Variational scaling law for atmospheric propagation

Sophia Potoczak Bragdon; Daniel Cargill; Jacob Grosek

doi:10.1364/JOSAA.417705

Journal of the Optical Society of America A
Vol. 38,
Issue 5,
pp. 690-700
(2021)
•https://doi.org/10.1364/JOSAA.417705

Variational scaling law for atmospheric propagation

Sophia Potoczak Bragdon, Daniel Cargill, and Jacob Grosek

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Sophia Potoczak Bragdon, Daniel Cargill, and Jacob Grosek, "Variational scaling law for atmospheric propagation," J. Opt. Soc. Am. A 38, 690-700 (2021)

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- Numerical Methods and Simulation
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About this Article
History
- Original Manuscript: December 16, 2020
- Revised Manuscript: March 24, 2021
- Manuscript Accepted: March 29, 2021
- Published: April 22, 2021

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Abstract

A new scaling law model for propagation of optical beams through atmospheric turbulence is presented and compared to a common scalar stochastic waveoptics technique. This methodology tracks the evolution of the important beam wavefront and phasefront parameters of a propagating Gaussian-shaped laser field as it moves through atmospheric turbulence, assuming a conservation of power. As with other scaling laws, this variational technique makes multiple simplifying assumptions about the optical beam to capture the essential features of interest, while significantly reducing the computational cost of calculation. This variational scaling law is shown to work reliably with moderately high turbulence strengths.

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Supplementary Material (1)

Name	Description
Code 1	Python3 code for the variational scaling law (VSL) and the scalar paraxial stochastic Helmholtz equation, both being for laser atmospheric propagation. A README.txt file provides instructions for running the codes and other useful information.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (52)

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${\hat{C_{n}}}^{2}$	$\hat{r_{0}}$	$σ_{l o g - a m p}^{2}$	Turbulence Strength
$1 \cdot 10^{- 16}$	0.18	0.046	Weak
$4 \cdot 10^{- 16}$	0.10	0.18	Medium
$9 \cdot 10^{- 16}$	0.06	0.41	Strong

Physical Quantity	Symbol	Value
Wavelength	$\hat{λ}$	$10^{- 6} m^{- 1}$
Inner-scale	$\hat{l_{0}}$	$10^{- 3} m$
Outer-scale	$\hat{L_{0}}$	$10^{2} m$
Aperture diameter	$\hat{D}$	$2 \cdot 10^{- 2} m$
Propagation distance	$\hat{L_{z}}$	6 km
Background index	$\hat{n}$	1.000273
Transverse length $x$	$\hat{L_{x}}$	1.25 m
Transverse length $y$	$\hat{L_{y}}$	1.25 m

Computational Quantity	Symbol	Value
$x$ scaling	$L_{x} = \hat{L_{x}} / \hat{l_{0}}$	625
$y$ scaling	$L_{y} = \hat{L_{y}} / \hat{l_{0}}$	625
Scaled distance	$L_{z} = \hat{L_{z}} / \hat{L_{0}}$	60
Scaled aperture	$D = \hat{D} / \hat{l_{0}}$	20
Wavenumber strength	$ξ = {\hat{l_{0}}}^{2} \hat{k_{0}^{ℓ}} / \hat{L_{0}}$	0.0623
Loss strength	$ζ = {\hat{l_{0}}}^{2} \hat{k_{0}^{ℓ}} \hat{α_{l o s s}^{ℓ}}$	0

$σ_{l o g - a m p}^{2}$	$x$ -Slice Error	$y$ -Slice Error
0.046	$2.30 \cdot 10^{- 1}$	$2.41 \cdot 10^{- 1}$
0.18	$3.62 \cdot 10^{- 1}$	$3.41 \cdot 10^{- 1}$
0.41	$7.52 \cdot 10^{- 1}$	$8.13 \cdot 10^{- 1}$

$σ_{l o g - a m p}^{2}$	Center Irradiance Error
0.046	$9.6 \cdot 10^{- 2}$
0.18	$3.68 \cdot 10^{- 1}$
0.41	$6.73 \cdot 10^{- 1}$

$σ_{l o g - a m p}^{2}$	$x$ Beam Width Error	$y$ Beam Width Error
0.046	$2.3 \cdot 10^{- 2}$	$2.3 \cdot 10^{- 2}$
0.18	$7.46 \cdot 10^{- 2}$	$7.16 \cdot 10^{- 2}$
0.41	$1.83 \cdot 10^{- 1}$	$1.72 \cdot 10^{- 1}$

$σ_{l o g - a m p}^{2}$	Relative Error in $\hat{z_{w}}$
0.046	$3.12 \cdot 10^{- 2}$
0.18	$8.11 \cdot 10^{- 2}$
0.41	$9.35 \cdot 10^{- 2}$

$σ_{l o g - a m p}^{2}$	$x$ -Coord.	$y$ -Coord.	Center Irradiance
0.046	$8.66 \cdot 10^{- 3}$	$2.08 \cdot 10^{- 2}$	$3.41 \cdot 10^{- 2}$
0.18	$1.93 \cdot 10^{- 2}$	$4.24 \cdot 10^{- 2}$	$1.57 \cdot 10^{- 1}$
0.41	$2.82 \cdot 10^{- 2}$	$7.15 \cdot 10^{- 2}$	$2.83 \cdot 10^{- 1}$

Abstract

Supplementary Material (1)

Data Availability

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Tables (8)

Equations (52)

Journal of the Optical Society of America A