W. Miller, Jr., Symmetry and Separation of Variables (Addison-Wesley Publ. Co., 1977).
Google Scholar
D. L. Andrews, Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic Press, New York, 2008).
Google Scholar
V. P. Aksenov and Ch. E. Pogutsa, “The effect of optical vortex on random Laguerre–Gauss shifts of a laser beam propagating in a turbulent atmosphere,” Atmos. Ocean. Opt. 26 (1), 13–17 (2013).
Article
Google Scholar
V.A. Banakh and A. V. Falits, “Turbulent broadening of Laguerre-Gaussian beam in the atmosphere,” Opt. Spectrosc. 117 (6), 942–948 (2014).
ADS
Article
Google Scholar
A. V. Falits, “The wander and optical scintillation of focused Laguerre–Gaussian beams in turbulent atmosphere,” Opt. Atmos. Okeana 28 (9), 763–771 (2015).
Google Scholar
V. A. Banakh and L. O. Gerasimova, “Diffraction of short-pulse Laguerre–Gaussian beams,” Atmos. Ocean. Opt. 29 (5), 441–446 (2016).
Article
Google Scholar
D. A. Marakasov and D. S. Rychkov, “Estimate of the change in the effective beam width by the streamline method for axisymmetric laser beams in a turbulent atmosphere,” Atmos. Ocean. Opt. 29 (5), 447–451 (2016).
Article
Google Scholar
V. A. Banakh, L. O. Gerasimova, and A. V. Falits, “Statistics of pulsed Laguerre–Gaussian beams in the turbulent atmosphere,” Opt. Atmos. Okeana 29 (5), 369–376 (2016).
Google Scholar
Ch. Xie, R. Giust, V. Jukna, L. Furfaro, M. Jacquot, P. Lacourt, L. Froehly, J. Dudley, A. Couairon, and F. Courvoisier, “Light trajectory in Bessel–Gauss vortex beams,” J. Opt. Soc. Am., A 32 (7), 1313–1316 (2015).
ADS
Article
Google Scholar
P. Birch, I. Ituen, R. Young, and Ch. Chatwin, “Longdistance Bessel beam propagation through Kolmogorov turbulence,” J. Opt. Soc. Am., A 32 (11), 2066–2073 (2015).
ADS
Article
Google Scholar
M. Cheng, L. Guo, J. Li, and Q. Huang, “Propagation properties of an optical vortex carried by a Bessel–Gaussian beam in anisotropic turbulence,” J. Opt. Soc. Am., A 33 (8), 1442–1450 (2016).
ADS
Article
Google Scholar
Sh. Chen, Sh. Li, Y. Zhao, J. Liu, L. Zhu, A. Wang, J. Du, L. Shen, J. Wang, “Demonstration of 20-Gbit/s high-speed Bessel beam encoding/decoding link with adaptive turbulence compensation,” Opt. Lett. 41 (20), 4680–4683 (2016).
ADS
Article
Google Scholar
Y. Zhang, D. Ma, X. Yuan, and Z. Zhou, “Numerical investigation of flat-topped vortex hollow beams and Bessel beams propagating in a turbulent atmosphere,” Appl. Opt. 55 (32), 9211–9216 (2016).
ADS
Article
Google Scholar
T. Doster and A. T. Watnik, “Laguerre–Gauss and Bessel–Gauss beams propagation through turbulence, Analysis of channel efficiency,” Appl. Opt. 55 (36), 10239–10246 (2016).
ADS
Article
Google Scholar
M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1970), 4th ed.
Google Scholar
E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, Cambridge, 2007).
MATH
Google Scholar
G. Gbur and T. D. Visser, “The structure of partially coherent fields,” Prog. Opt. 55, 285–341 (2010).
Article
Google Scholar
G. V. Bogatyryova, Ch. V. Fel’de, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28 (11), 878–880 (2003).
ADS
Article
Google Scholar
G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222 (1-6), 117–125 (2003).
ADS
Article
Google Scholar
G. Gbur, T. D. Visser, and E. Wolf, “Hidden” singularities in partially coherent wavefields,” J. Opt. A, Pure Appl. Opt. 6 (5), 239–S242 (2004).
ADS
Article
Google Scholar
I. D. Maleev, D. M. Palacios, A. S. Marathay, and G. A. Swartzlander, “Spatial correlation vortices in partially coherent light: Theory,” J. Opt. Soc. Am. 21 (11), 1895–1900.
Ch. Ding, L. Pan, and B. Lu, “Phase singularities and spectral changes of spectrally partially coherent higherorder Bessel–Gauss pulsed beams,” J. Opt. Soc. Am., A 26 (12), 2654–2661 (2009).
ADS
Article
Google Scholar
H. T. Eyyuboglu, Y. Baykal, and Y. Cai, “Complex degree of coherence for partially coherent general beams in atmospheric turbulence,” J. Opt. Soc. Amer., A 24 (9), 2891–2901 (2007).
ADS
Article
Google Scholar
R. Martinez-Herrero and A. Manjavacas, “Overall second-order parametric characterization of light beams propagating through spiral phase elements,” Opt. Commun. 282 (4), 473–477 (2009).
ADS
Article
Google Scholar
R. Borghi, M. Santarsiero, and F. Gori, “Axial intensity of apertured Bessel beams,” J. Opt. Soc. Am., A 14 (1), 23–26 (1997).
ADS
Article
Google Scholar
B. Chen, Z. Chen, and J. Pu, “Propagation of partially coherent Bessel–Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40 (6), 820–827 (2008).
ADS
Article
Google Scholar
K. Zhu, G. Zhou, X. Li, X. Zheng, and H. Tang, “Propagation of Bessel–Gaussian beams with optical vortices in turbulent atmosphere,” Opt. Express 16 (26), 21315–21320 (2008).
ADS
Article
Google Scholar