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Journals >Chinese Optics Letters >Volume 16 >Issue 8 >Page 080102 > Article

Chinese Optics Letters
Vol. 16, Issue 8, 080102 (2018)

Anisotropy effect on multi-Gaussian beam propagation in turbulent ocean

Yalçın Ata^1、* and Yahya Baykal²

Author Affiliations

¹TÜBİTAK Defense Industries Research and Development Institute (TÜBİTAK SAGE), P.K. 16 Mamak, 06261 Ankara, Turkey

²Çankaya University, Department of Electrical-Electronics Engineering, Yukarıyurtçu mah. Mimar Sinan cad., 06790 Ankara, Turkey

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DOI: 10.3788/COL201816.080102 Cite this Article Set citation alerts

Yalçın Ata, Yahya Baykal. Anisotropy effect on multi-Gaussian beam propagation in turbulent ocean[J]. Chinese Optics Letters, 2018, 16(8): 080102 Copy Citation Text

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Abstract

Average transmittance of multi-Gaussian (flat-topped and annular) optical beams in an anisotropic turbulent ocean is examined analytically based on the extended Huygens–Fresnel principle. Transmittance variations depending on the link length, anisotropy factor, salinity and temperature contribution factor, source size, beam flatness order of flat-topped beam, Kolmogorov microscale length, rate of dissipation of turbulent kinetic energy, rate of dissipation of the mean squared temperature, and thickness of annular beam are examined. Results show that all these parameters have effects in various forms on the average transmittance in an anisotropic turbulent ocean. Hence, the performance of optical wireless communication systems can be improved by taking into account the variation of average transmittance versus the above parameters.

〈 τ (L) 〉 = \frac{〈 I (L) 〉}{I^{v} (L)},

(1)

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〈 I (L) 〉 = {(\frac{1}{λ L})}^{2} \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} d^{2} s_{1} d^{2} s_{2} u (s_{1}) u^{*} (s_{2}) \times \exp [\frac{j k}{2 L} ({| s_{1} |}^{2} + {| s_{2} |}^{2})] \times 〈 \exp [ψ (s_{1}) + ψ^{*} (s_{2})] 〉,

(2)

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u (s, z = 0) = \sum_{n = 1}^{N} A_{n} \exp (- k α_{n} {| s |}^{2}),

(3)

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〈 \exp [ψ (s_{1}) + ψ^{*} (s_{2})] 〉 = \exp (- \frac{{| s_{1} - s_{2} |}^{2}}{ρ_{o c ξ}^{2}}),

(4)

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ρ_{o c ξ} = {[\frac{π^{2}}{3} k^{2} L ξ^{- 4} \int_{0}^{\infty} κ_{ξ}^{3} φ_{n} (κ_{ξ}) d κ_{ξ}]}^{- 1 / 2} .

(5)

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φ_{n} (κ_{ξ}, ξ) = \frac{0.388 \times 10^{- 8} ε^{- 1 / 3} ξ^{2} X_{T}}{w^{2}} κ_{ξ}^{- 11 / 3} [1 + 2.35 {(κ_{ξ} η)}^{2 / 3}] \times (w^{2} e^{- A_{T} δ} + e^{- A_{S} δ} - 2 w e^{- A_{TS} δ}),

(6)

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ρ_{o c ξ} = ξ | w | 1.802 \times 10^{- 7} k^{2} L {(ε η)}^{- 1 / 3} X_{T} {[(0.483 w^{2} - 0.835 w + 3.380)]}^{- 1 / 2} .

(7)

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〈 I (L) 〉 = {(\frac{k}{2 π L})}^{2} \sum_{l_{1} = 1}^{N} \sum_{l_{2} = 1}^{N} \int_{- \infty}^{\infty} d s_{1 x} \int_{- \infty}^{\infty} d s_{1 y} \int_{- \infty}^{\infty} d s_{2 x} \int_{- \infty}^{\infty} d s_{2 y} \times A_{l_{1}} A_{l_{2}} \exp [(- k α_{l_{1}} - \frac{1}{ρ_{o c ξ}^{2}} + \frac{j k}{2 L}) s_{1 x}^{2} + \frac{2}{ρ_{o c ξ}^{2}} s_{1 x} s_{2 x}] \times \exp [(- k α_{l_{1}} - \frac{1}{ρ_{o c ξ}^{2}} + \frac{j k}{2 L}) s_{1 y}^{2} + \frac{2}{ρ_{o c ξ}^{2}} s_{1 y} s_{2 y}] \times \exp [(- k α_{l_{2}} - \frac{1}{ρ_{o c ξ}^{2}} - \frac{j k}{2 L}) s_{2 x}^{2}] \times \exp [(- k α_{l_{2}} - \frac{1}{ρ_{o c ξ}^{2}} - \frac{j k}{2 L}) s_{2 y}^{2}] .

(8)

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\int_{- \infty}^{\infty} \exp (- p^{2} x^{2} \pm q x) d x = \exp (\frac{q^{2}}{4 p^{2}}) \frac{\sqrt{π}}{p}, R e (p^{2}) > 0,

(9)

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〈 I (L) 〉 = {(\frac{k}{2 π L})}^{2} \sum_{l_{1} = 1}^{N} \sum_{l_{2} = 1}^{N} \frac{A_{l_{1}} A_{l_{2}} π^{2}}{(k α_{l_{1}} + \frac{1}{ρ_{o c ξ}^{2}} - \frac{j k}{2 L}) (k α_{l_{2}} + \frac{1}{ρ_{o c ξ}^{2}} + \frac{j k}{2 L}) - \frac{1}{ρ_{o c ξ}^{4}}} .

(10)

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I^{v} (L) = {(\frac{k}{2 π L})}^{2} \sum_{l_{1} = 1}^{N} \sum_{l_{2} = 1}^{N} \frac{A_{l_{1}} A_{l_{2}} π^{2}}{(k α_{l_{1}} - \frac{j k}{2 L}) (k α_{l_{2}} + \frac{j k}{2 L})} .

(11)

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Yalçın Ata, Yahya Baykal. Anisotropy effect on multi-Gaussian beam propagation in turbulent ocean[J]. Chinese Optics Letters, 2018, 16(8): 080102

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