Complex-valued neural networks have many advantages over their real-valued counterparts. Conventional digital electronic computing platforms are incapable of executing truly complex-valued representations and operations. In contrast, optical computing platforms that encode information in both phase and magnitude can execute complex arithmetic by optical interference, offering significantly enhanced computational speed and energy efficiency. However, to date, most demonstrations of optical neural networks still only utilize conventional real-valued frameworks that are designed for digital computers, forfeiting many of the advantages of optical computing such as efficient complex-valued operations. In this article, we highlight an optical neural chip (ONC) that implements truly complex-valued neural networks. We benchmark the performance of our complex-valued ONC in four settings: simple Boolean tasks, species classification of an Iris dataset, classifying nonlinear datasets (Circle and Spiral), and handwriting recognition. Strong learning capabilities (i.e., high accuracy, fast convergence and the capability to construct nonlinear decision boundaries) are achieved by our complex-valued ONC compared to its real-valued counterpart.

The past two decades have witnessed the revolutionary development of optical trapping of nanoparticles, most of which deal with trapping stiffness larger than 10⁻⁸ N/m. In this conventional regime, however, it remains a formidable challenge to sort out sub–50-nm nanoparticles with single-nanometer precision, isolating us from a rich flatland with advanced applications of micromanipulation. With an insightfully established roadmap of damping, the synchronization between optical force and flow drag force can be coordinated to attempt the loosely overdamped realm (stiffness, 10⁻¹⁰ to 10⁻⁸ N/m), which has been challenging. This paper intuitively demonstrates the remarkable functionality to sort out single gold nanoparticles with radii ranging from 30 to 50 nm, as well as 100- and 150-nm polystyrene nanoparticles, with single nanometer precision. The quasi-Bessel optical profile and the loosely overdamped potential wells in the microchannel enable those aforementioned nanoparticles to be separated, positioned, and microscopically oscillated. This work reveals an unprecedentedly meaningful damping scenario that enriches our fundamental understanding of particle kinetics in intriguing optical systems, and offers new opportunities for tumor targeting, intracellular imaging, and sorting small particles such as viruses and DNA.

Lateral optical forces induced by linearly polarized laser beams have been predicted to deflect dipolar particles with opposite chiralities toward opposite transversal directions. These “chirality-dependent” forces can offer new possibilities for passive all-optical enantioselective sorting of chiral particles, which is essential to the nanoscience and drug industries. However, previous chiral sorting experiments focused on large particles with diameters in the geometrical-optics regime. Here, we demonstrate, for the first time, the robust sorting of Mie (size ~ wavelength) chiral particles with different handedness at an air–water interface using optical lateral forces induced by a single linearly polarized laser beam. The nontrivial physical interactions underlying these chirality-dependent forces distinctly differ from those predicted for dipolar or geometrical-optics particles. The lateral forces emerge from a complex interplay between the light polarization, lateral momentum enhancement, and out-of-plane light refraction at the particle-water interface. The sign of the lateral force could be reversed by changing the particle size, incident angle, and polarization of the obliquely incident light.

Strong mode coupling and Fano resonances arisen from exceptional interaction between resonant modes in single nanostructures have raised much attention for their advantages in nonlinear optics, sensing, etc. Individual electromagnetic multipole modes such as quadrupoles, octupoles, and their counterparts from mode coupling (toroidal dipole and nonradiating anapole mode) have been well investigated in isolated or coupled nanostructures with access to high $Q$ factors in bound states in the continuum. Albeit the extensive study on ordinary dielectric particles, intriguing aspects of light-matter interactions in single chiral nanostructures is lacking. Here, we unveil that extraordinary multipoles can be simultaneously superpositioned in a chiral nanocylinder, such as two toroidal dipoles with opposite moments, and electric and magnetic sextupoles. The induced optical lateral forces and their scattering cross sections can thus be either significantly enhanced in the presence of those multipoles with high-$Q$ factors, or suppressed by the bound states in the continuum. This work for the first time reveals the complex correlation between multipolar effects, chiral coupling, and optical lateral force, providing a distinct way for advanced optical manipulation.