# Investigation of 3 dB Optical Intensity Spot Radius of Laser Beam under Scattering Underwater Channel

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## Abstract

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## 1. Introduction

## 2. Monte Carlo Simulation Method

#### 2.1. Scattering Phase Function

#### 2.2. Photon Propagation

#### 2.2.1. Propagation Distance

#### 2.2.2. Photon Weight

#### 2.2.3. Propagation Direction

#### 2.3. Photons Termination

#### 2.4. Photons Reception

## 3. The 3 dB Optical Intensity Spot Radius

## 4. Numerical Results and Analysis

#### 4.1. Pure Seawater Channel

#### 4.2. Clean Seawater Channel

#### 4.3. Coastal Seawater Channel

#### 4.4. Harbor Seawater Channel

#### 4.5. Verification for the 3 dB Optical Intensity

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**The ${r}_{3dB}$ versus ${R}_{PD}$ for pure seawater laser channel for a link distance of (

**a**) 44 m and (

**b**) 52 m.

**Figure 4.**2D intensity distribution of laser beam for pure seawater channel (

**a**) Pur-44 with T-Phai = 1 mrad, (

**b**) Pur-44 with T-Phai = 5 mrad, (

**c**) Pur-44 with T-Phai = 10 mrad, (

**d**) Pur-52 with T-Phai = 1 mrad, (

**e**) Pur-52 with T-Phai = 5 mrad and (

**f**) Pur-52 with T-Phai = 10 mrad.

**Figure 5.**The ${r}_{3dB}$ versus ${Z}_{0}$ for pure seawater laser channel for a half-aperture of (

**a**) ${R}_{PD}$ = 0.25m and (

**b**) ${R}_{PD}$ = 0.35 m.

**Figure 6.**The ${r}_{3dB}$ versus ${R}_{PD}$ for the clean seawater laser channel for a link distance of (

**a**) 34 m and (

**b**) 42 m.

**Figure 7.**The 2D intensity distribution of the laser beam for the clean seawater channel (

**a**) Cle-34 with T-Phai = 1 mrad, (

**b**) Cle-34 with T-Phai = 5 mrad, (

**c**) Cle-34 with T-Phai = 10 mrad, (

**d**) Cle-42 with T-Phai = 1 mrad, (

**e**) Cle-42 with T-Phai = 5 mrad and (

**f**) Cle-42 with T-Phai = 10 mrad.

**Figure 8.**The ${r}_{3dB}$ versus ${Z}_{0}$ for the clean seawater laser channel for a half-aperture of (

**a**) ${R}_{PD}$ = 0.25 m and (

**b**) ${R}_{PD}$ = 0.35 m.

**Figure 9.**The ${r}_{3dB}$ versus ${R}_{PD}$ for the coastal seawater laser channel for a link distance of (

**a**) 24 m and (

**b**) 32 m.

**Figure 10.**The 2D intensity distribution of the laser beam for coastal seawater channel (

**a**) Coa-24 with T-Phai = 1 mrad, (

**b**) Coa-24 with T-Phai = 5 mrad, (

**c**) Coa-24 with T-Phai = 10 mrad, (

**d**) Coa-32 with T-Phai = 1 mrad, (

**e**) Coa-32 with T-Phai = 5 mrad and (

**f**) Coa-32 with T-Phai = 10 mrad.

**Figure 11.**The ${r}_{3dB}$ versus ${Z}_{0}$ for coastal seawater laser channel for a half-aperture of (

**a**) ${R}_{PD}$ = 0.25 m and (

**b**) ${R}_{PD}$ = 0.35 m.

**Figure 12.**The ${r}_{3dB}$ versus ${R}_{PD}$ for harbor seawater laser channel for a link distance of (

**a**) 6 m and (

**b**) 8 m.

**Figure 13.**The 2D intensity distribution of a laser beam for harbor seawater channel (

**a**) Har-6 with T-Phai = 1 mrad, (

**b**) Har-6 with T-Phai = 5 mrad, (

**c**) Har-6 with T-Phai = 10 mrad, (

**d**) Har-8 with T-Phai = 1 mrad, (

**e**) Har-8 with T-Phai = 5 mrad and (

**f**) Har-8 with T-Phai = 10 mrad.

**Figure 14.**The ${r}_{3dB}$ versus ${Z}_{0}$ for the harbor seawater laser channel for a half-aperture of (

**a**) ${R}_{PD}$ = 0.25 m and (

**b**) ${R}_{PD}$ = 0.35 m.

**Figure 15.**The ${r}_{3dB}$ versus T-Phai for the harbor seawater laser channel for a link distance of (

**a**) 6 m and (

**b**) 10 m.

Ref. No. | Methods | Contribution Highlights |
---|---|---|

[4] | VRT theory | Path losses. Received waveform degradation. Link bit error rate. |

[5] | BSF | Optical power distribution on the receiving plane. |

[6,7,8] | Experiments | Modulation depth, degree of polarization of modulated light. |

[9] | MC | CIR. Channel capacity. |

[10] | MC | Path losses. CIR. Bit error rate. Received photons distribution. |

[11] | Experiments | Effects of misalignment, scattering agents on temporal response. |

[12] | MC | Path losses for various channel configurations. |

[13] | MC | Wavelength-dependent path losses based on the bio-optical model of seawater given by [14]. |

[15] | RTE | Path losses modeled by direct RTE solver. |

[16] | Closed expression | CIR modeled by double gamma functions. |

[17] | Closed expression | MIMO CIR modeled by weight gamma function polynomial. |

[18] | Stochastic model | Spatial and temporal probability characteristics of photons. |

[19] | Closed expression | Path losses modeled by weighted function of two exponentials. |

[20] | MC | CIR and normalized received optical power. |

[21] | MC | Different effects of two scattering angle computational principle on CIR. |

[22] | Experiments | Statistical distribution of optical intensity fluctuations caused by temperature-induced oceanic turbulence. |

[23] | MC | Probability density function of oceanic turbulence channel. Turbulence-induced scintillation index and path losses. |

[24] | MC | Empirical model of transmission distance-dependent path losses. |

[25] | MC | Channel estimation and evaluation under geometric losses. |

[26] | MC | Scattering regimes of photons. |

[27] | MC | Optical receiving power, CIR based on a newly developed scattering phase function which better fit for real seawater. |

[28] | Experiments | Statistical model of intensity fluctuations caused by random temperature and salinity variations and air bubbles. Channel coherence time. |

[29] | Closed expression | New CIR model that is superior to the weighted double gamma functions. |

[30] | Ray tracing | CIR and path losses for blocking and shadowing channel. |

[31] | Modified BL law | Path losses. |

[32] | Experiments | Air bubble and temperature gradient-induced channel irradiance fluctuations presented by mixture exponential-generalized gamma distribution. |

[33] | Numerical Model | Influences of group velocity dispersion and time jitter at the pulse width, probability fade and maximum bit rate. |

[34] | BSF | Lower mathematical complexity and simplicity. |

[35] | RTE | Improved accurate solver for time-dependent RTE. |

[36] | Experiments | Beam’s wave-front distortion caused by turbulence. Real-time associated Zernike coefficients. Transmission of polarized light and light with OAM. |

[37] | Experiments | Impacts of temperature gradient-induced turbulence, population and size of air bubbles on non-line-of-sight channel. |

**Table 2.**Underwater optical channel parameters based on [10].

Items | Channel Parameters | |||
---|---|---|---|---|

Pure | Clean | Coastal | Harbor | |

${K}_{a}\left(\lambda \right)\left({\mathrm{m}}^{-1}\right)$ | 0.053 | 0.069 | 0.088 | 0.295 |

${K}_{s}\left(\lambda \right)\left({\mathrm{m}}^{-1}\right)$ | 0.003 | 0.080 | 0.216 | 1.875 |

${K}_{att}\left(\lambda \right)\left({\mathrm{m}}^{-1}\right)$ | 0.056 | 0.150 | 0.305 | 2.170 |

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## Share and Cite

**MDPI and ACS Style**

Wang, W.; Li, X.; Rajbhandari, S.; Li, Y.
Investigation of 3 dB Optical Intensity Spot Radius of Laser Beam under Scattering Underwater Channel. *Sensors* **2020**, *20*, 422.
https://doi.org/10.3390/s20020422

**AMA Style**

Wang W, Li X, Rajbhandari S, Li Y.
Investigation of 3 dB Optical Intensity Spot Radius of Laser Beam under Scattering Underwater Channel. *Sensors*. 2020; 20(2):422.
https://doi.org/10.3390/s20020422

**Chicago/Turabian Style**

Wang, Wei, Xiaoji Li, Sujan Rajbhandari, and Yanlong Li.
2020. "Investigation of 3 dB Optical Intensity Spot Radius of Laser Beam under Scattering Underwater Channel" *Sensors* 20, no. 2: 422.
https://doi.org/10.3390/s20020422