Theoretical research progress on the influence of atmospheric turbulence and thermal blooming on characteristics and beam quality of laser array beams propagating in the atmosphere

Xiaoqing Li; Xiaoling Ji

doi:10.11884/HPLPB202335.220411

Journals >High Power Laser and Particle Beams >Volume 35 >Issue 4 >Page 041007 > Article

High Power Laser and Particle Beams
Vol. 35, Issue 4, 041007 (2023)

Theoretical research progress on the influence of atmospheric turbulence and thermal blooming on characteristics and beam quality of laser array beams propagating in the atmosphere

Xiaoqing Li and Xiaoling Ji^*

Author Affiliations

College of Physics and Electronic Engineering, Sichuan Normal University, Chengdu 610068, China

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DOI: 10.11884/HPLPB202335.220411 Cite this Article

Xiaoqing Li, Xiaoling Ji. Theoretical research progress on the influence of atmospheric turbulence and thermal blooming on characteristics and beam quality of laser array beams propagating in the atmosphere[J]. High Power Laser and Particle Beams, 2023, 35(4): 041007 Copy Citation Text

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Abstract

We provide a review of the theoretical research progress on the influence of atmospheric turbulence and thermal blooming on the characteristics and beam quality of laser array beams propagating in the atmosphere. The analytical and numerical simulation methods to study the propagation of laser array beams in the atmosphere are introduced. The influence of the atmospheric turbulence on the intensity, angular spread, directionality, curvature radius and turbulence distance of laser array beams is reviewed, and the influence of the atmospheric thermal blooming on the intensity, propagation efficiency, beam centroid, time scale of thermal blooming and focal shift of laser array beams is also reviewed. It is shown that the influence of atmospheric turbulence and thermal blooming on the beam quality of laser array beams is closely related with the beam combination methods, beam parameters and atmospheric parameters.

Keywords

atmospheric propagation atmospheric turbulence beam quality laser array beam thermal blooming effect

\begin{aligned} < W ({\boldsymbol r}_{1}, {\boldsymbol r}_{2}, z) >= & {(\frac{k}{2 π z})}^{2} \int_{}^{} \int_{}^{} d^{2} {r^{'}}_{1} \int_{}^{} \int_{}^{} d^{2} {r^{'}}_{2} W ({\boldsymbol r^{'}}_{1}, {\boldsymbol r^{'}}_{2}, z = 0) \exp {\frac{i k}{2 z} [({\boldsymbol r^{'}}_{1}^{2} - {\boldsymbol r^{'}}_{2}^{2}) - 2 ({\boldsymbol r}_{1} \cdot {\boldsymbol r^{'}}_{1} - {\boldsymbol r}_{2} \cdot {\boldsymbol r^{'}}_{2})]} \times \\ < \exp [ψ ({\boldsymbol r^{'}}_{1}, {\boldsymbol r}_{1}, z) + ψ^{*} ({\boldsymbol r^{'}}_{2}, {\boldsymbol r}_{2}, z)] >_{m} \end{aligned}

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$ < \exp [\psi ({{{\boldsymbol{r'}}}_1},{{\boldsymbol{r}}_1},{\textit{z}}) + {\psi ^*}({{{\boldsymbol{r'}}}_2},{{\boldsymbol{r}}_2},{\textit{z}})]{ > _m} = \exp \left\{ { - 4{\pi ^2}{k^2}{\textit{z}}\displaystyle\int\limits_0^1 {\displaystyle\int\limits_0^\infty {\kappa {{\mathit{\Phi}} _n}(\kappa )\left\{ {1 - {J_0}\left[ {(\kappa \left| {\left( {1 - \xi } \right)\left( {{{\boldsymbol{r}}_2} - {{\boldsymbol{r}}_1}} \right){\text{ + }}\xi \left( {{{{\boldsymbol{r'}}}_2} - {{{\boldsymbol{r'}}}_1}} \right)} \right|)} \right]} \right\}} } {\text{d}}\kappa {\text{d}}\xi } \right\} $

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$ < \exp [\psi ({{\boldsymbol{r'}}_1},{{\boldsymbol{r}}_1},{\textit{z}}) + {\psi ^*}({{\boldsymbol{r'}}_2},{{\boldsymbol{r}}_2},{\textit{z}})]{ > _m} = \exp \left[ { - \dfrac{{{{({{{\boldsymbol{r'}}}_1} - {{{\boldsymbol{r'}}}_2})}^2}{\text{ + }}({{{\boldsymbol{r'}}}_1} - {{{\boldsymbol{r'}}}_2})({{\boldsymbol{r}}_1} - {{\boldsymbol{r}}_2}) + {{({{\boldsymbol{r}}_1} - {{\boldsymbol{r}}_2})}^2}}}{{\rho _0^2}}} \right] $

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$ h\left( {{{\boldsymbol{r}}_{\rm{s}}},{\boldsymbol{\theta }},{\textit{z}}} \right) = {\left( {\dfrac{k}{{2\pi }}} \right)^2}\displaystyle\int_{ - \infty }^\infty {W({{\boldsymbol{r}}_{\rm{s}}},{{\boldsymbol{r}}_{\rm{d}}},{\textit{z}})\exp \left( { - {\text{i}}k{\boldsymbol{\theta }} \cdot {{\boldsymbol{r}}_{\rm{d}}}} \right){{\text{d}}^{\text{2}}}{{\boldsymbol{r}}_{\rm{d}}}} $

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$ \left\langle {{x^{{l_1}}}{y^{{l_2}}}\theta _x^{{m_1}}\theta _y^{{m_2}}} \right\rangle = {{\displaystyle\int_{ - \infty }^\infty {\displaystyle\int_{ - \infty }^\infty {{x^{{l_1}}}{y^{{l_2}}}\theta _x^{{m_1}}\theta _y^{{m_2}}} } h\left( {{{\boldsymbol{r}}_{\rm{s}}},{\boldsymbol{\theta }},{\textit{z}}} \right){{\text{d}}^{\text{2}}}{{\boldsymbol{r}}_{\rm{s}}}{{\text{d}}^{\text{2}}}\theta } \mathord{\left/ {\vphantom {{\displaystyle\int_{ - \infty }^\infty {\displaystyle\int_{ - \infty }^\infty {{x^{{n_1}}}{y^{{n_2}}}\theta _x^{{m_1}}\theta _y^{{m_2}}} } h\left( {{{\boldsymbol{r}}_{\rm{s}}},{\boldsymbol{\theta }},{\textit{z}}} \right){{\text{d}}^{\text{2}}}{{\boldsymbol{r}}_{\rm{s}}}{{\text{d}}^{\text{2}}}\theta } P}} \right. } P} $

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$ 2{\rm{i}}k\dfrac{{\partial E}}{{\partial {\textit{z}}}} = \nabla _ \bot ^2E + {k^2}\Bigg(\dfrac{{{n^2}}}{{n_0^2}} - 1\Bigg)E $

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$ {E^{l + 1}} = \exp \Bigg( - \dfrac{{\text{i}}}{{4k}}\Delta {\textit{z}}{\nabla _ \bot }^2\Bigg)\exp \Bigg[ - \dfrac{{{\text{i}}k}}{2}\displaystyle\int\limits_{{{\textit{z}}^l}}^{{{\textit{z}}^l} + \vartriangle {\textit{z}}} {\Bigg(\dfrac{{{n^2}}}{{{n_0}}} - 1\Bigg)} {\text{d}}{\textit{z}}\Bigg]\exp \Bigg( - \dfrac{{\text{i}}}{{4k}}\Delta {\textit{z}}{\nabla _ \bot }^2\Bigg){E^l} $

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$ \dfrac{{I(x,y,{\textit{z}})}}{{I(x,y,0){{\rm{e}}^{ - \alpha {\textit{z}}}}}} = \exp \left\{ { - \dfrac{{2{n_T}\alpha }}{{{n_0}{\rho _0}{c_{\rm{p}}}v}}\displaystyle\int_0^{\textit{z}} {\displaystyle\int_0^{{{\textit{z}}'}} {\left[ {\dfrac{{\partial I}}{{\partial x}} + \dfrac{1}{2}\dfrac{{{\partial ^2}}}{{\partial {y^2}}}\displaystyle\int_{ - \infty }^x {I{\rm{d}}{x'}} + \dfrac{1}{{2I}}\dfrac{{\partial I}}{{\partial y}}\displaystyle\int_{ - \infty }^x {\dfrac{{\partial I}}{{\partial y}}} {\rm{d}}{x'}} \right]{\rm{d}}{{\textit{z}}'}{\rm{d}}{{\textit{z}}''}} } } \right\} $

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