Metasurface diffraction-order polarization control and Mueller matrix microscopy (<italic>invited</italic>)

ObjectivePolarization imaging, particularly Mueller matrix microscopy, holds significant value in biomedical diagnosis and material characterization due to its ability to provide abundant microscopic structural information regarding anisotropy. However, conventional polarization microscopy systems are often bulky and suffer from cumbersome measurement procedures. Although recent metasurface-based imaging solutions utilizing superpixels have achieved compactness, their inherent reliance on spatial multiplexing leads to restricted fields of view, reduced spatial resolution, and edge vignetting. To address these limitations, this study proposes a Silicon Nanoantenna Metasurface Diffraction-order Polarization Control (SNM-DOPC) technique. By realizing parallel polarization transformation at non-zero diffraction orders, we aim to construct a compact, transmissive Mueller matrix microscopy system free of spatial multiplexing, shared apertures, and moving parts, thereby facilitating high-precision characterization of fine sample structures.MethodsBased on matrix Fourier optics, we designed a silicon nano-antenna polarization-control metasurface featuring four specific non-zero diffraction orders—$ \{(\pm 1{,}0),(0,\pm 1)\} $. These orders function as quarter-waveplates with distinct fast-axis orientations ($ \pm 50{^{\circ}} $ and $ \pm 75{^{\circ}} $ ). To determine the optimal phase profile and orientation of the 15×15 silicon nano-antenna unit cells, a nonlinear constrained optimization algorithm (damped quasi-Newton method with Broyden–Fletcher–Goldfarb–Shanno (BFGS) update) was employed to iteratively solve the phase distribution, ensuring high and uniform diffraction efficiency. The metasurface structure was subsequently encoded using silicon nanoantennas that simultaneously modulate geometric and propagation phases. The device was fabricated on a fused silica substrate using electron-beam lithography (EBL) and inductively coupled plasma (ICP) etching. The fabricated metasurface was experimentally characterized, and polarization parameters of the non-zero diffraction orders were extracted using the Mueller Matrix Polar Decomposition (MMPD) method. To validate the system's imaging capability, we integrated the metasurface into an infinity-corrected microscopic optical path to construct a Mueller microscopic imaging system, and eliminated systematic errors using the Eigenvalue Calibration Method (ECM). Subsequently, we conducted a time-series monitoring experiment on fresh Epipremnum aureum leaf tissue. The Mueller matrix was calculated via the intensity projection matrix to extract polarization characteristics.Results and DiscussionsComprehensive experimental characterization of the fabricated metasurface was conducted. The results demonstrate excellent agreement between the measured polarization responses and the design specifications. The maximum deviations of the phase delay and fast-axis orientation from the theoretical values are merely 6.7% and 4%, respectively. Regarding diffraction efficiency, a low coefficient of variation (0.021) indicates high uniformity across the diffraction orders, with an absolute transmission efficiency of 62.8%. Upon integration into the Mueller microscopy system, a spatial resolution superior to 1.55 μm was achieved. Following calibration, the experimentally measured average Mueller matrix elements show good agreement with theoretical predictions, with a maximum deviation of only 0.0094. The calibrated system was utilized to perform imaging analysis on fresh Epipremnum aureum leaf sections. The results demonstrated that the average depolarization index decreases with increasing storage time, which is consistent with conclusions from conventional Mueller matrix microscopy studies. These results indicate that the system successfully achieves high-fidelity polarization information extraction without spatial multiplexing.ConclusionsThe Silicon Nanoantenna Metasurface Diffraction-order Polarization Control (SNM-DOPC) technique proposed in this paper offers an innovative solution for compact Mueller microscopic imaging systems. By leveraging a nonlinear optimization algorithm and the principles of matrix Fourier optics, and by combining geometric and propagation phase modulation in silicon nanoantennas, this approach successfully realizes highly uniform parallel polarization transformations without redundant components, spatial multiplexing, or shared apertures. Experimental results within the Mueller microscopic imaging system demonstrate that this technique effectively enhances imaging resolution and provides high-precision polarization responses. It proves practical for biological tissue characterization, enabling the precise extraction of polarization parameters at the sub-tissue scale. By overcoming the trade-off between resolution and compactness encountered in prior research, this approach showcases broad application prospects in fields such as material characterization and cellular biological imaging.