The design of liquid-crystal diffractive phase plate coronagraphs for ground-based and space-based high-contrast imaging systems is limited by the trade-off between spectral bandwidth and polarization leakage. We demonstrate that by combining phase patterns with a polarization grating (PG) pattern directly followed by one or several separate PGs, we can suppress the polarization leakage terms by additional orders of magnitude by diffracting them out of the beam. textcolor{black}{Using two PGs composed of a single-layer liquid crystal structure in the lab, we demonstrate a leakage suppression of more than an order of magnitude over a bandwidth of 133 nm centered around 532 nm. At this center wavelength we measure a leakage suppression of three orders of magnitude.} Furthermore, simulations indicate that a combination of two multi-layered liquid-crystal PGs can suppress leakage to $<10^{-5}$ for 1-2.5 $mu$m and $<10^{-10}$ for 650-800 nm. We introduce multi-grating solutions with three or more gratings that can be designed to have no separation of the two circular polarization states, and offer even deeper suppression of polarization leakage. We present simulations of a triple-grating solution that has $<10^{-10}$ leakage on the first Airy ring from 450 nm to 800 nm. We apply the double-grating concept to the Vector-Vortex coronagraph of charge 4, and demonstrate in the lab that polarization leakage no longer limits the on-axis suppression for ground-based contrast levels. Lastly, we report on the successful installation and first-light results of a double-grating vector Apodizing Phase Plate pupil-plane coronagraph installed at the Large Binocular Telescope. We discuss the implications of these new coronagraph architectures for high-contrast imaging systems on the ground and in space.
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