  Vortex fiber nulling (VFN) is a method that may enable the detection and
characterization of exoplanets at small angular separations (0.5-2 $\lambda/D$)
with ground- and space-based telescopes. Since the field of view is within the
inner working angle of most coronagraphs, nulling accesses non-transiting
planets that are otherwise too close to their star for spectral
characterization by other means, thereby significantly increasing the number of
known exoplanets available for direct spectroscopy in the near-infrared.
Furthermore, VFN targets planets on closer-in orbits which tend to have more
favorable planet-to-star flux ratios in reflected light. Here, we present the
theory and applications of VFN, show that the optical performance is
approximately equivalent for a variety of implementations and aperture shapes,
and discuss the trade-offs between throughput and engineering requirements
using numerical simulations. We compare vector and scalar approaches and,
finally, show that beam shaping optics may be used to significantly improve the
throughput for planet light. Based on theoretical performance, we estimate the
number of known planets and theoretical exoEarths accessible with a VFN
instrument linked to a high-resolution spectrograph on the future Thirty Meter
Telescope.
