  One possible solution to achieve high contrast direct imaging at a small
inner working angle (IWA) is to use a vector vortex coronagraph (VVC), which
provides a continuous helical phase ramp in the focal plane of the telescope
with a phase singularity in its center. Such an optical vortex is characterized
by its topological charge, i.e., the number of times the phase accumulates
2{\pi} radians along a closed path surrounding the singularity. Over the past
few years, we have been developing a charge-2 VVC induced by rotationally
symmetric subwavelength gratings (SGVC2), also known as the Annular Groove
Phase Mask (AGPM). Since 2013, several SGVC2s (or AGPMs) were manufactured
using synthetic diamond substrate, then validated on dedicated optical benches,
and installed on 10-m class telescopes. Increasing the topological charge seems
however mandatory for cancelling the light of bright stars which will be
partially resolved by future Extremely Large Telescopes in the near-infrared.
In this paper, we first detail our motivations for developing an SGVC4 (charge
4) dedicated to the near-infrared domain. The challenge lies in the design of
the pattern which is unrealistic in the theoretically perfect case, due to
state-of-the-art manufacturing limitations. Hence, we propose a new realistic
design of SGVC4 with minimized discontinuities and optimized phase ramp,
showing conclusive improvements over previous works in this field. A
preliminary validation of our concept is given based on RCWA simulations, while
full 3D finite-difference time-domain simulations (and eventually laboratory
tests) will be required for a final validation.
