Propagation characteristics of non-uniformly Sinc-correlated blue-green laser beam through oceanic turbulence

Wang Mingjun; Zhang Jialin; Wang Jiao

doi:10.3788/irla20190370

Journals >Infrared and Laser Engineering >Volume 49 >Issue 6 >Page 20190370 > Article

Infrared and Laser Engineering
Vol. 49, Issue 6, 20190370 (2020)

Propagation characteristics of non-uniformly Sinc-correlated blue-green laser beam through oceanic turbulence

Wang Mingjun^1、2, Zhang Jialin^1、*, and Wang Jiao¹

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¹[in Chinese]

²[in Chinese]

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DOI: 10.3788/irla20190370 Cite this Article

Wang Mingjun, Zhang Jialin, Wang Jiao. Propagation characteristics of non-uniformly Sinc-correlated blue-green laser beam through oceanic turbulence[J]. Infrared and Laser Engineering, 2020, 49(6): 20190370 Copy Citation Text

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Abstract

The propagation model of non-uniformly Sinc-correlated blue-green laser beam in oceanic turbulence was developed according to generalized Huygens-Fresnel principles. Based on the cross-spectral density, intensity variations in different propagation distances were discussed. When the oceanic turbulence parameters were varied, intensity and lateral shifted intensity maximum were numerically simulated. The results show that the propagation distance and ocean turbulence parameters have a certain influence on the intensity self-focusing effect of the non-uniformly Sinc-correlated blue-green laser beam. When the propagation distance is certain, the effect of the rate of dissipation of mean-square temperature on the intensity self-focusing is greater than the rate of dissipation of kinetic energy and the relative strength of temperature and salinity fluctuations.

Keywords

intensity lateral shifted intensity maximum non-uniformly Sinc-correlated beam oceanic turbulence

${W^{\left( 0 \right)}}\left( {{{\bf{\rho }}_{\bf{1}}},{{\bf{\rho }}_{\bf{2}}}} \right) = \left\langle {E\left( {{{\bf{\rho }}_{\bf{1}}}} \right){E^ * }\left( {{{\bf{\rho }}_{\bf{2}}}} \right)} \right\rangle $

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$\int {\int {{{\rm{d}}^2}{{\bf{\rho }}_{\bf{1}}}} } {{\rm{d}}^2}{{\bf{\rho }}_{\bf{2}}}{W^{\left( 0 \right)}}\left( {{{\bf{\rho }}_{\bf{1}}},{{\bf{\rho }}_{\bf{2}}}} \right)f\left( {{{\bf{\rho }}_{\bf{1}}}} \right)f\left( {{{\bf{\rho }}_{\bf{2}}}} \right) \geqslant 0$

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${W^{\left( 0 \right)}}\left( {{{\bf{\rho }}_{\bf{1}}},{{\bf{\rho }}_{\bf{2}}}} \right) = \int {p\left( v \right)H_0^ * \left( {{{\bf{\rho }}_{\bf{1}}},v} \right){H_0}\left( {{{\bf{\rho }}_{\bf{2}}},v} \right){\rm{d}}v} $

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${H_0}\left( {{\bf{\rho }},v} \right) = \tau \left( {\bf{\rho }} \right)\exp \left[ { - if\left( {\bf{\rho }} \right)v} \right]$

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$p\left( v \right) = \frac{1}{a} \cdot {\rm{rect}}\left( {\frac{v}{a}} \right) = \left\{ {\begin{array}{*{20}{c}} {1/a,\;\;\; \left| v \right| \leqslant a/2} \\ {0,\;\;\; \left| v \right| > a/2} \end{array}} \right.$

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${H_0}\left( {{\bf{\rho }},v} \right) = \tau \left( {\bf{\rho }} \right)\exp \left[ { - 2{\text{π}} iv{{\left( {{\bf{\rho }} - {\rho _0}} \right)}^2}} \right]$

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$ {W^{\left( 0 \right)}}\left( {{{\bf{\rho }}_{\bf{1}}},{{\bf{\rho }}_{\bf{2}}}} \right) = \exp \left[ { - \left( {{\bf{\rho }}_{\bf{1}}^{\bf{2}} + {\bf{\rho }}_{\bf{2}}^{\bf{2}}} \right)/\left( {2{\sigma ^2}} \right)} \right]\mu \left( {{{\bf{\rho }}_{\bf{1}}},{{\bf{\rho }}_{\bf{2}}}} \right) $

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$\mu \left( {{{\bf{\rho }}_{\bf{1}}},{{\bf{\rho }}_{\bf{2}}}} \right) = {\rm{sinc}}\left\{ {c\left[ {{{\left( {{{\bf{\rho }}_{\bf{1}}} - {\rho _0}} \right)}^2} - {{\left( {{{\bf{\rho }}_{\bf{2}}} - {\rho _0}} \right)}^2}} \right]} \right\}$

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$\begin{split} & W\left( {{{{\bf{\rho '}}}_{\bf{1}}},{{{\bf{\rho '}}}_{\bf{2}}},z} \right) =\\ & \quad\frac{{{k^2}}}{{4{{\text{π}} ^2}{z^2}}}\iint {{W^{\left( 0 \right)}}\left( {{{\bf{\rho }}_{\bf{1}}},{{\bf{\rho }}_{\bf{2}}}} \right)}\times \\ & \quad\exp \left[ { - ik\frac{{{{\left( {{{{\bf{\rho '}}}_{\bf{1}}} - {{\bf{\rho }}_{\bf{1}}}} \right)}^2}{\rm{ - }}{{\left( {{{{\bf{\rho '}}}_{\bf{2}}} - {{\bf{\rho }}_{\bf{2}}}} \right)}^2}}}{{2z}}} \right]\times \\ & \quad \left\langle {\exp \left[ {\phi \left( {{{{\bf{\rho '}}}_{\bf{1}}},{{\bf{\rho }}_{\bf{1}}}} \right) + {\phi ^ * }\left( {{{{\bf{\rho '}}}_{\bf{2}}},{{\bf{\rho }}_{\bf{2}}}} \right)} \right]} \right\rangle {{\rm{d}}^2}{{\bf{\rho }}_{\bf{1}}}{{\rm{d}}^2}{{\bf{\rho }}_{\bf{2}}} \end{split} $

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$\begin{split} & \left\langle {\exp \left[ {\phi \left( {{{{\bf{\rho '}}}_{\bf{1}}},{{\bf{\rho }}_{\bf{1}}}} \right) + {\phi ^ * }\left( {{{{\bf{\rho '}}}_{\bf{2}}},{{\bf{\rho }}_{\bf{2}}}} \right)} \right]} \right\rangle=\\ & {\rm{exp}}\left\{ { - 4{{\text{π}} ^2}{k^2}z\int {\int {\kappa {{\varPhi _n}}\left( \kappa \right)} } \left\{ {1 - {J_0}\left[ {\left| {\left( {1 - \gamma } \right){{u}} + \gamma {{q}}} \right|\kappa } \right]} \right\}} \right\}{\rm{d}}\kappa {\rm{d}}\gamma \end{split} $

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$\left\langle {\exp \left[ {\phi \left( {{{{\bf{\rho '}}}_{\bf{1}}},{{\bf{\rho }}_{\bf{1}}}} \right) + {\phi ^ * }\left( {{{{\bf{\rho '}}}_{\bf{2}}},{{\bf{\rho }}_{\bf{2}}}} \right)} \right]} \right\rangle = \exp \left\{ { - P\left[ {{{{u}}^2} + {{uq}} + {{{q}}^2}} \right]} \right\}$

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$W\left( {{{{\bf{\rho '}}}_{\bf{1}}},{{{\bf{\rho '}}}_2},z} \right) = \frac{{{k^2}}}{{4{{\text{π}} ^2}{z^2}}}\int {p\left( v \right){H^ * }\left( {{{{\bf{\rho '}}}_{\bf{1}}},z,v} \right)H\left( {{{{\bf{\rho '}}}_{\bf{2}}},z,v} \right){\rm{d}}v} $

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$\begin{split} & {H^ * }\left( {{{{\bf{\rho '}}}_{\bf{1}}},z,v} \right)H\left( {{{{\bf{\rho '}}}_{\bf{2}}},z,v} \right) = \\ & \quad\frac{\sigma }{{\omega \left( {z,v} \right)}}\exp \left[ { - {{\left( {\frac{{k\sigma }}{{2z}}} \right)}^2}{{\left( {{{{\bf{\rho '}}}_1} - {{{\bf{\rho '}}}_{\bf{2}}}} \right)}^2} - \frac{{ik}}{{2z}}\left( {{{{\bf{\rho '}}}_{\bf{1}}}^2 - {{{\bf{\rho '}}}_{\bf{2}}}^2} \right)} \right] \times \\ & \quad\exp \left\{ { - \frac{1}{{{\omega ^2}\left( {z,v} \right)}}{{\left[ {\frac{{{{{\bf{\rho '}}}_{\bf{1}}} + {{{\bf{\rho '}}}_{\bf{2}}}}}{2} - \frac{{ik{\sigma ^2}}}{{2z}}\left( {{{{\bf{\rho '}}}_{\bf{1}}} - {{{\bf{\rho '}}}_{\bf{2}}}} \right)-\frac{{4{\text{π}} vz{\rho _0}}}{k}} \right]}^2}} \right\} \end{split} $

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${\left| {H\left( {r,v,z} \right)} \right|^2} = \frac{\sigma }{{\omega \left( {z,v} \right)}}\exp \left[ { - \frac{{{{\left( {r - 4{\text{π}} vz{\rho _0}/k} \right)}^2}}}{{{\omega ^2}\left( {z,v} \right)}}} \right]$

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$\begin{split} & \omega \left( {z,v} \right)= \\ & \quad\sqrt {{{\left( {\dfrac{z}{{k\sigma }}} \right)}^2} + {\sigma ^2}{{\left( {1 - \dfrac{{4{\text{π}} zv}}{k}} \right)}^2} + \dfrac{{{{\text{π}} ^2}{k^2}z}}{3}\int_0^\infty {{\kappa ^3}{\varPhi _n}\left( \kappa \right)} {\rm{d}}\kappa } \end{split} $

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