  Dynamically encircling exceptional points (EPs) in two-dimensional
Hamiltonian parameter space has enabled intriguing chiral dynamics in which the
final state of the system depends on the encircling direction. Here, we show
that full Hamiltonian parameter space can be described in a Riemann sphere, and
those points on the parameter space boundary with the eigenstates of the system
Hamiltonian being convergent, converge to the north vertex. We present that
encircling one EP on the Riemann sphere leads to chiral response, and a
continuous encircling trajectory passing through the north vertex can realize
near-unity asymmetrical transmission. An asymmetric polarization-locked devices
are designed by mapping the encircling path onto the L-shaped silicon
waveguides. We experimentally demonstrate near 100% asymmetrical polarization
conversion efficiency between TE and TM modes with the mode crosstalk below -20
dB at 1550 nm. Our results bring the study of EP-associated dynamics into the
realm of highly-efficient asymmetrical polarization conversion and power up new
application opportunities for EP physics.
