  The coupling of large telescopes to astronomical instruments has historically
been challenging due to the tension between instrument throughput and
stability. Light from the telescope can either be injected wholesale into the
instrument, maintaining high throughput at the cost of point-spread function
(PSF) stability, or the time-varying components of the light can be filtered
out with single-mode fibers (SMFs), maintaining instrument stability at the
cost of light loss. Today, the field of astrophotonics provides a potential
resolution to the throughput-stability tension in the form of the photonic
lantern (PL): a tapered waveguide which can couple a time-varying and aberrated
PSF into multiple diffraction-limited beams at an efficiency that greatly
surpasses direct SMF injection. As a result, lantern-fed instruments retain the
stability of SMF-fed instruments while increasing their throughput. To this
end, we present a series of numerical simulations characterizing PL performance
as a function of lantern geometry, wavelength, and wavefront error (WFE), aimed
at guiding the design of future diffraction-limited spectrometers. These
characterizations include a first look at the interaction between PLs and
phase-induced amplitude apodization (PIAA) optics.
