High extinction ratio, low insertion loss, optical switch based on an electrowetting prism

: An optical switch based on an electrowetting prism coupled to a multimode ﬁber has demonstrated a large extinction ratio with speeds up to 300 Hz. Electrowetting prisms provide a transmissive, low power, and compact alternative to conventional free-space optical switches, with no moving parts. The electrowetting prism performs beam steering of ± 3 ◦ with an extinction ratio of 47 dB between the ON and OFF state and has been experimentally demonstrated at scanning frequencies of 100–300 Hz. The optical design is modeled in Zemax to account for secondary rays created at each surface interface (without scattering). Simulations predict 50 dB of extinction, in good agreement with experiment.


Electrowetting principle and fabrication
Electrowetting is a technique to change liquid's wetting properties by an external electric field [28][29][30][31][32][33]. Modern electrowetting devices incorporate an electrode, a dielectric, and a hydrophobic layer. The dielectric layer insulates the conductive fluid from the actuating electrode(s), preventing any electrochemical reactions [28][29][30][31][32][33][34]. The hydrophobic layer lowers contact angle hysteresis while enhancing the initial contact angle [68][69][70][71]. This is a more robust actuation mechanism known as electrowetting-on-dielectric (EWOD). The contact angle modulation is described by the Lippmann-Young equation [30,33], cos θ = cos θ • + ( • /2γd)V 2 , where θ is the contact angle after actuation with the applied voltage V, θ • is the initial contact angle at V = 0 V, and d are the effective permittivity of the dielectric layers and its thickness, and γ is the surface tension of the liquid-liquid interface. EWOD devices are often assembled in a cylindrical glass tube filled with a polar and nonpolar liquids, and by applying a voltage through the dielectric layer the curvature of the liquid-liquid interface is altered. EWOD lenses use a uniform electrode coated around the cylindrical glass tube and are implemented in optical applications that benefit from tunable variable focal length, such as cameras [12,72] and microscopy [73][74][75]. Two or more electrode EWOD devices, functioning as an EWOD prism, have been implemented in beam steering [16][17][18] applications like two-photon scanning microscopy [76] and light detection and ranging (LiDAR) [77]. By increasing the number of electrodes to 8 or 16, we can generate a custom shape liquid-liquid interface that can be used for both on-and off-axis optical aberration correction [46,78,79]. In addition to individual EWOD devices, an array of lenses and prisms has been studied extensively [13,14,16,19].
The EWOD prism is constructed in a cylindrical glass tube based on our previous work [41,76,77] as depicted in Fig. 1. The cylindrical glass tube has an inner diameter of 4 mm, outer diameter of 6 mm, and a height of 5 mm. Transparent Indium Tin Oxide (ITO) electrodes are deposited on the sidewalls of the glass tube using a direct current sputtering process. The EWOD prism consists of two separated electrodes on the sidewalls of the glass tube patterned using a 3D printing assisted shadow masking technique. The electrode patterning and deposition step is layer. An anti-reflection (AR) coated optical window patterned with an annular pattern of Ti/Au/Ti serves as the ground electrode. The device is filled with deionized (DI) water and 1-Phenyl-1-cyclohexene (PCH). The device is capped with an AR coated optical window. followed by coating the inner sidewalls of the glass tube with a ∼3.7 µm Parylene HT layer using a vapor phase deposition process (Specialty Coating Systems). The device is then dip coated in a 10% Cytop solution (CTL-809M in CTSOLVE-100E, AGC Chemical Company). The glass tube with thus functionalized sidewalls is epoxy bonded to a 12.7 mm diameter anti-reflection (AR) coated glass window with annular Titanium/Gold (Ti/Au, 20 nm/ 300 nm) electrode patterned on it. The Ti/Au annulus has an inner diameter of 3.75 mm and acts as the ground electrode for the device. The device is sequentially filled with ∼31.5 µL of deionized (DI) water and 1-phenyl-1-cyclohexene (PCH), followed by placing the AR coated optical window on top of the device [see Fig. 1(b)]. The ratio of gravitational to surface tension forces is characterized by the Bond number, B • = ρgR 2 /γ. In our case, the two liquids are density matched, with a Bond number << 1, resulting in an optical device that is insensitive to gravitational distortions. The EWOD device is actuated by applying a sinusoidal AC voltage, with a carrier frequency of 3 kHz and no offset voltage. The reliability and performance of an electrowetting device can be strongly affected by the dielectric layer properties and the characteristics of the liquids. Typically, a pinhole free material with high dielectric constant and a high breakdown strength is deposited as a thin layer. Many studies have been carried out on improving the reliability of EWOD devices based on the choice of single-and multi-layer dielectrics [80][81][82][83]. The choice of liquid combinations is critical in developing a reliable electrowetting device. One of the main challenges is to increase the refractive index difference between the two liquids while maintaining density match condition and having a low freezing point, low viscosity, and low turbidity after thermal shock [42]. The dielectric thickness (Parylene HT ∼3.7 µm and Cytop ∼500 nm) are chosen based on our previous work [41], so as to provide contact angle tuning range from 173 • at 0 V to 60 • at 170 V rms . In this work, we numerically simulate the liquid-liquid interface of a two-electrode EWOD device used in the experiment and implement it into an optical design to demonstrate a high-extinction ratio optical switch using non-sequential ray tracing.

Optical setup and simulation
The optical setup (shown in Fig. 2) used to test the switch is composed of a single two-electrode EWOD device (prism) followed by an achromatic doublet lens (effective focal length of 4.4 mm) and a multimode fiber with a core diameter of 50 µm. A tunable pressure-driven lens (Optotune EL10-30) is positioned 140 mm from the EWOD prism to adjust the focusing condition while coupling to the multimode fiber. The schematic of the setup, modeled in Zemax OpticStudio [84] (ray tracing software), is shown in Fig. 2 without the tunable pressure driven lens. To simulate the optical setup, we have modeled the curvature of the meniscus between the two liquids by using Young-Laplace equation [69][70][71][85][86][87][88][89][90], which describes the equilibrium shape of the liquid-liquid interface. The general Young-Laplace equation with contact condition is given by, ∇u(x, y)/(1 + |∇u(x, y)| 2 ) 1/2 ) = cos γ, where u(x, y) is the equilibrium surface profile and γ is the contact angle at the glass sidewall boundary. The steady-state contact angles of the DI water and PCH combination were experimentally determined to be 173 • with no applied voltage and 60 • at 170 V rms [41]. The contact angle variation is used as the boundary condition in the Young-Laplace equation. We have used Matlab's partial differential equation (PDE) toolbox to solve the Young-Laplace equation and the results are compared to computational fluid dynamics simulation based on two-phase Laminar flow in COMSOL Multiphysics [78,[91][92][93][94][95]. The simulated liquid-liquid interface is imported into Zemax OpticStudio to perform ray tracing. Figure 2 depicts the modeled setup in Zemax OpticStudio sequential mode with the 3 configurations that represent the simulated liquid-liquid interface for steering angles of 0 • and ±3 • . The distances between all the optical elements are kept fixed (similar to the experimental conditions), while the focal length of the tunable pressure-driven lens is optimized for minimum spot size in the imaging plane. A similar procedure has been implemented in the experiments. Next, the optical design is converted from sequential to non-sequential mode in Zemax. Nonsequential ray tracing is a powerful tool for tracing rays in a system with multiple optical paths in which certain types of analysis such as stray and scattered light are practical [84]. Twenty-one liquid-liquid interfaces are simulated in Matlab and imported to Zemax corresponding to a steering of ±3 • . A total of one million rays were traced to fill a 0.5 mm diameter detector plane with pixel size of 2 µm. An incoherent irradiance map (incoherent ray intensity distribution for various incident angles) is generated in the detector plane for various steering angles. Examples of these irradiance maps for steering angles of 0 • , 0.87 • , 1.7 • , and 2.3 • are shown in Fig. 3(a)-3(d).
The dark circle at (0,0) with 50 µm diameter represents the fiber core in these figures.
In non-sequential ray tracing, a ray that strikes a surface can either reflect, refract, total internal reflect (TIR), scatter, split, diffract, or get absorbed (or a combination of these) depending on the properties of the surface. Effects such as ray splitting divide each reflected beam into a large number of secondary rays that dominate the detector plane and appear as scattered pattern in Fig. 3(a)-3(d). Figure 3(a) shows the point-spread function without any steering (on-axis configuration). The shape of the point spread function is altered at larger steering angles (> 1 • ) as the optical aberrations such as coma take effect when a beam travels through a tilted slightly curved liquid-liquid surface [see Fig. 3(d)]. In general, optical switches are characterized by the extinction ratio, defined as: 10log(P max /P min ), where P max and P min are the power transmitted between the ON and OFF states, respectively. To evaluate the extinction ratio, the irradiance map for each steering angle is integrated within the 25 µm radius. The normalized power is plotted in linear and log scale, respectively, as shown in Fig. 3(e)-3(f). At the ON state the beam is aligned to the multimode fiber (at 0 • -on the optical axis), with high transmission, while steering the beam to angles larger than ±2.5 • diminished the transmission through the fiber corresponding to OFF state. This results in optical switching with an extinction ratio of 50 dB by steering the beam between the ON and OFF states (or steering the beam to angles larger than ±2.5 • ).

Experimental results and discussions
We used a continuous-wave 650 nm diode laser, with a collimated beam diameter of 1.2 mm (1/e 2 ), to characterize the extinction ratio of the EWOD prism as a function of steering angle. In addition, we have investigated the scanning frequency of the proposed optical switch. The experimental setup resemble the optical design sketched in Fig. 2. The apparatus is composed of a two-electrode, 4-mm inner diameter EWOD prism followed by an achromatic doublet lens (effective focal length of 4.4 mm) and a multimode 50 µm core fiber patch coupled into a Si-biased detector (Thorlabs DET36A). A tunable pressure-driven lens (Optotune EL10-30) is placed 140 mm behind the EWOD prism to adjust the focusing condition while coupling to the fiber. The power transmitted through the design is measured by collecting the light onto Si-biased detector which is connected to a lock-in amplifier (SRS SR830). We have coupled a laser power of 0.1 mW through the system with coupling efficiency of 80%. To actuate the EWOD prism, we have generated two sinusoidal voltages at 3 kHz with zero voltage offset using a high-speed analog output device (NI PCIe 6738) and amplified them with an 8-channel high-voltage amplifier (OKO Bipolar HV amplifier).
The initial contact angle of the liquid-liquid interface is 173 • with no applied voltages. The contact angle can be tuned to 60 • by applying 170 V [41]. Actuating the two electrodes symmetrically generates a curvature change similar to an EWOD lens device. We apply a voltage difference between the two electrodes to perform beam steering in the EWOD prism that will generate a tilt across the liquid-liquid interface as shown in Fig. 2. The collimated beam is first coupled to the multimode fiber. The EWOD prism is added to the optical path and actuated symmetrically by applying 72 V rms to both electrodes. The fiber coupling is optimized by adjusting the alignment of the EWOD prism and fine-tuning the pressure driven lens. To achieve beam steering, the EWOD prism is driven at the bias voltage of 72 V rms with a voltage difference of ± 10 V applied out of phase between the two electrodes, resulting in one-dimensional beam scanning corresponding to steering angles of ± 3 • . The scanning frequency was chosen to be 0.2 Hz due to the long time constant setting of the lock-in amplifier (a large time constant > 100 ms is mandatory to improve the signal to noise ratio (SNR) of the system and it also greatly increases the response time of the lock-in amplifier).
The optical performance of the optical switch is characterized in terms of extinction ratio in the ON and OFF states, and the scanning frequency. The power transmitted through the optical switch as a function of steering angle is shown in Fig. 4 in linear and log scales, respectively. We measure an extinction ratio of ∼47 dB for the beam that is transmitted through the device (ON state) versus the beam steered to angles > ± 2 • (OFF state). To ensure measurement reliability, the results presented here were repeated 20 times. The standard deviation errors are evaluated from 20 measurements and added to the data points in Fig 4(a) and 4(b). The standard deviation error bars are smaller than the data points (circle marker). The results show that the extinction ratio was maintained at 47 dB without altering the driving voltages of the electrowetting prism in the 20 measurements. The measured extinction ratio of 47 dB is comparable, but slightly smaller than the 50 dB predicted by simulation results. This is mainly due to lack of scattering in the optical simulation. The effect of optical scattering from the EWOD prism can be discarded due to the ultrasmooth surface of the liquid-liquid interface (in the sub-nanometer range) [65][66][67]. The other surfaces make a large contribution to optical scattering, such as the AR coated windows mounted on the top and bottom of the device and the coupling lens. Modeling the scattering from these surfaces in conjunction with non-sequential ray tracing is rather complex and beyond the scope of our work. The scattering from these surfaces reduces the extinction rate in the simulation which is consistent with observed experimental results. The extinction ratio limitation is mainly due to the secondary (stray) rays that circulate within the optical setup.
To perform dynamic beam scanning, the electrodes are driven with two amplitude modulated sinusoidal voltage functions, π out of phase, with a set sweeping frequency. The sweeping frequencies ranged from 100-300 Hz, well below the carrier wave frequency (3 kHz). The electrowetting prism is initially biased by applying 72 V (3 kHz) to both electrodes. The liquid-liquid interface is stable in this state and the voltage differential is defined as: (V left − V right ), applied symmetrically around the voltage of 72 V with various sweeping frequencies.
Due to the faster scan frequency, the transmission through the multimode fiber is collected on a photodiode by a data acquisition card (MC USB201) for various sweeping frequencies.  Hz over a period of 50 ms. The fiber core is positioned at the center of the scan cycle (at 0 • -on the optical axis, the scan starts from -3 • to 3 • and back to -3 • to complete one cycle) hence, in every scanning cycle, two intensity peaks will be recorded on the photodetector. Intensity measurements from the photodetector were analyzed using Fourier analysis as illustrated in  Fig. 5(c)], respectively. The scanning angles decrease by increasing the sweeping frequencies at a given differential voltages. Increasing the differential voltage between the two electrodes compensates for the scanning angle reduction [41].
The optical switch presented here is capable of hundreds of Hz scanning frequency, has ∼1 dB of insertion loss, a high extinction ratio of 47 dB, and can perform over a wide range of wavelengths. The PCH has an optical transmission of > 90% in the wavelength range of 500-1100 nm, while DI-water has a transmission of > 90% for 400-700 nm range. The extinction ratio of the demonstrated optical switch is mainly limited by the secondary rays created through glass substrates, the coupling lens, and the sidewalls of the EWOD prism.

Conclusion
We demonstrated a novel switching concept based on an EWOD prism coupled into a multimode fiber. The EWOD prism is filled with DI-water and PCH liquids, enabling optical switching with extinction ratio of 47 dB between the ON (high transmission) and OFF state (no transmission). The ultrasmooth, sub-nanometer surface roughness at the liquid-liquid interface enables us to perform switching with a large extinction ratio and low insertion loss. The liquid-liquid interface of the EWOD prism is modeled in Zemax to perform non-sequential ray tracing with secondary rays. The simulation predicts an extinction ratio of 50 dB between the ON and OFF state, while experimentally, we measured an extinction ratio of 47 dB. The discrepancy between the optical model and measured results are due to lack of scattering in the simulation model. We have explored the dynamic scanning speed of the EWOD prism in the proposed optical switch and find that scanning frequencies of up to 300 Hz are feasible in our design. Reducing the size of the EWOD prism can significantly enhance the scanning speed of these devices further as the response time is proportional to device radius, τ ∼ r 3/2 [12]. Lastly, a fiber coupled optical switch based on an EWOD prism is appealing for many applications due to the transmissive nature of the EWOD prism, independence from polarization, high extinction ratio, and low insertion loss.