Quadratic approximation of Bessel Gaussian beams propagation through non-Kolmogorov and marine atmosphere

The quadratic approximation of the high order Bessel Gaussian beams propagation through the non-Kolmogorov and the marine atmosphere is studied in this paper. Based on the extended Huygens-Fresnel principle, the intensity of the Bessel Gaussian beams propagation through the turbulence atmosphere is a quadruple integral, which could be simplified to a double integral when the spherical wave structure function is approximate to a quadratic function. And the intensity calculated by the Rytov method is a triple integral and studied as a comparison. In this paper, the accuracy of two methods is analyzed and the applicable condition is provided. The result of the Gaussian beam is also calculated to verify to presumption. And there will be a large bias between the extended Huygens-Fresnel principle with the quadratic approximation and the Rytov method when the inner scale of the turbulence is small and the Rytov method is better at this circumstance. This paper provides the theoretical basis for the application of the quadratic approximation.