Abstract

We examine the propagation of optical beams possessing different polarization states and spatial modes through the Ottawa River in Canada. A Shack-Hartmann wavefront sensor is used to record the distorted beam’s wavefront. The turbulence in the underwater channel is analysed, and associated Zernike coefficients are obtained in real-time. Finally, we explore the feasibility of transmitting polarization states as well as spatial modes through the underwater channel for applications in quantum cryptography.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2019 (2)

2018 (3)

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Quantum cryptography with twisted photons through an outdoor underwater channel,” Opt. Express 26(17), 22563–22573 (2018).
[Crossref]

F. Bouchard, K. Heshami, D. England, R. Fickler, R. W. Boyd, B.-G. Englert, L. L. Sánchez-Soto, and E. Karimi, “Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons,” Quantum 2, 111 (2018).
[Crossref]

B. Guo, G. Yuan, J. Yu, H. Liu, W. Xu, and R. Hou, “Simulations and measurements of polarization states changing in underwater laser transmission,” Proc. SPIE 10850, 108500U (2018).
[Crossref]

2017 (5)

Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, “A survey of underwater optical wireless communications,” IEEE Commun. Surv. Tutorials 19(1), 204–238 (2017).
[Crossref]

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref]

G. Nootz, S. Matt, A. Kanaev, K. P. Judd, and W. Hou, “Experimental and numerical study of underwater beam propagation in a Rayleigh–Bénard turbulence tank,” Appl. Opt. 56(22), 6065–6072 (2017).
[Crossref]

L. Ji, J. Gao, A.-L. Yang, Z. Feng, X.-F. Lin, Z.-G. Li, and X.-M. Jin, “Towards quantum communications in free-space seawater,” Opt. Express 25(17), 19795–19806 (2017).
[Crossref]

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Gunthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4(9), 1006–1010 (2017).
[Crossref]

2016 (2)

G. Nootz, E. Jarosz, F. R. Dalgleish, and W. Hou, “Quantification of optical turbulence in the ocean and its effects on beam propagation,” Appl. Opt. 55(31), 8813–8820 (2016).
[Crossref]

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref]

2015 (2)

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
[Crossref]

P. Shi, S.-C. Zhao, Y.-J. Gu, and W.-D. Li, “Channel analysis for single photon underwater free space quantum key distribution,” J. Opt. Soc. Am. A 32(3), 349–356 (2015).
[Crossref]

2014 (1)

M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, “Communication with spatially modulated light through turbulent air across vienna,” New J. Phys. 16(11), 113028 (2014).
[Crossref]

2013 (1)

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88(3), 032305 (2013).
[Crossref]

2009 (2)

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

J. C. Brock and S. J. Purkis, “The emerging role of lidar remote sensing in coastal research and resource management,” J. Coastal Res. 10053, 1–5 (2009).
[Crossref]

2007 (1)

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98(1), 010504 (2007).
[Crossref]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

1981 (1)

1980 (1)

T. Wiener and S. Karp, “The role of blue/green laser systems in strategic submarine communications,” IEEE Trans. Commun. 28(9), 1602–1607 (1980).
[Crossref]

1941 (1)

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Akademiia Nauk SSSR Doklady 30, 299–303 (1941).

Abbas, A.

Ahmed, N.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref]

Allen, L.

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Arbabi, A.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref]

Arbabi, E.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref]

Ashrafi, S.

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref]

Bacco, D.

S. Tarantino, D. Cozzolino, K. Rottwitt, and D. Bacco, Feasibility of quantum communications in aquatic scenario, in 2018 IEEE Photonics Conference (IPC), (IEEE, 2018), pp. 1–2.

Baker, K. S.

Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Bennett, C. H.

C. H. Bennett and G. Brassard, Quantum cryptography: public key distribution and coin tossing, in Int. Conf. on Comput. Syst. Signal Process. (IEEE, 1984), pp. 175–179.

Bouchard, F.

Boyd, R. W.

F. Bouchard, A. Sit, F. Hufnagel, A. Abbas, Y. Zhang, K. Heshami, R. Fickler, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “Quantum cryptography with twisted photons through an outdoor underwater channel,” Opt. Express 26(17), 22563–22573 (2018).
[Crossref]

F. Bouchard, K. Heshami, D. England, R. Fickler, R. W. Boyd, B.-G. Englert, L. L. Sánchez-Soto, and E. Karimi, “Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons,” Quantum 2, 111 (2018).
[Crossref]

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Gunthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4(9), 1006–1010 (2017).
[Crossref]

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
[Crossref]

Brassard, G.

C. H. Bennett and G. Brassard, Quantum cryptography: public key distribution and coin tossing, in Int. Conf. on Comput. Syst. Signal Process. (IEEE, 1984), pp. 175–179.

Brock, J. C.

J. C. Brock and S. J. Purkis, “The emerging role of lidar remote sensing in coastal research and resource management,” J. Coastal Res. 10053, 1–5 (2009).
[Crossref]

Cai, M.

Cai, W.-Q.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref]

Cao, M.-M.

Y. Chen, W.-G. Shen, Z.-M. Li, C.-Q. Hu, Z.-Q. Yan, Z.-Q. Jiao, J. Gao, M.-M. Cao, K. Sun, and X.-M. Jin, “Underwater transmission of high-dimensional twisted photons over 55 meters,” arXiv preprint arXiv:1902.01392 (2019).

Cao, Y.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref]

Y. Ren, L. Li, Z. Wang, S. M. Kamali, E. Arbabi, A. Arbabi, Z. Zhao, G. Xie, Y. Cao, N. Ahmed, Y. Yan, C. Liu, A. J. Willner, S. Ashrafi, M. Tur, A. Faraon, and A. E. Willner, “Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications,” Sci. Rep. 6(1), 33306 (2016).
[Crossref]

Cerf, N. J.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Chen, X.-W.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref]

Chen, Y.

Y. Chen, W.-G. Shen, Z.-M. Li, C.-Q. Hu, Z.-Q. Yan, Z.-Q. Jiao, J. Gao, M.-M. Cao, K. Sun, and X.-M. Jin, “Underwater transmission of high-dimensional twisted photons over 55 meters,” arXiv preprint arXiv:1902.01392 (2019).

C.-Q. Hu, Z.-Q. Yan, J. Gao, Z.-Q. Jiao, Z.-M. Li, W.-G. Shen, Y. Chen, R.-J. Ren, L.-F. Qiao, A.-L. Yang, H. Tang, and X.-M. Jin, “Transmission of photonic polarization states through 55-meter water: Towards air-to-sea quantum communication,” arXiv preprint arXiv:1811.11176 (2018).

Chen, Y.-A.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref]

Cheng, J.

Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, “A survey of underwater optical wireless communications,” IEEE Commun. Surv. Tutorials 19(1), 204–238 (2017).
[Crossref]

Cozzolino, D.

S. Tarantino, D. Cozzolino, K. Rottwitt, and D. Bacco, Feasibility of quantum communications in aquatic scenario, in 2018 IEEE Photonics Conference (IPC), (IEEE, 2018), pp. 1–2.

Dalgleish, F. R.

Deng, L.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
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Figures (5)

Fig. 1.
Fig. 1. Experimental setup. Two breadboards positioned on the beach are used for the sender and receiver, Alice and Bob respectively. A CW laser at $\lambda =532$ nm is sent to an SLM, polarizing beamsplitter (PBS), and half-wave plate (HWP) for state preparation at Alice’s side of the link. This is then sent to a first periscope (composed of two mirrors) which brings the beam underwater, where it propagates to the second periscope 5.5 m away. The receiver has a PBS and HWP for polarization measurements, and a beam splitter allows a CCD camera and Shack-Hartmann wavefront sensor (WFS) to take images.
Fig. 2.
Fig. 2. Polarization probability-of-detection matrix. The sender generates the linear polarization states of $\{\left | H \right \rangle ,\left | V \right \rangle \}$ or $\{\left | A \right \rangle ,\left | D \right \rangle \}$, chosen at random. The receiver randomly picks up one of the bases $\{\left | H \right \rangle ,\left | V \right \rangle \}$ or $\{\left | A \right \rangle ,\left | D \right \rangle \}$, and records the projection probability, whose numerical values are shown.
Fig. 3.
Fig. 3. Wavefront measurements. A Gaussian beam is sent through the underwater channel to measure the wavefront. Plot a shows the average value for the magnitude of the Zernike coefficients taken from the wavefront sensor. The coefficients are separated by their radial degree corresponding to the color bars. of The inset is a plot of the wavefront given by these values. The plots in b are wavefronts measured at different times of a guassian beam through the 5 m underwater link. The wavefront measurements are taken using an array of $150\,\mathrm {\mu }$m diameter lenses.
Fig. 4.
Fig. 4. Time dependence of tip-tilt aberrations. The intensity of a Gaussian beam was measured at the receiver using a CCD camera. The tip-tilt variations were then calculated by measuring the positional shift ($x$,$y$) of the Gaussian beam from the center. The x and y center of mass, relative to the their respective beam waists $\sigma _x$ and $\sigma _y$, are plotted as a function of time in a and b, respectively.
Fig. 5.
Fig. 5. Observed turbulence effects on spatial modes. The images in the first, second, third and fourth rows correspond to $\textrm {LG}_{0,0}$, $\left ( \textrm {LG}_{4,0}+\textrm {LG}_{-4,0} \right )/\sqrt {2}$, $\textrm {LG}_{4,0}$, and $\textrm {LG}_{9,0}$, respectively. The original beam profile is shown in a, and the images after propagation through the underwater channel are shown in b. The images are taken over a 6 second interval. The exposure time for the last three rows are set to $108$ ms, while it is set to $20$ ms for the Gaussian beam. The inhomogeneity in the beams’ intensity profiles are due primarily to Mie scattering from floating objects in the underwater channel. Lower and higher-order aberrations are manifested in the beam wandering (LG$_{0,0}$) and singularity splitting.