Fig. 1. UGR from topological charge evolution.
(A) Schematic of L-shaped grating coupler. Light travels through and radiates upward from the grating with downward radiation being forbidden. (B) The electrical field (Ey) of the UGR which radiates upward only. (C) Left: Band structures with the UGR marked by a circle, for C2 symmetric (black) and asymmetric (red) structures. Middle: The quality factors of the TE bands for the symmetric and asymmetric unit cell. A symmetry-protected BIC is located at the Γ point. By breaking the symmetry, the quality factor reduces from infinite to a friendly value of 134 for broadband operation. Right: The asymmetry ratio reaches 65.8 dB at kx = − 0.1192, which indicates a UGR. (D) Trajectories traced by the two half-charges (red and blue) for downward radiation in momentum space by varying the height of block B1, showing that the integer charge q = − 1 splits and restores with varying h1. The insets are the vectorial polarization field of the downward radiation in the momentum space for different h1.