Characterizing the intensity, phase, and polarization of engineered light is fundamental to understanding and applying metasurfaces. However, existing characterization frameworks are hindered by several limitations, most notably their inability to account for the polarization of the field. Here, we report polarization sensitive coherent modulation imaging (PS-CMI), a light-weight but robust, high-resolution platform for the full-field characterization of metasurface-modulated light. By supplementing the orthogonal x- and y- complex amplitude components with an additional 45°-component, this approach calculates the retardance between two orthogonal polarization components while eliminating phase offsets, thereby enabling the subsequent recovery of the complete polarization state. We demonstrate the versatility of our method by characterizing light fields produced by a United States Air Force (USAF) target, two kinds of complex polarization field, and a metalens. This compact solution addresses a critical gap in metasurface metrology and is broadly applicable to other fields requiring the mapping of complex, polarized light distributions.
Metasurfaces, the planar optical architectures consisting of subwavelength optical antenna arrays (1) , have emerged as a powerful paradigm. They can simultaneously control the fundamental degree of freedom in light, including phase, amplitude, and polarization. By consolidating complex wavefront manipulation into a single, ultra-thin layer, metasurface devices offer a compelling alternative to conventional bulk optics, such as lenses, waveplates, and polarizers (2)(3)(4), particularly for weight-and compactness-sensitive applications in mobile telephony and autonomous navigation. However, fully unlocking the potential of these devices necessitates a simultaneous, full-field, and high-resolution recovery of all modulated properties in the emergent light field, which remains elusive.
Metasurface-modulated light field characterization has long relied on interferometry as the standard benchmark (5,6). However, its implementation is frequently hampered by a reliance on complex, dualpath optical architectures. These configurations are notoriously sensitive to environmental perturbations such as mechanical vibrations and thermal drifts, which degrade measurement stability. In contrast, coherent diffraction imaging (CDI) methods, such as coherent modulation imaging (CMI), Fourier ptychographic microscopy (FPM), and multi-distance CDI, have emerged as robust, common-path alternatives (7,8). However, current CDI frameworks for metasurface characterization are restricted to scalar wave-field recovery. They map only amplitude and phase and fail to resolve the polarization information.
Beyond the specific domain of metasurface characterization, several CDI-derived modalities have sought to bridge this gap by recovering both the complex amplitude and the polarization state of optical beams. One strategy integrates polarization-sensitive detectors into FPM (9,10) , though often at the expense of spatial resolution. Alternatively, structured illumination has been employed to reconstruct the full vectorial distribution of tightly focused fields in three-dimensions (3Ds) (11). While such illumination encoding promotes the resolution, it compromises the ability to characterize samples sensitive to incident polarization and angle, such as metasurfaces. In contrast, measurement-encoding schemes-for example, combining multi-distance CDI with time-sequential polarization measurement (12)-provide a more robust approach for characterizing these samples. Nevertheless, these approaches remain restricted to the paraxial regime, inherently limiting the achievable resolution for characterizing metasurfaces with sub-wavelength structures.
To overcome these challenges, we present polarization sensitive coherent modulation imaging (PS-CMI), a framework for the high-resolution characterization of both wavefront and polarization profiles emergent from metasurfaces. Our new design provides two major improvements over the original works (7)(8)(9)(11)(12)(13)(14):
Comprehensive characterization and nondestructive diagnosis for metasurfaces: We demonstrate that the phase offset, an intrinsic ambiguity in CDI methods, is not globally consistent and must be addressed through regional analysis. Based on this insight, we develop a phase-offset removal algorithm that accurately retrieves the polarization map. While maintaining consistency with prior works on phase modulation (7,8,14), our method incorporates reconstructed maps to characterize the metasurface’s impact on polarization. Furthermore, reconstructed polarization maps enable nondestructive diagnosis of fabrication errors in metasurfaces, which provide guidance for subsequent design optimization and fabrication refinement. Broad Sample Compatibility: By employing measurement encoding rather than illumination encoding, our PS-CMI enables the characterization of angle-and polarization-sensitive samples, a category epitomized by metasurfaces. This framework is readily integrable with conventional microscopy. Rather than compromising the performance, the addition of PS-CMI enhances the resolution of the base system. This renders our method uniquely suited for high-resolution applications and samples that induce large-angle beam modulations.
The full field is reconstructed using CMI-based phase retrieval and time-division polarization modulation.
Theoretically, the vectorial light field can be reconstructed using Jones vector once the complex amplitudes for the x-and y-polarization components are established. Due to its ill-posed nature, phase retrieval suffers from an inherent ambiguity manifesting as a phase offset within the CMI framework (15). This ambiguity leads to incorrect retardance values between x-and y-polarization components, and the Jones vector of the reconstructed field ( ’ U ) containing phase offset can be expressed as: 12). This allows ∆𝜃𝜃 to be determined via a one-dimensional search (detailed in part A of the Supplementary Materials). Distinguished from the previo
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