As the third pillar of fabrication apart from subtractive and formative techniques, the additive manufacturing method of two-photon polymerization (2PP) 3D printing has been a growing technology for the fabrication of microoptics and photonics over the last years [1][2][3]. 2PP has been utilized to manufacture a multitude of optical parts, from typical refractive lenses [4][5][6] and diffractive optical elements [7,8] to photonic crystals [9,10] and polarization optics [11]. Furthermore, 3D printed microoptics enable applications ranging from micro-needles and endoscopy in biomedicine [12][13][14] to quantum technology [15][16][17] and photonic networks [18,19]. The usual drawback of 3D printed microoptics are long fabrication times, which can easily reach times of a day for larger elements [6]. For more complex designs, such as lens stacks, some of the printing time and design effort needs to be utilized to produce supporting structures that hold the optical elements in place. We dramatically reduce the fabrication time to 2 minutes per lens by utilizing diffractive lens designs together with two-photon polymerization grayscale lithography (2GL). With 2GL, we are able to increase the distance between printed layers while preserving the typical shape-accuracy and smoothness, reducing manufacturing times further [20,21]. Additionally, performing 3D printing inside a porous medium eases the need for supporting structures, enabling efficient volumetric integration of complex optics design [19,22,23].
We demonstrate singlet and doublet diffractive lenses for focusing and imaging that are rapidly manufactured by 2GL. The lenses with diameters in the half-millimeter range are embedded in a 60 µm film of porous SiO 2 (PSiO 2 ), allowing to omit supporting structures typically necessary to anchor structures, especially lens stacks to the substrate [17,21,24]. We first highlight the capability of diffractive lenses fabricated in PSiO 2 with simple singlet lenses with four different numerical apertures (NAs) from 0.15 to 0.60. They show close to diffraction limited performance in focusing Gaussian light beams with a wavelength of 600 nm. In the second part we highlight an imaging optical system consisting of two diffractive lenses. This doublet lens with a physical diameter of 600 µm and optical diameter of 575 µm offers high resolution imaging in a thin form factor, as it also fits in the 60 µm thick PSiO 2 film. To first test the capabilities of 2GL fabricated diffractive optics in PSiO 2 , we design and print four different singlet lenses with a diameter of 500 µm and numerical apertures of 0.15, 0.30, 0.45 and 0.60. We use the ray-optical design software Zemax OpticStudio 20.1. The basic layout of the optical system is sketched in Fig. 1(a), with light traveling along the z-axis. The diffractive lens is defined as a binary2-surface located 10 µm below the surface of the 60 µm thick PSiO 2 film. With the refractive indices of the lens n lens and of the surrounding medium n medium as well as the design wavelength λ = 600 nm, the height is given as
Here, a 2m are the term numbers that give the optimal phase and M the maximum order to which the parameters are optimized. In case of the singlet lenses, the maximum order M is 20, while the phase will approach a parabolic shape during optimization of the term parameters. The diffractive singlet lenses have spatial frequencies of up to 250 mm -1 , 500 mm -1 , 750 mm -1 and 1000 mm -1 at the edge of the lenses with NA's 0.15, 0.30, 0.45, and 0.60. This results in spatial extents of the outmost Fresnel zones of 4 µm, 3 µm, 2 µm, and 1 µm. The refractive index of the polymerized photoresist IP-n162 in PSiO 2 is derived using Maxwell-Garnett theory [25]. As the porosity of PSiO 2 is 68.29%, the diffractive lens will, to 68.29%, consist of polymerized IP-162 with a refractive index of 1.6221 at the design wavelength of 600 nm [26], while the other 31.71% are made up of PSiO 2 . Air-filled PSiO 2 has a refractive index of 1.1394 at 600 nm, with low dispersion [22]. These values result in an effective refractive index of the polymerized IP-n162 in PSiO 2 of 1.5714 at 600 nm, used to define the shape of the lens. The designed height of each Fresnel zone given by Eq. ( 1) is circa 1.389 µm.
The diffractive lenses are depicted in the two columns on the left of Fig. 1(b) in ascending numerical aperture from top to bottom. A zoom-in of the 0.30 NA lens is illustrated in Fig. 1(c), which highlights all diffractive zones and shows some aliasing due to the resolution of the image. Additionally, we fabricate the 0.30 NA lens on top of a microscopy glass slide, with the same design and fabrication parameters as the one inside PSiO 2 . The zoom-in of this lens is depicted in Fig. 1(d) and compares well in the shape and look to the lens fabricated in PSiO 2 . The remaining difference in appearance can be explained by the increased refractive index difference between at the interfaces of the resist IP-n162 and air to IP-n162 and PSiO 2 .
To examine the focusing ability of the 3D printed singlet lenses, we use the setup illustrated in Fig. 2(a). Laser light (NKT SuperK Extreme) at a wavelength of 600 nm, filtered by an Acousto-Optic Tunable Filter (NKT SuperK Select+, specified full width at half maximum 2.5-8.5 nm in the visible), is collimated by a triplet fiber collimator (Thorlabs PAF2-A4A) and strikes a pinhole with a diameter of 500 µm, matching the designed aperture of our 3D printed singlet lenses. The sample as seen in Fig. 1(b) is situated on a piezo-electric z-stage (P-736 PI nano Z) that can be moved with high accuracy. The laser is subsequently focused by the printed lens and analyzed by a basic microscopy setup consisting of a 0.7 NA, 60x magnification microscope objective (Nikon CFI S Plan Fluor 60x ELWD MRH08630), a tube lens and a camera (Allied Vision GC2450C). To measure the 3D intensity distribution, an image is taken in steps of 0.1 µm for the entire traveling range of 200 µm. The normalized intensity cross sections in the xy-focal plane and along the optical axis as a zy-plot for the four different types of singlet are depicted in Fig. 2(b). Here, the measurements depicts compact and symmetric Gaussian-shaped focal spots. Small artifacts in the intensity from the fabrication and diffractive nature of the lenses are visible for the two lower NA lenses with NA's of 0.15 and 0.30 but vanish almost completely for the higher NA lenses with NA's 0.45 and 0.60. To quantize the focusing performance, we fit Gaussian profiles through the intensity maximum of the focus along all three spatial axes. The full width at half maximum (FWHM) of the Gaussian profiles depict a symmetric behavior in the xy-focal plane with values from a FWHM of 2.64 µm in x-and 2.52 µm in y-direction for the 0.15 NA lens (design 2.06 µm) to a FWHM of 1.01 µm in x-and 0.99 µm in y-direction for the 0.60 NA lens (design 0.52 µm). The better focusing performance of the higher NA lenses is especially visible when looking at the intensity distribution in the zy-plane plotted on the right column of Fig. 2(b). Here, the FWHM along the optical axis is 53.78 µm for the 0.15 NA lens, decreasing to 7.65 µm for the 0.60 NA lens. See Table 1 for the comparison of designed and measured FWHM values for all four singlet diffractive lens types. The focusing performance of the diffractive singlets is close to the designed values. The deviations, however, increase with the NA of the singlets. This leads us to assume, that the fabrication resolution and tolerances are the likely culprit of the reduced optical performance. At high spatial frequencies of the diffractive elements, the lateral voxels dimensions in fabrication approach the feature size and period of the outer Fresnel zones.
Table 1. Full width at half maximum spot dimensions in lateral (denoted by the subscripts xy, x, and y) and axial direction (denoted by the subscript z) for the four diffractive singlet lenses. We give the designed as well as measured values, as extracted from Gaussian fits seen in Fig. 2. design (µm) measured (µm) NA FWHM xy FWHM z FWHM x FWHM y FWHM z 0.15 2.06 47.73 2.64 2.52 53.78 0.30 1.03 11.72 1.28 1.28 14.84 0.45 0.68 5.05 1.05 1.01 8.41 0.60 0.52 2.70 1.01 0.99 7.65
For imaging optics, the system requires a more advanced optical design. We achieve better performance at off-axis light fields, by utilizing a second diffractive surface in the system, resulting in a doublet diffractive lens stack, graphed schematically on the right of Fig. 1(a). Typically, at least one of the lenses of a 3D printed optical doublet needs to be anchored to the substrate or fiber by a supporting structure. This is the case both for refractive [17,21], and diffractive lens stacks [24,27]. Additionally, the supporting structure has to have openings to give the liquid resist room to dissolve into the developing solution. Printing lens stacks in porous media, such as the porous SiO 2 , there is no need for a supporting structure, as the lenses are held in place by the porous media itself and the developing solution can penetrate through the pores of the medium. This allows for a faster and more feasible fabrication of strongly overhanging or even free-floating structures. Moreover, the optically active area for arrays of lens stacks can be as large as 100%. A top view microscope image of optical doublets is depicted in Fig. 1(b).
The design of the diffractive doublet lens system is illustrated in Fig. 3. As design parameters we choose a wavelength of 633 nm, an aperture diameter of 550 µm, an optical diameter of 575 µm, and a physical diameter of 600 µm. At the design wavelength of 633 nm, the polymerized IP-n162 inside the PSiO 2 has a refractive index of 1.5687. We place the top diffractive lens 5 µm inside of the 60 µm thick PSiO 2 film and the bottom lens 45 µm below the top lens. With a working distance of 1000 µm in air, the diffractive doublet boasts an effective focal length of 1032 µm which result in an f# of 1.86 and an NA of 0.258. The modulation transfer function (MTF) of the diffractive doublet is plotted in Fig. 5, and discussed below. To achieve a field of view of roughly 20°, three ray fields at 0°, 5°, and 10°are implemented. We optimize the two diffractive lenses in Zemax OpticStudio 20.1, where they are defined by Eq. ( 1). The performance of the diffractive doublet is diffraction limited for field angles below about 3°, after which astigmatism, spherical aberrations and coma reduce the optical performance as is visible in the MTF shown in Fig. 5.
The optimized parameters give a maximum spatial frequency of circa 201 mm -1 for the bottom and 639 mm -1 for the top lens. Both diffractive surfaces can thereby be fabricated easier than the singlet 0.45 NA and 0.60 NA lenses, which both have higher maximum spatial frequencies. The diffractive lens doublet is manufactured with the same technique as described above. Multiple doublets are shown in the right two columns of Fig. 1(b).
To examine the optical performance of the doublet diffractive stack, we take images of an USAF 1951 resolution test chart at several magnifications. The basic setup is depicted in Fig. 4(a) and was previously utilized in [6,21]. Collimated white LED light (Thorlabs MCWHLP1 and Thorlabs AC254-040-A) first strikes a diffusor (Thorlabs DG10-1500-A) before being optically filtered using a band-pass filter. The filter is centered at 633 nm with a spectral FWHM of 10 nm (Thorlabs FL05632.8-10). The light is subsequently focused through a 10x magnification microscope objective (Mitutoyo M Plan Apo HR 10x, part number 378-788-4) and illuminates the USAF 1951 resolution test chart (Edmund Optics USAF HI-RES Target 2IN SQ NEG) before it strikes the diffractive doublet stack. We change the beam diameter in front of the first microscope objective with an iris (Thorlabs SM1D12C) to match the designed aperture of the diffractive doublet lens. The image is then analyzed by a basic microscopy setup in order to soley investigate the doublet system under test and not introduce pixilation, caused by direct imaging onto a camera. The microscopy setup consists of a 20x magnification microscope objective (Mitutoyo M Plan Apo 20x, part number 378-804-3), a tube lens and a camera (iDS UI-3180CP-C-HQ R2.1). We increase the magnification by reducing the distance between the USAF 1951 resolution test chart and the diffractive lens stack as well as centering on the relevant groups. Three different magnifications are illustrated in Fig. 4(b) through (d). The images show high contrast and quality throughout the groups. Some slight vignetting is visible at the edge of the higher elements of group 2 in Fig. 4(b), as well as some field curvature that is apparent at the edge of the image, visible in Fig. 4(c). Group 6 and 7 illustrated in Fig. 4(d) shows a slightly higher background intensity and therefore reduced contrast compared to the images in Fig. 4(b) and (c), which could be caused by light scattering at the various interfaces and in the porous medium itself. We quantify the resolution through the contrast, defined as With a resolution limit of 10%, the diffractive doublet stack is able to resolve element 2 of group 8, corresponding to a resolution of 287 lp /mm. Groups 6 and lower can be resolved clearly with higher contrast, which is plotted in the intensity profile in the left of Fig. 4(d). Taking the contrast for groups 2 to 8 of the USAF 1951 resolution test chart using the intensity levels depicted in Fig. 4(b) to (d), we construct the MTF, graphed in Fig. 5 for one diffractive doublet system. We then compare it to the design at the three different fields, 0°, 5°and 10°as well as 2), of one element from the USAF 1951 resolution test chart, going from group 2, element 1 to group 8, element 3. The contrast exceeds 10% for a resolution of up to 287 lp /mm. The designed MTF is shown for the tangential rays at field angles of 0°, 5°and 10°, as shown in Fig. 3. While a wavelength of 633 ± 5 nm is used to measure the MTF of the doublet, the diffraction limit and MTF at field angles of the design are given for a wavelength of 633 nm.
giving the theoretical diffraction limit, also plotted in Fig. 5. The MTF of the diffractive doublet lens exhibits some oscillations in the lower frequencies. This could be owed to the fact, that the elements of the resolution test chart are imaged with different field angles and are prone to vignetting, which is visible in Fig. 4(b). The contrast remains at above 20% for resolutions up to roughly 160 lp /mm and above 10% for up to 287 lp /mm. All but the measured MTF are calculated for monochromatic light at 633 nm. Polychromatic light, even for the narrow bandpass filter spectral range of 633 ± 5 nm, reduces the designed MTF. A study on achromatic doublet microoptical systems in PSiO 2 is given in [23].
A thorough description of the porousification of the silicon via etching as well as its thermal oxidation and transfer is given in [22,23]. The transferred film of PSiO 2 is visible as the ragged film on top of the glass substrate, as seen in Fig. 1(b). The average pore size of PSiO 2 produced by this method is 60 nm, which minimizes light scattering in the visible and infrared regions [22]. After transferring PSiO 2 onto quartz, the average total transmission (from 450 nm to 800 nm) increases from 95.6% (quartz only) to 97.2% due to the antireflection effect. This indicates that visible light perceives PSiO 2 as a homogeneous, transparent material, and the pores do not negatively affect the optical performance of the lenses printed within. Small cracks can develop during film transfer or the fabrication and developing process as described below, which can be seen on the right side of the sample. To prepare the sample for printing, the PSiO 2 -film is infilled with the photoresist IP-n162 over night. While not utilized in this study, infilling of the photoresist can be accelerated by placing the samples on a hot plate at 55-60°C for 3-5 minutes [19], and can be further accelerated by applying a lower than ambient pressure during the infilling process.
All lenses are fabricated using by the commercially available 3D printer Nanoscribe Quantum X (Nanoscribe GmbH & Co. KG) using two-photon polymerization grayscale lithography (2GL). The photoresist is polymerized by a femtosecond pulsed laser at a central wavelength of 780 nm. The lenses are fabricated in the dip-in mode with the medium feature set consisting of a 25x magnification objective with an NA of 0.8 (LCI Plan-Neofluar 25x/0.8 Imm Korr DIC M27 420852-9973). This objective has a maximum calibrated writing field diameter of 700 µm. Larger structures can be fabricated by lower magnification objectives [6], usually at the cost of resolution, or by stitching together multiple writing fields. We utilize grayscale lithography to increase manufacturing throughput while achieving smoother structures [20,21]. During the 2GL fabrication, the laser power is modulated by an acousto-optical modulator instead of the constant power applied during the typical 2PP fabrication processes [6]. We utilize average powers between 0 mW and 65 mW, dynamically changing the voxels size, resulting in step-free surfaces even at comparatively large slicing distances of 1 µm. We employ a hatching distance of 0.2 µm. The laser is scanned through the resist using a pair of Galvo mirrors at 70 mm s -1 for the singlet diffractive lenses and the top lens of the diffractive doublet. The bottom lens of the diffractive doublet is scanned slightly faster with a speed of 85 mm s -1 . These parameters result in fabrication times of about 2 minutes for the singlet and 4 minutes for the doublet lenses. Typical fabrication on glass substrates takes the same laser powers, slicing and hatching distances while using a faster scan speed of 200 mm s -1 [21], reducing the fabrication time in the PSiO 2 by a factor of two to three for the same fabrication volume. As discussed in [22], PSiO 2 is non-absorptive in the visible and near-infrared range and its far sub-wavelength pore size (averaging 60 nm in diameter) limits light scattering at visible and infrared frequencies. During printing, the pore is filled with liquid IP-n162, which has a refractive index closer to SiO 2 compared to air, further reducing the light scattering. Therefore, the porous medium won't compromise the resolution and repeatability. Following the polymerization of the print, the liquid photoresist is removed in a bath of mr-dev 600 (micro resist technology) inside an air-tight container at 40 °C for 5.5 h. The sample is subsequently placed into an isopropyl alcohol bath overnight and then critical point dried with in a fresh bath of isopropyl alcohol in a CO 2 critical point dryer (Leica EM CPD300). Typical drying with air or gaseous nitrogen is also possible but can cause cracks due to the capillary forces inside the small channels within the PSiO 2 . After fabrication, the samples can be handled the same way as 3D printed microoptics on glass substrates.
We have successfully fabricated singlet and doublet diffractive lenses by grayscale lithography femtosecond 3D printing inside porous SiO 2 . The singlet lenses with NAs of up to 0.60 illustrate high focusing performance and are rapidly fabricated due to the small spatial extent. We save fabrication time and design effort for the diffractive imaging lens stack by utilizing an approach that does not require any supporting structures. The fabrication time is further reduced by utilizing grayscale lithography, allowing large slicing distances while keeping the shape accuracy. We observe high contrast and low aberrated images of the diffractive lens stack and analyse the contrast MTF, which shows great resolution of up to 287 lp /mm at over 10% contrast.
In the future, optical performance could be increased further with a third lens element in thicker films of porous SiO 2 or higher NA writing objectives. The porous SiO 2 matrix can also be infilled with liquids, providing a way to change the optical capabilities of the system.
For applications in more extreme environments, e.g., a thin protection layer of Al 2 O 3 could be applied using different methods. Additionally, future research could also investigate the impact of porosity levels of SiO 2 on optical performance. Furthermore, fabrication times can be reduced further with light-sheet 3D-microprinting [28] or printing via digital holography [29].