title: Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems.
abstract: We introduce the generalized vector Helmholtz-Gauss (gVHzG) beams that constitute a general family of localized beam solutions of the Maxwell equations in the paraxial domain. The propagation of the electromagnetic components through axisymmetric ABCD optical systems is expressed elegantly in a coordinate-free and closed-form expression that is fully characterized by the transformation of two independent complex beam parameters. The transverse mathematical structure of the gVHzG beams is form-invariant under paraxial transformations. Any paraxial beam with the same waist size and transverse spatial frequency can be expressed as a superposition of gVHzG beams with the appropriate weight factors. This formalism can be straightforwardly applied to propagate vector Bessel-Gauss, Mathieu-Gauss, and Parabolic-Gauss beams, among others.
authors.forename: Raul I
authors.initials: RI
authors.lastname: Hernandez-Aranda
authors.forename: Julio C
authors.initials: JC
authors.lastname: Gutiérrez-Vega
authors.forename: Manuel
authors.initials: M
authors.lastname: Guizar-Sicairos
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Bandres