Multi-electrode tunable liquid crystal lenses with one lithography step

Transcription

1 Letter Optics Letters 1 Multi-electrode tunable liquid crystal lenses with one lithography step JEROEN BEECKMAN 1,*, TZU-HSUAN YANG 1,2, INGE NYS 1, JOHN PUTHENPARAMPIL GEORGE 1, TSUNG-HSIEN LIN 2, AND KRISTIAAN NEYTS 1 1 Department of Electronics and Information Systems, Ghent University, Technologiepark 15, 9052 Gent, Belgium 2 Department of Photonics, National Sun Yat-Sen University, Kaohsiung, Taiwan * Corresponding author: jeroen.beeckman@ugent.be Compiled December 2, 2017 Electrically tunable lenses offer the possibility to control the focal distance by applying an electric field. Different liquid crystal tunable lenses have been demonstrated. In order to minimize lens aberrations, multielectrode designs allow to fine-tune the applied voltages for every possible focal distance. In this article we provide a novel multi-electrode design in which only one lithography step is necessary, thereby offering a greatly simplified fabrication procedure compared to earlier proposed designs. The key factor is the use of a high-permittivity layer in combination with floating electrodes Optical Society of America OCIS codes: ( ) Lasers, distributed feedback; ( ) Fibers, polarization-maintaining;( ) Fiber Bragg gratings INTRODUCTION Quite a number of physical principles can be utilized to realize lenses with an electrically controllable focal distance. Some rely on pushing a liquid mechanically between flexible substrates [1] or rely on movement of a fluid due to electro-wetting [2]. Another important class of tunable lenses is based on liquid crystals (LCs) [3, 4]. In LC devices, a voltage is applied over the LC layer, such that the average molecular orientation is changed, aligning it along the electric field direction (for LCs with positive dielectric anisotropy). Due to this reorientation, light that is passing through the LC layer experiences a different refractive index. A suitable positional dependent refractive index profile then leads to a curvature of the phase profile of the transmitted light such that the beam is focused. A wide number of approaches have been studied to realize LC tunable lenses, using a non-uniform LC layer thickness [5], a non-uniform distance to the electrodes [6], an optically hidden dielectric structure [7], a spatially varying polymer stabilized LC [8] or a uniform weakly conductive layer [9 12]. An important class of LC lenses that offers very good control of the optical phase profile is based on multi-electrode designs. A schematic cross-section of such a multi-electrode device is depicted in Fig. 1(a). In this device, different voltages are applied over a series of ring-shaped electrodes [13 15]. Thanks to the fact that for every focal distance, the phase profile can be set accurately by finetuning the different applied voltages, the lens offers a good gradual tuning of the focal distance. This is in contrast to other types of LC lenses for which the structure can usually only be optimized for one certain focal distance. In such multi-electrode devices however it was found that the fringe fields at the edges of the electrodes result in aberrations and scattering. Fringe field effects due to electrode edges are well known in many types of LC devices and they can be used as a mechanism for fast switching Fringe-Field displays [16], but they can also result in unwanted behavior in microdisplays [17]. The unwanted fringe field effects in multi-electrode lenses were succesfully tackled by Li et al. [13] who solved this issue by adding a second layer of floating electrodes on top of the electrodes that are contacted (as depicted in Fig. 1(b)). Thanks to the very thin SiO 2 layer in between the two electrode layers, the floating electrodes are strongly capacitively coupled with the contacted electrodes. Hence, the floating electrodes exhibit a potential that is the average of the potential of the two electrodes in the close neighborhood. The fringe fields around the electrode edges are reduced due to the presence of the contacted electrodes in the bottom electrode layer. As such, the haze of the lens was drastically reduced and a lens with low aberrations was realized. However, due to the complex design, several lithography steps need to be carried out to define the electrode pattern and tedious alignment is necessary to align the floating electrodes with the contacted electrodes. Recently it was shown that a layer of high permittivity material on top of the contacted electrodes can greatly reduce fringe fields [15]. The high permittivity layer acts like a weakly conductive layer without the issue of current flowing through the conductive layer (and the associated power consumption). Moreover, it was shown that the distance between the electrodes could be increased drastically, thereby allowing for much larger apertures with the same number of electrodes. The distance between the electrodes is essentially limited by the maximum value of the permittivity that is possible materialwise and the thickness of that layer. In [15], a thin film with a permittivity of around 500 was used. The high permittivity layer is based on a lead zirconate titanate (PZT) thin film, which is deposited on glass by

2 Letter Optics Letters 2 means of a thin buffer layer [18]. In order to allow for even larger apertures, we propose a novel scheme that combines the idea of using high permittivity thin films with the benefit of using floating electrodes. Thanks to the fact that both the contacted and the floating electrodes are in one plane, only one lithography step is required. Fig. 2. Simulation of the electric potential distribution for different configurations (equipotential lines are shown). Contacting electrodes are colored red, floating electrodes are colored blue and the edge of the PZT layer is indicated in a dashed line. Fig. 1. Schematic showing different types of multi-electrode liquid crystal designs: (a) classic multi-electrode design, (b) floating electrode design as used in [13], (c) current design with floating electrodes and high permittivity layer. 2. SIMULATIONS In order to demonstrate the working principle of our devices based on floating electrodes covered with a PZT layer, electrical simulations were carried our using a 2D finite element solver. The electric potential distribution V is found by solving the equation (ε V) = 0. As the simulations are merely used as proof-of-principle, the full LC behavior is not simulated and the LC layer is modeled as an isotropic material with ε = 10 with a layer thickness of 20 µm. The top electrode is set to 0V and the bottom contacted electrodes to 5V. To reduce unwanted effects due to fringe fields and to minimize the reduction of electric field strength due to the gap between the contacting electrodes, it is essential that the electric field is as uniform as possible when the two contacting electrodes are at the same potential. In a multielectrode LC lens, typically the voltage on consecutive electrodes varies slowly in order to create a smooth refractive index profile. In Figure 2 four cases are simulated in which the contacting electrodes are 44 µm apart. The two left (right) figures show the equipotential lines without (with) floating electrodes. The two top figures show the case when no PZT layer is deposited on the glass, while the bottom figures show the case when a PZT thin film with a thickness of 800 nm and a relative permittivity of 500 is on the bottom glass plate. The potential distribution inside the bottom glass (with ε = 8) is included in the simulations, but not shown in the figures. It is clear from Figure 2(a) that the equipotential lines are drawn towards the gap between the contacting electrodes, which means that there is a considerable drop of the electric field strength inside the LC layer. As a result, the LC will switch very non-uniformly. Using a PZT layer on top of the bottom glass plate (Figure 2(c)) results in a smaller drop of the electric field in the LC layer. No PZT layer, but 3 floating electrodes in between the contacting electrodes also results in an increase of the electric field in the LC layer, but it gives rise to strong curvature of the equipotential lines and consequently also strong fringe fields. Clearly, the configuration which combines the PZT layer with floating electrodes gives rise to equipotential lines that are almost horizontal, which should result in uniform LC switching. It is clear that the effect of the floating electrodes is only important when the capacitive coupling between the bottom electrodes is much larger than the capacitive coupling with the ground electrode at the top glass plate. As a very rough approximation, assuming that the thickness of the PZT layer d PZT is much smaller than the inter electrode distance L g, we can write the capacitance between the floating electrodes as C f = ε PZTd PZT L g. The capacitance between the floating electrode and the ground electrode at the top can be approximated as C t = ε LCL e d. Note LC that the influence of the PZT layer can be neglected in C t due to the fact that ε PZT is much larger than ε LC. Stating that C f C t, then leads to ε PZT d PZT d LC ε LC L g L e. The latter equation offers clear guidelines for the device design. 3. LENS DESIGN AND EXPERIMENTS Two multi-electrode lens designs were used in this research. One design includes concentric rings of Indium Tin Oxide (ITO) of 12.4 µm width and spacing of 45 µm between adjacent electrodes as shown in figure 3(a). The spacing between the electrodes is based on the fact that this is getting close to the distance that can be bridged using a PZT layer. The other design is similar, but includes three unconnected rings of ITO electrodes of 12.4 µm width and 2 µm distance in between as shown in figure 3(b). The outer edge of the outer connected electrode has a radius of 470 µm in both designs. The ITO patterns were obtained from uniform ITO coated samples (sheet resistance 100 Ω/sq) through conventional UV lithography and wet etching. Some substrates were then coated with a 800 nm thick layer of PbZr 0.52 Ti 0.48 O 3. The next step involved depositing an alignment layer and uni-

3 Letter directional rubbing to ensure planar anchoring of the LC at the interfaces. A LC layer thickness of about 20 µm is ensured by gluing two substrates together with spacers in the glue. Measurements of the fabricated devices revealed a spacing of 19.8 µm for the device with PZT and 20.9 µm for the device without PZT. The device is then filled with the LC E7 (Merck). Each multi-electrode lens has eight contacted electrodes which can be driven separately by means of a computer controlled data acquisition device. The voltage signals are 1 khz sine waves with varying rms voltages. Optics Letters 3 adjacent (non-floating) electrodes. In this way, for the four devices (with or without PZT, with or without floating electrodes) we obtain a 2D plot with the position on the x axis and the applied voltage on the y axis. The color in the figure is a false color denoting the grayscale response of the pixels of the camera. At low voltages the contrast is not high, but it improves for higher voltages. This is due to the combination of the spectral width of the green LED (34 nm at FWHM) in combination with the large retardation at low voltages. It is clear from the four figures that the addition of a PZT layer greatly improves the switching uniformity as was already demonstrated in [15]. In case there is no PZT layer, the floating electrodes do not offer a noticeable improvement to the switching uniformity. In case there is a PZT layer, it is clear that the lines at low voltages become more horizontal. Also in the high voltage region, the influence of the floating electrodes can be observed. Fig. 3. Reflection microscope image of the ITO electrode pat- tern for a lens without floating electrodes (a) and with floating electrodes (b). Polarization microscope image of the LC devices with PZT without floating electrodes (c) and with floating electrodes (d) when 5 V is applied to all electrodes. The rubbing direction is denoted with a white arrow. The position of the contacted electrodes is indicated with a white dashed line. ages show the evolution of the intensity in the region between two adjacent connected electrodes as a function of the applied voltage on these electrodes. The left images are without floating electrodes, the top images are without PZT. Before the devices were tested as a lens, they are observed under the polarization microscope using a green LED as light source. In this way, the spatial response of the LC is visualized when voltages are applied to the electrodes. The situation when all electrodes are set to the same voltage gives a good indication of how well the LC switches in between adjacent connected electrodes. Figures 3(c) and (d) show the polarization microscope images of two PZT based LC devices when 5 V is applied to all electrodes. Note that due to the fairly large LC layer thickness, any non-uniformity of the LC switching is strongly enhanced and visible through crossed polarizers. Figures for the devices without PZT are not shown, but will be discussed later. It is clear from the microscope pictures that the LC between the contacted electrodes responds differently in devices with and without floating electrodes. Careful observation reveals the presence of the three floating electrodes in Figure 3(d). A more elaborate study of the response of the LC is shown in Figure 4. For every applied voltage, the intensity profile is recorded from a line along the rubbing direction between two From the analysis of figures 4(a)-(d), it is clear that the combination of a thin PZT layer with floating electrodes offers almost uniform switching in the region between two contacted electrodes. The PZT layer is necessary for providing sufficient capacitive coupling between the contacted electrodes and the floating electrodes. Next to the more uniform switching, the combination of a PZT layer and floating electrodes also offers the possibility for much larger spacing between contacted electrodes compared to the situation without floating electrodes, thereby reducing the need for many parallel voltage inputs for the lens. The effect of the additional electrodes does not look prominent in Figure 4, but one has to keep in mind that in the voltage range between 1 V and 3 V, there are closely spaced intensity variations. A slight improvement in the curvature of the equi-intensity lines will give a considerable improvement in the uniformity of the LC switching. The capacitive coupling could be improved further if the electrodes are placed closer together. However this is technologically challenging. Finally, the lens operation of the devices was tested by focus- Fig. 4. Analysis of polarization microscope images. The im-

4 Letter Optics Letters 4 ing a linearly polarized plane wave originating from a white LED into a spot. The voltages applied to the eight different electrodes are found by starting from the voltages that should theoretically result in a parabolic phase profile with a predefined focal length. These theoretical voltage values are obtained by first solving the one-dimensional differential equations governing the liquid crystal orientation as a function of applied voltage, followed by the calculation of optical path length for light propagating through this layer by means of the Jones calculus. This results in an expected optical path length as a function of applied voltage, by which the necessary voltage values can be estimated for a given phase profile. These voltages are then slightly changed in order to get the highest intensity into the central spot for the PZT device without floating electrodes. The same set of voltages is then used for the other devices. The central spot at the predefined focal length is recorded by an RGB CMOS camera. The resulting image at the focal distance of the lens is recorded and the grayscale value for the red channel is shown in Figure 5 (ranging from 0 to 255). The focal distance in this case was set to 40 mm with rms voltages from the inner electrode to the outer electrode going from 2.1 V to 4.0 V (sine wave, 1 khz). The results for the devices without PZT layer are not shown. The light intensity is very low compared to the PZT devices, because the operation as a lens is poor. This is expected from the analysis of Figure 4. The two images of the focal spot in Figure 5(a) and (b) reveal that the intensity for the device with floating electrodes is much higher than for the device without floating electrodes. On the other hand, the spot width is only marginally better. The same measurement was repeated for a number of other focal distances and every time, a much higher intensity was obtained at the central spot for the device with floating electrodes. The higher intensity in the focal spot for the device with floating electrodes clearly indicates that the aberrations from the ideal parabolic phase profile is much smaller than in the device without floating electrodes. Due to the smaller aberrations, less light is going into unwanted directions and more light into the central spot. Fig. 5. Grayscale intensity at the focal distance of 40 mm when the PZT lenses are driven with optimized voltage values, without floating electrodes (a) and with floating electrodes (b). Intensity profile at the focal distance, including the theoretical diffraction limited spot. The current devices are designed for demonstrating the beneficial effect of using closely spaced floating electrodes in order to enhance the switching uniformity. The lens design does not include any flyback regions (with 2π phase jumps) which means that the minimum possible focal distance is still fairly large. Using the equation f min = (R) 2 /(r nd) which gives the minimum focal distance f min for an LC lens with radius R, LC layer thickness d and LC birefringence n [19], we find a minimal focal distance of about 2.7 cm, whereby a LC thickness of 20µm is assumed. Future designs can include flyback regions, while also minimizing the area with the straight electrodes that are used to connect the circular ones. This undesirable area is still quite large in the current designs, representing a sector with an angle of 18.7 (as can be seen on Figure 3(a) and (b)). This is equivalent to about 5% of the lens area that is not focusing the light properly and causing unwanted diffraction and stray light. 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