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.

High contrast imaging at small inner working angles can be achieved using a vector vortex coronagraph in the focal plane of the telescope providing a helical phase ramp with a singularity at its center. The form birefringence of full-diamond subwavelength gratings has proven to be well suited to manufacture such vortex phase masks for coronagraphic applications (Subwavelength Grating Vortex Coronagraph, SGVC). In the past years our group has developed and manufactured SGVCs of topological charge 2 (Annular Groove Phase Mask, AGPM) made of a concentric diamond subwavelength grating. For future applications including ELT-class telescopes in the near-to mid-infrared that will partly resolve nearby stars, it is however useful to increase the topological charge of the vortex. After shortly reviewing our previous attempts at optimizing the grating structure for SGVC of charge 4, we present the first laboratory results obtained with such devices. We then introduce and discuss more realistic simulations compared to prior studies using finite-difference time-domain methods. The quality of the simulation results obtained with the open source software MEEP for an AGPM is shown to be appropriate for developing and assessing the performance of future vortex phase masks. We therefore perform updated simulations for SGVC of charge 4 including various designs with straight and curved grating lines. We conclude with a perspective on the potential of metasurfaces and their applications to design novel vortex coronagraphs based on subwavelength structures.