  There are several high-performance adaptive optics systems that deliver
diffraction-limited imaging on ground-based telescopes, which renewed the
interest of single-mode fiber (SMF) spectroscopy for exoplanet
characterization. However, the fundamental mode of a telescope is not well
matched to those of conventional SMFs. With the recent progress in asphere
manufacturing techniques it may be possible to reshape the fundamental mode of
a SMF into any arbitrary distribution. An optimization problem is setup to
investigate what the optimal mode field distribution is and what the
fundamental throughput limit is for SMF spectroscopy. Both single-object
spectrographs and integral-field spectrographs are investigated. The optimal
mode for single-object spectrographs is found to be the aperture function of
the exit pupil, while for integral-field spectrographs the optimal mode depends
on the spatial sampling of the focal plane. For dense sampling, a uniform mode
is optimal, while for sparse sampling, the mode of a conventional SMF is near
optimal. With the optimal fiber mode, high throughput (>80%) can be achieved
when the focal plane is (super) Nyquist sampled. For the Nyquist sampled cases,
the optimal mode has almost 20% more throughput than a conventional SMF.
