Propagation of auto-focusing hypergeometric Gaussian beams along a slant path in oceanic&#x00A0;turbulence

Wenhai Wang; Zhou Yu; Chengzhao Liu; Xu Zhou; Zheng-Da Hu; Zheng-Da Hu; Yun Zhu; Yun Zhu

doi:10.1364/JOSAA.519982

Journal of the Optical Society of America A
Vol. 41,
Issue 5,
pp. 943-951
(2024)
•https://doi.org/10.1364/JOSAA.519982

Propagation of auto-focusing hypergeometric Gaussian beams along a slant path in oceanic turbulence

Wenhai Wang, Zhou Yu, Chengzhao Liu, Xu Zhou, Zheng-Da Hu, and Yun Zhu

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Wenhai Wang, Zhou Yu, Chengzhao Liu, Xu Zhou, Zheng-Da Hu, and Yun Zhu, "Propagation of auto-focusing hypergeometric Gaussian beams along a slant path in oceanic turbulence," J. Opt. Soc. Am. A 41, 943-951 (2024)

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Table of Contents Category
- Atmospheric and Oceanic Optics
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About this Article
History
- Original Manuscript: January 25, 2024
- Revised Manuscript: April 2, 2024
- Manuscript Accepted: April 2, 2024
- Published: April 24, 2024

Abstract

Compared to horizontal transmission, the oceanic dissipation rate and temperature-salinity distribution ratio are no longer constant but vary with depth, imposing greater complexity on oceanic turbulence when beams propagate through a slant path and resulting in more limitations on the performance of underwater wireless optical communication (UWOC) links. This study focuses on investigating the performance, especially the auto-focusing characteristic, of auto-focusing hypergeometric Gaussian (AHGG) beams propagating along slant paths in oceanic turbulence. We theoretically derive the spatial coherence radius and the relative probability of the orbital angular momentum (OAM) mode for AHGG beams passing through such links. Numerical simulations reveal that AHGG beams exhibit superior propagation performance compared to hypergeometric Gaussian beams. Lower beam orders and OAM numbers contribute to improved performance, while careful selection of auto-focusing length can tangibly enhance detection performance as well. Additionally, tidal velocities and wind speeds have nonnegligible effects on OAM signal probability. Our results further demonstrate that surface buoyancy flux, temperature gradients, and waterside friction velocity significantly affect beam transmission under varying wind conditions. These findings, particularly controlling the auto-focusing length of AHGG beams to match the transmission distance, provide valuable insights for enhancing the quality of UWOC links.

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Parameters	Value
Initial OAM number $(m_{0})$	1
Wavelength $(λ)$	532 nm
Propagation distance $(z)$	50 m
Auto-focusing length $(z_{e})$	45.9 m
Depth below sea level of the uplink receiver $(h_{0})$	0.1 m
Order of AHGG beam $(p)$	3
Beam waist $(w_{0})$	0.05 m
Receiver radius $(D)$	0.09 m
Zenith angle $(ζ)$	$π / 3$

Parameters	Value
Outer scale $(L_{0})$	10 m
Inner scale $(l_{0})$	0.001 m
Wind speed $(W)$	1 m/s
Specific heat $(c_{p})$	$3932 J \cdot {k g}^{- 1} / K$
Surface buoyancy flux $(J_{b}^{0})$	$6 {W / m}^{2}$
Kinematic viscosity $(v)$	$10^{- 4} m^{2} / s$
Density of air $(ρ_{a})$	$1.2 {k g / m}^{3}$
Density of seawater $(ρ_{w})$	$1025 {k g / m}^{3}$
Waterside friction velocity $(u_{w})$	$0.0012 m / s$
Depth-averaged tidal velocity $(u)$	0.5 m/s
Temperature-salinity distribution ratio $(ω)$	−3
Weak wind or strong wind conditions $(J)$	1
Eddy diffusivity ratio of temperature to salinity $(θ)$	1
Largest eddy size proportional to the seawater depth $(ϑ)$	$6 \times 10^{- 3}$
Sources of turbulent temperature fluctuations $({T_{0}}^{'})$	0.003 K
Coefficient of drag between sea water surface and wind $(C_{D})$	0.0015

Parameters	Value
Initial OAM number $(m_{0})$	1
Wavelength $(λ)$	532 nm
Propagation distance $(z)$	50 m
Auto-focusing length $(z_{e})$	45.9 m
Depth below sea level of the uplink receiver $(h_{0})$	0.1 m
Order of AHGG beam $(p)$	3
Beam waist $(w_{0})$	0.05 m
Receiver radius $(D)$	0.09 m
Zenith angle $(ζ)$	$π / 3$

Parameters	Value
Outer scale $(L_{0})$	10 m
Inner scale $(l_{0})$	0.001 m
Wind speed $(W)$	1 m/s
Specific heat $(c_{p})$	$3932 J \cdot {k g}^{- 1} / K$
Surface buoyancy flux $(J_{b}^{0})$	$6 {W / m}^{2}$
Kinematic viscosity $(v)$	$10^{- 4} m^{2} / s$
Density of air $(ρ_{a})$	$1.2 {k g / m}^{3}$
Density of seawater $(ρ_{w})$	$1025 {k g / m}^{3}$
Waterside friction velocity $(u_{w})$	$0.0012 m / s$
Depth-averaged tidal velocity $(u)$	0.5 m/s
Temperature-salinity distribution ratio $(ω)$	−3
Weak wind or strong wind conditions $(J)$	1
Eddy diffusivity ratio of temperature to salinity $(θ)$	1
Largest eddy size proportional to the seawater depth $(ϑ)$	$6 \times 10^{- 3}$
Sources of turbulent temperature fluctuations $({T_{0}}^{'})$	0.003 K
Coefficient of drag between sea water surface and wind $(C_{D})$	0.0015

Abstract

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Equations (25)

Journal of the Optical Society of America A