Abstract

Non-line-of-sight (NLOS) ultraviolet communication (UVC) uses the atmosphere as a propagation medium. In previous literature, various scatter propagation models have been derived based on the premise that atmospheric turbulence was ignored and the atmosphere was considered as a turbid medium, also called random scatterers. In this Letter, a NLOS single-scatter propagation model is proposed to describe the singly scattered radiation in a turbulent medium, also called a random continuum, such as the clear atmosphere. The model is established based on the relationship between the scattered power and the characteristics of the random turbulent medium. The scattering cross section is further investigated in terms of different correlation distances and wavelengths. The received power dependence for NLOS UVC is also analyzed for different factors, including refractive-index structure parameter and transceiver range.

© 2013 Optical Society of America

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References

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    [CrossRef]
  10. H. Xiao, Y. Zuo, J. Wu, Y. Li, and J. Lin, Opt. Lett. 37, 4143 (2012).
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    [CrossRef]
  14. C. Chatfield, The Analysis of Time Series—An Introduction, 4nd ed. (Chapman and Hall, 1989).
  15. C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (Massachusetts Institute of Technology, 2006).
  16. P. Gao, Firm Characteristics, Covariances, and Cross-Sectional Expected Returns (University of Chicago, 2010).
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    [CrossRef]
  19. F. Du Castel, Tropospheric Radiowave Propagation Beyond the Horizon (Pergamon, 1966).
  20. V. M. Sorokin, V. M. Chmyrev, and A. K. Yaschenko, J. Atmos. Sol.-Terr. Phys. 63, 1681 (2001).
    [CrossRef]
  21. L. G. Hector and H. L. Schultz, Physics 7, 133 (1936).
    [CrossRef]
  22. Y. Yang and S. Danyluk, Tribol. Lett. 10, 211 (2001).
    [CrossRef]
  23. H. G. Booker and W. E. Gordon, J. Geophys. Res. 55, 241 (1950).
    [CrossRef]
  24. R. S. Cole, A. D. Sarma, and G. L. Siqueira, Appl. Opt. 27, 2261 (1988).
    [CrossRef]
  25. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

2012 (2)

2011 (2)

H. Xiao, Y. Zuo, J. Wu, H. Guo, and J. Lin, Opt. Express 19, 17864 (2011).
[CrossRef]

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, Proc. SPIE 8038, 80380J (2011).
[CrossRef]

2009 (1)

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, IEEE J. Sel. Areas Commun. 27, 1535 (2009).
[CrossRef]

2001 (2)

Y. Yang and S. Danyluk, Tribol. Lett. 10, 211 (2001).
[CrossRef]

V. M. Sorokin, V. M. Chmyrev, and A. K. Yaschenko, J. Atmos. Sol.-Terr. Phys. 63, 1681 (2001).
[CrossRef]

1991 (1)

1988 (1)

1977 (1)

1975 (1)

R. L. Fante, Proc. IEEE 63, 1669 (1975).
[CrossRef]

1966 (1)

J. B. Keller and F. C. Karal, J. Math. Phys. 7, 661 (1966).
[CrossRef]

1957 (1)

R. A. Silverman, J. Appl. Phys. 28, 506 (1957).
[CrossRef]

1950 (2)

H. G. Booker and W. E. Gordon, Proc. IRE 38, 401 (1950).
[CrossRef]

H. G. Booker and W. E. Gordon, J. Geophys. Res. 55, 241 (1950).
[CrossRef]

1936 (1)

L. G. Hector and H. L. Schultz, Physics 7, 133 (1936).
[CrossRef]

Andrews, L. C.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

Booker, H. G.

H. G. Booker and W. E. Gordon, J. Geophys. Res. 55, 241 (1950).
[CrossRef]

H. G. Booker and W. E. Gordon, Proc. IRE 38, 401 (1950).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, 1964).

Chatfield, C.

C. Chatfield, The Analysis of Time Series—An Introduction, 4nd ed. (Chapman and Hall, 1989).

Chen, G.

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, Proc. SPIE 8038, 80380J (2011).
[CrossRef]

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, IEEE J. Sel. Areas Commun. 27, 1535 (2009).
[CrossRef]

Chmyrev, V. M.

V. M. Sorokin, V. M. Chmyrev, and A. K. Yaschenko, J. Atmos. Sol.-Terr. Phys. 63, 1681 (2001).
[CrossRef]

Cole, R. S.

Danyluk, S.

Y. Yang and S. Danyluk, Tribol. Lett. 10, 211 (2001).
[CrossRef]

Ding, H.

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, Proc. SPIE 8038, 80380J (2011).
[CrossRef]

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, IEEE J. Sel. Areas Commun. 27, 1535 (2009).
[CrossRef]

Du Castel, F.

F. Du Castel, Tropospheric Radiowave Propagation Beyond the Horizon (Pergamon, 1966).

Fante, R. L.

R. L. Fante, Proc. IEEE 63, 1669 (1975).
[CrossRef]

Gao, P.

P. Gao, Firm Characteristics, Covariances, and Cross-Sectional Expected Returns (University of Chicago, 2010).

Gordon, W. E.

H. G. Booker and W. E. Gordon, J. Geophys. Res. 55, 241 (1950).
[CrossRef]

H. G. Booker and W. E. Gordon, Proc. IRE 38, 401 (1950).
[CrossRef]

Guo, H.

Hector, L. G.

L. G. Hector and H. L. Schultz, Physics 7, 133 (1936).
[CrossRef]

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Karal, F. C.

J. B. Keller and F. C. Karal, J. Math. Phys. 7, 661 (1966).
[CrossRef]

Keller, J. B.

J. B. Keller and F. C. Karal, J. Math. Phys. 7, 661 (1966).
[CrossRef]

Li, Y.

Lin, J.

Liu, C. H.

Luettgen, M. R.

Majumdar, A. K.

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, Proc. SPIE 8038, 80380J (2011).
[CrossRef]

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, IEEE J. Sel. Areas Commun. 27, 1535 (2009).
[CrossRef]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

Rasmussen, C. E.

C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (Massachusetts Institute of Technology, 2006).

Reilly, D. M.

Sadler, B. M.

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, Proc. SPIE 8038, 80380J (2011).
[CrossRef]

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, IEEE J. Sel. Areas Commun. 27, 1535 (2009).
[CrossRef]

Sarma, A. D.

Schultz, H. L.

L. G. Hector and H. L. Schultz, Physics 7, 133 (1936).
[CrossRef]

Shapiro, J. H.

Silverman, R. A.

R. A. Silverman, J. Appl. Phys. 28, 506 (1957).
[CrossRef]

Siqueira, G. L.

Sorokin, V. M.

V. M. Sorokin, V. M. Chmyrev, and A. K. Yaschenko, J. Atmos. Sol.-Terr. Phys. 63, 1681 (2001).
[CrossRef]

Strohbehn, J. W.

J. W. Strohbehn, Laser Beam Propagation in the Atmosphere (Springer, 1978).

Williams, C. K. I.

C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (Massachusetts Institute of Technology, 2006).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, 1964).

Wu, J.

Xiao, H.

Xu, Z.

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, Proc. SPIE 8038, 80380J (2011).
[CrossRef]

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, IEEE J. Sel. Areas Commun. 27, 1535 (2009).
[CrossRef]

Yang, Y.

Y. Yang and S. Danyluk, Tribol. Lett. 10, 211 (2001).
[CrossRef]

Yaschenko, A. K.

V. M. Sorokin, V. M. Chmyrev, and A. K. Yaschenko, J. Atmos. Sol.-Terr. Phys. 63, 1681 (2001).
[CrossRef]

Yeh, K. C.

Zuo, Y.

Appl. Opt. (1)

IEEE J. Sel. Areas Commun. (1)

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, IEEE J. Sel. Areas Commun. 27, 1535 (2009).
[CrossRef]

J. Appl. Phys. (1)

R. A. Silverman, J. Appl. Phys. 28, 506 (1957).
[CrossRef]

J. Atmos. Sol.-Terr. Phys. (1)

V. M. Sorokin, V. M. Chmyrev, and A. K. Yaschenko, J. Atmos. Sol.-Terr. Phys. 63, 1681 (2001).
[CrossRef]

J. Geophys. Res. (1)

H. G. Booker and W. E. Gordon, J. Geophys. Res. 55, 241 (1950).
[CrossRef]

J. Math. Phys. (1)

J. B. Keller and F. C. Karal, J. Math. Phys. 7, 661 (1966).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Express (2)

Opt. Lett. (1)

Physics (1)

L. G. Hector and H. L. Schultz, Physics 7, 133 (1936).
[CrossRef]

Proc. IEEE (1)

R. L. Fante, Proc. IEEE 63, 1669 (1975).
[CrossRef]

Proc. IRE (1)

H. G. Booker and W. E. Gordon, Proc. IRE 38, 401 (1950).
[CrossRef]

Proc. SPIE (1)

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, Proc. SPIE 8038, 80380J (2011).
[CrossRef]

Tribol. Lett. (1)

Y. Yang and S. Danyluk, Tribol. Lett. 10, 211 (2001).
[CrossRef]

Other (9)

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

F. Du Castel, Tropospheric Radiowave Propagation Beyond the Horizon (Pergamon, 1966).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, 1964).

J. W. Strohbehn, Laser Beam Propagation in the Atmosphere (Springer, 1978).

C. Chatfield, The Analysis of Time Series—An Introduction, 4nd ed. (Chapman and Hall, 1989).

C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (Massachusetts Institute of Technology, 2006).

P. Gao, Firm Characteristics, Covariances, and Cross-Sectional Expected Returns (University of Chicago, 2010).

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Figures (5)

Fig. 1.
Fig. 1.

Geometry showing transmitter, receiver, and random medium.

Fig. 2.
Fig. 2.

Geometry defining quantities.

Fig. 3.
Fig. 3.

Spherical coordinate system.

Fig. 4.
Fig. 4.

Scattering cross section versus correlation distance and wavelength.

Fig. 5.
Fig. 5.

Single-scatter irradiance versus turbulence intensity and transceiver range.

Equations (25)

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δP0=PTexp(τ1)ΩTl2δV,
δPR=ARcosζδP04πσ(o^,i^)4πL2exp(τ2),
PR=VPTARcosζexp(τ1τ2)ΩTl2L2σ(o^,i^)dV.
ε(r⃗,t)=ε(r⃗,t)(1+ε1(r⃗,t)),n(r⃗,t)=n(r⃗,t)(1+n1(r⃗,t)),
ε1(r⃗)2n1(r⃗).
E⃗(r⃗)=e^iexp(iki^·r⃗),f⃗(o^,i^)=k24πδV{o^×[o^×E⃗(r⃗)]}ε1(r⃗)exp(ikr⃗·o^)dV,
e^ssinχ=o^×(o^×e^i).
k⃗s=k(i^o^),ks=|k⃗s|=2ksin(θS/2),
f⃗(o^,i^)=e^sk2sinχ2πδVn1(r⃗)exp(ik⃗s·r⃗)dV.
σ(o^,i^)=|f⃗(o^,i^)|2/δV=f⃗(o^,i^)f⃗*(o^,i^)/δV.
Bn(rd)=n1(r⃗1)n1(r⃗2).
σ(o^,i^)=k4sin2χ(2π)2δV·δVdVcBn(rd)exp(ik⃗s·r⃗d)dVd,
Φn(K⃗)=1(2π)3Bn(r⃗d)exp(iK⃗·r⃗d)dVd,
Bn(r⃗d)=Bn(rd),Φn(K⃗)=Φn(K),
Bn(rd)exp(ik⃗s·r⃗d)dVd=(2π)3Φn(ks).
σ(o^,i^)=2πk4sin2χΦn(ks).
Φn(ks)=1(2π)3002π0πBn(rd)rd2sinαexp(iksrdcosα)drddϕdα.
Φn(ks)=12π2ks0Bn(rd)sin(ksrd)rddrd.
τ1=0lα(r)dr,
τ2=0Lα(r)dr.
α=4π2k202kΦn(ks)ksdks+kε(ε)1/2,
Bn(rd)=n12exp(rd/d0).
Φn(ks)=n12d03π2(1+ks2d02)2.
Cn2=1.91n12L02/3,
σ(o^,i^)=21.91πCn2k4d03L023[1+ks2d02]2.

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