An array of long slots, oriented along x, etched on a ground plane that separates two infinite dielectric materials constitutes the basic canonical problem investigated in this article. In a single slot structure, the direction of radiation and the attenuation constant could be directly linked to the dominant leaky wave pole (kxlw) that dominates the pertinent Green’s Function (GF) spectrum in the longitudinal direction, x. In a multi slot problem, the number of poles that appear in the GF is equal to the number (N) of slots composing the array and in view of this two problems arise. First, how to locate efficiently these N poles in the kx spectrum of the GF parameters. Secondly to asses which of these poles are significant, i.e. dominate the behaviour of the array.