolution. In this case, the voxel size is mainly defined by NA of the objective. Certainly, it could be enlarged and tuned by the applied laser power, i.e., laser exposure dose. If the laser beam is not covering the front aperture of the objective completely, then this effect would lead to a numerical aperture drop and, hence, to a larger voxel size. We have done numerical calculations in order to calculate the point spread function (PSF) dependence on laser beam size to the entrance of the objective aperture. The amount of laser light covering the input aperture of the objective we define as a filling factor T = $\omega /a$, i.e., simply the ratio of the Gaussian beam waist radius ($\omega$) (at the $1/e^2$) to the objective’s aperture radius ($a$) [18,19]. As reported in [19], the focused Gaussian beam is unclipped for the values $T$ < 0.5. The moderate filling ratio increases the achievable resolution. However, it also provides a hybrid focused beam spot size, as the Gaussian beam starts to be truncated and transforms into an Airy pattern as $T$ $\rightarrow$ $\infty$. Moreover, a further increase of filling factor ($T$ > 1) provides just a minor change in focused beam spot size, while the total power loss increases together with intensities of the diffraction rings of the Airy pattern [19,20].

Contrary, if the filling ratio T is below 1, then underfilling of the objective input aperture leads to a drop of effective numerical aperture (NA$_{\textrm {eff}}$), which could be recalculated using NA$_{\textrm {eff}}$=$n\sin \theta _{\textrm {max}}$, where $n$ - refractive index of the propagation medium, $\theta _{\textrm {max}}$ - highest marginal ray angle. By simply changing the incident beam waist, the voxel could be enlarged in the lateral and the axial directions. If the NA$_{\textrm {eff}}$ of the objective is lower, the voxel aspect ratio increases and becomes even more elongated in respect to the optical axis. Under low-NA focusing condition, the beam propagation could be treated using standard scalar theory [20].

For the scalar model, the focused beam spot dimensions could be calculated through the following equations: laser beam radius at the new waist position (after the lens) (at $1/e^2$):

On the other hand, higher NA objectives are typically employed for MPP process to ensure high feature resolution. In that case, the marginal ray angle $\theta _{\textrm {max}}$ is much larger, therefore a paraxial approximation could not be used anymore. To calculate the PSF under the tight focusing conditions with a high NA objective, spherical aberrations and the polarization effects have to be considered. For this purpose, the PSF needs to be calculated using vectorial Debye theory [20,21].

The theoretical simulation of the light intensity distribution for different objective underfilling conditions were done using vectorial and scalar models. The equations used for the vectorial Debye model can be found elsewhere [18,22]. This model takes into account the polarization state (circular in our case), the contribution of spherical aberrations due to several interfaces (see Fig. 2 (a)) between the objective lens and the focal point. Figures 2 (b)-(g) show the variation of the PSF of intensity distribution calculations for different $T$ (from 0.2 to over 1) filling factors for 0.95 NA objective with 515 nm laser wavelength. For instance, the filling factor $T$ of 0.5 would mean that the diameter of the Gaussian laser beam is twice smaller than the objective’s entrance diameter. It is worth noting that the underfilling of the aperture mostly affects the axial voxel resolution, while the lateral is enlarged at much lower scale. As can be clearly seen by incrementally changing the filling factor, the feature axial size could be tuned from sub-micron to tens of microns regime within the same high NA objective.

 

Fig. 2. (a) Schematic illustration of laser beam propagation through stratified media. Calculated PSF by vectorial theory for 0.95 NA objective with $\lambda$=515 nm laser wavelength with different filling factors T for the input aperture of the objective. Parameters: (b)$\,$T $\gg$ 1, (c)$\,$T = 1, (d)$\,$T = 0.5, (e)$\,$T = 0.33, (f)$\,$T = 0.25, (g)$\,$T = 0.2.

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To quantitatively investigate the voxel dimensions change dependence on the input filling factor, we chose to fabricate suspended fibers between supporting pillars [22]. A series of narrow parallel fibers were done with incrementally increasing the laser power for each of the following fiber and covering the whole dynamic range from polymerization to damage threshold. In this work, we used tight focusing conditions with a 1.4 NA oil-immersion objective, which is very common for the MPP application. The fabricated structures were investigated under the SEM to measure the lateral and axial feature size dimensions, as shown in Fig. 3.

 

Fig. 3. Top- and side-views of SEM images of suspended fibers between supporting pillars for NA$_{\textrm {eff}}$ of (a) 1.4 and (b) 0.32. The set of individual lines shows voxel growth dynamics with an increasing laser power for (a) 1.4 NA$_{\textrm {eff}}$, near the (left) polymerization (0.09-0.14 mW) and close to (right) damage threshold (0.16-0.21 mW). While for (b) 0.32 NA$_{\textrm {eff}}$, in the ranges of (left) 0.17-0.25 mW and (right) 0.43-0.53 mW, respectively.

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Figure 4 depicts a graphical representation of experimental data, as well as theoretical simulations are plotted as a function of filling factor $T$. Modelling and experiment were done with 1.4 NA objective and $\lambda$=515 nm wavelength. As can be seen for underfilling conditions for this objective, there is a good agreement between vectorial and scalar models as the beam diameter is small, up to $\sim$0.7 of $T$. When exceeding this value, the paraxial approximation cannot be applied anymore, then only the vectorial model is valid. The numerical calculations fit quite well with experimental data, which represent the polymerization threshold for each set of experiment with different filling factor $T$. In a complete filling case ($T=1$), the theoretical modeling predicts better feature resolution than it was achieved during the experiment. It is worth noting that feature size could be experimentally improved by narrowing the distance between the supporting pillar, as well as applying additional post-processing techniques, as critical point dryer for development process.

 

Fig. 4. Comparison of modeled PSF size by using scalar and vectorial theories for 1.4 NA objective. Bullet points represent experimental measurements of polymerization threshold under different filling factor conditions.

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A variation of dynamic range, from polymerization to damage threshold, with different light filling conditions is depicted in Fig. 5. The measurements were done through SEM analysis, each of suspended fiber was measured at the middle of the line. The depicted graph is indicative, showing the trend of the feature size growth. Our motorized telescope allowed to change the laser beam expansion from 8x to 1x magnification, which enabled to have the NA$_{\textrm {eff}}$ of 1.4 with a complete filling of the aperture while the least expanded beam dropped the NA$_{\textrm {eff}}$ to 0.32, respectively. The experiments showed that the 1.4 NA$_{\textrm {eff}}$ allowed to produce fine voxels, but had a short fabrication window of features from 0.25 to 0.5 µm in lateral and from 0.62 to 1.27 µm in axial dimensions. In contrast, 0.32 NA$_{\textrm {eff}}$ suffered from limited resolution, but exhibited large dynamic range from 0.6 to $\sim$2 µm transversely and from 3.7 to 22 µm longitudinally. A dynamic variation of NA$_{\textrm {eff}}$ would give the ability to overlap those high and low NA objective regimes, and largely extend the dynamic range within the same single objective.

 

Fig. 5. Measured (a) lateral and (b) axial voxel dimensions fabricated with a single objective by varying its NA$_{\textrm {eff}}$ and laser exposure dose over the entire fabrication window.

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In order to demonstrate the potential capability of the dynamics of the voxel size in one structure, we fabricated a woodpile structure, which fully reveals the single voxel size contrast by changing the incident beam on-demand. The grating structure consisted of two different optimized pattern sets (see Fig. 6). The upper and lower sections of the structure were done with first pattern with horizontal periods ${d_{\textrm {xy}}}$=5 µm and vertical spacing $d_{\textrm {z}}$=6 µm, NA$_{\textrm {eff}}$=0.54, laser average power $P$=0.4 mW, while the middle part with second pattern of $d_{\textrm {xy}}$=2.5 µm and $d_{\textrm {z}}$=1.5 µm, NA$_{\textrm {eff}}$=1.23, $P$=0.12 mW. With the fixed scanning speed of 100 µm/s the structure was printed in 8 min.

 

Fig. 6. SEM image of the woodpile structure having two different voxel segments: upper and lower parts were done with NA$_{\textrm {eff}}$=0.54, while the middle section with NA$_{\textrm {eff}}$=1.23. Whole structure was fabricated using the same microscope objective as well as constant translation velocity.

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In microscopy, the principles of the resolving power (or resolution) dependence on the lens aperture was already known by E. Abbe more than a century ago, however, this straightforward method has never been applied for the additive manufacturing. For the MPP technique, a high NA objective is not always considered as the first choice for all applications. For instance, scaffolds in bio-medicine, the lower NA objectives are even more desired for bigger structures, which provide larger voxels and faster structuring [23]. However, the large-size structures with small features require tight focusing conditions, which could prolong the fabrication process to an unreasonable time. In this case, compared to the traditional MPP scheme, the dynamic voxel control gives an extra degree of freedom in the MPP fabrication process for the same objective. A large NA$_{\textrm {eff}}$ tuning range has been achieved from 1.4 to 0.32 NA. It should be noted that we were limited by the least magnification of the telescope. A further reduction of the beam size would result in even lower achievable NA$_{\textrm {eff}}$. However, from an engineering point of view, this method requires a precise alignment of the optical system, otherwise variation of beam diameter may introduce laser focus shift in the field of the objective. In addition, the focal spot size could be easily scaled by this technique, however, the physical focal length and field of view remain unaffected. As the high NA objectives have a short working distance, the overall height of the achievable structures could be a limiting factor for some of the applications. Nonetheless, this beam expansion/reduction approach could easily be integrated into MPP systems and applied for large-size (mm) prototype structures with tiny features with hundred of nanometers of feature resolution. It could be used as an alternative to currently used approaches or solve the need to change objectives for up-scaling the voxel size with different objectives.

4. Conclusion

In this paper we present the possibility to employ dynamic voxel control by changing the incident beam diameter to the input of the objective with a motorized beam expander. An expanded beam with almost complete filling of the input aperture for 1.4 NA objective allowed to obtain the voxel feature size of 0.25 µm in the lateral and 0.62 µm in the axial direction, while unexpanded beam ($T=0.2$) allowed to enlarge the voxel up to $\sim$2 µm transversely and 22 µm longitudinally, respectively. This ability provides a huge extension of the fabrication window for high NA objective. We have modeled the PSF by vectorial and scalar models, which had a quite good agreement with our experimental results. It should be noted that a straightforward scalar model well describes the PSF variation up to 0.7 of the filling factor for 1.4 NA objective, then the vectorial theory should be used. Finally, we successfully demonstrated the realization of dynamically tunable voxel size. The presented approach extends the technology capabilities and could significantly increase the fabrication speed while maintaining the possibility to obtain high resolution features at the same time.