We control the point-spread-function of high numerical aperture objectives used for direct laser writing with a spatial light modulator. Combining aberration correction with different types of amplitude filters to reduce the aspect ratio of the point-spread-function enhances the structural and optical quality of woodpile photonic crystals. Here, aberration correction is crucial to ensure the functionality of the filters. Measured point-spread-functions compare well with numerical calculations and with structures generated by direct laser writing. The shaped point-spread-function not only influences the maximum achievable three-dimensional resolution but also proximity effect and optical performance of woodpile photonic crystals.
© 2012 Optical Society of America
Direct laser writing (DLW) [1, 2] is a versatile technique for the fabrication of almost arbitrarily complex three-dimensional nano- and microstructures. Recent examples are templates for cell-biology , optical cloaks , three-dimensional photonic metamaterials [5, 6], bi-chiral photonic crystals  and mechanical metamaterials .
Most direct laser writing setups base upon focussing femtosecond laser pulses through a high numerical aperture (NA) objective lens into a photoresist, triggering polymerization in the very focal volume via two-photon absorption. Scanning of the photoresist with respect to the focus allows then the fabrication of three-dimensional structures .
The smallest achievable feature, a single volume pixel (voxel), is defined by the iso-intensity surfaces of the focus marking the exposure threshold . Due to the finite NA the voxel is of ellipsoidal shape with the elongated axis oriented along the axis of propagation (z-axis) . Obviously, it is this axis that determines the limits on resolution and feature size in three-dimensional structures.
Hence, an active control of the aspect ratio between axial and lateral dimensions is highly desirable. Several approaches have been reported in recent years:  used a special arrangement of lenses to illuminate a slit on the entrance pupil, effectively reducing the numerical aperture of the objective along one axis, resulting in a fixed aspect ratio of almost one for the xz-intensity distribution. [13, 14] implemented an amplitude filter directly in front of the objective, consisting of a ring with reduced transmission (shaded-ring filter, SRF) and slightly reducing the aspect ratio for both, the xz- as well as the yz distribution. Here, alignment of the filter with respect to the optical axis is extremely crucial for the performance. Compared to these hardware approaches, modifying the focal intensity distribution via spatial light modulators (SLM) offers more flexibility:  optimized the aspect ratio of the point-spread-function (PSF) for microscopy purposes,  and  implemented a slit filter for writing of optical waveguides with controlled cross-section. Another advantage of using an SLM is the possibility to correct for aberrations [18, 19]. Surprisingly, none of the SLM based approaches aimed towards high resolution (below 1 μm) three-dimensional structures with feature sizes below 500 nm.
Here, we combine direct laser writing using high NA oil immersion objectives (NA=1.4) with the strength of an SLM based approach to find the limits in feature size and resolution for different types of amplitude filters. Furthermore, we correct for aberrations introduced by the optical setup, the objective and the choice of photoresist.
2. Experimental setup
The experimental setup is depicted in Fig. 1(a). A Ti:Sa oscillator (Coherent Chameleon Ultra II) generates 140 fs pulses at a wavelength of 780 nm and with a repetition rate of 80 MHz. The laser power is adjusted by an acousto-optical modulator (AOM). The laser beam is expanded to overfill the aperture of an SLM (liquid-crystal phase modulator, Hamamatsu LCOS X10468-02). The SLM diffracts the desired intensity and phase patterns in the first diffraction order, which is then imaged onto the entrance pupil of the objective (plan apochromat, oil-immersion, NA=1.4). A three-axis piezo (300 μm × 300 μm × 300 μm, PhysikInstrumente) is used to scan the sample relative to the fixed beam.
Almost arbitrary intensity and phase patterns can be generated with the SLM by spatially adjusting the piston and bias of a blazed grating. The piston controls the diffraction efficiency and therefore the intensity distribution while the bias controls the phase distribution [20, 21]. Here, we slightly modify this approach by pre-adjusting the desired amplitude values to achieve the correct output values, thus, linearizing the input-greyscale – output-greyscale curve. Our modified approach guarantees independent modification of the phase patterns for aberration correction and highly accurate amplitude patterns for different kinds of filters.
The intensity distribution of the resulting PSF is measured by scanning a gold nano-sphere (100 nm diameter) through the focus. The sphere resides on a glass substrate (170 μm thickness) and is covered with immersion oil. The scattered intensity is collected by the same objective used for focussing and detected by a CCD camera. Since the sphere is assumed to act as a point-scatterer, the scattered intensity is proportional to the intensity distribution in the focus and we therefore obtain an accurate three-dimensional intensity distribution map . A tracking algorithm ensures correct positioning while several consecutive measurements are taken and finally averaged to reduce measurement noise.
Aberration correction is performed by iteratively applying phase patterns calculated from the first order Zernike polynomials with varying coefficients and evaluating the effect on the Strehl intensity deduced from PSF scans. The coefficient is set to the minimal value that maximizes the Strehl intensity.
3. Methods and results
We start our discussion by comparing the influence of aberration correction on the PSF. For all cases the SLM displays a blazed grating and a backplane correction pattern as background to which the corresponding holograms are added. Figure 2 shows in the top row the lateral extent of the PSF (xy-plane), in the middle row the axial extent (xz-plane) and in the bottom row the xz-plane for numerical calculated PSFs. Column (a) depicts the uncorrected PSF, column (b) the aberration corrected PSF. The lateral width of the PSF is almost unchanged, while the axial width reduces. The experimental aspect ratio decreases to χ = 2.6, close to the theoretically predicted value of χ = 2.44, by applying the correcting Zernike polynomials, mostly spherical aberration and coma. Additionally, the Strehl intensity increases by 20%. For the numerical calculation , we assume an ideal objective with NA=1.4 to represent the corrected PSF. We include the experimentally found aberrations into the calculations for the uncorrected case. The overall good qualitative agreement shows the validity of our approach. Deviations from the theory are mainly due to the finite spectral width of the laser pulses, whereas the calculations are performed for a wavelength of 780 nm.
To further reduce the axial elongation without compromising the lateral extent, we introduce two different SRFs (SRFa: r1 = 0.179rp; r2 = 0.982rp; t1 = 10.2%; SRFb: r1 = 0.26rp; r2 = 0.95rp; t1 = 10.2%, the definitions of the parameters are depicted in Fig. 1(b)). The corresponding PSFs are shown in column (c) and (d) for SRFa and SRFb. The absolute diffraction efficiencies of the underlying blazed gratings are adjusted to yield approximately the same Strehl intensity for all cases, causing the power on the entrance pupil to differ (around 11 mW on the unobscured pupil, 60 mW for SRFa and 42 mW for SRFb). While the two SRFs do not visually differ much in axial and lateral line widths SRFa results in a measured aspect ratio of χ = 1.9 and SRFb even in χ = 1.7. These values nicely correspond to theory (χ = 1.82 and χ = 1.75 respectively). Compared to the uncorrected objective, the aspect ratio improves by almost 41% (47%), compared to the aberration corrected objective still almost 27% (35%) are reached. However, the sidelobes of SRFa are considerably lower than the sidelobes of SRFb (23% compared to 35% of the peak intensity). Here, the question arises whether the smaller aspect ratio outweighs the increased sidelobe intensity. Without aberration correction the sidelobe intensities reach values above 50%, rendering the filters basically useless.
As the PSF alone does not necessarily allow conclusions regarding resolution and structural quality, we fabricate woodpile photonic crystals  as benchmark structures in the commercially available liquid negative-tone photo resist IP-L (Nanoscribe). IP-L is drop-cast onto a glass-substrate, structured (scan-speed 100 μm/s) and developed for 20 min in isopropanol. For each of the PSF in Fig. 2 a whole set of structures is written with laser power varying in 0.5% steps and with rod-distance of 700 nm, 500 nm, 450 nm, and 400 nm. All samples are characterized by spectrally resolved transmittance and reflectance measurements. Probing a substantial sample volume, spectroscopy is often more revealing than electron micrographs. However, for the samples showing the highest reflectance electron-micrographs are taken after sputtering 5 nm of Chromium. Cross-sections to analyze the aspect ratio are prepared via focused ion beam milling.
Results for 700 nm rod distance woodpile photonic crystals are depicted in Fig. 3. Top views and cross-sectional views for two samples written with the corrected objective without (black frame, left column of the figure) and with SRFa (blue frame, center column) are on the left hand side. The average aspect ratio of the rods are χ = 2.6 and χ = 1.9 respectively (visualized by the dashed ellipse, six rods have been analyzed). The correspondence with theoretical expectations (χ = 2.45 and χ = 1.84, ) is very good. The samples also show the typical shrinkage on the order of 10%.
The corresponding transmittance and reflectance spectra are shown on the right hand side of Fig. 3. At first sight, the influence of the SRF on the spectra is small compared to the corrected blaze. This is not surprising, as the optimum stop-band for 700 nm woodpiles is relatively easily reached — even with comparatively high aspect ratios . This can directly be seen in Fig. 4 (top row). Here, numerically calculated (FDTD, Lumerical) transmittance spectra for varying aspect ratio and rod diameter are plotted, high values are marked in red, low ones in blue. The shaded areas at the bottom of the graphs mark the parameters for which the samples are not any longer mechanically connected. As linewidths of 150 nm are not challenging for state-of-the-art direct laser writing, even for large aspect ratio decent sample quality is reached. For reduced aspect ratio — despite the broader linewidth and higher filling fraction at the optimum stop-band — no red-shift of the spectral position is observed. Additionally, the greater parameter tolerance leads to an enhanced likelyhood to achieve structures with their stop-band close to the optimum thus resulting in broader stop-bands, especially if linewidth variations in the experiment are taken into account.
This behavior is also observed for the experimental spectra shown in Fig. 3 on the right hand side. Hence, reducing the aspect ratio is especially beneficial for woodpiles with smaller rod distance: Structures do not require any longer extremely small rod diameters to reach strong spectral response (see Fig. 4 (bottom row)). For the here depicted 450 nm woodpile photonic crystals, optimum performance at χ = 1.6 is reached with rod diameters above 100 nm. This is of great practical importance since rod diameters well below 80 nm tend to loose mechanical stability due to the reduced cross-linking density in direct consequence of reduced laser power. Collapsing or heavily deformed structures without clear spectral response are the result.
The improvement in spectral response due to reduced aspect ratio for smaller rod distances is shown in Fig. 5. Reflectance and transmittance spectra for woodpiles with rod distances of 500 nm, 450 nm and 400 nm are shown for the corrected unobscured pupil, SRFa, and SRFb. The grey lines mark the strength of the reflectance peak for the samples fabricated without SRF and serve as a reference in the other plots. Obviously, the samples written with the SRFs outperform the corrected objective. At 400 nm rod distance the higher sidelobe intensities introduced by SRFb cause the stop band to vanish: The structure is not any longer open due to the proximity effect. In contrast, the structures written with the unobscured pupil and SRFa still show a stop-band. However, the stop-band for the sample written without SRF almost vanishes, while the SRF written sample still clearly shows decent reflectance. This suggests that for small rod distances the advantageous aspect ratio is outweighed by sidelobe intensities of about 35% of the Strehl intensity. However, sidelobe intensities of 23% of the Strehl intensity are still acceptable even in high resolution applications.
As it is known from numerical calculations that body-centered-cubic woodpiles possess stronger stop-bands compared to face-centered-cubic ones, one might suspect that the results for the SRFs could also originate from an increased shrinkage along the axial direction. However, the focused ion beam cuts show no evidence of increased shrinkage. Such an increased shrinkage would additionally be accompanied by a substantial blue-shift of the spectral features which we observe neither.
Compared to the best so far published direct laser written woodpiles with 400 nm rod distance , our aspect ratio corrected samples clearly outperform these samples. Even in comparison to woodpiles written with STED inspired lithography , optical quality is comparable. While STED inspired lithography allows for further reduction of the rod distance without reducing the cross-linking density too much, this comes at the expense of a complex experimental setup and with the limitation to very few photoresists. With respect to the considerable less complex experimental setup and still being compatible with all photoresist materials suited for conventional direct laser writing, SLM based direct laser writing is another way to improve three-dimensional resolution.
In conclusion, we have demonstrated SLM based direct laser writing with high numerical aperture oil immersion objectives, combining aberration correction with different amplitude filters. Aberration correction enables the use of proper designed shaded-ring filters, able to reduce the aspect ratio of the voxel from the original 2.6 down to 1.7. Point-spread-function scans as well as written woodpile photonic crystals clearly demonstrate the validity of this approach. Due to the reduced aspect ratio, woodpile photonic crystals with rod distances down to 400 nm are realized, still showing decent optical properties. Important for the design of shaded-ring filters is the sidelobe intensity. Here, a level of 23% of the maximum intensity in the focal volume seems tolerable. Sidelobe intensity levels of above 30% prevent the fabrication of 400 nm rod distance structures of high quality. Being compatible with all photoresist types used in conventional direct laser writing, SLM based direct laser writing might be the way to further improve resolution in three-dimensional laser lithography.
We acknowledge support through the German Research Foundation under grant FR 1671/6-1 in the framework of the DFG priority program SPP-1327. We thank the team from the Nano Structuring Center for their support with scanning electron microscopy and focussed ion beam milling.
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