Quantum mechanics

Engineering

Discrete mathematics

Theoretical computer science

Vertex (graph theory)

Eigenvalues and eigenvectors

Computer science

Mathematical optimization

Hamiltonian (control theory)

Classical mechanics

Physical chemistry

Polarization (electrochemistry)

Mechanical engineering

Physics

Riemann hypothesis

Graph

Mathematics

Optics

Parameter space

Mathematical analysis

Geometry

Combinatorics

Chemistry

Topology (electrical circuits)

Manifold (fluid mechanics)

Physical Review Letters

Dynamically encircling exceptional points (EPs) have 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.

Riemann-Encircling Exceptional Points for Efficient Asymmetric Polarization-Locked Devices