  (abridged) The Atacama Large Aperture Submillimeter Telescope (AtLAST) is
undergoing a design study for a large (50 meter) single-dish submm-wavelength
Ritchey-Chr\'etien telescope to be located 5050 meters above sea level in the
Atacama Desert in northern Chile. It will allow for observations covering 30 to
950 GHz. Observing at such high frequencies with a 50~m primary mirror will be
challenging, and has never been attempted thus far. This observational
capability demands exquisite control of systematics to ensure a reliable beam
shape, and to mitigate the expected sidelobe levels. Among them, critical
issues that large telescopes like AtLAST need to deal with are introduced by
the panel gap pattern, the secondary mirror supporting struts, mirror
deformations produced by thermal and gravitational effects, and Ruze scattering
due to surface roughness. Proprietary software such as TICRA-Tools allows for
full-wave, complex-field physical optics simulations taking into account these
features. Such calculations can be computationally expensive since the mirror
surfaces are gridded (meshed) into a fine array in which each element is
treated as a current source. If the telescope size is large and the wavelengths
are short this may lead to very long running times. Here we present a set of
physical optics results that allow us to estimate the performance of the
telescope in terms of beam shape, directivity, sidelobes level and stray light.
We also discuss how we addressed the computational challenges, and provide
caveats on how to shorten the run times. Above all, we conclude that the
scattering effects from the gaps and tertiary support structure are minimal,
and subdominant to the Ruze scattering.
