Comparison between quadratic approximation and δ expansion in studying the spreading of multi-Gaussian beams in turbulent atmosphere

Abstract

Based on quadratic approximation and delta expansion in the first order, the analytical expressions for multi-Gaussian beams in a turbulent atmosphere have been derived. By comparing the two approaches with numerical calculations, the relative errors of average intensity are investigated. As special cases, the relative errors for Gaussian beams, flattened Gaussian beams, and annular beams are investigated. The investigation shows that the method of delta expansion in the first order agrees well with numerical calculations, no matter what the effect of turbulence. If the effect of turbulence is large enough, the relative error of on-axis intensity trends to a constant. The maximum of relative error is about 2.8%. However, quadratic approximation does not give satisfying results under some circumstance even when the effect of turbulence is small. The relative error of on-axis intensity reaches 9.2% when the effect of turbulence is large enough.

Short-term average intensity of a cosh-Gaussian beam in Kolmogorov turbulence

“…Studies show that the relative error due to the expansion of hard aperture is less than 1% when the Fresnel number is smaller than one [20,22]. The relative error due to the firstorder expansion of exp½Àð= 0 Þ 5=3 in Taylor series has been examined [23,24]. Study shows that the relative error is smaller than 2.8% [24].…”

“…The relative error due to the firstorder expansion of exp½Àð= 0 Þ 5=3 in Taylor series has been examined [23,24]. Study shows that the relative error is smaller than 2.8% [24].…”

“…Although the long-term average intensity of a cosh-Gaussian beam with aperture has been studied on the basis of the quadratic approximation [9], Equation (16) provides a more precise expression for the long-term average intensity [24].…”

Long- and short-term average intensity for multi-Gaussian beam with a common axis in turbulence

“…Our previous work showed that diverse intensity profiles could be obtained by choosing A n , w n and ϕ n . [18] On the basis of the extended Huygens-Fresnel principle, an expression for short-term average intensity was given in Ref. [2]…”

“…Our previous work showed that the first-order approximation of exp −x 5/3 could offer an accurate result to study MGB in turbulent atmosphere. [18] Following Ref. [18] the analytical formula for 014207-2 short-term average intensity can be derived as…”