Vortex phase masks have been shown to be an efficient means to reduce the blinding stellar light in high-contrast imaging instruments. Once placed at the focal plane of the telescope, the helical phase ramp of a vortex phase mask diffracts the light of a bright on-axis source outside the re-imaged telescope pupil, while transmitting the light of a faint off-axis companion nearly unaffected. The Annular Groove Phase Mask (AGPM) is a broadband metasurface implementation of a vector vortex phase mask using the artificial birefringence of a circular subwavelength grating etched onto a diamond substrate. To date, the AGPM design has been optimized using rigorous coupled-wave analysis (RCWA), which is a valid tool to simulate periodic straight gratings. However, we have now reached a performance level where the curvature of the grating lines at the center becomes a limiting factor. Here, we use a finite-difference time-domain (FDTD) method to correctly describe the AGPM performance, including the effect of the curved grating close to its center. We confirm the validity of this simulation framework by comparing its predictions with experimental results obtained on our infrared coronagraphic test bench, and we show that RCWA fails at reproducing correctly the central AGPM performance, confirming the need for a full 3d simulation tool such as FDTD. Finally, we use FDTD to optimize the grating parameters at the AGPM center, and conclude with a new optimal design.