No abstract

Vector vortex beams are conventionally created as the superposition of orbital angular momentum (OAM) modes with orthogonal polarizations, limiting the available degrees of freedom (DoFs) to 2, while their creation by complex optical devices such as metasurfaces, liquid crystals, and interferometers has hindered their versatility. Here we demonstrate a new class of vector vortex beam constructed from four DoFs as multiple ray-like trajectories with wave-like properties, which we create by operating a simple anisotropic microchip laser in a frequency-degenerate state. Our new structure is obtained by the superposition of two stable periodic ray trajectories, simultaneously fulfilling a completed oscillation in the cavity. By a simple external modulation, we can transform our ray trajectories into vortex beams with large OAM, multiple singularities, as well as exotic helical star-shaped patterns. Our experimental results are complemented by a complete theoretical framework for this new class of beam, revealing parallels to hybrid SU(2) coherent states. Our approach offers in principle unlimited DoFs for vectorial structured light with concomitant applications, for example, in engineering classically entangled light and in vectorial optical trapping and tweezing.

Vector beams, non-separable in spatial mode and polarisation, have emerged as enabling tools in many diverse applications, from communication to imaging. This applicability has been achieved by sophisticated laser designs controlling the spin and orbital angular momentum, but so far is restricted to only two-dimensional states. Here we demonstrate the first vectorially structured light created and fully controlled in eight dimensions, a new state-of-the-art. We externally modulate our beam to control, for the first time, the complete set of classical Greenberger–Horne–Zeilinger (GHZ) states in paraxial structured light beams, in analogy with high-dimensional multi-partite quantum entangled states, and introduce a new tomography method to verify their fidelity. Our complete theoretical framework reveals a rich parameter space for further extending the dimensionality and degrees of freedom, opening new pathways for vectorially structured light in the classical and quantum regimes.

Histological staining is the gold standard for tissue examination in clinical pathology and life-science research, which visualizes the tissue and cellular structures using chromatic dyes or fluorescence labels to aid the microscopic assessment of tissue. However, the current histological staining workflow requires tedious sample preparation steps, specialized laboratory infrastructure, and trained histotechnologists, making it expensive, time-consuming, and not accessible in resource-limited settings. Deep learning techniques created new opportunities to revolutionize staining methods by digitally generating histological stains using trained neural networks, providing rapid, cost-effective, and accurate alternatives to standard chemical staining methods. These techniques, broadly referred to as virtual staining, were extensively explored by multiple research groups and demonstrated to be successful in generating various types of histological stains from label-free microscopic images of unstained samples; similar approaches were also used for transforming images of an already stained tissue sample into another type of stain, performing virtual stain-to-stain transformations. In this Review, we provide a comprehensive overview of the recent research advances in deep learning-enabled virtual histological staining techniques. The basic concepts and the typical workflow of virtual staining are introduced, followed by a discussion of representative works and their technical innovations. We also share our perspectives on the future of this emerging field, aiming to inspire readers from diverse scientific fields to further expand the scope of deep learning-enabled virtual histological staining techniques and their applications.