Ink-jet printing of optical ink over SU-8 pillars is here proposed as a technology for obtaining microlenses with shape control. To demonstrate the flexibility of this method, microlenses with five different contour shapes (ranging from circular and elliptical to toric or more advanced geometries) have been fabricated. Furthermore, the optical properties of the different fabricated lenses have been experimentally investigated. Focal distance, numerical aperture (NA) and full-width at half maximum (FWHM) of the microlenses have been determined. Arrays of microlenses showed an identical behavior with a standard deviation in the total intensity of only 7%. Additionally, the focal plane of the fabricated symmetric microlenses and the Sturm interval of the non-symmetric ones have been obtained. The experimental results demonstrate the validity and flexibility of the proposed technology.
©2011 Optical Society of America
The progress of miniature optical systems has generated increased interest during the last years in the development of microlenses. Several fabrication methods (e.g. grayscale lithography  or ink-jet printing (IJP) ), have been proposed to obtain such micro-optical structures, all of them showing some advantages and disadvantages. Among these methods IJP is well known to be a cost-effective and flexible technique that has been successfully applied for the development of microlenses [3, 4]. Rapid prototyping capability, high precision dispensing, non-contact multi-material deposition, low material waste and 3D patterning are the key advantages of this technology . This method and others have been used to obtain microlenses that have been applied in the development of several systems and devices, as can be MOEMS  or lab-on-a-chip . It is common that microlenses used in such applications focus light into punctual spots. Nevertheless, there are some applications in which a more complex lens characteristics is required, as for example in the development of lab-on-a-chip using lenses that focus the light into lines [7, 8], to enhance optical fiber coupling efficiency using hemi-elliptic lenses  or in micro-optical systems where correction of astigmatism is required . Microlenses with such behavior have previously been fabricated following different methods, such as astigmatic diffractive microlenses by means of e-beam , using capillary forces , mechanically deforming fabricated soft microlenses  or performing IJP of adjacent drops to obtain microlenses with different contour shapes . However, some of these methods rely on complex and expensive fabrication techniques, or have limitations in terms of the sizes and shapes that can be obtained.
It has been previously demonstrated that it is possible to take into benefit the capability of IPJ to perform aligned local deposition to confine polymers into platforms. This allows controlling the final shape of the deposited structures . In this work we apply this simple, reliable and cost efficient method for the fabrication of microlenses with controlled contour shapes. Transparent platforms with different defined contour shapes have been designed and fabricated to confine an epoxy-based optical ink and to obtain microlenses with the desired shapes. Additionally, such microlenses have been optically characterized.
2. Concept and design
Behavior of the light focused by a microlens is directly related with the geometry of the lens. Different surface curvatures and contour shapes result in e.g. different focal distances, numerical apertures (NA), full-width at half maximum (FWHM), and different distribution of the light intensity in the lens focal planes. If the lens is not symmetric, meaning that it has different curvatures on the x- and y-axes, it will not focus on a single focal point, but it will form the so-called Sturm interval . It basically consists in three focal planes distributed along the direction of the light propagation: The horizontal line focus (HLF) appears in the plane in which the light in the vertical axis has been focused but not in the horizontal one, while the vertical line focus (VLF) corresponds to the plane in which the light is focused in the horizontal direction but not in the vertical one. The third element of the Sturm interval is the circle of least confusion (CLC) and it can be observed between the HLF and the VLF, at the plane where light is focused in the same degree in both directions. To validate the technology proposed in this work, microlenses with four different contour shapes have been designed and fabricated, two with a symmetric behavior and two with a non-symmetric one. Such microlenses are shown schematically in Fig. 1 , in which the x- and y-axes are in the microlenses planes, while the z-axis represents the light propagation direction. The first symmetric microlens is shown in Fig. 1a, corresponding to a spherical lens with circular contour shape. Such microlenses are the most commonly used and have been studied in this work only for validation purposes. The second symmetric lens that is investigated hereafter has a toric shape, as can be seen in Fig. 1b. A microlens with this shape will show a symmetric behavior, focusing the light in one single plane, but distributing the light intensity into a ring instead of a point. On the other hand, the first of the non-symmetric microlenses presents an elliptic contour shape, schematized in Fig. 1c. It will present different curvatures in the x- and y- axes, showing an induced astigmatic effect, focusing the light into the Sturm interval .
To provide an idea of the flexibility of the herein proposed technology, the second type of non-symmetric microlenses has been designed as a combination of two concentric identical ellipses tilted 90°, as it can be seen in Fig. 1d. The behavior of such a microlens will be a combination of the behavior of both elliptic shape lenses. Hence, instead of the standard Sturm interval, this microlens will focus the light into a zone that is a combination of the Sturm interval of the perpendicular elliptic lenses.
Fabrication of the controlled contour shape lenses starts with the preparation of platforms with the desired shapes on a transparent substrate. In this work, glass wafers with a thickness of 700 µm are used. The platforms are defined in SU-8 photostructurable epoxy material using conventional photolithography. Initially, the glass wafers are treated in O2 plasma for 7 min. Immediately after this pre-treatment procedure, a layer of 50 µm of SU-8 is spin coated over the wafers. Then a soft-bake is done at 130 °C for 30 min. and the wafers are exposed to UV light with a dose of 400 mJ/cm2. After the exposure, a post-exposure bake (PEB) is done at 100 °C for 30 min., followed by a relaxation time of 24h. Finally, the development of the structures is done in Propylene Glycol Methyl Ether Acetate (PGMEA) followed by a hard bake at 120 °C for 2h in N2 environment. At this point, the fabrication of the platforms is finished, as it is schematized in Fig. 2a .
In order to fabricated of the lenses, and considering the size of platforms, an IJP nozzle with a diameter of 70 µm was used. The ink-jetted material is an epoxy-based optical ink (Ink-Epo_1, Microresist GmbH, Germany)  which refractive index (@850 nm) after cross-linking is 1.55 ± 0.01. Alignment between nozzle and platform consisted of finding out the X-Y offset between an ink-jetted drop and an alignment mark on the substrate, visualized by means of a top view camera. Following an offset correction in the X-Y scan and theta rotation, the optical ink was then locally deposited onto each platform, as shown in Fig. 2b with a lateral precision of 5 µm. The total volume of ink was controlled by the number of drops deposited onto each platform. This printing procedure is done entirely automatic using computer aided design. In addition it has been previously demonstrated that by this method it is possible to control the contact angle of the deposited microlenses . When the platforms were fully covered with the polymer and before any overflowing, the samples were flood exposed to UV-light and a PEB was done at 140 °C for 20 min. At this point the lenses were finished as represented in Fig. 2c, and ready for subsequent characterization. Scanning electron microscope (SEM) images of the fabricated structures are presented in Fig. 3 .
Figure 3a shows a SEM image of a toric microlens fabricated over a platform with annular shape. Figure 3b shows the picture of two lenses obtained doing the IJP process over platforms with elliptic shape. Finally, Fig. 3c shows the profile of 5 different microlenses fabricated over circular platforms obtained using a surface profiler (Tencor Alpha-Step 500). This demonstrates that the size and curvature of the different the developed microlenses are equivalent, without any roughness or defect on their surfaces. These results validate the capability of the proposed technology to develop microlens structures with relatively arbitrary contour shapes.
Characterization of the fabricated microlenses was done using an optical fiber with a core diameter of 50 µm connected to a diode laser (Thorlabs GmbH, Germany) with a working wavelength of 635 nm. The lenses are placed on a holder at a fixed position and the light passing through is focused on a CCD camera (Pixelfly, Spain) by means of a microscope objective (x10). The lenses with symmetric contour shapes were considered first (Fig. 4 ).
Figure 4a shows a CCD image of the focal plane of a circular lens array with a diameter of 100 µm. Figure 4b shows a 3D spatial reconstruction of the experimental intensity distribution. As it can be observed, the focal points of all these microlenses are focused in the same plane and have a similar intensity, with a standard deviation of only 7%. The NA of these microlenses has been measured at 0.19 ± 0.01, the FWHM at 5.2 ± 0.7 µm and the focal distance at 260 ± 20 µm. Conversely, Fig. 4c presents the focal plane of a lens with a toric shape with D1 of 125 µm and D2 of 275 µm, as it was schematically represented in Fig. 1b. As it can be observed in this case, instead of a focal point, the light is focused into a ring, as it was expected. The NA of this toroid lens is 0.16 ± 0.01, the FWHM is 4.3 ± 1.5 µm and the focal distance is 480 ± 20 µm.
Lenses with asymmetric shapes were also characterized. As it was introduced in section 2, such microlenses present different curvatures in their orthogonal axes resulting in the formation of the Sturm interval. This phenomenon can be observed in Fig. 5 for a lens fabricated over a platform with an elliptic shape with D1 of 110 µm and D2 of 300 µm, as it was represented in Fig. 1c. Concretely, the VLF can be observed at Fig. 5a as a vertical line with a FWHM in the horizontal axis (FWHM-h) of 3.7 ± 1.0 µm and at a focal distance of 500 ± 24 µm. The CLC is shown in Fig. 5b at a distance of 1070 ± 42 µm as a blurred circle equally focused in both axes. Finally, Fig. 5c shows the HLF with a FWHM in the vertical axis (FWHM-v) of 5.4 ± 1.5 µm and a focal distance of 1640 ± 80 µm. Hence, the total distance of the Sturm interval for this microlens was 1140 ± 83 µm. The NA of this lens was 0.11 ± 0.01 in the vertical axis (NA-v) and 0.09 ± 0.01 in the horizontal axis (NA-h). Conversely, Fig. 6 shows the Strum interval of an array of three elliptic lenses with a D1 of 430 µm and a D2 of 100 µm. In this case the Sturm interval starts with the HLF due to the lens orientation, as it is observed in Fig. 6a. Its focal distance is 230 ± 25 µm and its FWHM-v is 1.9 ± 0.3 µm. The CLC is shown in Fig. 6b with a focal distance of 800 ± 15 µm. Finally, the VLF can be seen in Fig. 6c, it has a focal length of 1360 ± 20 µm and a FWHM-h of 11.2 ± 0.6 µm. In this case the total distance of the interval of Sturm is of 1130 ± 32 µm. As it can be observed both the CLC and the VLF of the three microlenses are overlapping due to the short distance between them. Furthermore, the different elements of the Sturm interval are located in the same focal planes for the three microlenses of the array, demonstrating that their size and curvature are equivalent.
Finally, a microlens structure consisting in the crossing of two identical ellipses was also characterized. Figure 7 shows the Sturm interval of this microlens system. In this case, instead of the standard HLF, CLC and VLF, a combination of these elements was observed. First a square focal shape is shown, as presented in Fig. 7a. Such distribution of the light power corresponds to the combination of the HLF of the horizontal lens and the VLF of the vertical lens. Its focal distance is 1000 ± 40 µm. Figure 7b shows a focal point that corresponds to the CLC of the Sturm interval, but in this case the blurring of this point is reduced since the lens system is almost symmetric and similar to a standard spherical microlens in the center. The focal distance of the CLC is 1065 ± 25 µm, while its FWHM-h is 11.1 ± 1.6 µm and its FWHM-v is 10.0 ± 0.9 µm. The low and similar values of both horizontal and vertical FWHM of the CLC demonstrate that in this region this microlens system behaves almost as a standard lens with circular shape. Finally, a rhombus focal shape is observed, as can be seen in Fig. 7c. This power distribution of the light corresponds to the combination of the VLF of the horizontal lens and the HLF of the vertical lens. This final element can be found at a focal distance of 1130 ± 25 µm. The NA of this optical system is similar in both axes, being the NA-h of 0.17 ± 0.01 and the NA-v of 0.15 ± 0.01, resulting in a short interval of Sturm of only 130 ± 50 µm. The results obtained from the characterization of both symmetrical and non-symmetrical microlenses validate the proposed technology for the reliable development of microlenses with an arbitrary contour shape.
Lenses with five different contour shapes have been designed, fabricated and characterized. We demonstrated that it is possible to achieve microlenses with different optical focusing characteristics using a simple and reliable method, consisting in the aligned local deposition of optical ink over transparent SU-8 platforms. Both symmetric and non-symmetric microlenses have been designed, fabricated and characterized as proof of concept. The first symmetric structure studied is an array of standard circular-shape microlenses. The second one is a microlens with toric shape showing a ring on its focal plane. Conversely, the non-symmetric microlenses have shown, as expected, the Sturm interval. Two elliptic lenses with different geometries have been studied; in both cases it was possible to clearly observe the horitzontal line focus, the circle of least confusion and the vertical line focus. Furthermore, a microlens system consisting in two identical ellipses crossed by the central point was also investigated. For this optical system, instead of the standard Sturm interval, a combination of the HLF, the CLC and the VLC of the two ellipses has been confirmed. These results validate both the proposed technology to develop microlenses with a large degree of freedom for the desired contour shape and the capability and flexibility of the fabrication procedure. Such micro-optical components are of great interest for the future development of systems where microlenses with particular optical characteristics are required, as can be optical scanning systems, imaging applications or lab-on-a-chip platforms.
This work has been funded by the IAPP Marie Curie action ACAPOLY nº PIAP-GA-2008-218075 and the European Research Council (FP7/2007-2013) / ERC n° 209243, both from the EC's 7th FP. The authors are pleased to acknowledge the EPFL CMi for their valuable discussions and help. J. Perera-Núñez acknowledges the Junta de Extremadura for her grant, the Spanish Ministry for Science and Technology (MAT2009-14695-C04-01) and FEDER.
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