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Abstract
Large aperture beam steering in a transmissive and compact device has been an important design objective for various technologies including LIDAR and 3D displays. We propose a new aperture variable beam steering method using an electrowetting prism array. By individually controlling the voltage of electrode, 3-dimensional beam steering is possible because it can manipulate beam steering and forming simultaneously. The total aperture of the prism array can be varied depending on the number of arrays. The operating speed was 25ms and the steering range was ±9.5° in the transverse and longitudinal directions, and ±13.2° in the diagonal direction. The range of optical power was −47.6D to 47.6D. Measurement of optical properties such as the RMS wavefront error as the sum of all aberrations of the prism and the radius of curvature, which is the flatness of the interface, and a demonstration of a 3-dimensional beam steering is also presented.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In modern optics, the beam steering component is an optical element just as important as the lens. Beam steering is used in many optical applications, including LIDAR [1–3], optical wireless communications [4], microscopes [5,6], laser engraving [7], beam forming [8], and 3D displays [9,10]. However, some technologies are still limited by the lack of a large aperture, light weight, and compact beam steering device. Most of the existing beam steering elements operate in a mechanical way. Several mechanical actuation methods have been proposed, including gimbal, micro electro mechanical systems (MEMS) [11–15], galvo [16,17] and voice coil motors (VCM) [18]. While mechanical movement has the advantage of providing accurate and reliable performance, it also brings problems, such as increasing the size and weight of the system, and high cost. It also consumes large amounts of power. Light and small devices such as MEMs are being studied, but the mechanical beam steering element is affected by external acceleration in a moving environment such as a vehicle. Also, as its size grows smaller, the actuating force becomes relatively weaker than the external force so it is more affected. And most mechanical beam steering elements are reflective type, using a mirror. The optical axis cannot be maintained because the optical axis is also reflected. It makes the overall system bulky and complex.
In order to improve these shortcomings, non-mechanical beam steering devices are being studied. A non-mechanical beam steering device controls the direction of the beam by adjusting a refraction interface. The refraction interface can be controlled by various methods, such as liquid crystals [19–22], optical phase array (OPA) [23–27] and electrowetting [28–33]. These actuating methods have advantages, including compact structure, fast operating speed and low power consumption, which is possible because there is no mechanical movement. However, the beam is steered through refraction so its light efficiency is degraded by polarization, reflection, or absorption. Among these methods, electrowetting has a high light efficiency because there is no polarizing element and little absorption in the visible light region. In our previous work, we studied 3-dimensional beam steering with an electrowetting prism and lens using the characteristics of electrowetting [30]. It enables accurate depth measurements when scanning objects because the focusing position can be adjusted. It is also compact and light weight because both elements are nonmechanical. However, it requires the use of two elements, a prism and a lens, which makes the system complex and difficult to control. Also, due to the nature of electrowetting, it has a small steering aperture.
Electrowetting [34] is a phenomenon in which the contact angle changes according to the potential difference between an electrolyte liquid and a conductor substrate. As the contact angle of electrolyte liquid changes on the substrate, it changes the curvature of the surface. Electrowetting prisms have been studied for their wide steering angle, fast operating speed, and high optical performance, but still has a limitation in that the steering aperture is small. This is related to the operating speed of electrowetting. Operating speed is an important characteristic in beam steering elements. The operating speed of the electrowetting prism decreases as the size of the EW prism increases, because the total mass increases with size, and it slows movement down.
2. Design of electrowetting prism array
2.1 Structure design
To solve the above limitation, we propose an electrowetting prism array in which a small cell prism is arranged for aperture variable beam steering. The total aperture of the prism array can be varied depending on the number of arrays. The electrowetting prism array is capable of not only large aperture beam steering, but also beam forming. Beam forming works by designing the steering direction of each cell prism. Since beam forming can be used to separate, focus, or defocus the beam, it is possible to simultaneously steer wide and multiple ranges or focus the beam to increase the beam power at a specific depth position. The structure of each cell prism has a square pillar shape. In the square pillar structure, the four electrode sidewalls are vertically positioned, and a liquid-liquid interface is formed in a prism shape by applying different voltages to each sidewall to adjust the contact angle between the electrolyte liquid and sidewalls. The square shape is suitable for not only controlling the direction when performing two-dimensional beam steering, but also for manufacturing as an array, because the fill-factor can be made 100% excluding the thickness of sidewall. Since the fill-factor of an individual electrowetting prism is high, beam steering with little loss is possible even when it is fabricated as an array.
The steering direction of the single cell prism is determined by the direction of the liquid interface, which is controlled by the contact angle between the liquid interface and each sidewall as shown in the following equation [32].
In this work, a 3 × 3 prism array was used as shown in the Fig. 2(a). ${V_1}$ - ${V_{12}}$ are required to control the all sidewall electrodes of prism array. ${a_1}$ - ${a_{12}}$ are contact angle according to the voltage ${V_1}$ - ${V_{12}}$. The contact angle according to the voltage of the electrolyte liquid is shown in the Fig. 2(b). Four contact angles in each cell prism follow Eq. (1). In addition, the sum of the two opposite contact angles in cell prism is 180°. This is the same condition as when beam steering is performed only in the direction perpendicular to the sidewall, that means the two opposite sidewalls control the beam steering in the vertical direction. Thus, the transverse sidewalls control the longitudinal direction and the longitudinal sidewalls control the steering in the transverse direction.
Fig. 2. (a) Voltages applied to each sidewall of the 3 × 3 array and contact angle and (b) contact angle of electrolyte liquid according to voltage.
2.2 Fabrication
ITO glass was used as the material for the chamber. In our previous electrowetting prism work [29], polycarbonate was used because it was strong and light, and it was easy to cut using a laser. However, it melts or bends when heated, there is a problem in that the cross section is not flat due to the melting during the process of electrode deposition and laser cutting. If the cross section is not flat, a space is created between adjacent sidewalls, and spacing causes distortion of the prism [35].
The process of fabricating the electrowetting prism array is shown in Fig. 3. The glass had a thickness of 0.5mm, and ITO was coated on both sides at a thickness of 185nm, with a resistance of 6ohm/sq. Thin glass has a high fill factor, but if it is too thin, it is difficult to handle, so a 0.5mm thickness was used. The ITO glass was cut into the shape shown in Fig. 3(c) using a laser (AMT355, Advanced Optowave Corporation) to make the sidewall. The shape of the sidewall is rectangular, with a groove the thickness of glass, so that the sidewalls can be joined to each other through the groove. The distance between the grooves determines the size of the cell prism.
Fig. 3. Fabrication process of the electrowetting prism array chamber. (a) Glass substrate, (b) double side ITO and dielectric layer coating, (c) shape of sidewall, (d) assembling the sidewalls, (e) attach the bottom ITO glass and 3D structure to the chamber, (f) liquid dosing and sealing and (g) electrowetting prism array
The prism array operates through the cell prism, and the operating speed of the prism array is determined by the size of the cell prism. Therefore, in order to design the operating speed of the entire prism array, it is necessary to adjust the size of the cell prism. Figure 4(a)shows the operating speed according to size. In addition, the size of the cell prism determines the fill factor of the entire prism array. When the sidewall thickness is 0.5mm, the fill factor compared to the size is shown in Fig. 4(b). As a result, when the size of cell prism is large, the fill factor is high but the operation speed is slow, and when the size of cell prism is small, the operation speed is fast but the fill factor is low. In this work, the size of the cell prism was 7mm with an operating speed of 25ms and a fill factor of 87%.
Fig. 4. (a) Operation speed and (b) fill factor of prism array according to the size of the cell prism.
In previous electrowetting prism array research, to fabricate a prism array, a 3-dimensional structure that becomes a chamber was fabricated, and then electrodes were deposited on the entire structure, and then all electrodes were separated or some single electrowetting prisms were tiled. However, the 3-dimensional structure makes it difficult to uniformly deposit the electrode, and there are many difficulties in the process of separating the electrode. Separating the electrodes creates a space between the electrodes, and as mentioned above, the space between the electrodes causes distortion of the prism. Also, as the number of arrays increases, there is a limit to the process of separating all the prism sidewall electrodes and connecting the electrodes of internal cell prism to the outside of the prism array. And the tiled prism array has a relatively low fill factor because of the bezel of a single prism.
In the proposed fabrication method, because ITO is deposited on the sidewalls for each line, the electrodes are already separated by line. The voltage can be controlled by each line and there is no need to connect the internal electrodes to the outside of the prism array. For these reasons, the proposed fabrication method has no major restrictions as long as the sidewall can be manufactured. Therefore, depending on the length of the sidewall, the number of arrays can be expanded to make the aperture size as large as desired. However, the sidewalls are manufactured using laser, the length of the sidewall is limited by the size of the laser cutting equipment.
2.3 Liquid selection
Two immiscible liquids were used for the electrowetting. Water was used as the electrolyte liquid and oil was used as the non-electrolyte liquid. The water contained 0.1wt% sodium dodecyl sulfate (SDS). SDS lowers the surface tension of water [36], so the contact angle can change even at low voltage. However, using too high SDS concentration will result in electrical breakdown, so an appropriate concentration should be used. The light beam is refracted more when it passes through an interface with a large refractive index difference, so having a larger difference between the refractive indexes of the two liquids in the electrowetting prism increases the steering range. The oil used was Series E oil (Cargille Laboratories), which has a high refractive index (n=1.63). Series E oil consisted of a mixture of hydrogenated terphenyl and 1-bromonaphthalene. However, Series E oil is denser than water; consequently, when it is used in electrowetting, there is a gravity effect [37] on its electrowetting operation. Gravity influences the shape of the refracting interface. By adding dodecane oil, which is less dense than water, the density of the oil mixture can be adjusted to be the same as that of water. The final oil had a 57:43 ratio of Series E oil and dodecane. Even with density matching, if a different acceleration is applied depending on the position, such as rotational motion, the interface can be perturbed. However, due to the small size of device, in most cases it is accelerated in the same direction and magnitude. Thus, it is not affected by external acceleration including gravity.
2.4 Oil isolation problem
The proposed square structure had an oil isolation problem. When the initial contact angle is ${\theta _i}$ and the side length of the square is d, the initial radius of curvature (RoC) of water is ${\rm{r}} = - {\rm{d}}/2\cos {\theta _i}$. Then, water is formed by the curvature distance from the center of the square, and the area farther than the RoC of water is filled with oil. When the oil is filled in the corners, the oil can penetrate to the bottom. As the contact angle decreases, the RoC of the water increases, and when the distance is the same as half of the diagonal farthest from the center, the water fills the entire square structure. Then the oil at the bottom is separated from the top; the oil is isolated and there is no way for it to come out. To solve this problem, a structure was used in a previous prism study [32]. The structure has the same shape as the oil when it is separated, so the structure replaces the area of isolated oil.
In the prism array, as shown in Fig. 5(a), the structures can be used for each of the cell prisms. However, this method has the disadvantage of lowering the fill factor of the prism array. Therefore, the rest of the prism array except the corners was made into an open structure to allow liquid to pass through the cells as shown in Fig. 5(b) by lifting the sidewalls from the bottom, and the structure was used only at the corners of the prism array.
Fig. 5. Two solutions of the oil isolation problem. (a) the structures were used each of the cell prisms and (b) lifting the sidewalls from the bottom, and the structure was used at the corners of the prism array.
3. Results
3.1 Optical properties
To measure the optical properties of the refracting interface of the proposed prism array, a Shack-Hartmann wavefront sensor (WFS10-7AR, Thorlab) [38] was used. A green LED with a wavelength of 520nm was used as a light source. A lens and two apertures were used to collimate the LED light. For each apex angle of the electrowetting prism, the RMS wavefront error and RoC were measured, as shown in Fig. 6. For the proposed prism array, the measured values of cell prisms were averaged, and the reference prism was also measured to compare with the proposed prism array. The reference prism was fabricated by forming the interface of two liquids by placing a flat glass between the two liquids. The apex angle range of the proposed prism array was 0 to 40°. Larger angles are not possible due to the contact angle limit. The RoC value means the flatness of the interface between two liquids. The prism must be flat with infinite curvature at the interface. However, The RoC value was considered flat if it was roughly larger than 1000mm because the size of the cell prism is relatively very small. The RMS wavefront error means the sum of all aberrations of the prism. As the RMS wavefront error and RoC value of the proposed prism are not significantly different from that of the reference prism, the proposed prism has a flat and low aberration interface. However, as the apex angle approaches the limit, the RMS wavefront error slightly increases.
Fig. 6. RMS wavefront aberration & RoC measurement of proposed prism array and reference prism. (a) Optical measurement setting, (b) wavefront shape of proposed prism and (c) RMS wavefront aberration & RoC according to apex angle of prism.
The optical power and beam steering angle range were also measured as shown in Fig. 7. In the case of the 3 × 3 array, the shortest focal length was 42mm and the optical power range is −23.8D to 23.8D. Therefore, the maximum steering angle of the prism array is ±9.5° in the horizontal and vertical direction and ±13.2° in the diagonal direction. The steering angle of the prism array is proportional to the apex angle of the prism and the refractive index difference of the two liquid. Because the prism array uses the same structure and liquid composition as a single prism, its performance is similar to the previous single prism work [32]. The range of optical power can increase as the size of the cell prism decreases, the maximum beam steering angle increases, or as fewer number of arrays are used. When the size of cell prism is L, the beam steering angle θ and the optical power of two adjacent cell prisms P are $\textrm{P} = {f^{ - 1}} = \textrm{L}/2\tan \theta $. The focal length range of two adjacent cell prisms is −21mm to 21mm, so the maximum optical power range of the proposed prism array is −47.6D to 47.6D.
Fig. 7. Measurement of the optical power range at a distance of 42 mm. (a) zero optical power, (b) negative optical power, (c) positive optical power and (d) maximum optical power.
3.2 3-dimensional beam steering with beam steering and forming
The schematic diagram and some situations of 3-dimensional beam steering are shown in Fig. 8. It shows a top view of the prism array and the beam. The blue arrow indicates the vertical beam steering vector of the sidewall line, and the red arrow indicates the final beam steering vector of the cell prism. The beam steering vector of the cell prism is represented by the sum of the transverse and longitudinal vectors of the line corresponding to the cell prism. Figure 8(a) shows only beam steering, Fig. 8(b) shows only beam forming (defocusing), and Fig. 8(c) shows both beam steering and beam forming (focusing).
Fig. 8. Demonstration of 3-dimensional beam steering. (a) Only beam steering, (b) only beam forming (defocusing) and (c) both beam steering and beam forming (focusing).
4. Conclusion
We have demonstrated the design, fabrication method, measurement of optical properties, and beam steering and forming by a compact electrowetting prism array. By precisely adjusting the tilt of the liquid in each chamber, the steering angle can be adjusted at high speed. Beam forming can be precisely controlled by individual electrode voltage control. 3-dimensional beam steering, which required two elements in our previous work [30], is now possible with only one element of the prism array because it can manipulate beam steering and forming simultaneously. The total aperture of the prism array can be varied depending on the number of arrays. The optical power was improved from −47.6D to 47.6D compared to the previous −5D to 15D. The operation speed and the optical power of beam forming can be improved as the size of the cell prism decreases. Therefore, the specifications can be designed according to the application. Liquids with a large refractive index difference were used to increase the beam steering angle, but it was the similar performance as the previous single prism. The prism array was made by separately fabricating and combining the sidewall structures. The spacing between the electrodes was minimized by separating each sidewall. This reduces the distortion of the prism. The oil isolation problem that occurs in electrowetting prisms was solved without loss of fill-factor by making the chamber an open structure and using a 3-dimensional structure. Future research will be conducted on increasing the range of beam steering angle and new applications.
Funding
National Research Foundation of Korea; Ministry of Science and ICT, South Korea.
Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF2020R1F1A107408912).
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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