title: Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions.
abstract: The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.
authors.affiliation: Teoría de la Señal y Comunicaciones e Ingeniería Telemática, University of Valladolid, Paseo de Belén, 15, 47011, Valladolid, Spain. raumah@tel.uva.es
authors.forename: R
authors.initials: R
authors.lastname: Mahillo-Isla
authors.forename: M J
authors.initials: MJ
authors.lastname: Gonźalez-Morales
authors.forename: C
authors.initials: C
authors.lastname: Dehesa-Martínez