The fundamental electromagnetic Gaussian beam is constructed from a single component of the electric vector potential oriented normal to the propagation direction. The potential is cylindrically symmetrical about the propagation direction. The paraxial beam and the first-order nonparaxial beam are obtained. In solving the inhomogeneous paraxial wave equation governing the evolution of the nonparaxial beam, both the particular integral and the complementary function are included. A procedure for deducing the proper asymptotic state of the nonparaxial beam is summarized. The amplitude coefficients of the cylindrically symmetric complex-argument Laguerre-Gauss beams, which constitute the complementary function are determined by requiring the potential to have the proper behavior asymptotically at infinity and near the input plane. From the potential function, the electromagnetic fields are developed and the electrodynamics of the fundamental electromagnetic Gaussian beam beyond the paraxial approximation is investigated. The role of the first-order nonparaxial beam in determining the average beam characteristics is examined.
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