Here we describe the results from the three different devices. Measurement results feature a 2D scan of the microwave cavity chamber for each configuration, with the red-green-blue colors representing the equivalent hue of visible light when the microwave frequencies are scaled by a factor of ×59,618. The microwave components have varying scattering parameters over the bandwidth of interest, a scan of the empty cavity is used to normalize device measurements to the total power injected into the cavity. Each device focuses to one or more of three separate pixels, depending on the desired functionality of the configuration. The pixels are depicted as either red, green, or blue, indicating the assigned color in the spectral splitting configuration with red as the lowest frequency bin (7.6-8.9 GHz), green as the middle frequency bin (8.9-10.2 GHz), and blue as the high frequency bin (10.2-11.6 GHz). These frequency bins are referred to simply as red, green, or blue from now on.
The focal plane is analyzed in simulation to determine the sorting efficiency, defined as the fraction of incident power transmitting through the target pixel. To quantitatively corroborate the measured intensity profile with the simulated intensity profile, the measured devices feature a series of plots that compare the normalized intensity integrated over the frequency bands of interest for each functionality.
The first device presented here changes its function by undergoing a 180° rotation. The device is designed only for TE light. It focuses broadband light to the center pixel when illuminated by a normally-incident planewave from one side, and focuses red, green, and blue light to the respectively colored pixels when illuminated from the other side, as shown in Fig. 2(a-d). The footprint of the device is 6.2 cm × 18.6 cm, which is 2λ × 6λ at the center wavelength of 3.1 cm, shown in Fig. 2(e). To ensure structural stability the device has a thin frame of PLA, and a connectivity constraint is enforced every ten iterations of the optimization so that the index distribution converges to a fully connected structure.
This device is uniquely simple among the devices presented, since a 180° rotation does not alter the scattering matrix beyond a transposition due to reciprocity. A reasonable concern is that this device will be limited in performance because of this. However, reciprocity does not strongly affect this device, since inputs from both sides are assumed to be normally incident. Thus, only scattering components mapping a normally incident input to a normally incident output are coupled by reciprocity, while the desired output fields are comprised of many more uncoupled planewave components.
The sorting efficiency as a function of frequency is shown in Fig. 2(f). The sorting efficiency averaged across the relevant frequencies for each function is 50.6%. This outperforms a traditional three-pixel absorptive Bayer filter arrays, which have a maximum theoretical sorting efficiency of 33% for each frequency band. To quantitatively compare the intensity profiles of measured and simulated results, normalized intensity profiles are shown in Fig. 2(g) for each function.
Fig. 2. Rotatable device performing broadband focusing in one configuration and spectral splitting in the other configuration. (a) Broadband focusing simulation, (b) spectral splitting simulation, (c) broadband focusing measurement, and (d) spectral splitting measurement. (e) Schematic of the device, where blue represents PLA and white represents air. The footprint of the device is 6.2 cm × 18.6 cm. (f) Analysis of the simulated fields at the focal plane showing the sorting efficiency for each function, defined as the fraction of incident power reaching the target pixel. Red, green, and blue light are focused to their respectively colored pixels, and sorting efficiency is drawn in red, green, and blue, respectively. The broadband focusing function focuses all light to the middle pixel and is drawn in black. (g) Comparison of simulated and measurement normalized intensity profiles at the focal plane. Configuration B intensities are integrated over (left) 7.6 to 8.9 GHz, (center-left) 8.9 GHz to 10.2 GHz, (center-right) 10.2 to 11.6 GHz. (right) Configuration A intensity integrated from 7.6 to 11.6 GHz.
3.2 Auxetic device
Auxetic metameterials have a negative Poisson’s ratio – they have the nonintuitive property of widening in the transverse direction when stretched and narrowing in the transverse direction when compressed. Such metamaterials are useful for tailoring the mechanical properties of devices, and can increase indentation resistance, shear resistance, energy absorption, hardness, and fracture toughness24. They can be fabricated at the macro-scale through techniques such as 3D printing and have been studied at the micro- and nanoscale25,26. Here we present a device capable of switching its optical functionality through the well-studied auxetic transformation of rotating rigid squares, yielding devices with -1 Poisson’s ratio27.
The two functions chosen here are broadband focusing and spectral splitting for TE polarization – the same as the rotatable device. The first configuration features a 0° rotation of all squares, while the second configuration features a ±90° of each square, with each square having an opposite angular rotation as its neighboring squares. The device is fully connected, with a frame around each square element to ensure structural stability. The device and its auxetic transformation are shown in Fig. 3(e).
Fig. 3. Auxetic device performing broadband focusing in one configuration and spectral splitting in the other configuration. (a) Broadband focusing simulation, (b) spectral splitting simulation, (c) broadband focusing measurement, and (d) spectral splitting measurement. (e) Demonstration of the auxetic transformation and device footprint, where blue represents PLA and white represents air. The footprint of the device is 6.2 cm × 18.6 cm. (f) Analysis of the focal plane of this device, showing the sorting efficiency for each function, defined as the fraction of incident power reaching the target pixel. Red, green, and blue light are focused to their respectively colored pixels, and sorting efficiency is drawn in red, green, and blue, respectively. The broadband focusing function focuses all light to the middle pixel and is drawn in black. (g) Comparison of simulated and measurement normalized intensity profiles at the focal plane. Configuration B intensities are integrated over (left) 7.6 to 8.9 GHz, (center-left) 8.9 GHz to 10.2 GHz, (center-right) 10.2 to 11.6 GHz. (right) Configuration A intensity integrated from 7.6 to 11.6 GHz.
A total of three devices were fabricated. The first device demonstrates the auxetic transformation. To fabricate this, the 3D-print was paused at half the thickness of the device, a nylon mesh was manually inserted, and the 3D-print was then resumed to completion. After the print, the nylon mesh was cut to leave only the required flexible hinges between each square. A video of this device being manually actuated is available in Visualization 1. The other two devices are the two different configurations printed directly, which were then measured.
The auxetic design and rotatable design have the same device size and focal length, so the performance of the two devices can be directly compared. The simulated sorting efficiency is shown in Fig. 3(f). Since the auxetic device has a frame around each square element, less of the design area is available for optimization. This detracts from the degrees of freedom of the device, which may explain why the device has a 48.0% average sorting efficiency, 2.6% less than the rotatable device. The difference in average efficiency may also arise from the different natures of the mechanical reconfiguration. The simulated and measured intensities within the full test chamber are shown in Fig 3(a-d). To quantitatively compare the intensity profiles of measured and simulated results, normalized intensity profiles are shown in Fig. 3(g) for each function.
3.3 Shearing device
The final device features a transformation based on shearing alternate layers. This action is achievable at the microscale through MEMS electrostatic actuation. Unlike the previous devices, this device switches between three different functionalities: spectral splitting shown in Fig. 4(a), broadband focusing shown in Fig. 4(b), and polarization splitting shown in Fig. 4(c). All functionalities are designed for both TE and TM polarizations.
The added polarization control demands more degrees of freedom than the rotatable and auxetic devices, and it was found that the device needed to be nearly 3× thicker than the rotatable and auxetic devices to achieve satisfactory performance of 59.2% average sorting efficiency. This device does not have a supporting frame and does not enforce connectivity like the previous devices.
This device was analyzed only in simulation due to limitations within the measurement system: the measurement chamber only supports a TE-polarized TEM mode, and the scannable region is too small to measure this device. A 4-layer device was designed and tested with similar agreement between simulation and measurement to the rotatable and auxetic devices, but the device could not achieve all objective functions. Data for this device is available on request.
The configurations and simulation results for the 8-layer simulated device are summarized in Fig. 4. The device is a stack of eight 8 cm × 2 cm layers. The mechanical actuation displaces adjacent layers in equal and opposite directions by 3 cm, which is approximately one wavelength. The first configuration, shown in Fig. 4(a), shows spectral splitting behavior with 42% average sorting efficiency for TE and 40% average sorting efficiency for TM. The crosstalk between the different spectral bins is worse than the rotatable and auxetic devices, with the worst case occurring for the TM-polarized green input which focuses only 1.2× more power to the desired green pixel than the undesired blue and red pixels.
The neutral position of the device, in which all layers are aligned as shown in Fig. 4(b), features broadband focusing with high efficiency. The aperture size of this configuration is smaller than the other two configurations, and the sorting efficiency is normalized to the power incident on this smaller aperture when analyzing this configuration. The sorting efficiency shown in Fig. 4(e) is expected to be uniformly high across all frequencies and both polarizations.
The final configuration sorts TE polarization to the leftmost pixel and TM polarization to the center pixel. The transmission through each pixel, averaged across the entire spectrum, is summarized in matrix form in Fig. 4(f): a TE input focuses 47% power to the correct pixel and 28% power to the incorrect pixel, the TM input focuses 62% power to the correct pixel and 24% power to the incorrect pixel. More power is coupled to the desired pixel than the undesired pixel at all frequencies except for the case of TE input frequencies below approximately 9 GHz. In this case more power is directed towards the incorrect green pixel than the correct red pixel. It is possible that this could be fixed by sacrificing performance in the other functionalities, such as by tuning the weighting scheme described in equation (1), or by increasing the thickness or index contrast of the device.
Fig. 4. TE and TM fields for a device based on a net shearing movement of 6 cm. (a) The spectral splitting configuration splits red, green, and blue light to the red, green, and blue pixels, respectively. This is analyzed for both TE and TM polarizations. (b) The neutral state of the device performs broadband focusing to the center pixel for both TE and TM polarizations. (c) The polarization sorting configuration sorts broadband TE light to the left (red) pixel and focuses broadband TM light to the center (green) pixel. (d-f) Sorting efficiency of the different configurations. The line color represents the sorting efficiency to the similarly colored pixel as depicted in the color plots. Solid lines represent the TE response, and dashed line represent the TM response. (d) Sorting efficiency in the spectral splitting configuration. (e) Sorting efficiency for the broadband focusing configuration. (f) Sorting efficiency for the polarization splitting configuration. (Inset) A confusion matrix representation of the sorting efficiency, with true input on the vertical axis and predicted input on the horizontal axis. Each matrix entry is determined by averaging the relevant trace over the full bandwidth.