The design, simulation, fabrication and characterization of 3-D modulable micro-optical system based on poly-dimethilsiloxane (PDMS) are presented in this paper. This system consists on two uncoupled PDMS lenses with different diameter (2 and 10 µm). Under stretching conditions, the dimensions of the small lens are not modified, whereas the geometry of the bigger lens is shifted from spherical to elliptical. A combination of different technologies is used to fabricate this microsystem: silicon, polymer and soft-lithography microfabrication techniques. This combination allows obtaining structures with a simple and mass production technology. Experimental results confirm the predicted numerical simulations, showing that, when the structure is under stretching conditions, the first focus is virtually invariable whereas the second focus becomes a Sturm zone.
©2008 Optical Society of America
Microlenses are the basic component of many optical devices and systems. Formation of a large variety of microlenses has been possible thanks to the development of accurate microfabrication processes: using both semiconductor  and polymer  technology. Two different configurations are usually chosen to define microlenses: either parallel configuration , when the lenses are implemented parallel to the substrate surface and light follows a path parallel to it; or orthogonal configurations , when the lenses are orthogonal to the substrate.
Some technologies have been employed to obtain microlenses on parallel configuration: either by using several masks  and then mounting them on a vertical holder , with complex technological steps , with grayscale masks  or with a combination of UV and soft lithographic techniques . However, the production cost of these micro-lenses is dramatically increased because it is required to develop complex technology processes and the alignment of the microlenses with the light sources.
Alternatively, in the orthogonal configuration, the light is injected from the backside of the substrate and the lenses are fabricated on the front side focussing the light at a fixed distance. Using this configuration is relatively simple to obtain a high density of microlenses and, since full wafer processing is possible, achieve mass production. A large number of technologies have been used to obtain microlenses on orthogonal configuration, as for example, reflow of photoresist microstructures [10,11], ink jet processes of UV curable polymers , soft lithography techniques (like hot embossing to transfer master lenses to plastic materials  and replication processes by moulding UV curable epoxies [14,15]) or a photoresist replication and reflow method . Recently, some researchers, as an effort to raise the microlenses capabilities and applications, have reported such devices with a variable focal length. Usually, these structures are based on a thin membrane that requires complex heating  or microfluidic systems [18,19] to achieve the actuation over the lenses; resulting on fragile devices.
Previous works have demonstrated that is possible to combine silicon micromachining technologies with polymer technologies (SU-8) and soft lithography  techniques to obtain optical devices based on polydimethylsiloxane (PDMS) . The PDMS is a silicon elastomer with interesting properties, such as transparency at visible range, physical and chemical stability, high flexibility (with a Young modulus between 300 and 800 kPa), and incompressibility.
In this work, the replication of complex micromechanized shapes on silicon to obtain a robust 3-D modulable micro-optical system based on PDMS has been performed. This system consists on a structure of two microlenses with uncoupled optical properties that, under a mechanical actuation, only one of the microlenses will change its shape, while the other is unaffected. Since in the approach presented in this paper the microlenses are solid structures (not based on membranes) and the modulation is stretching-induced, the resulting device is highly robust. Moreover, it is possible to obtain these complex structures with a low-cost (mass-production), simple and highly repetitive technology. Such devices can be easily applied to obtain robust optical scanners, since these scanners are usually fragile since they are based on micromechanized systems . A second application could be the improvement of photonic lab-on-a-chip systems. Generally, in such systems cylindrical lenses are implemented , which focuses the light only in one axis and additionally the focal plane depends on the refractive index of the liquid surrounding the microlens. With the usage of the proposed microlens system, both drawbacks are addressed and solved, since it allows obtaining a focal point (that is, obtaining a 2D confinement) that can vary its position upon actuation for a fixed liquid surrounding the microlens system. Alternatively, if the refractive index of this liquid vary, the curvature radius of one microlens can be changed so as to keep the position of its focal point fixed, while using the second microlens for sensing purposes.
2. Device concept and simulation
The proposed structure is presented on Fig. 1, it consists on a mechanically modulable microoptics structure based on PDMS that integrate two lenses of different sizes. The small lens (Sl) is placed at the centre of the large lens (Ll) conforming a solid structure and therefore both focuses are perfectly aligned. Since the light passes through both lenses simultaneously and not consecutively, we have defined the system as uncoupled. Figure 1(a) schematise the focus of the Sl and Ll lenses surrounded by rings. The focal of Sl, surrounded by the primary ring (PR), can be observed on the A-A’ cut; this PR is due to the light that will form the Ll focus at the B-B’ cut. This Ll focus is surrounded by the secondary ring (SR), which is the light that diverges from the Sl focus.
Due to the mechanical properties of the PDMS , it is easy to modify the shape of these micro-lenses stretching the structure by horizontal mechanical actuation (on the x-axis). Using this method is possible to modulate their behaviour; conceptual scheme of this can be show on the Fig. 1(b). When a uniaxial actuation force is applied over the whole structure, the Sl does not suffer measurable variation of his curvature. Conversely, the Ll will be highly stretched, due to its bigger diameter. Hence the first focus point will remain unaltered whereas, under stretching, the second focus is converted to an interval of Sturm . Three elements can be observed on this interval. On a surface at one end of the interval is the horizontal line focus (HLF), on the other surface end is the vertical line focus (VLC), and where the image is least blurred is the circle of least confusion (CLC). This behaviour is usual on an astigmatic lens and is due to the different curvatures of the Ll on the x-axis and the yaxis.
In order to obtain the optical and mechanical properties presented above, the diameter of the Sl (DS) has been fixed at the minimum value possible with the standard UV photolithographic techniques; hence DS has been fixed at 2 µm. On the other hand, the Ll has been designed to assure that the two micro-lenses are perfectly uncoupled, so it is possible to distinguish the different focuses, and that after stretching, the interval of Sturm can be observed. Hence, the diameter of the Ll (DL) has been fixed at 10 µm.
Due to the complexity of this design a numerical analysis has been done using the FIMMWAVE and FIMMPROP software (Photon Design, Oxford, UK). This tool uses eigenmode expansion (EME) [26,27] to solve the optical propagation problem in a rigorous manner. The algorithm can be understood simply as follows. First the structure is approximated by dividing in the propagation direction into many short sections and then maintaining a constant cross-section in each section to create a staircase approximation. Within each section the electromagnetic fields are expanded in terms of local modes:
Where βm is the propagation constant of the mth mode and c + m, c - m are the amplitudes of the modes in the +z and −z direction. The problem then reduces to finding the mode amplitudes in each section. At interfaces between sections coupling occurs both between co-propagating modes and potentially reflection into back-propagating modes. This coupling is computed using overlap integrals and matrix algebra, generating a scattering matrix for the interface. The s-matrices for all the interfaces and sections can be combined to create an smatrix for the whole lens. For this application, the method has the advantage over others in that a) it can model wide-angle effects correctly, b) it gives information on reflections, c) it can efficiently deal with relatively large volumes without requiring a fine grid and d) it is fully vectorial.
Numerically simulated intensity pattern of the proposed optical system with a Gaussian beam illumination and without the actuation force, are presented on Fig. 2(a) for A-A’ cut and on Fig. 2(b) for the B-B’ cut. Both patterns have revolution symmetry so, in plane vision, the simulations predict the expected situation of a focus surrounded by a ring. However some differences between Sl and Ll can be observed: the first focus has a smaller FWHM than the second focus and it focuses less power; on the other hand, the PR is wider and more complex than the SR and it carries more light intensity. These results are expectable when considering that the DS is smaller than the DL and hence less amount of light is coupled by the Sl. In addition, since Sl can be understood as a perturbation in the Ll, the focusing quality of this latter lens is reduced and hence its FWHM increases.
As it was explained previously, when the light of the first focus continues propagating it diverges and becomes the SR. On the other hand, when the light of the PR continues propagating will converge and become the second focus point. Therefore the PR and the second focus point have the same power and, on the other hand, the power of the first focus point and the power of the SR match as well. This clearly shows that the behaviour of both lenses is uncoupled.
When the micro-optical system is 10% stretched in horizontal direction the behaviour of the first focus is not modified. That is because the diameter of the Sl are only increased on 200 nm, so their optical performance does not suffer from appreciable variation, keeping the revolution symmetry as can be seeing in Fig. 3. On the other hand the Ll is highly stretched; its diameter is increased in 1 µm resulting on an elliptic lens. Because of that, the PR behaviour is highly modified and it does not keep the revolution symmetry. The y-axis cross section, Fig. 3(b), shows the same shape presented on the Fig. 2(a). Conversely, on the x-axis cross section, Fig. 3(a), the focal still shows the same shape presented on Fig. 2(a), but the PR structure has been significantly modified, resulting in a non-symmetrical light distribution. This variation on the PR behaviour is consistent since the PR behaviour will depend exclusively from the Ll shape and after stretching, this has been modified. Hence, when the light propagates the PR will form the interval of Sturm.
As it is expected on an elliptic lens, the x-axis and the y-axis can be studied separately. When the light of the PR on the y-axis is focused, on the x-axis it continues converging. This situation produces the HLF, a focus line wider on the x-axis (see Fig. 4(a)) than in the y-axis (see Fig. 4(b)). Then, the light on the x-axis continues converging and, on the y-axis, begins to diverge. At this point both axis are similar, the CLC is reached, as it is showed on Fig. 4(c) and Fig. 4(d) for the x and y-axis. Finally, the light on the x-axis is focused, as can be seen on Fig. 4(e), but on the y-axis has continued its defocusing, see Fig. 4(f). Hence, the VLF is obtained, wider on the y-axis than in the x-axis.
Three different technologies have been used all together to obtain the proposed microoptic system: Silicon micromachining, polymer technology (SU-8) and soft lithography. Using a combination of these three technologies it is possible to obtain the proposed systems. Conceptually, its fabrication can be resumed in three stages (one for each technology used): definition of rocket tips (combination of a shaft and an isotropic apex) on silicon, obtaining of the SU-8 master and, finally, replication process to form the micro-optical system in PDMS. DRIE is the most important technological process for the definition of rocket tips on silicon . High Density Low Pressure (HDLP) plasma tools improve ion directionality, reduce ion scattering and thus enhance the control of the anisotropy. HDLP plasmas can be generated by a wide range of techniques but Inductive Coupled Plasma (ICP) offers the widest operating window and therefore it is dominating the market for advanced anisotropic etching for MEMS. In this work, the DRIE used is based on the “Bosch process”  which couples the ion bombardment with the deposition of a chemical etch resistant polymer to achieve high vertical profiles .
The processing starts with the wet oxidation of a (100) oriented silicon wafer of 100 mm in diameter. This SiO2 is defined in a photolithographic step to be used as mask (Fig. 5(a)). A nearly isotropic etch is done by DRIE to obtain the sharp apex, as it is showed on Fig. 5(b)). After that, in the same DRIE step, etching conditions are modified so as to obtain a vertical etch profile process, as can be seen in Fig. 5(c). Then, the SiO2 mask is removed by wet etching and a new SiO2 layer is thermally growth to be used as a sacrificial layer, see Fig. 5(d). After this step, the rocket tips have been defined and they will be replicated to obtain the micro-optical system. The replication process involves the usage of this silicon master to define a polymer master over which PDMS will be cast to obtain the proposed system. This “double mastering” process starts with the spinning of a layer of SU-8 (SU-8 50, MicroChem Corporation, Newton, MA, USA) with the following spinning conditions: 400 rpm×30 sec. A thickness of 150 µm was obtained. After 10 minutes at 65 °C wafer is baked for 2 hours at 95 °C in a hot plate. When the wafer returns to room temperature it is exposed 60 seconds to UV without any kind of mask. Then a Post Exposure Bake (PEB) of 30 minutes at 95°C is done. Result is schematized in Fig. 5(e). After the PEB, the wafer is immersed in HF in order to etch the SiO2 sacrificial layer and release the patterned SU-8 layer from the silicon substrate, as can be seen in Fig. 5(f). As it has been previously mentioned, this SU-8 layer will be used as a master. The final process for defining the proposed micro-optical system starts with the preparation of the PDMS prepolymer by mixing the curing agent and the elastomer base in a 1:10 ratio (v/v) and degassing in a vacuum chamber. After pouring the prepolymer over the SU-8 master (Fig. 5(g)) the PDMS was cured on a hotplate at 80°C for 20 minutes. Once the PDMS has polymerized, the micro-optical system is mechanically released from the SU-8 master. The final structure is schematized on Fig. 5(h). At this point, it is possible to repeat steps (g) and (h) several times with the same SU-8 to obtain a large number of systems.
4. Experimental results
In order to structurally characterize the modulable micro-optical system, two microscopic techniques have been used: Scanning Electronic Microscopy (SEM) and confocal microscopy. Figure 6(a) and (b) show a SEM picture of a 3×3 array of the proposed system. As it can be seen on these pictures the fabricated micro-optical systems have a high quality and repeatability. The shape of the fabricated structures has been obtained using confocal microscopy, see Fig. 6(c). The expected diameters of both lenses, namely DS=2 µm and DL=10 µm have been achieved, with a high replication quality, as it can be observed from the facet smoothness of the micro-optical system presented. The results obtained from this structural characterization allow validating the technology proposed which, although is based on a non-standard double moulding process, it only requires one photolithographic mask and after the definition of the polymer master, the technology is simplified to a typical mastermould process.
Optical characterization of the proposed structures has been made using the experimental set up schematised on Fig. 7. The light emitted from a LED with a wavelength of 678 nm is coupled to a multimode fiber with a core diameter of 50 µm and faced towards the microoptical system, which is hold with two tweezers. The first tweezers remain fixed throughout the experiment, while the second ones are placed over a micropositioner and therefore they perform the modulation of the micro-optical system, that is, the stretching the structure. A microscope objective (×15) is used to collect the output light and focus it on a CCD camera Pixelfly 200 XS VGA (pco.imagin, Kelheim, Germany) connected to a computer. To optimise the alignment between all the elements of the set up to three additional three-axial micropositioners are used; the first one for the optical fiber, the second one for the microscope objective and the third one for the CCD camera.
The first and the second focus of the micro-optical system are presented on Fig. 8(a) and Fig. 8(b), respectively. Inlets show the original images of the power distribution taken with the CCD. The 3D figures show a spatial reconstruction of the experimental power distribution, obtained using the commercial software I+SOLEX (SOLEX, Madrid, Spain).
The presented experimental results match with the numerical simulations. As it was expected, both focuses are surrounded by a ring and presents revolution symmetry. Furthermore, the first focus is thinner than the second focus and has less power; on the other hand, the PR is wider than the SR and has more power.
To confirm the modulability of the system, the second tweezer is displaced so as to cause a stress on the structure and therefore convert the Ll to an elliptical microlens. 10% Stretched lens focuses are showed on Fig. 9.
The first focus point (Fig. 9(a)) keeps the revolution symmetry and it is equivalent to the non-stretched situation. The PR is drastically modified and do not keep the revolution symmetry. Due to this variation, it can be observed all the elements that conform the Sturm zone, namely the HLF (Fig. 9(b)), the CLC (Fig. 9(c)) and the VLF (Fig. 9(d)). These results were accurately predicted by the numerical simulations and hence they confirm both the technology and the principle of operation.
Finally, to demonstrate the usability of the proposed micro-optical system, a 3×3 matrix was implemented. The first focus without stretching (a) and with a stretching of 10% (b) is presented on Fig. 10. As it can be seen, the modulation of all the microlenses within the array is identical, confirming the possibility of make modulation of a whole array of micro-optical systems with a single stretching.
Experimental results show that the proposed micro-optical system can be easily modulated, leaving one of its focus invariant and changing the second one to become a Sturm zone. Moreover, the low cost of the fabrication process (which only requires one photolithographic mask), allows the mass-production, and the possibility of work with an array of such systems present this structure as interesting candidate for applications on telecommunications, photonic imaging or lab-on-a-chip systems.
A 3-D modulable micro-optical systems based on PDMS has been designed, simulated, fabricated and characterized. Designed systems consist on two bulk uncoupled lenses with diameters of 2 µm and 10 µm, respectively. Numerical simulations show that, when the structure is stretched, the first focus remains invariable and the second focus became a Sturm zone. Although such systems have a complex structure, the fabrication process (which combines silicon micromachining, polymer technology and soft lithography techniques) only requires one photolithographic mask and therefore are low cost processing. Characterization of the micro-optical system shows an agreement between the numerical and the experimental results: the first lens does not vary its shape when a stretch is applied, while the second lens is converted from spherical to elliptical under modulation conditions. Furthermore, experimental results confirm that a 3×3 array of these micro-optical systems can be simultaneously modulated.
This work has been made with founds of the project MINAHE 2, Micro/NanoHerramientas (TEC2005-07996-C02-01) para el estudio de células vivas, and the project 4Senses (PSE-020400-2007-1); both of them financed by the Spanish Ministerio de Educación y Ciencia (MEC).
The authors thank to Photon Design for his help and fruitful discussions. V.J.C. acknowledges the Consejo Superior de Investigaciones Científicas (CSIC) the grant conceded by the program I3P, cofinancing by the European Social Fund. A.L. acknowledges the Spanish Ministry of Science and Education for the award of a Ramón y Cajal contract.
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