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Abstract
In this paper, an optofluidic phase modulator based on electrowetting is presented. The modulator consists of an inner and outer chamber. Two immiscible liquids are filled into the chambers, and a transparent sheet is fixed between the liquid-liquid interface to obtain a flat interface. By applying different voltages to the modulator, the flat interface moves up and down leading to the change of optical path length. Consequently, the variation of the optical path in the proposed modulator exploits the ability to alter the optical phase. To prove the concept, a prototype of the phase modulator is fabricated in experiment, and the ability of phase modulation is detected. Our proposed modulator performs optical phase shift up to ∼6.68 π driven with 150 V. Widespread applications of such an optofluidic phase modulator is foreseeable.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical phase modulation by variable optical path has practical applications in industry and biomedicine [1–3]. For example, optical coherence tomography utilizes the optical path difference between reference beam and measured beam to obtain three-dimensional structural information [3]. In phase shifting interferometry, it is necessary to introduce phase shift into two coherent beams to measure various optical elements [4]. Polarization independent optical phase modulators with high efficiency have also related applications in adaptive optics [5,6]. In addition, large aperture and linear-isotropic medium are equally needed due to the increasing demand for large aperture optical elements.
Optofluidics has been developing rapidly in recent years, and the relative optofluidic devices are designed to replace the conventional solid devices such as optical switches [7,8], liquid lenses [9–12] and liquid prisms [13–16]. On account of the deformability of the liquid-liquid interface, the optofluidic devices can get a variable optical path to correct the wavefront error [17–19]. In 2012, Juliet T. Gopinath first demonstrated that electrowetting lens and prism technology can be used for wavefront correction, providing new application value for electrowetting-based devices. Then, they developed a linear array of focus-tunable electrowetting lenses, which can compensate optical phase distortion over a full wavelength in a transmission optical system [19–21]. In 2017, A. O. Ashtiani proposed an electrowetting driven liquid tunable optical phase shifter composed of multi-layer SU-8. The device can achieve a phase shift of 171° with a response time of 110 ms by applying 100 V voltage [22,23]. In 2019, Qiong-Hua Wang reported an optofluidic variable optical path modulator based on electrowetting, which is used in an imaging system to compensate the back focal length. The liquid-liquid interface of the device can move 7.5 mm and the optical path length change is 1.15 mm [24]. These electrowetting-based optofluidic devices can change optical phase via the variable optical path. However, an optofluidic phase modulating devices with simple structure and small volume is urgently needed.
In this paper, an electrowetting-actuated optofluidic phase modulator is proposed. The device consists of two chambers which filled with immiscible liquids. A transparent sheet is fixed between the liquid-liquid interface by an elastic film to get flat interface. We analyze its operating mechanism, and detect the performance of its optical phase modulation in the experiment. Compared with the liquid-crystal spatial light modulators [6], our modulator is polarization independence. The results show that our proposed modulator can achieve continuous optical phase shift. The relative results will promote the development of optofluidic phase modulator and has a wide range of applications.
2. Design and fabrication
2.1 Structure design
The structure of the proposed optofluidic phase modulator is depicted in Fig. 1. From the cross-section of the device in Fig. 1(a), the optical phase modulator consists an inner and an outer cylindrical chamber. In order to facilitate the flow of liquids inside the chamber, there are four circular holes on the inner cylindrical chamber, and the height of the inner chamber is slightly shorter than that of the outer chamber. An insulating droplet is deposited in the center of the bottom, which is surrounded by conductive liquid. A transparent sheet is on the top of the insulating droplet, and an elastic film is attached at the liquid-liquid interface to hold the transparent sheet. Therefore, a flat interface is formed in the inner chamber, which avoids introducing unnecessary aberrations. The inner chamber is the effective part of optical phase modulation, while the function of outer chamber is to store liquid. When the voltage is applied, the wettability of the conductive liquid on the solid surface is changed in term of electrowetting theory, consequently the shape of the insulating droplet changes with it [25].
Fig. 1. Schematic structure of the proposed optofluidic phase modulator. (a) The cross-section of the modulator. (b) Structure of the planar electrode (black parts).
An indium tin oxide (ITO) planar electrode is used in the optofluidic phase modulator to simplify the structure and fabrication procedure [26]. As shown in Fig. 1(b), the electrode consists of a central electrode and a peripheral electrode (black parts). The central electrode is connected by a line, and the tail line is enlarged to facilitate the connection with the power. The planar ITO electrode is coated with a dielectric layer and a hydrophobic layer.
2.2 Device fabrication
The fabrication procedure of the optofluidic phase modulator is shown in Fig. 2. In order to facilitate the passage and observation of light, all the elements of the optofluidic phase modulator are high transparency materials. The bottom planar electrode is a photoetching ITO glass (19 mm × 24 mm, SnO2: In2O3, ∼200 nm thickness) spin-coated with SU-8 2005 (∼5 µm thickness) and fluoropel cytop (∼400 nm thickness), as depicted in Fig. 2(a). Specially, the fluoropel cytop is only coated on the central area (∼7 mm in diameter) to ensure that the insulating droplet is fixed in the center of the electrode. The planar electrode pattern is shown in Fig. 1(b). A cylindrical polymethyl methacrylate (PMMA) cavity with the size of 15 mm (diameter) × 10 mm (height) is used as the outer chamber which fixed on the bottom substrate in Fig. 2(b). Figure 2(d) and (e) show the fabrication procedure of the inner chamber. A cylindrical PMMA cavity with four circular holes (2 mm in diameter) is used as the inner chamber. The size of the inner chamber is 7 mm (diameter) × 8 mm (height). The inner chamber is an effective part of the device which connected with a PMMA annular sheet. The transparent partition is a PMMA sheet (6 mm in diameter), which is fixed at the bottom of the inner chamber by an elastic film polydimethylsiloxane (PDMS, ∼100 µm thickness).
Fig. 2. Fabrication procedure of the optofluidic phase modulator. (a) Coating the dielectric and hydrophobic layer on the photoetching ITO glass. (b) Fixing the outer chamber. (c) Filling the conductive liquid and the insulating droplet. (d) Fixing the transparent sheet and annular sheet with the inner chamber. (e) Placing and fixing the whole inner chamber into the outer chamber. (f) Encapsulating the modulator with cover sheet. (g) Elements of the optofluidic phase modulator.
Then, filling the two liquids in the chamber as Fig. 2(c). The insulating droplet is dimethyl silicone oil (refractive index n1 = 1.400) and the conductive liquid is propylene glycol (refractive index n2 = 1.432) containing with 1 wt% tetrabutylammonium chloride (TBAC). The properties of the two liquids are listed in Table 1. The process of liquid packaging in this device is summarized as follows: the outer chamber is first filled with propylene glycol (1 wt% TBAC) and then the dimethyl silicone oil droplet is squeezed to the center by a syringe pipette with a sharp tip. After this step, the inner chamber with movable transparent sheet is put into the outer chamber. In the last, the volume of propylene glycol (1 wt% TBAC) is increased until the entire chamber is filled with liquids. The modulator is encapsulated by a PMMA cover sheet as shown in Fig. 2(f), and all the elements are glued together by an ultraviolet (UV) curable adhesive. The whole device is shown in Fig. 2(g), with the effective optical aperture of 5 mm.
Table 1. Properties of the liquids in the modulator (at 25°C).
2.3 Operating principle
The working mechanism of the proposed optofluidic phase modulator is depicted in Fig. 3. As shown in Fig. 3(a), in the initial state, the whole optical path length (OPL1) consists of two parts:
where n1 and n2 are the refractive indices of insulating liquid and conductive liquid, respectively, h1 and h2 are the heights of the two liquids in the inner chamber. When the voltage is applied to the planar electrode, the wettability of the conductive liquid changes due to electrowetting effect, and the insulating droplet is squeezed inward [22,25]. Since the overall volume of the droplet must remain constant, this squeezing means that the contact angle of the insulating droplet increases. As a result, the height of the insulating droplet increases, and the transparent sheet moves upward as shown in Fig. 3(b). The changed optical path length (OPL2) is: here ${\textrm{h}^{\prime}}_1$ and ${\textrm{h}^{\prime}}_2$ are the heights of the two liquids in the inner chamber after applying voltage, respectively.Fig. 3. Working mechanism of the proposed optofluidic phase modulator. (a) Initial state of the phase modulator. (b) Operating state of the phase modulator.
Due to the different refractive indices, the change of optical path length of the system can realize the function of phase modulation. The optical path difference (OPD) which defined as the variation of the optical path between Fig. 3(a) and (b) can be expressed as:
According to the Eq. (3), the relative variation of the phase can be written as [22]: where Δn is the refractive index difference between the two liquids, Δh is the variation of the droplet height after applying voltage, λ is the wavelength of the beam.From Fig. 3, we can see that the shape of the insulating droplet in the modulator can be described as the difference between two spherical caps. Since the volume of the droplet remains unchanged after applying voltage, the variation of the droplet height Δh can be deduced according to the geometrical relations:
When no voltage is applied, the interfacial surface tensions near the three-phase contact line among conductive liquid, insulating liquid, and dielectric layer are balanced with the initial contact angle θ0 [27]:
where γdi, γdc and γic represents the interfacial surface tension between the dielectric layer and insulating liquid, dielectric layer and conductive liquid, insulating liquid and conductive liquid separately.When a voltage is applied, the balance of the interfacial surface tensions meets the following equations [28]:
where ɛ0 is the permittivity of free space, ɛr is the dielectric relative electric permittivity, U is the voltage applied, and d is the hydrophobic dielectric thickness.According to Eqs. (6)–(8), the relationship between the contact angle θ of the droplet and the driving voltage U can be obtained:
According to Eqs. (4)–(9), the relationship between phase variation and voltage is:
3. Results and discussion
An optical interference system shown in Fig. 4 is built to measure the phase modulation ability of our optofluidic phase modulator with the help of Michelson interferometer. A He-Ne laser (λ = 632.8 nm) is employed as light source. After passing through the polarizers and auxiliary lens in turn, the laser is split into two beams by a beam splitter (BS). One beam is reflected as object light through our proposed modulator, and the other beam as reference light is directly reflected by the reflecting mirror. The two beams finally merge at the beam splitter and interfere with each other to from a fringe pattern. The optical path variation through our optofluidic phase modulator in an operating state causes noticeable differences in the phase of the combining light beams, which is reflected by the shift of fringe patterns. In order to capture the evolution of interference, a CCD camera (MV-GE202GM-T: 2/3” CMOS, MindVision Co. Ltd., Shenzhen, China) is placed at the end of the measurement system.
As shown in Fig. 5, the interference ring shrinks inward is observed when different voltages U are applied on our device. When U < 50 V is applied on the planar electrode, the interference rings does not move shown in Fig. 5(a) and (b). As the voltage increases gradually, the interference rings monitored by the CCD camera begin to shrink. When the voltage is increased, visible movements of the ring can be seen in Fig. 5(c)-(f), where U = 90 V, 110 V, 130 V, 150 V, respectively. The authors assume that the main factors of the non-standard interference rings and edge blurring problems caused in the shown interferograms are uneven coating of the dielectric layer and poor light-transmission of liquid in our device. The video of the interference ring movement is provided in Visualization 1.
Fig. 5. Fringe patterns changing during driven procedure. (a) Initial state U = 0 V. (b) U = 50 V. (c) U = 90 V. (d) U = 110 V. (e) U = 130 V. (f) U = 150 V.
The optical phase modulation values are obtained by detecting the intensities of the interference fringes, instead of calculating the movement of the interference fringes, which is shown as hollow circle (○) in Fig. 6. A Si Amplified Detector (PDA10A-EC, Thorlabs Inc., Newton, NJ, USA) is employed to replace the CCD camera in Fig. 4. The line with solid star (★) in Fig. 6 is the theoretical results calculated by the Eqs. (10), which shows good consistence with our relevant experimental results. When the applied voltage U < 50 V, the optical phase of our device has no change. Here 50 V is defined as the operating threshold of our device. The authors suggest that the existence of threshold is mainly determined by the pinning effect of electrowetting in conjunction with the potential required for mechanical deformation of the elastic film [29,30]. When the voltage gradually increases, the contact angle of oil droplet increases and the transparent sheet moves up. It means that the optical path length of oil in the inner chamber is lengthened while the optical path length of conductive liquid is shortened. Due to the different refractive indices of the two liquids, the total optical path length through the inner chamber changes, which leads to the variation of the optical phase. The largest phase shift reaches above ∼6.68 π when the applied voltage is 150 V. From Fig. 6, we can also find that the optical phase shift of our device varies linearly when the operating voltage is applied from 90 V to 150 V, which is called as the linear working range.
4. Conclusion
In this paper, an optofluidic phase modulator based on electrowetting is designed and fabricated. The modulator consists of two chambers which filled with immiscible insulating droplet and conductive liquid. A transparent sheet is fixed between the liquid-liquid interface by an elastic film PDMS at the bottom of chamber to get flat interface. When the voltage is applied to the planar electrode, the flat liquid interface will move up, resulting in the variable optical path length which can realize the function of phase adjustment. A phase shift of 6.68 π is achieved under a voltage of 150 V. The proposed modulator will promote the development of optofluidic devices and has potential high values for application on adaptive optics.
Funding
National Natural Science Foundation of China (61775102); Youth Program of National Natural Science Foundation of China (61905117); Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX19_0970); Technology Foundation of Basic Enhancement Program (2019-JCJQ-JJ-446).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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