Unlocking ultra-high holographic information capacity through nonorthogonal polarization multiplexing

Polarization multiplexing, a crucial technique in photonics, traditionally relies on orthogonal polarization states. This orthogonality, a consequence of the inner product of two output fields equaling zero, confines polarization multiplexing to two channels, dictated by a 2 × 2 Jones matrix. While suitable for polarization imaging and encryption, this limitation restricts the number of multiplexing channels free from cross-interference. Existing methods, like space- or time-division techniques, compromise spatial or temporal resolution and typically only expand to four orthogonal channels. Even advanced eigen-polarization modulation techniques remain constrained by orthogonal bases, limiting applications like dynamic holography and information transmission. Recent advancements in metasurfaces have shown potential for increased holographic information capacity, but the number of independent channels remains a challenge. This research aims to overcome the inherent limitations of orthogonal polarization multiplexing to achieve ultra-high holographic information capacity. The authors propose a novel approach using non-orthogonal polarization-basis multiplexing to significantly increase the number of independent channels achievable in holographic applications.

Previous research has explored various methods to enhance polarization multiplexing. Bao et al. used cascaded metasurfaces to manipulate light amplitude and phase for complex holographic applications. Wang et al. demonstrated high-efficiency metasurfaces for complex vectorial holography using polarization multiplexing. Xiong et al. introduced engineered noise to surpass the fundamental limit, achieving 11 independent holographic images. These studies highlight the potential of innovative strategies like engineered noise and complex light manipulation to improve polarization multiplexing, but the number of achievable independent channels remains a significant limitation. The use of orthogonal polarization bases in these studies represents a key limitation that the current research seeks to overcome.

This study introduces a nonorthogonal polarization-basis multiplexing technique. The authors engineer spatially variable eigen-polarization states at a subwavelength scale using metaatoms. By meticulously controlling the local eigen-polarization of each metaatom, a unique collective effect is achieved across multiple nonorthogonal polarization channels. This allows for a nonzero product of output fields, resulting in a precise overall polarization output. The Jones matrix is expanded to 10x10 using a controllable local eigen-polarization modulation mechanism. A vectorial diffraction neural network (VDNN) optimizes multiplexing efficiency and reduces crosstalk. The design principle centers around manipulating the local linear eigen-polarizations of metaatoms to construct globally nonorthogonal output polarization states. The authors use circular polarization basis vectors to derive equations describing the metaatom's response based on eigen-polarization modulation. This allows for the reconstruction of a control matrix over various non-orthogonal input-output polarization channels. The global response of the metasurface is the integral of this matrix with respect to position. A VDNN is then used to optimize parameters and selectively extract different channels. Experiments involved designing and fabricating metasurfaces to validate the approach, including tri-fold cyclic nonorthogonal linear polarization multiplexes, circular and elliptical polarization multiplexes, and 55 diverse nonorthogonal polarization multiplexes. The training process of the VDNN is illustrated, highlighting incident polarization, output polarization, and the target holographic pattern. The metasurface fabrication employed electron beam evaporation, spin coating, electron beam lithography, and ICP dry etching. Experimental characterization used mid-infrared light, polarizers, a liquid crystal retarder, and a focal plane array. For simulations, the authors employed the three-dimensional finite difference time domain (FDTD) method and the vector integration algorithm based on Rayleigh-Sommerfeld diffraction theory.

The research successfully demonstrates nonorthogonal polarization-basis multiplexing, achieving three-channel nonorthogonal polarization multiplexing with full degrees-of-freedom coverage. The method expands the Jones matrix dimensionality to 10 × 10. The VDNN optimization process resulted in the experimental creation of 55 intricate holographic patterns across these expanded channels, without compromising spatial, temporal, or other dimensions. The experiments validated the approach using different polarization states (linear, circular, elliptical), generating various holographic images (puppy, kitten, mouse, A, B, C, deer, squirrel, wolf, and elements from the periodic table). The correlation coefficient analysis confirms high isolation between different channels. Holographic efficiencies were measured for various configurations, demonstrating the feasibility and effectiveness of the approach. The analytical solution reveals that the maximum channel number without compromising other dimensions is three, and the method utilizes a controllable local eigen-polarization modulation mechanism and VDNN optimization to achieve a higher number of channels (55).

The findings address the research question by demonstrating a significant increase in the number of independent channels achievable in holographic polarization multiplexing. The success in generating 55 distinct holographic patterns across nonorthogonal polarization channels showcases the potential of this approach to significantly enhance information capacity in optical systems. The high isolation between channels demonstrates the practicality and robustness of the method. The results are highly relevant to the field of photonics, offering a significant advancement in polarization multiplexing for applications such as dynamic holography, optical encryption, and high-capacity information transmission. The compact nature of the metadevices makes them a versatile platform for advanced optical applications. The research suggests future research directions might involve expanding the Jones matrix to even higher dimensions and exploring functionalities beyond holography, like adaptive lenses and dynamic optical devices.

This study presents a significant breakthrough in polarization multiplexing by introducing nonorthogonal polarization-basis multiplexing. The integration of a controllable eigen-polarization modulation mechanism and a VDNN enabled the creation of 55 distinct holographic patterns, exceeding previous limitations. This work establishes a foundation for advanced hyper-polarization dynamic holography, enhancing information capacity and security in optical communication and quantum information sciences.

The study primarily focuses on mid-infrared wavelengths. Further research could explore the applicability of this method across a broader range of wavelengths. The fabrication process requires advanced nanofabrication techniques, which might limit scalability for mass production. While the VDNN optimization significantly reduces crosstalk, minor crosstalk might still exist in high-channel-count scenarios, necessitating further improvements in metaatom design and optimization algorithms.