A transport model for broadening of a linearly polarized, coherent beam due to inhomogeneities in a turbulent atmosphere

Traditional models for beam broadening include both a diffractive term, owing to the source aperture, and a beam 'wandering' term that stems from refractive index variations in the atmosphere. Here we derive a novel beam broadening term that depends on the properties of atmospheric turbulence. The derivation rests on a transport formulation of the propagation problem whereby the magnitude of the electric field is viewed as the density of a fluid, moving in a flow that is driven by the refractive index perturbations. Properties of the transport solutions are obtained using Lagrangian coordinates and are demonstrated to be entirely consistent with existing theory on the subject. The new factor predicts appreciable (25% in our example) increases in beam broadening for applications requiring propagation over very long optical paths and heavy turbulence.