Аннотация:We propose a general procedure to study double integrals arising when considering wave propagation inperiodic structures. This method, based on a complex deformation of the integration surface to bypass theintegrands’ singularities, is particularly efficient to estimate the Green’s functions of such structures in the farfield. We provide several illustrative examples and explicit asymptotic formulas. Special attention is devoted tothe pathological cases of degeneracies, such as Dirac conical points.