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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. We find that Gaussian-mapping beam-shaping optics can enhance coupling into 3-port lanterns but offer diminishing gains with larger lanterns. In the y- and J - band (0.97–1.35 µm) region, with moderately high WFE (∼ 10% Strehl ratio), a 3-port lantern in conjunction with beam-shaping optics strikes a good balance between pixel count and throughput gains. If pixels are not a constraint, and the flux in each port will be dominated by photon noise, then larger port count lanterns will provide further coupling gains due to a greater resilience to tip-tilt errors. Finally, we show that lanterns can maintain high operating efficiencies over large wavelength bands where the number of guided modes at the lantern entrance drops, if care is taken to minimize the attenuation of weakly radiative input modes.
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