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Optical beams with nonuniform polarization offer enhanced capabilities for information transmission, boasting increased capacity, security, and resilience. These beams possess vectorial features that are spatially organized within localized three-dimensional regions, forming tensors that can be harnessed across a spectrum of applications spanning quantum physics, imaging, and machine learning. However, when subjected to the effect of the transmission channel, the tensorial propagation leads to a loss of data integrity due to the entanglement of spatial and polarization degrees of freedom. The challenge of quantifying this spatial-polarization coupling poses a significant obstacle to the utilization of vector beams in turbulent environments, multimode fibers, and disordered media. Here, we introduce and experimentally investigate mosaic vector beams, which consist of localized polarization tesserae that propagate in parallel, demonstrating accurate measurement of their behavior as they traverse strongly disordered channels and decoding their polarization structure in single-shot experiments. The resultant transmission tensor empowers polarization-based optical communication and imaging in complex media. These findings also hold promise for photonic machine learning, where the engineering of tensorial flow can enable optical computing with high throughput.

Quantum metasurfaces, i.e., two-dimensional subwavelength arrays of quantum emitters, can be employed as mirrors towards the design of hybrid cavities, where the optical response is given by the interplay of a cavity-confined field and the surface modes supported by the arrays. We show that stacked layers of quantum metasurfaces with orthogonal dipole orientation can serve as helicity-preserving cavities. These structures exhibit ultranarrow resonances and can enhance the intensity of the incoming field by orders of magnitude, while simultaneously preserving the handedness of the field circulating inside the resonator, as opposed to conventional cavities. The rapid phase shift in the cavity transmission around the resonance can be exploited for the sensitive detection of chiral scatterers passing through the cavity. We discuss possible applications of these resonators as sensors for the discrimination of chiral molecules. Our approach describes a new way of chiral sensing via the measurement of particle-induced phase shifts.