Average intensity of Bessel–Gauss beams propagating through Kolmogorov turbulence with the quadratic structure function

It is well known that in free space propagations, Bessel–Gauss (BG) beams are non-diffractive, in the sense that over a finite distance the beam mainlobe does not spread. Non-diffraction beams have been found to offer advantages over diffractive beams, for example, in terms of power delivery. However, in random media, such as a turbulent atmosphere, the performance of BG beams is still an active area of research. For example, applying the extended Huygens–Fresnel (EHF) principle results in an intractable expression for the optical field and the average intensity. This work is concerned with finding a closed-form expression for the average intensity of BG beam propagating through weak and strong Kolmogorov turbulence under the quadratic structure function (QSF) assumption. This is achieved by considering the average intensity convolution integral of the free space intensity with the point spread function (PSF). This convolution integral is reduced to a one-dimensional integral that can be easily evaluated in closed form and plotted. Moreover, the beam root mean square (rms) width is also given in terms of one-dimensional integrals. The work presented can be used for assessing the utility of a BG beam for applications in emerging communication systems such as optical wireless communications (OWC).