ASTRI is a Flagship Project of the Italian Ministry of Education, University and Research, led by the Italian National Institute of Astrophysics, INAF. One of the main aims of the ASTRI Project is the design, construction and on-field verification of a dual mirror (2M) end-to-end prototype for the Small Size Telescope (SST) envisaged to become part of the Cherenkov Telescope Array. The ASTRI SST-2M prototype is designed according to the Schwarzschild-Couder optical scheme, and adopts a camera based on Silicon Photo Multipliers (SiPM); it will be assembled at the INAF astronomical site of Serra La Nave on mount Etna (Catania, Italy) in the second half of 2014, and will start scientific validation phase soon after. With its 4m wide primary dish, the telescope will be sensitive to multi-TeV Very High Energy (VHE) gamma rays up to 100 TeV and above, with a point spread function of ~2 arcminutes and a wide (semiaperture 4.8°) corrected field of view. The peculiarities of the optical design and of the SiPM bandpass pushed towards specifically optimized choices in terms of reflective coatings for both the primary and the secondary mirror. Fully dielectric multi-layer coatings have been developed and tested as an option for the primary mirror, aiming to filter out the large Night Sky Background contamination at wavelengths λ>~700 nm. On the other hand, for the large monolithic secondary mirror a simpler design with quartz-overcoated aluminium has been optimized for incidences far from normality. The conformation of the ASTRI camera in turn pushed towards the design of a reimaging system based on thin pyramidal light guides, that could be optionally integrated in the focal surface, aiming to increase the fill factor. An anti-reflective coating optimized for a wide range of incident angles faraway from normality was specifically developed to enhance the UV-optical transparency of these elements. The issues, strategy, simulations and experimental results are thoroughly presented.