This paper deals with the spatial domain parametrization and physical interpretationof the asymptotic high-frequency solution pertaining to the asymptotic Green’s functionfor an infinite periodic line array of phased parallel dipoles on an infinite stratified groundeddielectric slab. This Green’s function is the basic constituent for deriving the array Green’sfunction (AGF) for a semi-infinite array of dipoles, which is treated elsewhere. The lineararray is synthesized as a superposition of smoothly phased periodicity-matched line sources.Each smoothly phased line source excites surface and leaky conical waves and associatedcoupled space wave contributions, which exhibit a transitional behavior at their appropriateshadow boundaries. The spectral integral which represents this space wave contribution istreated asymptotically by the use of an appropriate transition function.