Simulation and verification of pulsed laser beam propagation underwater using Markov chains [Invited]

Tianhua Zhou; Jian Ma; Tingting Lu; Guyu Hu; Tingwei Fan; Xiaopeng Zhu; Xiaolei Zhu; Weibiao Chen

doi:doi:10.3788/COL201917.100003

Chinese Optics Letters, 2019, 17 (10): 100003, Published Online: Sep. 12, 2019

Simulation and verification of pulsed laser beam propagation underwater using Markov chains [Invited]

Tianhua Zhou ^*Jian Ma Tingting Lu Guyu Hu Tingwei Fan Xiaopeng Zhu Xiaolei Zhu Weibiao Chen

Author Affiliations

Key Laboratory of Space Laser Communication and Detection Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

Figures & Tables

Fig. 1. State transition matrix of water. (a) State transition matrix $M_{T}$ . (b) State transition matrix raised to the $15^{th}$ power $M_{T}^{15}$ .

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Fig. 2. Normalized angular probability distribution for increasing number of collisions $n_{c}$ .

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Fig. 3. Normalized probability distribution of the number of collisions $n_{c}$ for increasing transmission distance $D_{T}$ .

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Fig. 4. Energy loss on the receiving plane versus transmission distance $D_{T}$ . (a) Jerlov IB: a = 0.06 m⁻¹, b = 0.084 m⁻¹. (b) Pool water: a = 0.117 m⁻¹, b = 0.182 m⁻¹.

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Fig. 5. Transmission procedures of the successive layering model, $n_{c} = 1$ and $n_{c} = 2$ .

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Fig. 6. Temporal distributions of different transmission distances. (a) $D_{T} = 20 m$ , (b) $D_{T} = 40 m$ , (c) $D_{T} = 60 m$ , (d) $D_{T} = 80 m$ .

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Table1. Water Parameters

Water Parameter	$a (m^{- 1})$	$b (m^{- 1})$	$c (m^{- 1})$	$\bar{ω}$
Jerlov IB	0.060	0.084	0.144	0.58
Pool water	0.117	0.182	0.299	0.61

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Tianhua Zhou, Jian Ma, Tingting Lu, Guyu Hu, Tingwei Fan, Xiaopeng Zhu, Xiaolei Zhu, Weibiao Chen. Simulation and verification of pulsed laser beam propagation underwater using Markov chains [Invited][J]. Chinese Optics Letters, 2019, 17(10): 100003.

Simulation and verification of pulsed laser beam propagation underwater using Markov chains [Invited]

Fig. 1. State transition matrix of water. (a) State transition matrix $M_{T}$ . (b) State transition matrix raised to the $15^{th}$ power $M_{T}^{15}$ .

Fig. 2. Normalized angular probability distribution for increasing number of collisions $n_{c}$ .

Fig. 3. Normalized probability distribution of the number of collisions $n_{c}$ for increasing transmission distance $D_{T}$ .

Fig. 4. Energy loss on the receiving plane versus transmission distance $D_{T}$ . (a) Jerlov IB: a = 0.06 m⁻¹, b = 0.084 m⁻¹. (b) Pool water: a = 0.117 m⁻¹, b = 0.182 m⁻¹.

Fig. 5. Transmission procedures of the successive layering model, $n_{c} = 1$ and $n_{c} = 2$ .

Fig. 6. Temporal distributions of different transmission distances. (a) $D_{T} = 20 m$ , (b) $D_{T} = 40 m$ , (c) $D_{T} = 60 m$ , (d) $D_{T} = 80 m$ .

Table1. Water Parameters

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Simulation and verification of pulsed laser beam propagation underwater using Markov chains [Invited]

Fig. 1. State transition matrix of water. (a) State transition matrix MT. (b) State transition matrix raised to the 15th power MT15.

Fig. 2. Normalized angular probability distribution for increasing number of collisions nc.

Fig. 3. Normalized probability distribution of the number of collisions nc for increasing transmission distance DT.

Fig. 4. Energy loss on the receiving plane versus transmission distance DT. (a) Jerlov IB: a = 0.06 m−1, b = 0.084 m−1. (b) Pool water: a = 0.117 m−1, b = 0.182 m−1.

Fig. 5. Transmission procedures of the successive layering model, nc=1 and nc=2.

Fig. 6. Temporal distributions of different transmission distances. (a) DT=20 m, (b) DT=40 m, (c) DT=60 m, (d) DT=80 m.

Table1. Water Parameters

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Fig. 1. State transition matrix of water. (a) State transition matrix $M_{T}$ . (b) State transition matrix raised to the $15^{th}$ power $M_{T}^{15}$ .

Fig. 2. Normalized angular probability distribution for increasing number of collisions $n_{c}$ .

Fig. 3. Normalized probability distribution of the number of collisions $n_{c}$ for increasing transmission distance $D_{T}$ .

Fig. 4. Energy loss on the receiving plane versus transmission distance $D_{T}$ . (a) Jerlov IB: a = 0.06 m⁻¹, b = 0.084 m⁻¹. (b) Pool water: a = 0.117 m⁻¹, b = 0.182 m⁻¹.

Fig. 5. Transmission procedures of the successive layering model, $n_{c} = 1$ and $n_{c} = 2$ .

Fig. 6. Temporal distributions of different transmission distances. (a) $D_{T} = 20 m$ , (b) $D_{T} = 40 m$ , (c) $D_{T} = 60 m$ , (d) $D_{T} = 80 m$ .