Abstract

Although underwater wireless optical communication (UWOC) receives much interest lately, security issues associated with it get little attention. In this paper, we show how a message communicated using UWOC can be eavesdropped without a sender's or addressee's awareness, by employing a diffraction grating. We also analyze the propagation of multiple diffracted Gaussian beams in water, and show for the first time that UWOC is feasible even in natural ultra-salty water taken from the Dead-Sea. We evaluate how far from the addressee the message could be eavesdropped, and discuss different possibilities of tapping the channel – one from the air and one underwater.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

F. Mattoussi, M. A. Khalighi, and S. Bourennane, “Improving the performance of underwater wireless optical communication links by channel coding,” Appl. Opt. 57(9), 2115–2120 (2018).
[Crossref] [PubMed]

M. Kong, B. Sun, R. Sarwar, J. Shen, Y. Chen, F. Qu, J. Han, J. Chen, H. Qin, and J. Xu, “Underwater wireless optical communication using a lens-free solar panel receiver,” Opt. Commun. 426, 94–98 (2018).
[Crossref]

2017 (4)

2016 (5)

I. F. Akyildiz, P. Wang, and S. C. Lin, “SoftWater: Software-defined networking for next-generation underwater communication systems,” Ad Hoc Netw. 46, 1–11 (2016).
[Crossref]

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, “OFDM-based broadband underwater wireless optical communication system using a compact blue LED,” Opt. Commun. 369, 100–105 (2016).
[Crossref]

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

C. Shen, Y. Guo, H. M. Oubei, T. K. Ng, G. Liu, K. H. Park, K. T. Ho, M. S. Alouini, and B. S. Ooi, “20-meter underwater wireless optical communication link with 1.5 Gbps data rate,” Opt. Express 24(22), 25502–25509 (2016).
[Crossref] [PubMed]

H. H. Lu, C. Y. Li, H. H. Lin, W. S. Tsai, C. A. Chu, B. R. Chen, and C. J. Wu, “An 8 m/9.6 Gbps underwater wireless optical communication system,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

2015 (4)

2014 (2)

L. J. Johnson, F. Jasman, R. J. Green, and M. Leeson, “Recent advances in underwater optical wireless communications,” Underwat. Technol. 32(3), 167–175 (2014).
[Crossref]

S. Tang, Y. Dong, and X. Zhang, “Impulse response modeling for underwater wireless optical communication links,” IEEE Trans. Commun. 62(1), 226–234 (2014).
[Crossref]

2013 (3)

L. Savage, “Underwater imaging gets clearer,” Opt. Photonics News 24(7), 30–37 (2013).
[Crossref]

C. Gabriel, M. Khalighi, S. Bourennane, P. Leon, and V. Rigaud, “Monte-Carlo-based channel characterization for underwater optical communication systems,” J. Opt. Comm. Netw. 5(1), 1–12 (2013).
[Crossref]

E. Boss, H. Gildor, W. Slade, L. Sokoletsky, A. Oren, and J. Loftin, “Optical properties of the Dead Sea,” J. Geophys. Res. Oceans 118(4), 1821–1829 (2013).
[Crossref]

2010 (1)

S. Arnon, “Underwater optical wireless communication network,” Opt. Eng. 49(1), 015001 (2010).
[Crossref]

2009 (2)

X. Zhang and L. Hu, “Scattering by pure seawater at high salinity,” Opt. Express 17(15), 12685–12691 (2009).
[Crossref] [PubMed]

D. Pompili and I. F. Akyildiz, “Overview of networking protocols for underwater wireless communications,” IEEE Commun. Mag. 47(1), 97–102 (2009).
[Crossref]

2007 (1)

A. Martínez, M. M. Sánchez-López, and I. Moreno, “Phasor analysis of binary diffraction gratings with different fill factors,” Eur. J. Phys. 28(5), 805–816 (2007).
[Crossref]

1969 (1)

E. W. Ng and M. Geller, “A table of integrals of the error functions,” J. Research of the National Bureau of Standards – B. Mathematical Sciences 73B, 1 (1969).

Akyildiz, I. F.

I. F. Akyildiz, P. Wang, and S. C. Lin, “SoftWater: Software-defined networking for next-generation underwater communication systems,” Ad Hoc Netw. 46, 1–11 (2016).
[Crossref]

D. Pompili and I. F. Akyildiz, “Overview of networking protocols for underwater wireless communications,” IEEE Commun. Mag. 47(1), 97–102 (2009).
[Crossref]

Al-Halafi, A.

A. Al-Halafi, H. M. Oubei, B. S. Ooi, and B. Shihada, “Real-time video transmission over different underwater wireless optical channels using a directly modulated 520 nm laser diode,” in IEEE/OSA. J. Opt. Commun. Netw. 9(10), 826–832 (2017).
[Crossref]

Ali, T.

Alouini, M. S.

Arnon, S.

S. Arnon, “Underwater optical wireless communication network,” Opt. Eng. 49(1), 015001 (2010).
[Crossref]

Boss, E.

E. Boss, H. Gildor, W. Slade, L. Sokoletsky, A. Oren, and J. Loftin, “Optical properties of the Dead Sea,” J. Geophys. Res. Oceans 118(4), 1821–1829 (2013).
[Crossref]

Bourennane, S.

F. Mattoussi, M. A. Khalighi, and S. Bourennane, “Improving the performance of underwater wireless optical communication links by channel coding,” Appl. Opt. 57(9), 2115–2120 (2018).
[Crossref] [PubMed]

C. Gabriel, M. Khalighi, S. Bourennane, P. Leon, and V. Rigaud, “Monte-Carlo-based channel characterization for underwater optical communication systems,” J. Opt. Comm. Netw. 5(1), 1–12 (2013).
[Crossref]

Chen, B. R.

H. H. Lu, C. Y. Li, H. H. Lin, W. S. Tsai, C. A. Chu, B. R. Chen, and C. J. Wu, “An 8 m/9.6 Gbps underwater wireless optical communication system,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Chen, J.

M. Kong, B. Sun, R. Sarwar, J. Shen, Y. Chen, F. Qu, J. Han, J. Chen, H. Qin, and J. Xu, “Underwater wireless optical communication using a lens-free solar panel receiver,” Opt. Commun. 426, 94–98 (2018).
[Crossref]

Chen, Y.

M. Kong, B. Sun, R. Sarwar, J. Shen, Y. Chen, F. Qu, J. Han, J. Chen, H. Qin, and J. Xu, “Underwater wireless optical communication using a lens-free solar panel receiver,” Opt. Commun. 426, 94–98 (2018).
[Crossref]

M. Kong, J. Wang, Y. Chen, T. Ali, R. Sarwar, Y. Qiu, S. Wang, J. Han, and J. Xu, “Security weaknesses of underwater wireless optical communication,” Opt. Express 25(18), 21509–21518 (2017).
[Crossref] [PubMed]

Cheng, X.

H. Li, Y. He, X. Cheng, H. Zhu, and L. Sun, “Security and privacy in localization for underwater sensor networks,” IEEE Commun. Mag. 53(11), 56–62 (2015).
[Crossref]

Chu, C. A.

H. H. Lu, C. Y. Li, H. H. Lin, W. S. Tsai, C. A. Chu, B. R. Chen, and C. J. Wu, “An 8 m/9.6 Gbps underwater wireless optical communication system,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Cong, C.

Deng, N.

J. Xu, M. Kong, A. Lin, Y. Song, J. Han, Z. Xu, B. Wu, S. Gao, and N. Deng, “Directly modulated green-light diode-pumped solid-state laser for underwater wireless optical communication,” Opt. Lett. 42(9), 1664–1667 (2017).
[Crossref] [PubMed]

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, “OFDM-based broadband underwater wireless optical communication system using a compact blue LED,” Opt. Commun. 369, 100–105 (2016).
[Crossref]

Dong, Y.

S. Tang, Y. Dong, and X. Zhang, “Impulse response modeling for underwater wireless optical communication links,” IEEE Trans. Commun. 62(1), 226–234 (2014).
[Crossref]

Fang, Z.

Fletcher, S.

S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53(11), 49–55 (2015).
[Crossref]

Gabriel, C.

C. Gabriel, M. Khalighi, S. Bourennane, P. Leon, and V. Rigaud, “Monte-Carlo-based channel characterization for underwater optical communication systems,” J. Opt. Comm. Netw. 5(1), 1–12 (2013).
[Crossref]

Gao, S.

Geller, M.

E. W. Ng and M. Geller, “A table of integrals of the error functions,” J. Research of the National Bureau of Standards – B. Mathematical Sciences 73B, 1 (1969).

Gildor, H.

E. Boss, H. Gildor, W. Slade, L. Sokoletsky, A. Oren, and J. Loftin, “Optical properties of the Dead Sea,” J. Geophys. Res. Oceans 118(4), 1821–1829 (2013).
[Crossref]

Green, R. J.

L. J. Johnson, F. Jasman, R. J. Green, and M. Leeson, “Recent advances in underwater optical wireless communications,” Underwat. Technol. 32(3), 167–175 (2014).
[Crossref]

Guo, Y.

Hamilton, S. A.

S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53(11), 49–55 (2015).
[Crossref]

Han, J.

M. Kong, B. Sun, R. Sarwar, J. Shen, Y. Chen, F. Qu, J. Han, J. Chen, H. Qin, and J. Xu, “Underwater wireless optical communication using a lens-free solar panel receiver,” Opt. Commun. 426, 94–98 (2018).
[Crossref]

M. Kong, J. Wang, Y. Chen, T. Ali, R. Sarwar, Y. Qiu, S. Wang, J. Han, and J. Xu, “Security weaknesses of underwater wireless optical communication,” Opt. Express 25(18), 21509–21518 (2017).
[Crossref] [PubMed]

J. Xu, M. Kong, A. Lin, Y. Song, J. Han, Z. Xu, B. Wu, S. Gao, and N. Deng, “Directly modulated green-light diode-pumped solid-state laser for underwater wireless optical communication,” Opt. Lett. 42(9), 1664–1667 (2017).
[Crossref] [PubMed]

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, “OFDM-based broadband underwater wireless optical communication system using a compact blue LED,” Opt. Commun. 369, 100–105 (2016).
[Crossref]

Hanawa, M.

He, Y.

H. Li, Y. He, X. Cheng, H. Zhu, and L. Sun, “Security and privacy in localization for underwater sensor networks,” IEEE Commun. Mag. 53(11), 56–62 (2015).
[Crossref]

Ho, K. T.

Hu, L.

Jasman, F.

L. J. Johnson, F. Jasman, R. J. Green, and M. Leeson, “Recent advances in underwater optical wireless communications,” Underwat. Technol. 32(3), 167–175 (2014).
[Crossref]

Johnson, L. J.

L. J. Johnson, F. Jasman, R. J. Green, and M. Leeson, “Recent advances in underwater optical wireless communications,” Underwat. Technol. 32(3), 167–175 (2014).
[Crossref]

Kaddoum, G.

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

Kaushal, H.

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016).
[Crossref]

Khalighi, M.

C. Gabriel, M. Khalighi, S. Bourennane, P. Leon, and V. Rigaud, “Monte-Carlo-based channel characterization for underwater optical communication systems,” J. Opt. Comm. Netw. 5(1), 1–12 (2013).
[Crossref]

Khalighi, M. A.

Kong, M.

M. Kong, B. Sun, R. Sarwar, J. Shen, Y. Chen, F. Qu, J. Han, J. Chen, H. Qin, and J. Xu, “Underwater wireless optical communication using a lens-free solar panel receiver,” Opt. Commun. 426, 94–98 (2018).
[Crossref]

J. Xu, M. Kong, A. Lin, Y. Song, J. Han, Z. Xu, B. Wu, S. Gao, and N. Deng, “Directly modulated green-light diode-pumped solid-state laser for underwater wireless optical communication,” Opt. Lett. 42(9), 1664–1667 (2017).
[Crossref] [PubMed]

M. Kong, J. Wang, Y. Chen, T. Ali, R. Sarwar, Y. Qiu, S. Wang, J. Han, and J. Xu, “Security weaknesses of underwater wireless optical communication,” Opt. Express 25(18), 21509–21518 (2017).
[Crossref] [PubMed]

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, “OFDM-based broadband underwater wireless optical communication system using a compact blue LED,” Opt. Commun. 369, 100–105 (2016).
[Crossref]

Leeson, M.

L. J. Johnson, F. Jasman, R. J. Green, and M. Leeson, “Recent advances in underwater optical wireless communications,” Underwat. Technol. 32(3), 167–175 (2014).
[Crossref]

Leon, P.

C. Gabriel, M. Khalighi, S. Bourennane, P. Leon, and V. Rigaud, “Monte-Carlo-based channel characterization for underwater optical communication systems,” J. Opt. Comm. Netw. 5(1), 1–12 (2013).
[Crossref]

Li, C.

Li, C. Y.

H. H. Lu, C. Y. Li, H. H. Lin, W. S. Tsai, C. A. Chu, B. R. Chen, and C. J. Wu, “An 8 m/9.6 Gbps underwater wireless optical communication system,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Li, H.

H. Li, Y. He, X. Cheng, H. Zhu, and L. Sun, “Security and privacy in localization for underwater sensor networks,” IEEE Commun. Mag. 53(11), 56–62 (2015).
[Crossref]

Lin, A.

J. Xu, M. Kong, A. Lin, Y. Song, J. Han, Z. Xu, B. Wu, S. Gao, and N. Deng, “Directly modulated green-light diode-pumped solid-state laser for underwater wireless optical communication,” Opt. Lett. 42(9), 1664–1667 (2017).
[Crossref] [PubMed]

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, “OFDM-based broadband underwater wireless optical communication system using a compact blue LED,” Opt. Commun. 369, 100–105 (2016).
[Crossref]

Lin, H. H.

H. H. Lu, C. Y. Li, H. H. Lin, W. S. Tsai, C. A. Chu, B. R. Chen, and C. J. Wu, “An 8 m/9.6 Gbps underwater wireless optical communication system,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Lin, S. C.

I. F. Akyildiz, P. Wang, and S. C. Lin, “SoftWater: Software-defined networking for next-generation underwater communication systems,” Ad Hoc Netw. 46, 1–11 (2016).
[Crossref]

Liu, G.

Liu, R.

Liu, X.

Loftin, J.

E. Boss, H. Gildor, W. Slade, L. Sokoletsky, A. Oren, and J. Loftin, “Optical properties of the Dead Sea,” J. Geophys. Res. Oceans 118(4), 1821–1829 (2013).
[Crossref]

Lu, H. H.

H. H. Lu, C. Y. Li, H. H. Lin, W. S. Tsai, C. A. Chu, B. R. Chen, and C. J. Wu, “An 8 m/9.6 Gbps underwater wireless optical communication system,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Martínez, A.

A. Martínez, M. M. Sánchez-López, and I. Moreno, “Phasor analysis of binary diffraction gratings with different fill factors,” Eur. J. Phys. 28(5), 805–816 (2007).
[Crossref]

Mattoussi, F.

Mizukoshi, I.

Moores, J. D.

S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53(11), 49–55 (2015).
[Crossref]

Moreno, I.

A. Martínez, M. M. Sánchez-López, and I. Moreno, “Phasor analysis of binary diffraction gratings with different fill factors,” Eur. J. Phys. 28(5), 805–816 (2007).
[Crossref]

Nakamura, K.

Ng, E. W.

E. W. Ng and M. Geller, “A table of integrals of the error functions,” J. Research of the National Bureau of Standards – B. Mathematical Sciences 73B, 1 (1969).

Ng, T. K.

Ooi, B. S.

Oren, A.

E. Boss, H. Gildor, W. Slade, L. Sokoletsky, A. Oren, and J. Loftin, “Optical properties of the Dead Sea,” J. Geophys. Res. Oceans 118(4), 1821–1829 (2013).
[Crossref]

Oubei, H. M.

Park, K. H.

Pompili, D.

D. Pompili and I. F. Akyildiz, “Overview of networking protocols for underwater wireless communications,” IEEE Commun. Mag. 47(1), 97–102 (2009).
[Crossref]

Qin, H.

M. Kong, B. Sun, R. Sarwar, J. Shen, Y. Chen, F. Qu, J. Han, J. Chen, H. Qin, and J. Xu, “Underwater wireless optical communication using a lens-free solar panel receiver,” Opt. Commun. 426, 94–98 (2018).
[Crossref]

Qiu, Y.

Qiu, Z. J.

Qu, F.

M. Kong, B. Sun, R. Sarwar, J. Shen, Y. Chen, F. Qu, J. Han, J. Chen, H. Qin, and J. Xu, “Underwater wireless optical communication using a lens-free solar panel receiver,” Opt. Commun. 426, 94–98 (2018).
[Crossref]

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, “OFDM-based broadband underwater wireless optical communication system using a compact blue LED,” Opt. Commun. 369, 100–105 (2016).
[Crossref]

Rigaud, V.

C. Gabriel, M. Khalighi, S. Bourennane, P. Leon, and V. Rigaud, “Monte-Carlo-based channel characterization for underwater optical communication systems,” J. Opt. Comm. Netw. 5(1), 1–12 (2013).
[Crossref]

Sánchez-López, M. M.

A. Martínez, M. M. Sánchez-López, and I. Moreno, “Phasor analysis of binary diffraction gratings with different fill factors,” Eur. J. Phys. 28(5), 805–816 (2007).
[Crossref]

Sarwar, R.

M. Kong, B. Sun, R. Sarwar, J. Shen, Y. Chen, F. Qu, J. Han, J. Chen, H. Qin, and J. Xu, “Underwater wireless optical communication using a lens-free solar panel receiver,” Opt. Commun. 426, 94–98 (2018).
[Crossref]

M. Kong, J. Wang, Y. Chen, T. Ali, R. Sarwar, Y. Qiu, S. Wang, J. Han, and J. Xu, “Security weaknesses of underwater wireless optical communication,” Opt. Express 25(18), 21509–21518 (2017).
[Crossref] [PubMed]

Savage, L.

L. Savage, “Underwater imaging gets clearer,” Opt. Photonics News 24(7), 30–37 (2013).
[Crossref]

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Shihada, B.

A. Al-Halafi, H. M. Oubei, B. S. Ooi, and B. Shihada, “Real-time video transmission over different underwater wireless optical channels using a directly modulated 520 nm laser diode,” in IEEE/OSA. J. Opt. Commun. Netw. 9(10), 826–832 (2017).
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Slade, W.

E. Boss, H. Gildor, W. Slade, L. Sokoletsky, A. Oren, and J. Loftin, “Optical properties of the Dead Sea,” J. Geophys. Res. Oceans 118(4), 1821–1829 (2013).
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E. Boss, H. Gildor, W. Slade, L. Sokoletsky, A. Oren, and J. Loftin, “Optical properties of the Dead Sea,” J. Geophys. Res. Oceans 118(4), 1821–1829 (2013).
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J. Xu, M. Kong, A. Lin, Y. Song, J. Han, Z. Xu, B. Wu, S. Gao, and N. Deng, “Directly modulated green-light diode-pumped solid-state laser for underwater wireless optical communication,” Opt. Lett. 42(9), 1664–1667 (2017).
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M. Kong, B. Sun, R. Sarwar, J. Shen, Y. Chen, F. Qu, J. Han, J. Chen, H. Qin, and J. Xu, “Underwater wireless optical communication using a lens-free solar panel receiver,” Opt. Commun. 426, 94–98 (2018).
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S. Tang, Y. Dong, and X. Zhang, “Impulse response modeling for underwater wireless optical communication links,” IEEE Trans. Commun. 62(1), 226–234 (2014).
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M. Kong, B. Sun, R. Sarwar, J. Shen, Y. Chen, F. Qu, J. Han, J. Chen, H. Qin, and J. Xu, “Underwater wireless optical communication using a lens-free solar panel receiver,” Opt. Commun. 426, 94–98 (2018).
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M. Kong, J. Wang, Y. Chen, T. Ali, R. Sarwar, Y. Qiu, S. Wang, J. Han, and J. Xu, “Security weaknesses of underwater wireless optical communication,” Opt. Express 25(18), 21509–21518 (2017).
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J. Xu, M. Kong, A. Lin, Y. Song, J. Han, Z. Xu, B. Wu, S. Gao, and N. Deng, “Directly modulated green-light diode-pumped solid-state laser for underwater wireless optical communication,” Opt. Lett. 42(9), 1664–1667 (2017).
[Crossref] [PubMed]

J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, “OFDM-based broadband underwater wireless optical communication system using a compact blue LED,” Opt. Commun. 369, 100–105 (2016).
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Yi, S.

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S. Tang, Y. Dong, and X. Zhang, “Impulse response modeling for underwater wireless optical communication links,” IEEE Trans. Commun. 62(1), 226–234 (2014).
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[Crossref]

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H. H. Lu, C. Y. Li, H. H. Lin, W. S. Tsai, C. A. Chu, B. R. Chen, and C. J. Wu, “An 8 m/9.6 Gbps underwater wireless optical communication system,” IEEE Photonics J. 8(5), 1–7 (2016).
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in IEEE/OSA. J. Opt. Commun. Netw. (1)

A. Al-Halafi, H. M. Oubei, B. S. Ooi, and B. Shihada, “Real-time video transmission over different underwater wireless optical channels using a directly modulated 520 nm laser diode,” in IEEE/OSA. J. Opt. Commun. Netw. 9(10), 826–832 (2017).
[Crossref]

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E. Boss, H. Gildor, W. Slade, L. Sokoletsky, A. Oren, and J. Loftin, “Optical properties of the Dead Sea,” J. Geophys. Res. Oceans 118(4), 1821–1829 (2013).
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C. Gabriel, M. Khalighi, S. Bourennane, P. Leon, and V. Rigaud, “Monte-Carlo-based channel characterization for underwater optical communication systems,” J. Opt. Comm. Netw. 5(1), 1–12 (2013).
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J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, “OFDM-based broadband underwater wireless optical communication system using a compact blue LED,” Opt. Commun. 369, 100–105 (2016).
[Crossref]

M. Kong, B. Sun, R. Sarwar, J. Shen, Y. Chen, F. Qu, J. Han, J. Chen, H. Qin, and J. Xu, “Underwater wireless optical communication using a lens-free solar panel receiver,” Opt. Commun. 426, 94–98 (2018).
[Crossref]

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[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Sketch that demonstrates experimental model of underwater channel tapping by diffraction grating. A 7-sec voice signal modulates a 520 nm green laser beam that impinges on the grating, and is divided into several diffraction orders. A detector is placed at a position along the Line-of-Sight of the 0-order light beam, while the other beams continue to propagate in different directions. In Setup A, the grating is outside the water tank, and in Setup B the grating is inside the water tank.
Fig. 2
Fig. 2 (a) Simulation of the propagation of the Gaussian laser beam in Setup A. A green-color Gaussian beam impinges upon a binary amplitude diffraction grating, and splits into different orders with intensity coefficients of | sinc( am ) | 2 . The beams enter the water tank and propagate in the water for a distance of 1-m. Each beam diverges, spreads and experiences intensity loss due to absorption and scattering in water. A detector is placed to collect the 0-order beam. (b) A photo of the outputs of setup A. The green laser beam impinges upon the grating, and splits into several diffraction orders. Multiple beams are now propagating ins the water. A detector is placed in a position that is in the direction of the 0-order light beams, while the other beams continue to propagate in different directions.
Fig. 3
Fig. 3 Eavesdropping in free-space (Setup A). (a) Image of all diffraction orders on a screen behind the detector, which is positioned directly to detect the 0-order beam. (b) Part of the input voice signal (green), and detected voice signal from the 0-order beam (yellow). (c) Image of all diffraction orders on a screen behind the detector, which is positioned directly to detect the 1-order beam. (d) Part of the input voice signal (green), and detected voice signal from the 1-order beam (yellow). The SNR is ~52 dB (for 0-order beam) and ~41 dB (for 1-order beam).
Fig. 4
Fig. 4 Eavesdropping in pure water. (a) Part of the input voice signal (green), and detected voice signal from the 0-order beam (yellow) in Setup A. The SNR is ~42 dB. (b) Part of the input voice signal (green), and detected voice signal from the 0-order beam (yellow) in Setup B. The SNR is ~37 dB. (c) Part of the input voice signal (green), and detected voice signal from the 1-order beam (yellow) in Setup A. The SNR is ~35 dB. (d) Part of the input voice signal (green), and detected voice signal from the 1-order beam (yellow) in Setup B. The SNR is ~29 dB.
Fig. 5
Fig. 5 Eavesdropping in natural water from the Dead-Sea. (a) Collection of natural water from the Dead-Sea. (b) Part of the input voice signal (green), and detected voice signal from the 0-order beam (yellow) in Setup A. The SNR is ~37 dB. (c) Part of the input voice signal (green), and detected voice signal from the 1-order beam (yellow) in Setup A. The SNR is ~33 dB.
Fig. 6
Fig. 6 The relation between the location of the diffraction grating in the z-axis and the maximum displacement in the x-axis at which an attacker can place a secret detector for eavesdropping. The simulation was performed for an input power of 5 mW, a minimum detectable dark power of 40 nW, and for clear ocean water (c = 0.151 1/m).

Equations (21)

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mλ Λ = n i sin( θ i )+ n med sin( θ med )
u i (x,y,0)=exp(π x 2 + y 2 ω 0 2 )
t(x,y,0)=( rect( x aΛ )rect( y d ) m= δ(xmΛ) )rect( x B )rect( y B )
u t (x,y,0)=exp(π x 2 + y 2 ω 0 2 )t(x,y,0)
U t ( f x , f y )={ u t (x,y,0) }= u t (x,y,0)exp[ j2π( x f x +y f y ) ] dxdy= U i ( f x , f y )T( f x , f y )
T( f x )=( m= asinc(am)δ( f x m Λ ) )Bsinc(B f x )
1 Λ comb( x Λ )= m= δ(xmΛ )
{ 1 Λ comb( x Λ ) }=comb( Λ f x )= 1 Λ m= δ( f x m Λ )
U t ( f x )= ω 0 2 exp(π ω 0 2 f x 2 )( m= asinc(am)δ( f x m Λ ) )Bsinc(B f x )= a ω 0 2 ( m= sinc(am)exp(π ω 0 2 ( f x m Λ ) 2 )Bsinc(B f x )
U t ( f x )=a ω 0 3 m= sinc(am)exp(π ω 0 2 ( f x m Λ ) 2 )[ Re{ erf( B π 2 ω 0 +j π ω 0 ( f x m Λ )) }) ]
I m = | U m | 2 | sinc(am) | 2
P z = P 0 η T η R A π ( ztan( θ d ) ) 2 exp(cz)= P ˜ 0 exp(cz)
P zm = P in exp(cd) | sinc(am) | 2
P min = P d exp(c z max ) | sinc(a) | 2
z max = 1 c [ ln( P d P min )0.0676 ]
U t ( f x )=a ω 0 2 m= sinc(am) exp( π ω 0 2 ( f x f x ' m Λ ) 2 ) Bsinc(B f x ' )d f x '
f 0 = f x m Λ s=π ω 0 2 1 π 0 Bπ cos(β f x )d β=Bsinc(B f x )
U t ( f x )= a ω 0 2 π m= sinc(am) exp( s ( f 0 f x ' ) 2 ) d f x ' 0 Bπ cos(β f x ' )d β
U t ( f x )= a ω 0 2 π m= sinc(am) exp( s u 2 ) cos(βu+β f 0 )du 0 Bπ d β= a ω 0 2 π m= sinc(am) exp( s u 2 ) [ cos(βu)cos(β f 0 )sin(βu)sin(β f 0 ) ]du 0 Bπ d β
U t ( f x )= a ω 0 2 π m= sinc(am) exp( s u 2 ) cos(βu)du 0 Bπ cos(β f 0 )d β= = a ω 0 2 π m= sinc(am) 0 Bπ exp( β 2 4s )cos(β f 0 )d β
U t ( f x )= a ω 0 2 π m= sinc(am) 0 Bπ exp( β 2 4s ) [ exp(jβ f 0 )+exp(jβ f 0 ) ] 2 d β= a ω 0 2 2π m= sinc(am) 0 Bπ [ exp( ( β 2 s j s f 0 ) 2 s f 0 2 )+exp( ( β 2 s +j s f 0 ) 2 s f 0 2 ) ]d β= = a ω 0 2 2π m= sinc(am) [ 2 s exp( s f 0 2 ) j s f 0 Bπ 2 s j s f 0 exp( v 2 )d v+2 s exp( s f 0 2 ) j s f 0 Bπ 2 s +j s f 0 exp( t 2 )d t ]= a ω 0 3 2 m= sinc(am) exp( s f 0 2 )[ erf( Bπ 2 s j s f 0 )erf(j s f 0 )+erf( Bπ 2 s j s f 0 )erf(j s f 0 ) ]= a ω 0 3 m= sinc(am) exp( s f 0 2 )[ Re{ erf( Bπ 2 s +j s f 0 ) }) ]

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