  The vector-Apodizing Phase Plate (vAPP) is a pupil-plane coronagraph that
manipulates phase to create dark holes in the stellar PSF. The phase is induced
on the circular polarization states through the inherently achromatic geometric
phase by spatially varying the fast axis orientation of a half-wave
liquid-crystal layer. The two polarized PSFs can be separated, either by a
quarter-wave plate (QWP) followed by a polarizing beamsplitter (PBS) for
broadband operation, or a polarization sensitive grating (PSG) for narrowband
or IFS operation. Here we present new vAPP concepts that lift the restrictions
of previous designs and report on their performance. We demonstrated that the
QWP+PBS combination puts tight tolerances on the components to prevent leakage
of non-coronagraphic light into the dark-hole. We present a new broadband
design using an innovative two-stage patterned liquid-crystal element system
based on multi-color holography, alleviating the leakage problem and relaxing
manufacturing tolerances. Furthermore, we have shown that focal-plane wavefront
sensing (FPWFS) can be integrated into the vAPP by an asymmetric pupil.
However, such vAPPs suffer from a reduced throughput and have only been
demonstrated with a PSG in narrowband operation. We present advanced designs
that maintain throughput and enable phase and amplitude wavefront sensing. We
also present broadband vAPP FPWFS designs and outline a broadband FPWFS
algorithm. Finally, previous dual-beam vAPP designs for sensitive polarimetry
with one-sided dark holes were very complex. We show new dual-beam designs that
significantly reduce the complexity.
