Objective Polarization beam splitters are indispensable components in polarization imaging systems. These systems can acquire intensity information and polarization information almost simultaneously, enriching the information content of target images and significantly enhancing image detection accuracy. In recent years, polarization imaging detection technology has emerged as a key technology for target tracking and recognition in both civil and military sectors. The polarization beam splitting components of traditional polarization imaging systems mostly rely on various lens groups, which makes the imaging system structure complex and bulky and is not conducive to the development of miniaturization of imaging systems. Metasurfaces, artificially defined sub- wavelength periodic or aperiodic array structures, offer flexible electromagnetic wave regulation through phase and amplitude adjustments, leading to more compact electromagnetic control devices. A polarization beam splitter employing metasurfaces is lightweight and structurally simple, favoring integrated development in modern optical systems. Polarization imaging spans various optical bands; notably, the 3-5 mu m band in the mid- infrared serves as an atmospheric window band. This band boasts strong anti- interference capabilities, making it ideal for military applications like nighttime target detection and sea level measurement. Most existing polarization imaging systems utilize linearly polarized light, which is heavily influenced by environmental factors, causing significant losses and reducing imaging intensity and clarity when used in mist, clouds, and smoke. Circularly polarized light, conversely, offers superior anti- interference capabilities and propagation stability. Given this background, there is a pressing need to explore mid- infrared circularly polarized beam splitters. Methods Phase and amplitude are fundamental properties of electromagnetic waves, and their manipulation allows for beam control. According to the phase propagation principle, the phase of a metasurface varies with its unit structure size. Our designed metasurface, based on a rectangular pillar structure, enables arbitrary electromagnetic wave control by adjusting the unit structure's dimensions. Following the geometric phase principle, rotating the unit structure introduces an additional phase shift twice the rotation angle for incident circularly polarized light. We obtain essential phase data for metasurface design by transmitting phase and geometric phase. Leveraging the generalized Snell's law, we determine the minimum number of unit structures for metasurface structures and calculate the polarization beam splitting angle. Using the Fourier optics concept, we treat electromagnetic interference on a plane as superpositions of plane waves with varying incident angles. Viewing the metasurface as an obstruction in the path of light propagation, we incorporate polarization information and apply matrix Fourier optics to translate the metasurface's light field polarization state control into distinct diffraction orders. Using the time-tomain finite difference algorithm for simulation calculations, an electric field monitor is set up in Lumerical to obtain the effect of polarization beam splitting. Results and Discussions The mid- infrared (4 mu m) circular polarization beam splitter we developed based on metasurfaces achieves the desired polarization beam splitting [Figs. 5(a) -(d)]. We determine the polarization beam splitting angle by analyzing the electric field pattern, resulting in 8 =6. 52 degrees . This closely matches the theoretical value, demonstrating a strong correlation. Furthermore, we calculate the Jones vectors of four polarization states when interacting with the metasurface and compare these with the Jones vectors for those states [Figs. 5(i) - (l)]. Our results confirm that the metasurface polarization splitter designed in our research effectively operates as a polarizer. Conclusions Our study designs a mid- infrared (4 mu m), circularly polarized beam splitter based on metasurfaces composed solely of BaF2 substrate and rectangular silicon columns measuring 2.7 mu m. This configuration results in a device that is both simple and lightweight. Using the separately incident four different polarization states of light, we obtain the electric field distribution map for each polarization state. Electric field calculations reveal a deflection angle of 8=6.52 degrees for the metasurface circularly polarized beam splitter, closely matching the theoretical value 8=6.56 degrees. The theoretical maximum efficiency for our metasurface circularly polarized beam splitter is 50 degrees o, with simulations indicating an efficiency exceeding 45 degrees o. Transmittance for each polarization state exceeds 87 degrees o, demonstrating good polarization beam splitting effect. Future work could incorporate compensatory phase adjustments to the metasurface for broader bandwidth polarization beam splitting. Notably, the design concept of the metasurface circularly polarized beam splitter is wavelength- agnostic, offering universal applicability. Integrating this beam splitter into polarization imaging can markedly reduce system volume and pave new avenues for integration.
