Dynamically encircling exceptional points (EPs) has unveiled intriguing chiral dynamics in photonics. However, the traditional approach based on an open manifold of Hamiltonian parameter space fails to explore trajectories that pass through an infinite boundary. Here, by mapping the full parameter space onto a closed manifold of the Riemann sphere, we introduce a framework to describe encircling-EP loops. We demonstrate that an encircling trajectory crossing the north vertex can realize near-unity asymmetric transmission. An efficient gain-free, broadband asymmetric polarization-locked device is realized by mapping the encircling path onto L-shaped silicon waveguides.   , which makes  equal to zero.

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.Topological edge states (TESs), arising from topologically nontrivial phases, provide a powerful toolkit for the architecture design of photonic integrated circuits, since they are highly robust and strongly localized at the boundaries of topological insulators. It is highly desirable to be able to control TES transport in photonic implementations. Enhancing the coupling between the TESs in a finite-size optical lattice is capable of exchanging light energy between the boundaries of a topological lattice, hence facilitating the flexible control of TES transport. However, existing strategies have paid little attention to enhancing the coupling effects between the TESs through the finite-size effect. Here, we establish a bridge linking the interaction between the TESs in a finite-size optical lattice using the Landau–Zener model so as to provide an alternative way to modulate/control the transport of topological modes. We experimentally demonstrate an edge-to-edge topological transport with high efficiency at telecommunication wavelengths in silicon waveguide lattices. Our results may power up various potential applications for integrated topological photonics.

Optical wavefront engineering is essential for the development of next-generation integrated photonic devices. It is used for reflecting terahertz waves in a predesigned nonspecular direction with near-unitary efficiency, which is a longstanding challenge for high-performance functional devices. Recently, metagratings have offered an efficient solution for beam steering at large angles without the need for a discretization phase or impedance profile. Here, all-dielectric metagratings fabricated using a silicon cuboid complex lattice are proposed and demonstrated experimentally to achieve anomalous terahertz beam reflections above the diffraction cone with unitary diffraction efficiency. For the bipartite metagrating system, a single dispersive scatterer per unit is effective for achieving broadband beam steering because of Brillouin zone folding, and another perturbative synergetic scatterer is introduced to slightly tailor the array coupling and improve the performance. High-efficiency beam steering, including both retroreflection under oblique incidence and one-way diffraction under normal incidence, can be achieved by breaking structural symmetry and coherently suppressing unnecessary radiation channels. Moreover, silicon metagratings with spatially dispersive response features show perfect anomalous reflection operation in the broadband region, which is promising for leveraging terahertz spatially separated devices.