Abstract

The convex partially coherent beam (CPCB) is a special type of nonuniformly correlated beam with a convex-shaped complex degree of coherence (DoC) distributions. Previously our research has illustrated the potential of CPCBs with super-Gaussian DoCs in free-space optical communications (FSOC), mainly manifested as self-focusing which can be transferred into extra scintillation reduction and SNR gain. In this study, the effects of the DoC transition slopes are analyzed and more details about the turbulence propagation of CPCBs with super-Gaussian shaped DoC are revealed. By means of wave optics simulation, the longitudinal intensity evolution of the CPCB is explored, showing that the DoC slope has a profound influence on the self-focusing features such as the focusing plane and the peak intensity. Aperture scintillation and mean SNR at the receiver end of some short-range vertical turbulent links are numerically computed. The obtained results show that, with CPCBs, an ~2 dB SNR gain can be achieved as compared to conventional Gaussian Schell-modal (GSM) beams. However, CPCBs are preferred only in shorter links, which is found to be relevant to the power-in-the-bucket of the receiving aperture. Furthermore, the impacts of the ratio of the source coherence time to the detector integration time are investigated, implying that the CPCB is less susceptible than the GSM. We have also examined the off-axis scintillation of the CPCB. Due to its convex-shaped DoC, the CPCB has significantly reduced off-axis scintillation, which can be beneficial in the presence of pointing errors.

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

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References

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2017 (3)

H. Kaushal and G. Kaddoum, “Optical Communication in Space: Challenges and Mitigation Techniques,” IEEE Commun. Surveys Tuts. 19(1), 57–96 (2017).
[Crossref]

H. T. Eyyuboğlu, “The performance bounds of an optical communication system using irradiance profile modulation,” J. Mod. Opt. 64(20), 2110–2116 (2017).
[Crossref]

M. Wang, X. Yuan, and D. Ma, “Potentials of radial partially coherent beams in free-space optical communication: a numerical investigation,” Appl. Opt. 56(10), 2851–2857 (2017).
[Crossref] [PubMed]

2016 (3)

2015 (2)

D. Voelz, X. Xiao, and O. Korotkova, “Numerical modeling of Schell-model beams with arbitrary far-field patterns,” Opt. Lett. 40(3), 352–355 (2015).
[Crossref] [PubMed]

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

2014 (1)

2013 (3)

2012 (1)

2011 (1)

2010 (2)

2009 (1)

R. Betancur, J. Restrepo, and R. Castaneda, “Beam shaping by spatial coherence modulation based on spatial coherence wavelets,” Opt. Lasers Eng. 47(12), 1340–1347 (2009).
[Crossref]

2007 (1)

2006 (1)

2005 (1)

M. Toyoshima, “Trends in satellite communications and the role of optical free-spacecommunications [Invited],” Journal of Optical Networking 4(6), 300–311 (2005).
[Crossref]

2004 (2)

P. B. Harboe and J. Souza, “Free space optical communication systems: a feasibility study for deployment in Brazil,” J. Microw. Optoelectron. Electromagn. Appl. 3, 58–66 (2004).

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

2003 (2)

2002 (2)

1992 (1)

A. Parent, M. Morin, and P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quantum Electron. 24(9), S1071–S1079 (1992).
[Crossref]

1981 (1)

R. L. Fante, “Intensity fluctuations of an optical wave in a turbulent medium effect of source coherence,” Opt. Acta (Lond.) 28(9), 1203–1207 (1981).
[Crossref]

1979 (1)

Amarande, S.

Andrews, L. C.

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

Basu, S.

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

Baykal, Y.

Betancur, R.

R. Betancur, J. Restrepo, and R. Castaneda, “Beam shaping by spatial coherence modulation based on spatial coherence wavelets,” Opt. Lasers Eng. 47(12), 1340–1347 (2009).
[Crossref]

Borah, D. K.

Cai, Y.

Castaneda, R.

R. Betancur, J. Restrepo, and R. Castaneda, “Beam shaping by spatial coherence modulation based on spatial coherence wavelets,” Opt. Lasers Eng. 47(12), 1340–1347 (2009).
[Crossref]

Chen, Y.

Chen, Z.

Cui, S.

Davidson, F. M.

Davis, C. C.

S. D. Milner, S. Trisno, C. C. Davis, B. Epple, and H. Henniger, “A cross-layer approach to mitigate fading on bidirectional free space optical communication links,” in Military Communications Conference (MILCOM), (IEEE, 2008), 1–6.
[Crossref]

Dogariu, A.

Epple, B.

S. D. Milner, S. Trisno, C. C. Davis, B. Epple, and H. Henniger, “A cross-layer approach to mitigate fading on bidirectional free space optical communication links,” in Military Communications Conference (MILCOM), (IEEE, 2008), 1–6.
[Crossref]

Eyyuboglu, H. T.

H. T. Eyyuboğlu, “The performance bounds of an optical communication system using irradiance profile modulation,” J. Mod. Opt. 64(20), 2110–2116 (2017).
[Crossref]

Fante, R. L.

R. L. Fante, “Intensity fluctuations of an optical wave in a turbulent medium effect of source coherence,” Opt. Acta (Lond.) 28(9), 1203–1207 (1981).
[Crossref]

Gbur, G.

Gerçekcioglu, H.

Ghassemlooy, Z.

Gori, F.

Gu, Y.

Hameed, W.

W. Hameed, S. S. Muhammad, and N. M. Sheikh, “Integration scenarios for free space optics in next generation (4G) wireless networks,” in 7th International Symposium on Communication Systems Networks and Digital Signal Processing (CSNDSP), (IEEE, 2010), 571–575.

Harboe, P. B.

P. B. Harboe and J. Souza, “Free space optical communication systems: a feasibility study for deployment in Brazil,” J. Microw. Optoelectron. Electromagn. Appl. 3, 58–66 (2004).

Henniger, H.

S. D. Milner, S. Trisno, C. C. Davis, B. Epple, and H. Henniger, “A cross-layer approach to mitigate fading on bidirectional free space optical communication links,” in Military Communications Conference (MILCOM), (IEEE, 2008), 1–6.
[Crossref]

Hyde, M. W.

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

Kaddoum, G.

H. Kaushal and G. Kaddoum, “Optical Communication in Space: Challenges and Mitigation Techniques,” IEEE Commun. Surveys Tuts. 19(1), 57–96 (2017).
[Crossref]

Kaushal, H.

H. Kaushal and G. Kaddoum, “Optical Communication in Space: Challenges and Mitigation Techniques,” IEEE Commun. Surveys Tuts. 19(1), 57–96 (2017).
[Crossref]

Khalighi, M.-A.

Korotkova, O.

Lajunen, H.

Lavigne, P.

A. Parent, M. Morin, and P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quantum Electron. 24(9), S1071–S1079 (1992).
[Crossref]

Lee, I. E.

Liaw, S.-K.

Liu, X.

Ma, D.

Milner, S. D.

S. D. Milner, S. Trisno, C. C. Davis, B. Epple, and H. Henniger, “A cross-layer approach to mitigate fading on bidirectional free space optical communication links,” in Military Communications Conference (MILCOM), (IEEE, 2008), 1–6.
[Crossref]

Morin, M.

A. Parent, M. Morin, and P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quantum Electron. 24(9), S1071–S1079 (1992).
[Crossref]

Muhammad, S. S.

W. Hameed, S. S. Muhammad, and N. M. Sheikh, “Integration scenarios for free space optics in next generation (4G) wireless networks,” in 7th International Symposium on Communication Systems Networks and Digital Signal Processing (CSNDSP), (IEEE, 2010), 571–575.

Nakiboglu, C.

Ng, W. P.

Parent, A.

A. Parent, M. Morin, and P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quantum Electron. 24(9), S1071–S1079 (1992).
[Crossref]

Phillips, R. L.

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

Pu, J.

Restrepo, J.

R. Betancur, J. Restrepo, and R. Castaneda, “Beam shaping by spatial coherence modulation based on spatial coherence wavelets,” Opt. Lasers Eng. 47(12), 1340–1347 (2009).
[Crossref]

Ricklin, J. C.

Saastamoinen, T.

Santarsiero, M.

Sheikh, N. M.

W. Hameed, S. S. Muhammad, and N. M. Sheikh, “Integration scenarios for free space optics in next generation (4G) wireless networks,” in 7th International Symposium on Communication Systems Networks and Digital Signal Processing (CSNDSP), (IEEE, 2010), 571–575.

Shirai, T.

Souza, J.

P. B. Harboe and J. Souza, “Free space optical communication systems: a feasibility study for deployment in Brazil,” J. Microw. Optoelectron. Electromagn. Appl. 3, 58–66 (2004).

Tong, Z.

Toyoshima, M.

M. Toyoshima, “Trends in satellite communications and the role of optical free-spacecommunications [Invited],” Journal of Optical Networking 4(6), 300–311 (2005).
[Crossref]

Trisno, S.

S. D. Milner, S. Trisno, C. C. Davis, B. Epple, and H. Henniger, “A cross-layer approach to mitigate fading on bidirectional free space optical communication links,” in Military Communications Conference (MILCOM), (IEEE, 2008), 1–6.
[Crossref]

Valley, G. C.

Voelz, D.

Voelz, D. G.

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

D. K. Borah and D. G. Voelz, “Spatially partially coherent beam parameter optimization for free space optical communications,” Opt. Express 18(20), 20746–20758 (2010).
[Crossref] [PubMed]

Wang, F.

Wang, M.

M. Wang, X. Yuan, and D. Ma, “Potentials of radial partially coherent beams in free-space optical communication: a numerical investigation,” Appl. Opt. 56(10), 2851–2857 (2017).
[Crossref] [PubMed]

M. Wang and X. Yuan, “Effects of finite inner and outer scales on the scintillation index of turbulent slant path,” J. Mod. Opt. 64, 1–7 (2016).
[Crossref]

Wolf, E.

Xiao, X.

Yuan, X.

Yuan, Y.

Zhang, L.

Zhang, Y.

Zhou, Z.

Appl. Opt. (4)

IEEE Commun. Surveys Tuts. (1)

H. Kaushal and G. Kaddoum, “Optical Communication in Space: Challenges and Mitigation Techniques,” IEEE Commun. Surveys Tuts. 19(1), 57–96 (2017).
[Crossref]

J. Appl. Phys. (1)

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

J. Microw. Optoelectron. Electromagn. Appl. (1)

P. B. Harboe and J. Souza, “Free space optical communication systems: a feasibility study for deployment in Brazil,” J. Microw. Optoelectron. Electromagn. Appl. 3, 58–66 (2004).

J. Mod. Opt. (2)

H. T. Eyyuboğlu, “The performance bounds of an optical communication system using irradiance profile modulation,” J. Mod. Opt. 64(20), 2110–2116 (2017).
[Crossref]

M. Wang and X. Yuan, “Effects of finite inner and outer scales on the scintillation index of turbulent slant path,” J. Mod. Opt. 64, 1–7 (2016).
[Crossref]

J. Opt. Soc. Am. A (5)

Journal of Optical Networking (1)

M. Toyoshima, “Trends in satellite communications and the role of optical free-spacecommunications [Invited],” Journal of Optical Networking 4(6), 300–311 (2005).
[Crossref]

Opt. Acta (Lond.) (1)

R. L. Fante, “Intensity fluctuations of an optical wave in a turbulent medium effect of source coherence,” Opt. Acta (Lond.) 28(9), 1203–1207 (1981).
[Crossref]

Opt. Eng. (1)

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom,” Opt. Eng. 43(2), 330–341 (2004).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (1)

R. Betancur, J. Restrepo, and R. Castaneda, “Beam shaping by spatial coherence modulation based on spatial coherence wavelets,” Opt. Lasers Eng. 47(12), 1340–1347 (2009).
[Crossref]

Opt. Lett. (8)

Opt. Quantum Electron. (1)

A. Parent, M. Morin, and P. Lavigne, “Propagation of super-Gaussian field distributions,” Opt. Quantum Electron. 24(9), S1071–S1079 (1992).
[Crossref]

Other (12)

D. G. Voelz, Computational Fourier Optics: A MATLAB Tutorial (SPIE, Bellingham, WA, 2011).

J. D. Schmidt, Numerical simulation of optical wave propagation with examples in MATLAB (SPIE, Bellingham, WA, 2010).

R. R. Beland, “Propagation through atmospheric optical turbulence,” in The Infrared and ElectroOptical Systems Handbook, F. G. Smith, ed. (SPIE, Bellingham, WA, 1993).

M. Wang, X. Yuan, J. Li, and X. Zhou, “Radial partially coherent beams for free-space optical communications,” in Laser Communication and Propagation through the Atmosphere and Oceans VI, (SPIE, 2017), 1040813.

O. Korotkova, L. C. Andrews, and R. L. Phillips, “Phase diffuser at the transmitter for lasercom link: effect of partially coherent beam on the bit-error rate,” in High-Power Lasers and Applications (SPIE, 2003), 8.

L. C. Andrews and R. L. Philips, Laser beam propagation through random media, 2nd ed. (SPIE, Bellingham, WA, 2005).

S. D. Milner, S. Trisno, C. C. Davis, B. Epple, and H. Henniger, “A cross-layer approach to mitigate fading on bidirectional free space optical communication links,” in Military Communications Conference (MILCOM), (IEEE, 2008), 1–6.
[Crossref]

J. W. Goodman, Statistical Optics (Wiley, New York, 2000).

H. Willebrand and B. S. Ghuman, Free space optics: enabling optical connectivity in today's networks (SAMS, 2002).

Z. Ghassemlooy and W. O. Popoola, Terrestrial free-space optical communications (InTech, 2010).

C. C. M. Uysal, Z. Ghassemlooy, A. Boucouvalas, and E. Udvary, eds., Optical Wireless Communications - An Emerging Technology (Springer, Switzerland, 2016).

W. Hameed, S. S. Muhammad, and N. M. Sheikh, “Integration scenarios for free space optics in next generation (4G) wireless networks,” in 7th International Symposium on Communication Systems Networks and Digital Signal Processing (CSNDSP), (IEEE, 2010), 571–575.

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Figures (11)

Fig. 1
Fig. 1 The principle of CPCB generation process. a(x): cross-section of the spatial modulation function; μ0: original DoC of the coherent beam; μ: DoC of the beam after DoC modulation.
Fig. 2
Fig. 2 Profile of the phase screen modulation function a(r) with fixed β and different slopes.
Fig. 3
Fig. 3 On-axis intensity evolution of CPCBs compared with GSM and coherent beams.
Fig. 4
Fig. 4 Evolution of the beam profile with propagation distance for (a) GSM beam, (b) SG1-CPCB, (c) G-CPCB, (d) coherent super-Gaussian beam.
Fig. 5
Fig. 5 Partition boundaries for 21 unevenly distributed phase-screen representation of slant path turbulence effects under H-V5-7 turbulence model.
Fig. 6
Fig. 6 On-axis scintillation and the corresponding mean SNR of (a, d) H = 1 km, (b, e) H = 2 km and (c, f) H = 5 km uplinks.
Fig. 7
Fig. 7 On-axis scintillation and the corresponding mean SNR of (a, d) 1 km, (b, e) 2 km and (c, f) 5 km downlinks.
Fig. 8
Fig. 8 Power-in-the-bucket as a function of DoC modulation index β of (a) 1 km uplink, (b) 2 km uplink, (c) 5 km (uplink), (d) 1 km downlink, (e) 2 km downlink, (f) 5 km downlink.
Fig. 9
Fig. 9 Scintillation and SNR versus modulation depth for the uplinks: (a, d) 1 km, (b, e) 2 km and (c, f) 5 km
Fig. 10
Fig. 10 Scintillation and SNR versus modulation depth for the downlinks: (a, d) 1 km, (b, e) 2 km and (c, f) 5 km
Fig. 11
Fig. 11 Off-axis scintillation and mean SNR of 1 km uplink (a,c) and downlink (b,d).

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

W 0 ( r 1 , r 2 )=S( r 1 , r 2 )× μ 0 ( r 1 , r 2 )= I 0 exp[ ( r 1 + r 2 ) 2 ω 0 2 ]×exp( | r 1 r 2 | 2 l c0 2 ),
μ 0 ( r 1 , r 2 )= exp{ i[ φ( r 1 )φ( r 2 ) ] } exp( | r 1 r 2 | 2 4π σ f 4 / σ r 2 ),
μ( r 1 , r 2 )= exp{ ia[ φ( r 1 )φ( r 2 ) ] } =exp( | r 1 r 2 | 2 ( l c0 /a) 2 ).
β= A a(r) U 0 (r)dr A U 0 (r)dr ,
U i+1 ( r i+1 )= exp( jkL/m ) iλL/m U i ( r i ) exp( jk 2L/m | r i+1 r i | 2 )d r i ,i[1,m]
a( r )=1exp( ( r ω 0 × N 2 /200 ) N/d ),
C n 2 (h)=8.15× 10 26 w 2 h 10 exp(h)+2.7× 10 16 exp(1.5h)+ C n 2 (0)exp(10h),
h i h i+1 [ C n 2 (h)] 6/11 dh = C 0 / (m+1) ,
ψ( r )= F 1 [ R G (f) Φ ψ 0.5 (f) ],
Φ ψ (f)0.0097 k 2 C n 2 L exp[ (f/ f m ) 2 ] ( f 2 + f 0 2 ) 11/6 ,
U i+1 ( r i+1 )= exp( jkL/m ) iλL/m U i ( r i ) exp[ j ψ i ( r i ) ]exp( jk 2L/m | r i+1 r i | 2 )d r i .
σ I 2 (D)= ( S I(r) d 2 r ) 2 S I(r) d 2 r 2 1= P S 2 P S 2 1,
SNR = ( P S0 P S SNR 0 2 + σ I 2 (D) ) 1/2 ,

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