Abstract

The mean irradiance profile has been widely applied in performance analysis and atmospheric channel research for free space optical communication; however, the modeling method and a closed-form expression of the mean irradiance profile under random jitter have rarely been discussed. To the best of our knowledge, this work presents a modeling method and a closed-form expression for a mean irradiance profile under random jitter through the ensemble average principle for the first time. We find that, with an increase in random jitter variance, the mean irradiance profile varied from an approximately Gaussian profile to a flat-topped profile to a hollow profile. These findings were verified using multilayer random phase screen simulations. The model of the mean irradiance profile under random jitter developed in this study will improve the accuracy of performance analysis and atmospheric channel research.

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

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References

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  14. D. Jiang, Y. Yang, J. Huang, Z. Yao, B. Zhu, and K. Qin, “A variable aperture method to simultaneously estimate atmospheric extinction coefficient and refractive index structure constant,” Opt. Commun. 320(1), 138–144 (2014).
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2018 (1)

F. Boufalah, L. Dalil-Essakali, L. Ez-Zariy, and A. Belafhal, “Introduction of generalized Bessel–Laguerre–Gaussian beams and its central intensity travelling a turbulent atmosphere,” Opt. Quantum Electron. 50(8), 305 (2018).
[Crossref]

2017 (4)

V. A. Kulikov and M. A. Vorontsov, “Analysis of the joint impact of atmospheric turbulence and refractivity on laser beam propagation,” Opt. Express 25(23), 28524–28535 (2017).
[Crossref]

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

H. Kaushal, G. Kaddoum, V. K. Jain, and S. Karc, “Experimental investigation of optimum beam size for FSO uplink,” Opt. Commun. 400, 106–114 (2017).
[Crossref]

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Comm. Surv. and Tutor. 19(1), 57–96 (2017).
[Crossref]

2016 (1)

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4(1), 1518–1547 (2016).
[Crossref]

2014 (4)

D. Geng, P. Du, W. Wang, G. Gao, T. Wang, and M. Gong, “Single laser free-space duplex communication system with adaptive threshold technique and BER analysis in weak turbulent atmosphere,” Opt. Lett. 39(13), 3950–3953 (2014).
[Crossref] [PubMed]

D. Jiang, Y. Yang, J. Huang, Z. Yao, B. Zhu, and K. Qin, “A variable aperture method to simultaneously estimate atmospheric extinction coefficient and refractive index structure constant,” Opt. Commun. 320(1), 138–144 (2014).
[Crossref]

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: a communication theory perspective,” IEEE Comm. Surv. and Tutor. 16(4), 2231–2258 (2014).
[Crossref]

A. Viswanath, H. Kaushal, V. K. Jain, and S. Kar, “Evaluation of performance of ground to satellite free space optical link under turbulence conditions for different intensity modulation schemes,” Proc. SPIE 8971, 897106 (2014).
[Crossref]

2010 (2)

Y. Ren, A. Dang, B. Luo, and H. Guo, “Capacities for long-distance free-space optical links under beam wander effects,” IEEE Photonics Technol. Lett. 22(14), 1069–1071 (2010).
[Crossref]

H. Guo, B. Luo, Y. Ren, S. Zhao, and A. Dang, “Influence of beam wander on uplink of ground-to-satellite laser communication and optimization for transmitter beam radius,” Opt. Lett. 35(12), 1977–1979 (2010).
[Crossref] [PubMed]

2009 (2)

A. Prokes, “Atmospheric effects on availability of free space optics systems,” Opt. Eng. 48(6), 066001 (2009).
[Crossref]

L. B. Stotts, B. Stadler, D. Hughes, P. Kolodzy, A. Pike, D. W. Young, J. E. Sluz, J. C. Juarez, B. Graves, D. Dougherty, J. Douglas, and T. Martin, “Optical communications in atmospheric turbulence,” Proc. SPIE 7464, 746403 (2009).
[Crossref]

2008 (1)

2007 (1)

2006 (1)

J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, “Atmospheric channel effects on free-space laser communication,” J. Opt. Fiber. Commun. Rep. 3(2), 111–158 (2006).
[Crossref]

2005 (2)

A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Rep. 2(4), 345–396 (2005).
[Crossref]

M. Toyoshima, S. Yamakawa, T. Yamawaki, K. Arai, M. R. García-Talavera, A. Alonso, S. Sodnik, and B. Demelenne, “Long-term statistics of laser beam propagation in an optical ground-to-geostationary satellite communications link,” IEEE Trans. Antenn. Propag. 53(2), 842–850 (2005).
[Crossref]

1995 (1)

Alonso, A.

M. Toyoshima, S. Yamakawa, T. Yamawaki, K. Arai, M. R. García-Talavera, A. Alonso, S. Sodnik, and B. Demelenne, “Long-term statistics of laser beam propagation in an optical ground-to-geostationary satellite communications link,” IEEE Trans. Antenn. Propag. 53(2), 842–850 (2005).
[Crossref]

Arai, K.

M. Toyoshima, S. Yamakawa, T. Yamawaki, K. Arai, M. R. García-Talavera, A. Alonso, S. Sodnik, and B. Demelenne, “Long-term statistics of laser beam propagation in an optical ground-to-geostationary satellite communications link,” IEEE Trans. Antenn. Propag. 53(2), 842–850 (2005).
[Crossref]

Banzer, P.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Belafhal, A.

F. Boufalah, L. Dalil-Essakali, L. Ez-Zariy, and A. Belafhal, “Introduction of generalized Bessel–Laguerre–Gaussian beams and its central intensity travelling a turbulent atmosphere,” Opt. Quantum Electron. 50(8), 305 (2018).
[Crossref]

Boufalah, F.

F. Boufalah, L. Dalil-Essakali, L. Ez-Zariy, and A. Belafhal, “Introduction of generalized Bessel–Laguerre–Gaussian beams and its central intensity travelling a turbulent atmosphere,” Opt. Quantum Electron. 50(8), 305 (2018).
[Crossref]

Boyd, R. W.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Dalil-Essakali, L.

F. Boufalah, L. Dalil-Essakali, L. Ez-Zariy, and A. Belafhal, “Introduction of generalized Bessel–Laguerre–Gaussian beams and its central intensity travelling a turbulent atmosphere,” Opt. Quantum Electron. 50(8), 305 (2018).
[Crossref]

Dan, Y.

Dang, A.

Y. Ren, A. Dang, B. Luo, and H. Guo, “Capacities for long-distance free-space optical links under beam wander effects,” IEEE Photonics Technol. Lett. 22(14), 1069–1071 (2010).
[Crossref]

H. Guo, B. Luo, Y. Ren, S. Zhao, and A. Dang, “Influence of beam wander on uplink of ground-to-satellite laser communication and optimization for transmitter beam radius,” Opt. Lett. 35(12), 1977–1979 (2010).
[Crossref] [PubMed]

Demelenne, B.

M. Toyoshima, S. Yamakawa, T. Yamawaki, K. Arai, M. R. García-Talavera, A. Alonso, S. Sodnik, and B. Demelenne, “Long-term statistics of laser beam propagation in an optical ground-to-geostationary satellite communications link,” IEEE Trans. Antenn. Propag. 53(2), 842–850 (2005).
[Crossref]

Dougherty, D.

L. B. Stotts, B. Stadler, D. Hughes, P. Kolodzy, A. Pike, D. W. Young, J. E. Sluz, J. C. Juarez, B. Graves, D. Dougherty, J. Douglas, and T. Martin, “Optical communications in atmospheric turbulence,” Proc. SPIE 7464, 746403 (2009).
[Crossref]

Douglas, J.

L. B. Stotts, B. Stadler, D. Hughes, P. Kolodzy, A. Pike, D. W. Young, J. E. Sluz, J. C. Juarez, B. Graves, D. Dougherty, J. Douglas, and T. Martin, “Optical communications in atmospheric turbulence,” Proc. SPIE 7464, 746403 (2009).
[Crossref]

Du, P.

Eaton, F. D.

J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, “Atmospheric channel effects on free-space laser communication,” J. Opt. Fiber. Commun. Rep. 3(2), 111–158 (2006).
[Crossref]

Elser, D.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Ez-Zariy, L.

F. Boufalah, L. Dalil-Essakali, L. Ez-Zariy, and A. Belafhal, “Introduction of generalized Bessel–Laguerre–Gaussian beams and its central intensity travelling a turbulent atmosphere,” Opt. Quantum Electron. 50(8), 305 (2018).
[Crossref]

Farid, A. A.

Gao, G.

García-Talavera, M. R.

M. Toyoshima, S. Yamakawa, T. Yamawaki, K. Arai, M. R. García-Talavera, A. Alonso, S. Sodnik, and B. Demelenne, “Long-term statistics of laser beam propagation in an optical ground-to-geostationary satellite communications link,” IEEE Trans. Antenn. Propag. 53(2), 842–850 (2005).
[Crossref]

Geng, D.

Gong, M.

Graves, B.

L. B. Stotts, B. Stadler, D. Hughes, P. Kolodzy, A. Pike, D. W. Young, J. E. Sluz, J. C. Juarez, B. Graves, D. Dougherty, J. Douglas, and T. Martin, “Optical communications in atmospheric turbulence,” Proc. SPIE 7464, 746403 (2009).
[Crossref]

Günthner, K.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Guo, H.

H. Guo, B. Luo, Y. Ren, S. Zhao, and A. Dang, “Influence of beam wander on uplink of ground-to-satellite laser communication and optimization for transmitter beam radius,” Opt. Lett. 35(12), 1977–1979 (2010).
[Crossref] [PubMed]

Y. Ren, A. Dang, B. Luo, and H. Guo, “Capacities for long-distance free-space optical links under beam wander effects,” IEEE Photonics Technol. Lett. 22(14), 1069–1071 (2010).
[Crossref]

Hammel, S. M.

J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, “Atmospheric channel effects on free-space laser communication,” J. Opt. Fiber. Commun. Rep. 3(2), 111–158 (2006).
[Crossref]

Hranilovic, S.

Huang, J.

D. Jiang, Y. Yang, J. Huang, Z. Yao, B. Zhu, and K. Qin, “A variable aperture method to simultaneously estimate atmospheric extinction coefficient and refractive index structure constant,” Opt. Commun. 320(1), 138–144 (2014).
[Crossref]

Hughes, D.

L. B. Stotts, B. Stadler, D. Hughes, P. Kolodzy, A. Pike, D. W. Young, J. E. Sluz, J. C. Juarez, B. Graves, D. Dougherty, J. Douglas, and T. Martin, “Optical communications in atmospheric turbulence,” Proc. SPIE 7464, 746403 (2009).
[Crossref]

Jain, V. K.

H. Kaushal, G. Kaddoum, V. K. Jain, and S. Karc, “Experimental investigation of optimum beam size for FSO uplink,” Opt. Commun. 400, 106–114 (2017).
[Crossref]

A. Viswanath, H. Kaushal, V. K. Jain, and S. Kar, “Evaluation of performance of ground to satellite free space optical link under turbulence conditions for different intensity modulation schemes,” Proc. SPIE 8971, 897106 (2014).
[Crossref]

Jiang, D.

D. Jiang, Y. Yang, J. Huang, Z. Yao, B. Zhu, and K. Qin, “A variable aperture method to simultaneously estimate atmospheric extinction coefficient and refractive index structure constant,” Opt. Commun. 320(1), 138–144 (2014).
[Crossref]

Juarez, J. C.

L. B. Stotts, B. Stadler, D. Hughes, P. Kolodzy, A. Pike, D. W. Young, J. E. Sluz, J. C. Juarez, B. Graves, D. Dougherty, J. Douglas, and T. Martin, “Optical communications in atmospheric turbulence,” Proc. SPIE 7464, 746403 (2009).
[Crossref]

Kaddoum, G.

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Comm. Surv. and Tutor. 19(1), 57–96 (2017).
[Crossref]

H. Kaushal, G. Kaddoum, V. K. Jain, and S. Karc, “Experimental investigation of optimum beam size for FSO uplink,” Opt. Commun. 400, 106–114 (2017).
[Crossref]

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4(1), 1518–1547 (2016).
[Crossref]

Kar, S.

A. Viswanath, H. Kaushal, V. K. Jain, and S. Kar, “Evaluation of performance of ground to satellite free space optical link under turbulence conditions for different intensity modulation schemes,” Proc. SPIE 8971, 897106 (2014).
[Crossref]

Karc, S.

H. Kaushal, G. Kaddoum, V. K. Jain, and S. Karc, “Experimental investigation of optimum beam size for FSO uplink,” Opt. Commun. 400, 106–114 (2017).
[Crossref]

Kaushal, H.

H. Kaushal, G. Kaddoum, V. K. Jain, and S. Karc, “Experimental investigation of optimum beam size for FSO uplink,” Opt. Commun. 400, 106–114 (2017).
[Crossref]

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Comm. Surv. and Tutor. 19(1), 57–96 (2017).
[Crossref]

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4(1), 1518–1547 (2016).
[Crossref]

A. Viswanath, H. Kaushal, V. K. Jain, and S. Kar, “Evaluation of performance of ground to satellite free space optical link under turbulence conditions for different intensity modulation schemes,” Proc. SPIE 8971, 897106 (2014).
[Crossref]

Khalighi, M. A.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: a communication theory perspective,” IEEE Comm. Surv. and Tutor. 16(4), 2231–2258 (2014).
[Crossref]

Kolodzy, P.

L. B. Stotts, B. Stadler, D. Hughes, P. Kolodzy, A. Pike, D. W. Young, J. E. Sluz, J. C. Juarez, B. Graves, D. Dougherty, J. Douglas, and T. Martin, “Optical communications in atmospheric turbulence,” Proc. SPIE 7464, 746403 (2009).
[Crossref]

Kulikov, V. A.

Lachinova, S. L.

J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, “Atmospheric channel effects on free-space laser communication,” J. Opt. Fiber. Commun. Rep. 3(2), 111–158 (2006).
[Crossref]

Lavery, M. P. J.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Leuchs, G.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Luo, B.

H. Guo, B. Luo, Y. Ren, S. Zhao, and A. Dang, “Influence of beam wander on uplink of ground-to-satellite laser communication and optimization for transmitter beam radius,” Opt. Lett. 35(12), 1977–1979 (2010).
[Crossref] [PubMed]

Y. Ren, A. Dang, B. Luo, and H. Guo, “Capacities for long-distance free-space optical links under beam wander effects,” IEEE Photonics Technol. Lett. 22(14), 1069–1071 (2010).
[Crossref]

Majumdar, A. K.

A. K. Majumdar, “Free-space laser communication performance in the atmospheric channel,” J. Opt. Fiber Commun. Rep. 2(4), 345–396 (2005).
[Crossref]

Marquardt, C.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Martin, T.

L. B. Stotts, B. Stadler, D. Hughes, P. Kolodzy, A. Pike, D. W. Young, J. E. Sluz, J. C. Juarez, B. Graves, D. Dougherty, J. Douglas, and T. Martin, “Optical communications in atmospheric turbulence,” Proc. SPIE 7464, 746403 (2009).
[Crossref]

Padgett, M. J.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Peuntinger, C.

M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
[Crossref] [PubMed]

Pike, A.

L. B. Stotts, B. Stadler, D. Hughes, P. Kolodzy, A. Pike, D. W. Young, J. E. Sluz, J. C. Juarez, B. Graves, D. Dougherty, J. Douglas, and T. Martin, “Optical communications in atmospheric turbulence,” Proc. SPIE 7464, 746403 (2009).
[Crossref]

Prokes, A.

A. Prokes, “Atmospheric effects on availability of free space optics systems,” Opt. Eng. 48(6), 066001 (2009).
[Crossref]

Qin, K.

D. Jiang, Y. Yang, J. Huang, Z. Yao, B. Zhu, and K. Qin, “A variable aperture method to simultaneously estimate atmospheric extinction coefficient and refractive index structure constant,” Opt. Commun. 320(1), 138–144 (2014).
[Crossref]

Ren, Y.

H. Guo, B. Luo, Y. Ren, S. Zhao, and A. Dang, “Influence of beam wander on uplink of ground-to-satellite laser communication and optimization for transmitter beam radius,” Opt. Lett. 35(12), 1977–1979 (2010).
[Crossref] [PubMed]

Y. Ren, A. Dang, B. Luo, and H. Guo, “Capacities for long-distance free-space optical links under beam wander effects,” IEEE Photonics Technol. Lett. 22(14), 1069–1071 (2010).
[Crossref]

Ricklin, J. C.

J. C. Ricklin, S. M. Hammel, F. D. Eaton, and S. L. Lachinova, “Atmospheric channel effects on free-space laser communication,” J. Opt. Fiber. Commun. Rep. 3(2), 111–158 (2006).
[Crossref]

Sluz, J. E.

L. B. Stotts, B. Stadler, D. Hughes, P. Kolodzy, A. Pike, D. W. Young, J. E. Sluz, J. C. Juarez, B. Graves, D. Dougherty, J. Douglas, and T. Martin, “Optical communications in atmospheric turbulence,” Proc. SPIE 7464, 746403 (2009).
[Crossref]

Sodnik, S.

M. Toyoshima, S. Yamakawa, T. Yamawaki, K. Arai, M. R. García-Talavera, A. Alonso, S. Sodnik, and B. Demelenne, “Long-term statistics of laser beam propagation in an optical ground-to-geostationary satellite communications link,” IEEE Trans. Antenn. Propag. 53(2), 842–850 (2005).
[Crossref]

Stadler, B.

L. B. Stotts, B. Stadler, D. Hughes, P. Kolodzy, A. Pike, D. W. Young, J. E. Sluz, J. C. Juarez, B. Graves, D. Dougherty, J. Douglas, and T. Martin, “Optical communications in atmospheric turbulence,” Proc. SPIE 7464, 746403 (2009).
[Crossref]

Stotts, L. B.

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M. Toyoshima, S. Yamakawa, T. Yamawaki, K. Arai, M. R. García-Talavera, A. Alonso, S. Sodnik, and B. Demelenne, “Long-term statistics of laser beam propagation in an optical ground-to-geostationary satellite communications link,” IEEE Trans. Antenn. Propag. 53(2), 842–850 (2005).
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A. Viswanath, H. Kaushal, V. K. Jain, and S. Kar, “Evaluation of performance of ground to satellite free space optical link under turbulence conditions for different intensity modulation schemes,” Proc. SPIE 8971, 897106 (2014).
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L. B. Stotts, B. Stadler, D. Hughes, P. Kolodzy, A. Pike, D. W. Young, J. E. Sluz, J. C. Juarez, B. Graves, D. Dougherty, J. Douglas, and T. Martin, “Optical communications in atmospheric turbulence,” Proc. SPIE 7464, 746403 (2009).
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Yura, H. T.

Zhang, B.

Zhao, S.

Zhu, B.

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H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Comm. Surv. and Tutor. 19(1), 57–96 (2017).
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Y. Ren, A. Dang, B. Luo, and H. Guo, “Capacities for long-distance free-space optical links under beam wander effects,” IEEE Photonics Technol. Lett. 22(14), 1069–1071 (2010).
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M. Toyoshima, S. Yamakawa, T. Yamawaki, K. Arai, M. R. García-Talavera, A. Alonso, S. Sodnik, and B. Demelenne, “Long-term statistics of laser beam propagation in an optical ground-to-geostationary satellite communications link,” IEEE Trans. Antenn. Propag. 53(2), 842–850 (2005).
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H. Kaushal, G. Kaddoum, V. K. Jain, and S. Karc, “Experimental investigation of optimum beam size for FSO uplink,” Opt. Commun. 400, 106–114 (2017).
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A. Viswanath, H. Kaushal, V. K. Jain, and S. Kar, “Evaluation of performance of ground to satellite free space optical link under turbulence conditions for different intensity modulation schemes,” Proc. SPIE 8971, 897106 (2014).
[Crossref]

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M. P. J. Lavery, C. Peuntinger, K. Günthner, P. Banzer, D. Elser, R. W. Boyd, M. J. Padgett, C. Marquardt, and G. Leuchs, “Free-space propagation of high-dimensional structured optical fields in an urban environment,” Sci. Adv. 3(10), e1700552 (2017).
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Figures (6)

Fig. 1
Fig. 1 Schematic of the concept of the model of the mean irradiance profile under random jitter.
Fig. 2
Fig. 2 Procedure for obtaining the mean irradiance profile under random jitter.
Fig. 3
Fig. 3 Simulation validation under random jitter with varied standard variance.
Fig. 4
Fig. 4 Comparison of the results under random jitter with small variance for model validation.
Fig. 5
Fig. 5 The change of mean irradiance profile under large random jitter variance.
Fig. 6
Fig. 6 Mean irradiance at the propagation optical axis decreases with increasing random jitter.

Equations (11)

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I 0 (r,L) = W 0 2 W LT 2 exp( 2 r 2 W LT 2 ),
p(l)=f( l L ) 1 L = l L 2 σ θ 2 exp( l 2 2 L 2 σ θ 2 )= l W θ 2 exp( l 2 2 W θ 2 ).
I(r,L) =0.5 0 [ I 0 (r+l,L) + I 0 (rl,L) ] p(l)dl.
I(r,L) = W 0 2 2 W LT 2 0 { exp[ 2 (r+l) 2 W LT 2 ]+exp[ 2 (rl) 2 W LT 2 ] } lexp( l 2 W θ 2 ) W θ 2 dl .
I( r,L ) = W 0 2 exp( 2 r 2 W LT 2 ) ( W LT 2 +4 W θ 2 ) 2 ×[ W LT 2 +4 W θ 2 +2 2π W θ 2 r 4 W LT 2 + 1 W θ 2 exp( 8 W θ 2 r 2 W LT 4 +4 W LT 2 W θ 2 )erf( 2 2 r W LT 2 4 W LT 2 + 1 W θ 2 ) ].
U[x,y,(i+1)Δz]= F 1 { F{ U(x,y,iΔz)exp[ iΔϕ( x,y ) ] }exp( ikΔzi κ x 2 + κ y 2 2k Δz ) },
U ^ j [x,y,(i+1)Δz]=U[x θ xj (i+1)Δz,y θ yj (i+1)Δz,(i+1)Δz],
I( r,L ) = 1 M j=1 M | U ^ j [x,y,L] | 2 .
I(r,L) = W 0 2 W S 2 exp( 2 r 2 W S 2 ),
I( r,L ) = 2 W 0 2 ( 1 2 r 2 W LT 2 ) ( W LT 2 +4 W θ 2 ) 2 [ W LT 2 +4 W θ 2 + 16 W θ 2 r 2 W LT 2 ( 1+ 8 W θ 2 r 2 W LT 4 +4 W LT 2 W θ 2 ) ].
d 2 I( r,L ) d r 2 | r=0 = 8 W 0 2 ( W LT 2 4 W θ 2 ) W LT 2 ( W LT 2 +4 W θ 2 ) 2 ,

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