Effects of a modified spectrum on the wave structure function of a Gaussian beam

A general expression is developed for the wave structure function (WSF) of a Gaussian beam wave using a modified spectrum of refractive-index fluctuations that features a high wave number bump. Effective beam parameters that characterize the turbulent spot size and phase front radius of curvature are used to formally extend this expression into the strong turbulence regime. The implied spatial coherence length from this expression for the WSF is less than that predicted by conventional spectral models whenever the Fresnel zone size is much larger than the initial beam radius. In the case of a focused beam, the predicted coherence length is slightly greater than that predicted by conventional spectral models when the Fresnel zone size is much smaller than the initial beam radius. The presence of the spectral bump appears to have little effect on coherence when the Fresnel zone size and initial beam radius are of comparable size