EFFECTIVE BEAM PARAMETERS AND THE TURBULENT BEAM WAIST FOR CONVERGENTGAUSSIAN BEAMS

Expressions are developed for the location and the size of the beam wa ist for a convergent Gaussian beam in statistically homogeneous and is otropic atmospheric turbulence. Subsidiary expressions are presented t hat lead to the maximum distance from the transmitter at which the bea m waist can be located under given optical turbulence conditions and t he optimal initial radius of curvature required for placing the beam w aist at a desired location. The free-space beam radius W of a Gaussian beam satisfies the relationship partial derivative W/partial derivati ve z = -W/R, where z represents the path length and R is the phase-fro nt radius of curvature at z. By enforcing this relation on the effecti ve beam spot size in turbulence W-e, we can define an effective radius of curvature R(e). In addition to specifying the beam waist, R(e) lea ds to a pair of effective beam parameters theta(e) and Lambda(e) that provide a natural extension to the complex amplitude plane. Within thi s context, general propagation characteristics may be described, inclu ding the coherence properties of a Gaussian beam in both weak and stro ng optical turbulence.