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We consider diffraction of waves on a product cone. We first show thatdiffractive waves enjoy a one-step polyhomogeneous asymptotic expansion, whichis an improvement of Cheeger-Taylor's classical result of half-steppolyhomogeneity of diffractive waves in [CT82a], [CT82b]. We also conclude thaton product cones, the scattering matrix is the diffraction coefficient, whichis the principal symbol of the diffractive half wave kernel, for strictlydiffractively related points on the cross section. This generalize the resultof Ford, Hassell and Hillairet in 2-dimensional flat cone settings [FHH18]. Inthe last section, we also give a radiation field interpretation of therelationship between the scattering matrix and the diffraction coefficient.

Propagation of polyhomogeneity, Diffraction and Scattering on Product Cones