A physical optics characterization of the beam shape and sidelobe levels for the Atacama Large Aperture Submillimeter Telescope (AtLAST)

(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.