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    Journals >Infrared and Laser Engineering >Volume 49 >Issue 7 >Page 20190452 > Article
    • Infrared and Laser Engineering
    • Vol. 49, Issue 7, 20190452 (2020)
    Validity of beam propagation characteristics through oceanic turbulence simulated by phase screen method
    Chaojun Niu, Xiaobin Wang, Fang Lu, and Xiang’e Han
    Author Affiliations
  • 西安电子科技大学 物理与光电工程学院， 陕西 西安 710071
    • show less
    DOI: 10.3788/IRLA20190452 Cite this Article
    Chaojun Niu, Xiaobin Wang, Fang Lu, Xiang’e Han. Validity of beam propagation characteristics through oceanic turbulence simulated by phase screen method[J]. Infrared and Laser Engineering, 2020, 49(7): 20190452 Copy Citation Text show less

    Abstract

    Oceanic turbulence is an important factor to restrict the application of underwater optical communication. Phase screen method is a simple and effective way to simulate the propagation process of complex beams through turbulence. The constraints of parameter setting for phase screen simulated oceanic turbulence based on the sampling principle and turbulence effects were firstly discussed here. Furthermore, the theoretical expressions of propagation characteristics of Gaussian beam through oceanic turbulence from weak to strong fluctuation regime were derived. Our goal in this research was to testify the validity of phase screen method in oceanic turbulence by comparison of major statistical characteristics of Gaussian beam propagating in oceanic turbulence simulated by phase screen method and the theoretical expressions derived. Results show good match between simulation results and theory formulas for long exposure beam radius and centroid displacement under different turbulence conditions, as well as the scintillation index under weak fluctuation regime. However, results show significant mismatch between numerically estimated and theoretically predicted values for the on-axis scintillation index in strong fluctuation regime.

    Keywords

    $\begin{array}{l} {\varPhi _n}(\kappa ) = 0.388 \times {10^{ - 8}}{\varepsilon ^{ - 1/3}}{\kappa ^{ - 11/3}}[1 + 2.35{(\kappa \eta )^{2/3}}] \times \\ \dfrac{{{\chi _T}}}{{{\omega ^2}}}[{\omega ^2}\exp( - {A_T}{\delta _{TS}}) + \exp ( - {A_S}{\delta _{TS}}) - 2\omega \exp ( - {A_{TS}}{\delta _{TS}})] \\ \end{array} $(1)

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    ${W_{{{LE}}}} = W\sqrt {1 + T} $(2)

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    $\begin{split} T &= 4{\pi ^2}{k^2}L\int_0^1 {d\xi } \int_0^\infty {d\kappa \kappa {\varPhi _n}\left( \kappa \right)}\times \\ &\left[ {1 - \exp \left( { - \dfrac{{\varLambda L{\kappa ^2}{\xi ^2}}}{k}} \right)} \right] \\ \end{split} $(3)

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    $\begin{split} \left\langle {r_c^{\rm{2}}} \right\rangle & = 4{\pi ^2}{k^2}L\int_0^1 {d\xi } \int_0^\infty {d\kappa \kappa {\varPhi _n}\left( \kappa \right)} \\ &{H_{LS}}\left[ {1 - \exp \left( { - \dfrac{{\varLambda L{\kappa ^2}{\xi ^2}}}{k}} \right)} \right] \end{split} $(4)

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    ${H_{LS}} = \exp \left\{ { - {\kappa ^2}W_0^2\left[ {{{\left( {{\Theta _0} + {\Theta _0}\xi } \right)}^2} + \varLambda _0^2{{\left( {1 - \xi } \right)}^2}} \right]} \right\}$(5)

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    $\begin{split} \sigma _I^2\left( {0,L} \right)& = 8{\pi ^2}{k^2}L\int_0^1 {d\xi } \int_0^\infty {d\kappa \kappa {\varPhi _n}\left( \kappa \right)} \exp \left( { - \dfrac{{\varLambda L{\kappa ^2}{\xi ^2}}}{k}} \right) \times \\ & \left\{ {1 - \cos \left[ {\frac{{L{\kappa ^2}}}{k}\xi \left( {1 - \left( {1 - \Theta } \right)\xi } \right)} \right]} \right\} \end{split} $(6)

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    ${\varLambda _0} = \dfrac{{2L}}{{kw_0^2}},{\Theta _0} = 1 - \dfrac{L}{{{F_0}}}$(7)

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    $\varLambda = \dfrac{{{\varLambda _0}}}{{\Theta _0^2 + \varLambda _0^2}},\Theta = \dfrac{{{\Theta _0}}}{{\Theta _0^2 + \varLambda _0^2}}$(8)

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    ${\varLambda _e} = \dfrac{\varLambda }{{1 + 4q\varLambda /3}},{\Theta _e} = \dfrac{{\Theta - 2q\varLambda /3}}{{1 + 4q\varLambda /3}}$(9)

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    $\begin{split} u({{r}},{z_{j + 1}})& = {F^{ - 1}}\{ F\left[ {u({{r}},{z_j})\exp \left[ {{\rm{i}}\varphi (x,y)} \right]} \right]\times \\ & \exp ( - {\rm{i}}\dfrac{{\kappa _x^2 + \kappa _y^2}}{{2k}}\Delta {z_{j + 1}})\} \\ \end{split} $(10)

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    $\begin{split} \varphi \left( {x,\;y} \right) &= C\sum\limits_{{K_x}} {\sum\limits_{{K_Y}} {a\left( {{\kappa _x}{\rm{,}}\;{\kappa _y}} \right)\sqrt {{\varPhi _\theta }\left( {{\kappa _x}{\rm{,}}\;{\kappa _y}} \right)} } }\times \\ & \exp \left[ {i\left( {{\kappa _x}x + {\kappa _y}y} \right)} \right] \end{split} $(11)

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    ${\varPhi _\theta }({\kappa _x},{\kappa _y}) = 2\pi {k^2}\int\limits_z^{\Delta z} {{\varPhi _n}({\kappa _x},{\kappa _y},\xi )} {\rm{d}}\xi $(12)

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    $\Delta x = \dfrac{{\lambda L}}{x}$(13)

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    $\begin{split} &{\rho _0} = {[3.603 \times {10^{ - 7}}{k^2}\Delta z{\varepsilon ^{ - 1/3}}\dfrac{{{\chi _T}}}{{2{\omega ^2}}}(16.958{\omega ^2} - 44.175\omega + 118.923)]^{ - 1/2}}\;\;\;\;({\rho _0} < < \eta ) \\ &{\rho _0} = {[3.603 \times {10^{ - 7}}{k^2}\Delta z{\varepsilon ^{ - 1/3}}\dfrac{{{\chi _T}}}{{2{\omega ^2}}}(1.116{\omega ^2} - 2.235\omega + 1.119)]^{ - 3/5}}\;\;\;\;({\rho _0} > > \eta ) \\ \end{split} $(14)

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    ${N_{PS}} > {\left[ {10\sigma _R^2\left( L \right)} \right]^{6/11}}$(15)

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    $\begin{split} \sigma _R^2 &= 3.063 \times {10^{ - 7}}{k^{7/6}}{L^{11/6}}{\varepsilon ^{ - 1/3}}{\chi _T}× \\ &\left( {0.358{\omega ^2} - 0.725\omega + 0.367} \right)/{\omega ^2} \end{split} $(16)

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    $W_{{{LE}}}^2 = {{2\int\limits_{ - \infty }^\infty {{r^2}\left\langle {I\left( {{{r}},L} \right)} \right\rangle {\rm{d}}{{r}}} } / {\int\limits_{ - \infty }^\infty {\left\langle {I\left( {{{r}},L} \right)} \right\rangle {\rm{d}}{{r}}} }}$(17)

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    ${\sigma _c} = \sqrt {\left\langle {{{r}}_c^{\rm{2}}} \right\rangle } $(18)

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    ${{{r}}_c} = {{2\int\limits_{ - \infty }^\infty {{{r}}I\left( {{{r}},L} \right){\rm{d}}{{r}}} } / {\int\limits_{ - \infty }^\infty {\left\langle {I\left( {{{r}},L} \right)} \right\rangle {\rm{d}}{{r}}} }}$(19)

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    $\sigma _I^2 = {{\left\langle {{{\left[ {I(0,L) - \left\langle {I(0,L)} \right\rangle } \right]}^2}} \right\rangle }/ {{{\left\langle {I(0,L)} \right\rangle }^2}}}$(20)

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    Chaojun Niu, Xiaobin Wang, Fang Lu, Xiang’e Han. Validity of beam propagation characteristics through oceanic turbulence simulated by phase screen method[J]. Infrared and Laser Engineering, 2020, 49(7): 20190452
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