Résumé : This paper is mainly concerned with the structure of the singular and regular parts of the solution of time-harmonic Maxwell's equations in polygonal plane domains. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation. A detailed functional analysis of the solution shows that the boundary value problem does not belong locally to~$H^2$ when the boundary of the domain has non-acute angles, and explicit formulas for the singularity functions and their corresponding coefficients are given.