Leaky wave antenna of AFSIW structure comprising a top substrate layer and a bottom substrate layer sandwiching an intermediate layer comprising a longitudinal aperture of length L defining a waveguide and whose width W1 is delimited by two conductive lateral walls. The inner faces of the conductive lateral walls are coated with a layer of dielectric material of thickness w(z). The top layer has a longitudinal radiating slot of width Wf (z) facing the longitudinal aperture of the intermediate layer. The thickness w(z) of the dielectric coating varies along the longitudinal axis z according to a given law, defined so as to obtain variations along the axis z of the amplitude Alpha(z) and of the phase Beta(z) of the leaky wave of the guide.