Abstract

Hypersonic turbulence, causing the environment disturbance, is an important factor influencing optical propagation and optical communication. Based on the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function, we have derived the analytical expressions of the average intensity, the normalized propagation factor, and the normalized mean-squared beam width of Gaussian Schell-model beams in anisotropic hypersonic turbulence. The evolution properties demonstrate the severe beam expansion and beam quality degradation, and the influences of the source and turbulent parameters are discussed in detail. The comparison between anisotropic hypersonic turbulence and atmosphere turbulence is given, and it is proved that the influence of anisotropic hypersonic turbulence is much stronger. Our results play a guiding role in optical signal transmission in the turbulent environment induced by hypersonic aircraft.

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

Full Article  |  PDF Article
OSA Recommended Articles
Propagation properties of radially polarized multi-Gaussian Schell-model beams in oceanic turbulence

Zhenzhen Song, Zhiyuan Han, Jingfei Ye, Zhengjun Liu, Shutian Liu, and Bo Liu
J. Opt. Soc. Am. A 36(10) 1719-1726 (2019)

Evolution properties of Bessel-Gaussian Schell-model beams in non-Kolmogorov turbulence

Xiaoyang Wang, Mingwu Yao, Zhiliang Qiu, Xiang Yi, and Zengji Liu
Opt. Express 23(10) 12508-12523 (2015)

Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence

Hua-Feng Xu, Zhou Zhang, Jun Qu, and Wei Huang
Opt. Express 22(19) 22479-22489 (2014)

References

  • View by:
  • |
  • |
  • |

  1. X. Liu and J. Pu, “Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence,” Opt. Express 19(27), 26444–26450 (2011).
    [Crossref]
  2. X. Yi, Z. Liu, and P. Yue, “Inner-and outer-scale effects on the scintillation index of an optical wave propagating through moderate-to-strong non-Kolmogorov turbulence,” Opt. Express 20(4), 4232–4247 (2012).
    [Crossref]
  3. Y. Gu, O. Korotkova, and G. Gbur, “Scintillation of nonuniformly polarized beams in atmospheric turbulence,” Opt. Lett. 34(15), 2261–2263 (2009).
    [Crossref]
  4. W. Wen, Y. Jin, M. Hu, X. Liu, Y. Cai, C. Zou, M. Luo, L. Zhou, and X. Chu, “Beam wander of coherent and partially coherent Airy beam arrays in a turbulent atmosphere,” Opt. Commun. 415, 48–55 (2018).
    [Crossref]
  5. Y. Huang, A. Zeng, Z. Gao, and B. Zhang, “Beam wander of partially coherent array beams through non-Kolmogorov turbulence,” Opt. Lett. 40(8), 1619–1622 (2015).
    [Crossref]
  6. G. Gbur and E. Wolf, “Spreading of partially coherent beams in random media,” J. Opt. Soc. Am. A 19(8), 1592–1598 (2002).
    [Crossref]
  7. P. Zhou, Y. Ma, X. Wang, H. Zhao, and Z. Liu, “Average spreading of a Gaussian beam array in non-Kolmogorov turbulence,” Opt. Lett. 35(7), 1043–1045 (2010).
    [Crossref]
  8. L. Cui, “Analysis of angle of arrival fluctuations for optical waves’ propagation through weak anisotropic non-Kolmogorov turbulence,” Opt. Express 23(5), 6313–6325 (2015).
    [Crossref]
  9. X. Wang, M. Yao, Z. Qiu, X. Yi, and Z. Liu, “Evolution properties of Bessel-Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 23(10), 12508–12523 (2015).
    [Crossref]
  10. Y. Zhou, Y. Yuan, J. Qu, and W. Huang, “Propagation properties of Laguerre-Gaussian correlated Schell-model beam in non-Kolmogorov turbulence,” Opt. Express 24(10), 10682–10693 (2016).
    [Crossref]
  11. H. F. Xu, Z. Zhang, J. Qu, and W. Huang, “Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 22(19), 22479–22489 (2014).
    [Crossref]
  12. T. C. Lin and L. K. Sproul, “Influence of reentry turbulent plasma fluctuation on EM wave propagation,” Comput. Fluids 35(7), 703–711 (2006).
    [Crossref]
  13. M. Kim, M. Keidar, and I. D. Boyd, “Electrostatic manipulation of a hypersonic plasma layer: Images of the two-dimensional sheath,” IEEE Trans. Plasma Sci. 36(4), 1198–1199 (2008).
    [Crossref]
  14. J. T. Li and L. X. Guo, “Research on electromagnetic scattering characteristics of reentry vehicles and blackout forecast model,” J. Electromagnet. Wave. 26(13), 1767–1778 (2012).
    [Crossref]
  15. B. Bai, X. Li, Y. Liu, J. Xu, L. Shi, and K. Xie, “Effects of reentry plasma sheath on the polarization properties of obliquely incident EM waves,” IEEE Trans. Plasma Sci. 42(10), 3365–3372 (2014).
    [Crossref]
  16. Y. Zhao, S. Yi, L. Tian, L. He, and Z. Cheng, “The fractal measurement of experimental images of supersonic turbulent mixing layer,” Sci. China, Ser. G: Phys., Mech. Astron. 51(8), 1134–1143 (2008).
    [Crossref]
  17. J. Li, S. Yang, L. Guo, and M. Cheng, “Anisotropic power spectrum of refractive-index fluctuation in hypersonic turbulence,” Appl. Opt. 55(32), 9137–9144 (2016).
    [Crossref]
  18. J. Li, S. Yang, L. Guo, M. Cheng, and T. Gong, “Bit error rate performance of free-space optical link under effect of plasma sheath turbulence,” Opt. Commun. 396, 1–7 (2017).
    [Crossref]
  19. Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38(2), 91–93 (2013).
    [Crossref]
  20. E. Wolf and G. Gbur, “Spreading of partially coherent beams in random media,” J. Opt. Soc. Am. A 19(8), 1592–1598 (2002).
    [Crossref]
  21. J. Yu, Y. Chen, L. Liu, X. Liu, and Y. Cai, “Splitting and combining properties of an elegant Hermite-Gaussian correlated Schell-model beam in Kolmogorov and non-Kolmogorov turbulence,” Opt. Express 23(10), 13467–13481 (2015).
    [Crossref]
  22. X. Peng, L. Liu, Y. Cai, and Y. Baykal, “Statistical properties of a radially polarized twisted Gaussian Schell-model beam in an underwater turbulent medium,” J. Opt. Soc. Am. A 34(1), 133–139 (2017).
    [Crossref]
  23. M. Tang and D. Zhao, “Regions of spreading of Gaussian array beams propagating through oceanic turbulence,” Appl. Opt. 54(11), 3407–3411 (2015).
    [Crossref]
  24. J. Gao, Y. Zhu, D. L. Wang, Y. X. Zhang, Z. D. Hu, and M. J. Cheng, “Bessel-Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence,” Photonics Res. 4(2), 30–34 (2016).
    [Crossref]
  25. Y. Wu, Y. Zhang, and Y. Zhu, “Average intensity and directionality of partially coherent model beams propagating in turbulent ocean,” J. Opt. Soc. Am. A 33(8), 1451–1458 (2016).
    [Crossref]
  26. X. Huang, Z. Deng, X. Shi, Y. Bai, and X. Fu, “Average intensity and beam quality of optical coherence lattices in oceanic turbulence with anisotropy,” Opt. Express 26(4), 4786–4797 (2018).
    [Crossref]
  27. M. Tang, D. Zhao, X. Li, and J. Wang, “Propagation of radially polarized multi-cosine Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Commun. 407, 392–397 (2018).
    [Crossref]
  28. M. Tang and D. Zhao, “Propagation of multi-Gaussian Schell-model vortex beams in isotropic random media,” Opt. Express 23(25), 32766–32776 (2015).
    [Crossref]
  29. L. Cui, B. Xue, and F. Zhou, “Generalized anisotropic turbulence spectra and applications in the optical waves’ propagation through anisotropic turbulence,” Opt. Express 23(23), 30088–30103 (2015).
    [Crossref]
  30. M. Cheng, L. Guo, and Y. Zhang, “Scintillation and aperture averaging for Gaussian beams through non-Kolmogorov maritime atmospheric turbulence channels,” Opt. Express 23(25), 32606–32621 (2015).
    [Crossref]
  31. J. Li, T. Gong, L. Guo, and S. Yang, “Wave structure function of electromagnetic waves propagating through anisotropic hypersonic turbulence,” In 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2017), pp. 1843–1844.
  32. S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
    [Crossref]
  33. Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009).
    [Crossref]
  34. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products. (Academic, 2007).
  35. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti, and P. Vahimaa, “Spreading properties of beams radiated by partially coherent Schell-model sources,” J. Opt. Soc. Am. A 16(1), 106–112 (1999).
    [Crossref]
  36. X. Ji, X. Li, and G. Ji, “Propagation of second-order moments of general truncated beams in atmospheric turbulence,” New J. Phys. 13(10), 103006 (2011).
    [Crossref]
  37. Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation factors of multi-sinc Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 24(2), 1804–1813 (2016).
    [Crossref]
  38. S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photonics Res. 4(5), B1–B4 (2016).
    [Crossref]

2018 (3)

W. Wen, Y. Jin, M. Hu, X. Liu, Y. Cai, C. Zou, M. Luo, L. Zhou, and X. Chu, “Beam wander of coherent and partially coherent Airy beam arrays in a turbulent atmosphere,” Opt. Commun. 415, 48–55 (2018).
[Crossref]

M. Tang, D. Zhao, X. Li, and J. Wang, “Propagation of radially polarized multi-cosine Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Commun. 407, 392–397 (2018).
[Crossref]

X. Huang, Z. Deng, X. Shi, Y. Bai, and X. Fu, “Average intensity and beam quality of optical coherence lattices in oceanic turbulence with anisotropy,” Opt. Express 26(4), 4786–4797 (2018).
[Crossref]

2017 (2)

X. Peng, L. Liu, Y. Cai, and Y. Baykal, “Statistical properties of a radially polarized twisted Gaussian Schell-model beam in an underwater turbulent medium,” J. Opt. Soc. Am. A 34(1), 133–139 (2017).
[Crossref]

J. Li, S. Yang, L. Guo, M. Cheng, and T. Gong, “Bit error rate performance of free-space optical link under effect of plasma sheath turbulence,” Opt. Commun. 396, 1–7 (2017).
[Crossref]

2016 (6)

2015 (8)

L. Cui, “Analysis of angle of arrival fluctuations for optical waves’ propagation through weak anisotropic non-Kolmogorov turbulence,” Opt. Express 23(5), 6313–6325 (2015).
[Crossref]

Y. Huang, A. Zeng, Z. Gao, and B. Zhang, “Beam wander of partially coherent array beams through non-Kolmogorov turbulence,” Opt. Lett. 40(8), 1619–1622 (2015).
[Crossref]

M. Tang and D. Zhao, “Regions of spreading of Gaussian array beams propagating through oceanic turbulence,” Appl. Opt. 54(11), 3407–3411 (2015).
[Crossref]

X. Wang, M. Yao, Z. Qiu, X. Yi, and Z. Liu, “Evolution properties of Bessel-Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 23(10), 12508–12523 (2015).
[Crossref]

J. Yu, Y. Chen, L. Liu, X. Liu, and Y. Cai, “Splitting and combining properties of an elegant Hermite-Gaussian correlated Schell-model beam in Kolmogorov and non-Kolmogorov turbulence,” Opt. Express 23(10), 13467–13481 (2015).
[Crossref]

L. Cui, B. Xue, and F. Zhou, “Generalized anisotropic turbulence spectra and applications in the optical waves’ propagation through anisotropic turbulence,” Opt. Express 23(23), 30088–30103 (2015).
[Crossref]

M. Cheng, L. Guo, and Y. Zhang, “Scintillation and aperture averaging for Gaussian beams through non-Kolmogorov maritime atmospheric turbulence channels,” Opt. Express 23(25), 32606–32621 (2015).
[Crossref]

M. Tang and D. Zhao, “Propagation of multi-Gaussian Schell-model vortex beams in isotropic random media,” Opt. Express 23(25), 32766–32776 (2015).
[Crossref]

2014 (2)

B. Bai, X. Li, Y. Liu, J. Xu, L. Shi, and K. Xie, “Effects of reentry plasma sheath on the polarization properties of obliquely incident EM waves,” IEEE Trans. Plasma Sci. 42(10), 3365–3372 (2014).
[Crossref]

H. F. Xu, Z. Zhang, J. Qu, and W. Huang, “Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 22(19), 22479–22489 (2014).
[Crossref]

2013 (2)

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38(2), 91–93 (2013).
[Crossref]

2012 (2)

X. Yi, Z. Liu, and P. Yue, “Inner-and outer-scale effects on the scintillation index of an optical wave propagating through moderate-to-strong non-Kolmogorov turbulence,” Opt. Express 20(4), 4232–4247 (2012).
[Crossref]

J. T. Li and L. X. Guo, “Research on electromagnetic scattering characteristics of reentry vehicles and blackout forecast model,” J. Electromagnet. Wave. 26(13), 1767–1778 (2012).
[Crossref]

2011 (2)

X. Ji, X. Li, and G. Ji, “Propagation of second-order moments of general truncated beams in atmospheric turbulence,” New J. Phys. 13(10), 103006 (2011).
[Crossref]

X. Liu and J. Pu, “Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence,” Opt. Express 19(27), 26444–26450 (2011).
[Crossref]

2010 (1)

2009 (2)

2008 (2)

M. Kim, M. Keidar, and I. D. Boyd, “Electrostatic manipulation of a hypersonic plasma layer: Images of the two-dimensional sheath,” IEEE Trans. Plasma Sci. 36(4), 1198–1199 (2008).
[Crossref]

Y. Zhao, S. Yi, L. Tian, L. He, and Z. Cheng, “The fractal measurement of experimental images of supersonic turbulent mixing layer,” Sci. China, Ser. G: Phys., Mech. Astron. 51(8), 1134–1143 (2008).
[Crossref]

2006 (1)

T. C. Lin and L. K. Sproul, “Influence of reentry turbulent plasma fluctuation on EM wave propagation,” Comput. Fluids 35(7), 703–711 (2006).
[Crossref]

2002 (2)

1999 (1)

Bai, B.

B. Bai, X. Li, Y. Liu, J. Xu, L. Shi, and K. Xie, “Effects of reentry plasma sheath on the polarization properties of obliquely incident EM waves,” IEEE Trans. Plasma Sci. 42(10), 3365–3372 (2014).
[Crossref]

Bai, Y.

Baykal, Y.

Borghi, R.

Boyd, I. D.

M. Kim, M. Keidar, and I. D. Boyd, “Electrostatic manipulation of a hypersonic plasma layer: Images of the two-dimensional sheath,” IEEE Trans. Plasma Sci. 36(4), 1198–1199 (2008).
[Crossref]

Cai, Y.

Chen, Y.

Cheng, M.

Cheng, M. J.

J. Gao, Y. Zhu, D. L. Wang, Y. X. Zhang, Z. D. Hu, and M. J. Cheng, “Bessel-Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence,” Photonics Res. 4(2), 30–34 (2016).
[Crossref]

Cheng, Z.

Y. Zhao, S. Yi, L. Tian, L. He, and Z. Cheng, “The fractal measurement of experimental images of supersonic turbulent mixing layer,” Sci. China, Ser. G: Phys., Mech. Astron. 51(8), 1134–1143 (2008).
[Crossref]

Chu, X.

W. Wen, Y. Jin, M. Hu, X. Liu, Y. Cai, C. Zou, M. Luo, L. Zhou, and X. Chu, “Beam wander of coherent and partially coherent Airy beam arrays in a turbulent atmosphere,” Opt. Commun. 415, 48–55 (2018).
[Crossref]

Cincotti, G.

Cui, L.

Deng, Z.

Du, S.

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Eyyuboglu, H. T.

Fu, S.

S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photonics Res. 4(5), B1–B4 (2016).
[Crossref]

Fu, X.

Gao, C.

S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photonics Res. 4(5), B1–B4 (2016).
[Crossref]

Gao, J.

J. Gao, Y. Zhu, D. L. Wang, Y. X. Zhang, Z. D. Hu, and M. J. Cheng, “Bessel-Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence,” Photonics Res. 4(2), 30–34 (2016).
[Crossref]

Gao, Z.

Gbur, G.

Gong, T.

J. Li, S. Yang, L. Guo, M. Cheng, and T. Gong, “Bit error rate performance of free-space optical link under effect of plasma sheath turbulence,” Opt. Commun. 396, 1–7 (2017).
[Crossref]

J. Li, T. Gong, L. Guo, and S. Yang, “Wave structure function of electromagnetic waves propagating through anisotropic hypersonic turbulence,” In 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2017), pp. 1843–1844.

Gori, F.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products. (Academic, 2007).

Gu, Y.

Guo, L.

J. Li, S. Yang, L. Guo, M. Cheng, and T. Gong, “Bit error rate performance of free-space optical link under effect of plasma sheath turbulence,” Opt. Commun. 396, 1–7 (2017).
[Crossref]

J. Li, S. Yang, L. Guo, and M. Cheng, “Anisotropic power spectrum of refractive-index fluctuation in hypersonic turbulence,” Appl. Opt. 55(32), 9137–9144 (2016).
[Crossref]

M. Cheng, L. Guo, and Y. Zhang, “Scintillation and aperture averaging for Gaussian beams through non-Kolmogorov maritime atmospheric turbulence channels,” Opt. Express 23(25), 32606–32621 (2015).
[Crossref]

J. Li, T. Gong, L. Guo, and S. Yang, “Wave structure function of electromagnetic waves propagating through anisotropic hypersonic turbulence,” In 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2017), pp. 1843–1844.

Guo, L. X.

J. T. Li and L. X. Guo, “Research on electromagnetic scattering characteristics of reentry vehicles and blackout forecast model,” J. Electromagnet. Wave. 26(13), 1767–1778 (2012).
[Crossref]

He, L.

Y. Zhao, S. Yi, L. Tian, L. He, and Z. Cheng, “The fractal measurement of experimental images of supersonic turbulent mixing layer,” Sci. China, Ser. G: Phys., Mech. Astron. 51(8), 1134–1143 (2008).
[Crossref]

Hu, M.

W. Wen, Y. Jin, M. Hu, X. Liu, Y. Cai, C. Zou, M. Luo, L. Zhou, and X. Chu, “Beam wander of coherent and partially coherent Airy beam arrays in a turbulent atmosphere,” Opt. Commun. 415, 48–55 (2018).
[Crossref]

Hu, Z. D.

J. Gao, Y. Zhu, D. L. Wang, Y. X. Zhang, Z. D. Hu, and M. J. Cheng, “Bessel-Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence,” Photonics Res. 4(2), 30–34 (2016).
[Crossref]

Huang, W.

Huang, X.

Huang, Y.

Ji, G.

X. Ji, X. Li, and G. Ji, “Propagation of second-order moments of general truncated beams in atmospheric turbulence,” New J. Phys. 13(10), 103006 (2011).
[Crossref]

Ji, X.

X. Ji, X. Li, and G. Ji, “Propagation of second-order moments of general truncated beams in atmospheric turbulence,” New J. Phys. 13(10), 103006 (2011).
[Crossref]

Jin, Y.

W. Wen, Y. Jin, M. Hu, X. Liu, Y. Cai, C. Zou, M. Luo, L. Zhou, and X. Chu, “Beam wander of coherent and partially coherent Airy beam arrays in a turbulent atmosphere,” Opt. Commun. 415, 48–55 (2018).
[Crossref]

Keidar, M.

M. Kim, M. Keidar, and I. D. Boyd, “Electrostatic manipulation of a hypersonic plasma layer: Images of the two-dimensional sheath,” IEEE Trans. Plasma Sci. 36(4), 1198–1199 (2008).
[Crossref]

Kim, M.

M. Kim, M. Keidar, and I. D. Boyd, “Electrostatic manipulation of a hypersonic plasma layer: Images of the two-dimensional sheath,” IEEE Trans. Plasma Sci. 36(4), 1198–1199 (2008).
[Crossref]

Korotkova, O.

Li, J.

J. Li, S. Yang, L. Guo, M. Cheng, and T. Gong, “Bit error rate performance of free-space optical link under effect of plasma sheath turbulence,” Opt. Commun. 396, 1–7 (2017).
[Crossref]

J. Li, S. Yang, L. Guo, and M. Cheng, “Anisotropic power spectrum of refractive-index fluctuation in hypersonic turbulence,” Appl. Opt. 55(32), 9137–9144 (2016).
[Crossref]

J. Li, T. Gong, L. Guo, and S. Yang, “Wave structure function of electromagnetic waves propagating through anisotropic hypersonic turbulence,” In 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2017), pp. 1843–1844.

Li, J. T.

J. T. Li and L. X. Guo, “Research on electromagnetic scattering characteristics of reentry vehicles and blackout forecast model,” J. Electromagnet. Wave. 26(13), 1767–1778 (2012).
[Crossref]

Li, X.

M. Tang, D. Zhao, X. Li, and J. Wang, “Propagation of radially polarized multi-cosine Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Commun. 407, 392–397 (2018).
[Crossref]

B. Bai, X. Li, Y. Liu, J. Xu, L. Shi, and K. Xie, “Effects of reentry plasma sheath on the polarization properties of obliquely incident EM waves,” IEEE Trans. Plasma Sci. 42(10), 3365–3372 (2014).
[Crossref]

X. Ji, X. Li, and G. Ji, “Propagation of second-order moments of general truncated beams in atmospheric turbulence,” New J. Phys. 13(10), 103006 (2011).
[Crossref]

Liang, C.

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Lin, T. C.

T. C. Lin and L. K. Sproul, “Influence of reentry turbulent plasma fluctuation on EM wave propagation,” Comput. Fluids 35(7), 703–711 (2006).
[Crossref]

Liu, L.

Liu, S.

Liu, X.

Liu, Y.

B. Bai, X. Li, Y. Liu, J. Xu, L. Shi, and K. Xie, “Effects of reentry plasma sheath on the polarization properties of obliquely incident EM waves,” IEEE Trans. Plasma Sci. 42(10), 3365–3372 (2014).
[Crossref]

Liu, Z.

Luo, M.

W. Wen, Y. Jin, M. Hu, X. Liu, Y. Cai, C. Zou, M. Luo, L. Zhou, and X. Chu, “Beam wander of coherent and partially coherent Airy beam arrays in a turbulent atmosphere,” Opt. Commun. 415, 48–55 (2018).
[Crossref]

Ma, Y.

Mei, Z.

Peng, X.

Pu, J.

Qiu, Z.

Qu, J.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products. (Academic, 2007).

Santarsiero, M.

Shi, L.

B. Bai, X. Li, Y. Liu, J. Xu, L. Shi, and K. Xie, “Effects of reentry plasma sheath on the polarization properties of obliquely incident EM waves,” IEEE Trans. Plasma Sci. 42(10), 3365–3372 (2014).
[Crossref]

Shi, X.

Song, Z.

Sproul, L. K.

T. C. Lin and L. K. Sproul, “Influence of reentry turbulent plasma fluctuation on EM wave propagation,” Comput. Fluids 35(7), 703–711 (2006).
[Crossref]

Sun, Q.

Tang, M.

Tian, L.

Y. Zhao, S. Yi, L. Tian, L. He, and Z. Cheng, “The fractal measurement of experimental images of supersonic turbulent mixing layer,” Sci. China, Ser. G: Phys., Mech. Astron. 51(8), 1134–1143 (2008).
[Crossref]

Vahimaa, P.

Wang, D. L.

J. Gao, Y. Zhu, D. L. Wang, Y. X. Zhang, Z. D. Hu, and M. J. Cheng, “Bessel-Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence,” Photonics Res. 4(2), 30–34 (2016).
[Crossref]

Wang, J.

M. Tang, D. Zhao, X. Li, and J. Wang, “Propagation of radially polarized multi-cosine Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Commun. 407, 392–397 (2018).
[Crossref]

Wang, X.

Wen, W.

W. Wen, Y. Jin, M. Hu, X. Liu, Y. Cai, C. Zou, M. Luo, L. Zhou, and X. Chu, “Beam wander of coherent and partially coherent Airy beam arrays in a turbulent atmosphere,” Opt. Commun. 415, 48–55 (2018).
[Crossref]

Wolf, E.

Wu, Y.

Xie, K.

B. Bai, X. Li, Y. Liu, J. Xu, L. Shi, and K. Xie, “Effects of reentry plasma sheath on the polarization properties of obliquely incident EM waves,” IEEE Trans. Plasma Sci. 42(10), 3365–3372 (2014).
[Crossref]

Xu, H. F.

Xu, J.

B. Bai, X. Li, Y. Liu, J. Xu, L. Shi, and K. Xie, “Effects of reentry plasma sheath on the polarization properties of obliquely incident EM waves,” IEEE Trans. Plasma Sci. 42(10), 3365–3372 (2014).
[Crossref]

Xue, B.

Yang, S.

J. Li, S. Yang, L. Guo, M. Cheng, and T. Gong, “Bit error rate performance of free-space optical link under effect of plasma sheath turbulence,” Opt. Commun. 396, 1–7 (2017).
[Crossref]

J. Li, S. Yang, L. Guo, and M. Cheng, “Anisotropic power spectrum of refractive-index fluctuation in hypersonic turbulence,” Appl. Opt. 55(32), 9137–9144 (2016).
[Crossref]

J. Li, T. Gong, L. Guo, and S. Yang, “Wave structure function of electromagnetic waves propagating through anisotropic hypersonic turbulence,” In 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2017), pp. 1843–1844.

Yao, M.

Yi, S.

Y. Zhao, S. Yi, L. Tian, L. He, and Z. Cheng, “The fractal measurement of experimental images of supersonic turbulent mixing layer,” Sci. China, Ser. G: Phys., Mech. Astron. 51(8), 1134–1143 (2008).
[Crossref]

Yi, X.

Yu, J.

Yuan, Y.

Yue, P.

Zeng, A.

Zhang, B.

Zhang, Y.

Zhang, Y. X.

J. Gao, Y. Zhu, D. L. Wang, Y. X. Zhang, Z. D. Hu, and M. J. Cheng, “Bessel-Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence,” Photonics Res. 4(2), 30–34 (2016).
[Crossref]

Zhang, Z.

Zhao, D.

Zhao, H.

Zhao, Y.

Y. Zhao, S. Yi, L. Tian, L. He, and Z. Cheng, “The fractal measurement of experimental images of supersonic turbulent mixing layer,” Sci. China, Ser. G: Phys., Mech. Astron. 51(8), 1134–1143 (2008).
[Crossref]

Zhou, F.

Zhou, K.

Zhou, L.

W. Wen, Y. Jin, M. Hu, X. Liu, Y. Cai, C. Zou, M. Luo, L. Zhou, and X. Chu, “Beam wander of coherent and partially coherent Airy beam arrays in a turbulent atmosphere,” Opt. Commun. 415, 48–55 (2018).
[Crossref]

Zhou, P.

Zhou, Y.

Zhu, Y.

Y. Wu, Y. Zhang, and Y. Zhu, “Average intensity and directionality of partially coherent model beams propagating in turbulent ocean,” J. Opt. Soc. Am. A 33(8), 1451–1458 (2016).
[Crossref]

J. Gao, Y. Zhu, D. L. Wang, Y. X. Zhang, Z. D. Hu, and M. J. Cheng, “Bessel-Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence,” Photonics Res. 4(2), 30–34 (2016).
[Crossref]

Zou, C.

W. Wen, Y. Jin, M. Hu, X. Liu, Y. Cai, C. Zou, M. Luo, L. Zhou, and X. Chu, “Beam wander of coherent and partially coherent Airy beam arrays in a turbulent atmosphere,” Opt. Commun. 415, 48–55 (2018).
[Crossref]

Appl. Opt. (2)

Comput. Fluids (1)

T. C. Lin and L. K. Sproul, “Influence of reentry turbulent plasma fluctuation on EM wave propagation,” Comput. Fluids 35(7), 703–711 (2006).
[Crossref]

IEEE Trans. Plasma Sci. (2)

M. Kim, M. Keidar, and I. D. Boyd, “Electrostatic manipulation of a hypersonic plasma layer: Images of the two-dimensional sheath,” IEEE Trans. Plasma Sci. 36(4), 1198–1199 (2008).
[Crossref]

B. Bai, X. Li, Y. Liu, J. Xu, L. Shi, and K. Xie, “Effects of reentry plasma sheath on the polarization properties of obliquely incident EM waves,” IEEE Trans. Plasma Sci. 42(10), 3365–3372 (2014).
[Crossref]

J. Electromagnet. Wave. (1)

J. T. Li and L. X. Guo, “Research on electromagnetic scattering characteristics of reentry vehicles and blackout forecast model,” J. Electromagnet. Wave. 26(13), 1767–1778 (2012).
[Crossref]

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

New J. Phys. (1)

X. Ji, X. Li, and G. Ji, “Propagation of second-order moments of general truncated beams in atmospheric turbulence,” New J. Phys. 13(10), 103006 (2011).
[Crossref]

Opt. Commun. (3)

M. Tang, D. Zhao, X. Li, and J. Wang, “Propagation of radially polarized multi-cosine Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Commun. 407, 392–397 (2018).
[Crossref]

J. Li, S. Yang, L. Guo, M. Cheng, and T. Gong, “Bit error rate performance of free-space optical link under effect of plasma sheath turbulence,” Opt. Commun. 396, 1–7 (2017).
[Crossref]

W. Wen, Y. Jin, M. Hu, X. Liu, Y. Cai, C. Zou, M. Luo, L. Zhou, and X. Chu, “Beam wander of coherent and partially coherent Airy beam arrays in a turbulent atmosphere,” Opt. Commun. 415, 48–55 (2018).
[Crossref]

Opt. Express (13)

X. Liu and J. Pu, “Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence,” Opt. Express 19(27), 26444–26450 (2011).
[Crossref]

X. Yi, Z. Liu, and P. Yue, “Inner-and outer-scale effects on the scintillation index of an optical wave propagating through moderate-to-strong non-Kolmogorov turbulence,” Opt. Express 20(4), 4232–4247 (2012).
[Crossref]

L. Cui, “Analysis of angle of arrival fluctuations for optical waves’ propagation through weak anisotropic non-Kolmogorov turbulence,” Opt. Express 23(5), 6313–6325 (2015).
[Crossref]

X. Wang, M. Yao, Z. Qiu, X. Yi, and Z. Liu, “Evolution properties of Bessel-Gaussian Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 23(10), 12508–12523 (2015).
[Crossref]

Y. Zhou, Y. Yuan, J. Qu, and W. Huang, “Propagation properties of Laguerre-Gaussian correlated Schell-model beam in non-Kolmogorov turbulence,” Opt. Express 24(10), 10682–10693 (2016).
[Crossref]

H. F. Xu, Z. Zhang, J. Qu, and W. Huang, “Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 22(19), 22479–22489 (2014).
[Crossref]

M. Tang and D. Zhao, “Propagation of multi-Gaussian Schell-model vortex beams in isotropic random media,” Opt. Express 23(25), 32766–32776 (2015).
[Crossref]

L. Cui, B. Xue, and F. Zhou, “Generalized anisotropic turbulence spectra and applications in the optical waves’ propagation through anisotropic turbulence,” Opt. Express 23(23), 30088–30103 (2015).
[Crossref]

M. Cheng, L. Guo, and Y. Zhang, “Scintillation and aperture averaging for Gaussian beams through non-Kolmogorov maritime atmospheric turbulence channels,” Opt. Express 23(25), 32606–32621 (2015).
[Crossref]

J. Yu, Y. Chen, L. Liu, X. Liu, and Y. Cai, “Splitting and combining properties of an elegant Hermite-Gaussian correlated Schell-model beam in Kolmogorov and non-Kolmogorov turbulence,” Opt. Express 23(10), 13467–13481 (2015).
[Crossref]

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation factors of multi-sinc Schell-model beams in non-Kolmogorov turbulence,” Opt. Express 24(2), 1804–1813 (2016).
[Crossref]

X. Huang, Z. Deng, X. Shi, Y. Bai, and X. Fu, “Average intensity and beam quality of optical coherence lattices in oceanic turbulence with anisotropy,” Opt. Express 26(4), 4786–4797 (2018).
[Crossref]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009).
[Crossref]

Opt. Laser Technol. (1)

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[Crossref]

Opt. Lett. (4)

Photonics Res. (2)

S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photonics Res. 4(5), B1–B4 (2016).
[Crossref]

J. Gao, Y. Zhu, D. L. Wang, Y. X. Zhang, Z. D. Hu, and M. J. Cheng, “Bessel-Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence,” Photonics Res. 4(2), 30–34 (2016).
[Crossref]

Sci. China, Ser. G: Phys., Mech. Astron. (1)

Y. Zhao, S. Yi, L. Tian, L. He, and Z. Cheng, “The fractal measurement of experimental images of supersonic turbulent mixing layer,” Sci. China, Ser. G: Phys., Mech. Astron. 51(8), 1134–1143 (2008).
[Crossref]

Other (2)

J. Li, T. Gong, L. Guo, and S. Yang, “Wave structure function of electromagnetic waves propagating through anisotropic hypersonic turbulence,” In 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2017), pp. 1843–1844.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products. (Academic, 2007).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1. The normalized average intensity in hypersonic turbulence with $w_0=0.02\textrm {m}$, $\lambda =3.8\mu\textrm {m}$, $\xi _y=1$, $\delta _0=5\textrm {mm}$ for (a) propagation distance $z$, (b) outer scale $L_0$, (c) anisotropic parameter $\xi _x$ and (d) variance of the refractive-index fluctuation $<n_1^2>$.
Fig. 2.
Fig. 2. The normalized mean-squared beam width versus propagation distance under different source parameters with $L_0=0.1m$, $\xi _x=3$, $\xi _y=1$, $<n_1^2>=0.2\times 10^{-24}$ for (a) $\lambda =3.8\mu\textrm{m}$, $z=0.4\textrm {m}$, $\delta _0=5\textrm {mm}$ and (b) $\lambda =3.8\mu\textrm {m}$, $w_0=2\textrm {cm}$, $z=0.4\textrm {m}$.
Fig. 3.
Fig. 3. The normalized mean-squared beam width versus the variance of the refractive-index fluctuation under different hypersonic turbulent parameters with $w_0=2\textrm {cm}$, $\delta _0=5\textrm {mm}$, $z=0.4\textrm {m}$ for (a) the outer scale and (b) the anisotrpic parameter.
Fig. 4.
Fig. 4. The normalized propagation factor versus propagation distance under different source parameters with $L_0=0.1\textrm {m}$, $\xi _x=3$, $\xi _y=1$, $<n_1^2>=0.2\times 10^{-24}$ for (a) $\lambda =3.8\mu\textrm {m}$, $z=0.4\textrm {m}$, $\delta _0=5\textrm {mm}$ and (b) $\lambda =3.8\mu\textrm {m}$, $w_0=2\textrm {cm}$, $z=0.4\textrm {m}$.
Fig. 5.
Fig. 5. The normalized propagation factor under different turbulent parameters with $\lambda =3.8\mu\textrm {m}$, $w_0=2\textrm {cm}$, $\delta _0=5\textrm {mm}$, $z=0.4\textrm {m}$ for (a) $<n_1^2>=0.2\times 10^{-24}$, $\xi _x=3$, $\xi _y=1$ and (c) $<n_1^2>=0.2\times 10^{-24}$, $L_0=0.1\textrm {m}$, $\xi _y=1$.
Fig. 6.
Fig. 6. The spatial coherence radius versus the variance of the refractive-index fluctuation under different hypersonic turbulence parameters, for (a) and (b) anisotropic parameter, (c) the outer scale.
Fig. 7.
Fig. 7. The results comparison between anisotropic hypersonic turbulence ((a1)–(a3)) and atmosphere turbulence ((b1)–(b3)) with $\lambda =3.8\mu\textrm {m}$, $w_0=2\textrm {cm}$, $\delta _0=5\textrm {mm}$.

Equations (29)

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

W ( r 1 , r 2 , 0 ) = exp ( | r 1 | 2 + | r 2 | 2 4 w 0 2 ) exp [ ( r 1 r 2 ) 2 2 δ 0 2 ] ,
W ( ρ 1 , ρ 2 , z ) = ( k 2 π z ) 2 d 2 r 1 d 2 r 1 W ( r 1 , r 2 , 0 ) × exp ( i k 2 z [ ( ρ 1 r 1 ) 2 ( ρ 2 r 2 ) 2 ] ) × exp [ Ψ ( ρ 1 , r 1 ) + Ψ ( ρ 2 , r 2 ) ] ,
exp [ Ψ ( ρ 1 , r 1 ) + Ψ ( ρ 2 , r 2 ) ] = exp [ ( ρ 1 ρ 2 ) ( r 1 r 2 ) + ( r 1 r 2 ) 2 ρ 0 ξ 2 ] × exp [ ( ρ 1 ρ 2 ) 2 ρ 0 ξ 2 ] ,
ρ 0 ξ 2 = π 2 k 2 z 3 0 κ 3 ψ ~ a n ( κ ) d κ ,
ψ ~ a n ( κ ) = a 64 π < n 1 2 > L 0 2 ( m 1 ) ( 1 + 100 κ L 0 2 ) m exp ( κ κ 0 ) ,
ρ 0 ξ = [ 64 a 10 4 π 3 k 2 z n 1 2 L 0 2 ( m 1 ) ξ x 2 + ξ y 2 6 ξ x 3 ξ y 3 Γ ( 4 ) 1 L 0 8 ] 1 / 2 × [ ( Γ ( m 4 ) Γ ( m ) + Γ ( 4 m ) Γ ( 4 ) ( 1 100 L 0 2 κ 0 ) m 4 ) ] 1 / 2 ,
W ( r 1 , r 2 , 0 ) = W ( r , r d , 0 ) = W ( r + r d 2 , r r d 2 , 0 ) ,
[ Ψ ( ρ 1 , r 1 ) + Ψ ( ρ 1 , r 1 ) ] = 1 ρ 0 ξ 2 ( r d 2 + r d ρ d + ρ d 2 ) ,
W ( r 1 , r 2 , 0 ) = W ( r , r d + z k κ d , 0 ) = exp [ r 2 2 σ 2 ( 1 8 σ 2 + 1 2 δ 2 ) ( r d + z k κ d ) 2 ] ,
exp [ Ψ ( ρ 1 , r 1 ) + Ψ ( ρ 2 , r 2 ) ] = exp [ ( 3 ρ d 2 + 3 z k κ d ρ d + z 2 k 2 κ d 2 ) ρ 0 ξ 2 ] ,
W ( ρ 1 , ρ 2 , z ) = W ( ρ , ρ d , z ) = ( 1 2 π ) 2 d 2 r d 2 κ d × exp [ r 2 2 w 0 2 ( 1 8 w 0 2 + 1 2 δ 0 2 ) ( r d + z k κ d ) 2 ] × exp [ 1 ρ 0 ξ 2 ( 3 ρ d 2 + 3 z k κ d ρ d + z 2 k 2 κ d 2 ) ] × exp ( i ρ κ d + i r κ d ) ,
I ( ρ , z ) = w 0 2 k 2 2 a 0 z 2 exp ( a 1 2 ρ 2 4 a 0 ) ,
h ( ρ , θ , z ) = ( k 2 z ) 2 W ( ρ , ρ d , z ) exp ( i k θ ρ d ) d 2 ρ d ,
h ( ρ , θ , z ) = k 2 w 0 2 8 π 3 d 2 ρ d d 2 κ d exp ( b ρ d 2 c κ d 2 d ρ d κ d ) × exp ( i ρ κ d i k θ ρ d ) ,
ρ x n 1 ρ y n 2 θ x m 1 θ y m 2 = ρ x n 1 ρ y n 2 θ x m 1 θ y m 2 h ( ρ , θ , z ) d 2 ρ d 2 θ h ( ρ , θ , z ) d 2 ρ d 2 θ ,
M 2 ( z ) = k [ ρ 2 θ 2 ρ θ 2 ] 1 / 2 ,
ρ 2 = ρ x 2 + ρ y 2 ,
θ 2 = θ x 2 + θ y 2 ,
ρ θ = ρ x θ x + ρ y θ y ,
ρ 2 = 2 w 0 2 + ( 1 2 w 0 2 + 2 δ 0 2 ) z 2 k 2 + 4 z 2 k 2 ρ 0 ξ 2 ,
θ 2 = ( 1 2 w 0 2 + 2 δ 0 2 ) 1 k 2 + 12 k 2 ρ 0 ξ 2 ,
ρ θ = ( 1 2 w 0 2 + 2 δ 0 2 ) z k 2 + 6 z k 2 ρ 0 ξ 2 ,
M 2 ( z ) = ( 1 + 4 w 0 2 δ 0 2 + 24 w 0 2 ρ 0 ξ 2 + 2 z 2 k 2 ρ 0 ξ 2 w 0 2 + 8 z 2 k 2 ρ 0 ξ 2 δ 0 2 + 12 z 2 k 2 ρ 0 ξ 4 ) 1 / 2 ,
M N 2 ( z ) = 1 + 4 w 0 2 δ 0 2 + 24 w 0 2 ρ 0 ξ 2 + 2 z 2 k 2 ρ 0 ξ 2 w 0 2 + 8 z 2 k 2 ρ 0 ξ 2 δ 0 2 + 12 z 2 k 2 ρ 0 ξ 4 1 + 4 w 0 2 δ 0 2 ,
w N ( z ) = w ( z ) w ( 0 ) = 2 w 0 2 + ( 1 2 w 0 2 + 2 δ 0 2 ) z 2 k 2 + 4 z 2 k 2 ρ 0 ξ 2 2 w 0 2 .
M 2 ( z ) = 1 + 4 w 0 2 δ 0 2 + 8 π 2 k 2 T w 0 2 z + 2 π 2 T z 3 3 w 0 2 + 8 π 2 T z 3 3 δ 0 2 + 4 π 4 k 2 T 2 z 4 3 ,
w ( z ) = 2 2 w 0 2 + ( 1 2 w 0 2 + 2 δ 0 2 ) z 2 k 2 + 4 z 3 π 2 T 3 ,
T = A ( α ) 2 α 4 C ~ n 2 [ κ m 2 α ( 2 κ 0 2 2 κ m 2 + α κ m 2 ) exp ( κ 0 2 κ m 2 ) × Γ ( 2 α 2 , κ 0 2 κ m 2 ) 2 κ 0 4 α ] ,
ρ 0 = ( 3 π 2 k 2 z T ) 1 / 2 .

Metrics