  The detection and characterization of Earth-like exoplanets around Sun-like
stars for future flagship missions requires coronagraphs to achieve contrasts
on the order of 1e-10 at close angular separations and over large spectral
bandwidths (>=20%). We present our progress thus far on exploring the potential
for scalar vortex coronagraphs (SVCs) in direct exoplanet imaging. SVCs are an
attractive alternative to vector vortex coronagraphs (VVCs), which have
recently demonstrated 6e-9 raw contrast in 20% broadband light but are
polarization dependent. SVCs imprint the same phase ramp on the incoming light
and do not require polarization splitting, but are inherently limited by their
chromatic behavior. Several SVC designs have been proposed in recent years to
solve this issue by modulating or wrapping the azimuthal phase function
according to specific patterns. For one such design, the staircase SVC, we
present our best experimental SVC results demonstrating raw contrast of 2e-7 in
10% broadband light. Since SVC broadband performance and aberration
sensitivities are highly dependent on topology, we conducted a comparative
study of several SVC designs to optimize for high contrast across a range of
bandwidths. Furthermore, we present a new coronagraph optimization tool to
predict performance in order to find an achromatic solution.
