Millimeter-scale focal length tuning with MEMS-integrated meta-optics employing high-throughput fabrication

Miniature varifocal lenses are crucial for many applications requiring compact optical systems. Here, utilizing electro-mechanically actuated 0.5-mm aperture infrared Alvarez meta-optics, we demonstrate 3.1 mm (200 diopters) focal length tuning with an actuation voltage below 40 V. This constitutes the largest focal length tuning in any low-power electro-mechanically actuated meta-optic, enabled by the high energy density in comb-drive actuators producing large displacements at relatively low voltage. The demonstrated device is produced by a novel nanofabrication process that accommodates meta-optics with a larger aperture and has improved alignment between meta-optics via flip-chip bonding. The whole fabrication process is CMOS compatible and amenable to high-throughput manufacturing.

lists the design dimensions for the two complementary Alvarez meta-optics, including the square array layouts and the individual nanoposts used to map the cubic surface profiles. The six linear steps of nanopost duty cycles and their corresponding diameters are selected from the simulated transmitted coefficients (presented in Figure 1 of the main paper) to produce a near-unity amplitude and a phase range from 0 to 2π.  Table S1. Design dimensions of the silicon nitride cylindrical nanoposts for the pair of complementary Alvarez meta-optics.

Device images and tuning data for Alvarez lens with actuator Design 2
Here we present the results of an Alvarez metalens fabricated with the same optical elements as the one presented in the main paper but different parameters for the actuator design.

Fabricated device
Design 2 here has the same Alvarez metasurfaces as Design 1 presented in the main paper. In contrast, the Design 2 electrostatic actuator for the mobile metasurface has a higher spring constant due to its shorter springs of 500 µm and wider finger width of 3 µm. Given the same comb-drive footprint and finger gap, Design 2 has fewer finger pairs involved in actuation. Table 1 of the main paper summarizes the complete comparison between actuator Designs 1 and 2. Compared to Design 1 presented in the main paper, although Design 2 requires a higher voltage to produce a similar focal tuning range, the higher stiffness also leads to a higher natural frequency, giving a more extensive range of actuation frequencies before reaching the instability regime. The differences here show that the users can flexibly modify the actuator designs to boost specific attributes to fulfill different application requirements without changing the device footprint.

Electrostatic tuning
Similar to Design 1 in the main paper, the actuated displacement in actuator Design 2 follows the voltage squared curve with negligible hysteresis in Figure S2(b). Figure S2

Alvarez focal tuning
As shown in Figure S3(a), the increasing actuation voltage and actuated displacement shift the focal profile closer to the device plane and concentrate it to a smaller region. Figure S3

Power consumption calculation
For the MEMS tunable Alvarez meta-optic lens presented in the main paper, we calculate the DC power consumption based on the measured current values and estimate the power consumption per switching based on the measured spring constants and design capacitor dimensions. (1) Figure S4 plots the power calculated as the product of measured current and actuation DC voltage. The calculated power closely follows the theoretical quadratic dependence on the applied voltage.

Energy consumed per switching
Besides the static power calculated in Section 2.1 for a device held at a constant voltage, we expect a small amount of power consumption whenever the voltage switches and the capacitive energy stored in the comb-drive is built up or released.
There are N = 252 finger pairs on each actuation side of the device presented in the main paper, and the comb drive dimensions are summarized in Table 1, where finger height h = 11 µm and finger gap dsep = 2 µm. The initial finger overlap is l0 = 5 µm. For estimation, we will calculate the largest power consumption at the highest application voltage V = 40 V, which induces a maximum lateral actuation of Δd = 18.1 µm. With the dielectric medium being air, when the actuator is at its maximum displacement, the capacitance in the comb drive is Assuming the actuator is operating right below the natural resonance f0 = 1300 Hz (see Section 4.1 in the main paper) before instability sets in, the maximum power consumption can be estimated from the energy required to charge the capacitor per period realizing low power consumption when operating at kHz tuning frequencies.

Error analysis
For the MEMS actuation data and Alvarez focal tuning data presented in Figure 3 and Figure 4 in the main paper, we estimate the corresponding error based on the uncertainties of the analysis methods and the physical camera limitations.

Uncertainties in edge detection of MEMS platform actuation
The infrared camera captures the actuated displacement of the MEMS platform induced by various voltages. We perform edge detection of actuated features at multiple locations in each video frame to analyze local displacements. The algorithm automatically omits outliers and ambiguous readout due to camera defects or resolution limitations. Given the valid local displacements 1 , 2 , … , with a standard deviation , the overall device displacement is calculated as their mean We estimate the associated uncertainty by the standard deviation of the mean ̅ 1 , calculated as Another source of uncertainty can come from the resolution limit of the camera, which limits the location reading accuracy to the distance corresponding to half of a pixel. Therefore, in the actuated displacement data presented in the main paper, the error bars have been calculated as the corresponding standard deviation of the mean from the edge detection results or the distance of a half camera pixel, whichever is larger.

Uncertainties in focal tracking of Alvarez tuning
The infrared camera we have used to monitor the Alvarez metalens has intrinsic artifacts and defects such as uneven stripes and dead pixels, as shown in Figure S5(a). They are visible in raw device images captured by the camera, as shown in Figure S5(b). In focal tracking, we analyze the in-plane distribution of intensities to identify the bright clusters near the center as the potential focal spot. All the potential focal spots found from images taken along the optical axis are then compared to search for the brightest spot as the focus and the corresponding image plane as the focal plane at the given actuation voltage. Therefore, it is crucial to remove the abnormalities in the images prior to focal tracking. Since the camera artifacts and defects are mostly static, we use an algorithm to extract their locations and intensity deviation relative to the background to correct the corresponding abnormalities in the raw device images. As shown in Figure S5(c), although there is some faint stripe residue left, probably due to random intensity noise intervening with the correction process, the majority of the abnormalities have been removed, producing images ready for focal tracking. However, just as the camera artifacts introduce local intensity offsets, the corresponding correction process will inevitably modify the captured pixel intensities at the potential focal spots, and the exact values of modification are affected by the artifact locations relative to the focal spots. Therefore, the most predominant uncertainty in focal tracking comes from the possible deviation in the search results caused by the spatially varying intensity abnormalities and the corresponding correction process. To estimate the range of uncertainties, we find the nominal focal plane first. Then we offset the intensity value of every pixel in the focal spot by a sigma of the dark reference image used to perform the image correction, mimicking the