H. Deng, X. Ji, X. Li, H. Zhang, X. Wang, and Y. Zhang, “Effect of spatial coherence on laser beam self-focusing from orbit to the ground in the atmosphere,” Opt. Express 24(13), 14429–14437 (2016).

[Crossref]
[PubMed]

X. Ji, H. Chen, and G. Ji, “Characteristics of annular beams propagating through atmospheric turbulence along a downlink path and an uplink path,” Appl. Phys. B 122(8), 221 (2016).

[Crossref]

S. V. Chekalin and V. P. Kandidov, “From self-focusing light beams to femtosecond laser pulse filamentation,” Phys. Uspekhi 56(2), 123–140 (2013).

[Crossref]

L. Dou, X. Ji, and P. Li, “Propagation of partially coherent annular beams with decentered field in turbulence along a slant path,” Opt. Express 20(8), 8417–8430 (2012).

[Crossref]
[PubMed]

C. A. Palla, C. Pacheco, and M. E. Carrín, “Production of structured lipids by acidolysis with immobilized Rhizomucor miehei lipases: selection of suitable reaction conditions,” J. Mol. Catal., B Enzym. 76, 106–115 (2012).

[Crossref]

A. M. Rubenchik, S. K. Turitsyn, and M. P. Fedoruk, “Modulation instability in high power laser amplifiers,” Opt. Express 18(2), 1380–1388 (2010).

[Crossref]
[PubMed]

H. Gerçekcioğlu, Y. Baykal, and C. Nakiboğlu, “Annular beam scintillations in strong turbulence,” J. Opt. Soc. Am. A 27(8), 1834–1839 (2010).

[Crossref]
[PubMed]

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Laser beam self-focusing in the atmosphere,” Phys. Rev. Lett. 102(23), 233902 (2009).

[Crossref]
[PubMed]

S. Gladysz, J. C. Christou, L. W. Bradford, and L. C. Roberts, “Temporal Variability and Statistics of the Strehl Ratio in Adaptive-Optics,” Publ. Astron. Soc. Pac. 120(872), 1132–1143 (2008).

[Crossref]

F. E. S. Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE 5160, 86–97 (2004).

[Crossref]

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, “Compensation of nonlinear self-focusing in high-power lasers,” IEEE J. Quantum Electron. 36(6), 687–691 (2000).

[Crossref]

A. E. Siegman, “How to (maybe) measure laser beam quality,” OSA Trends Opt. Phonotic Ser. 17, 184–199 (1998).

J. T. Hunt, J. A. Glaze, W. W. Simmons, and P. A. Renard, “Suppression of self-focusing through low-pass spatial filtering and relay imaging,” Appl. Opt. 17(13), 2053–2057 (1978).

[Crossref]
[PubMed]

J. A. Fleck, J. R. Morris, and E. S. Bliss, “Small-scale self-focusing effects in a high-power glass laser amplifier,” IEEE J. Quantum. Electron. 14(5), 353–363 (1978).

[Crossref]

S. N. Vlasov, V. A. Petrishev, and V. I. Talanov, “Average description of wave beams in linear and nonlinear media,” Radiophys Quant. El. 14(9), 1062–1070 (1974).

[Crossref]

R. H. Hardin and F. D. Tappert, “Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equation,” SIAM Rev. Chronicles 15(2), 805–809 (1973).

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).

[Crossref]

F. E. S. Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE 5160, 86–97 (2004).

[Crossref]

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, “Compensation of nonlinear self-focusing in high-power lasers,” IEEE J. Quantum Electron. 36(6), 687–691 (2000).

[Crossref]

J. A. Fleck, J. R. Morris, and E. S. Bliss, “Small-scale self-focusing effects in a high-power glass laser amplifier,” IEEE J. Quantum. Electron. 14(5), 353–363 (1978).

[Crossref]

S. Gladysz, J. C. Christou, L. W. Bradford, and L. C. Roberts, “Temporal Variability and Statistics of the Strehl Ratio in Adaptive-Optics,” Publ. Astron. Soc. Pac. 120(872), 1132–1143 (2008).

[Crossref]

C. A. Palla, C. Pacheco, and M. E. Carrín, “Production of structured lipids by acidolysis with immobilized Rhizomucor miehei lipases: selection of suitable reaction conditions,” J. Mol. Catal., B Enzym. 76, 106–115 (2012).

[Crossref]

S. V. Chekalin and V. P. Kandidov, “From self-focusing light beams to femtosecond laser pulse filamentation,” Phys. Uspekhi 56(2), 123–140 (2013).

[Crossref]

X. Ji, H. Chen, and G. Ji, “Characteristics of annular beams propagating through atmospheric turbulence along a downlink path and an uplink path,” Appl. Phys. B 122(8), 221 (2016).

[Crossref]

S. Gladysz, J. C. Christou, L. W. Bradford, and L. C. Roberts, “Temporal Variability and Statistics of the Strehl Ratio in Adaptive-Optics,” Publ. Astron. Soc. Pac. 120(872), 1132–1143 (2008).

[Crossref]

H. Deng, X. Ji, X. Li, H. Zhang, X. Wang, and Y. Zhang, “Effect of spatial coherence on laser beam self-focusing from orbit to the ground in the atmosphere,” Opt. Express 24(13), 14429–14437 (2016).

[Crossref]
[PubMed]

H. Deng, X. Ji, X. Li, and X. Wang, “Effect of spherical aberration on laser beam self-focusing in the atmosphere,” Opt. Lett. 40(16), 3881–3884 (2015).

[Crossref]
[PubMed]

A. M. Rubenchik, S. K. Turitsyn, and M. P. Fedoruk, “Modulation instability in high power laser amplifiers,” Opt. Express 18(2), 1380–1388 (2010).

[Crossref]
[PubMed]

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Laser beam self-focusing in the atmosphere,” Phys. Rev. Lett. 102(23), 233902 (2009).

[Crossref]
[PubMed]

J. A. Fleck, J. R. Morris, and E. S. Bliss, “Small-scale self-focusing effects in a high-power glass laser amplifier,” IEEE J. Quantum. Electron. 14(5), 353–363 (1978).

[Crossref]

S. Gladysz, J. C. Christou, L. W. Bradford, and L. C. Roberts, “Temporal Variability and Statistics of the Strehl Ratio in Adaptive-Optics,” Publ. Astron. Soc. Pac. 120(872), 1132–1143 (2008).

[Crossref]

R. H. Hardin and F. D. Tappert, “Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equation,” SIAM Rev. Chronicles 15(2), 805–809 (1973).

X. Ji, H. Chen, and G. Ji, “Characteristics of annular beams propagating through atmospheric turbulence along a downlink path and an uplink path,” Appl. Phys. B 122(8), 221 (2016).

[Crossref]

X. Ji, H. Chen, and G. Ji, “Characteristics of annular beams propagating through atmospheric turbulence along a downlink path and an uplink path,” Appl. Phys. B 122(8), 221 (2016).

[Crossref]

H. Deng, X. Ji, X. Li, H. Zhang, X. Wang, and Y. Zhang, “Effect of spatial coherence on laser beam self-focusing from orbit to the ground in the atmosphere,” Opt. Express 24(13), 14429–14437 (2016).

[Crossref]
[PubMed]

H. Deng, X. Ji, X. Li, and X. Wang, “Effect of spherical aberration on laser beam self-focusing in the atmosphere,” Opt. Lett. 40(16), 3881–3884 (2015).

[Crossref]
[PubMed]

L. Dou, X. Ji, and P. Li, “Propagation of partially coherent annular beams with decentered field in turbulence along a slant path,” Opt. Express 20(8), 8417–8430 (2012).

[Crossref]
[PubMed]

S. V. Chekalin and V. P. Kandidov, “From self-focusing light beams to femtosecond laser pulse filamentation,” Phys. Uspekhi 56(2), 123–140 (2013).

[Crossref]

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).

[Crossref]

H. Deng, X. Ji, X. Li, H. Zhang, X. Wang, and Y. Zhang, “Effect of spatial coherence on laser beam self-focusing from orbit to the ground in the atmosphere,” Opt. Express 24(13), 14429–14437 (2016).

[Crossref]
[PubMed]

H. Deng, X. Ji, X. Li, and X. Wang, “Effect of spherical aberration on laser beam self-focusing in the atmosphere,” Opt. Lett. 40(16), 3881–3884 (2015).

[Crossref]
[PubMed]

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, “Compensation of nonlinear self-focusing in high-power lasers,” IEEE J. Quantum Electron. 36(6), 687–691 (2000).

[Crossref]

J. A. Fleck, J. R. Morris, and E. S. Bliss, “Small-scale self-focusing effects in a high-power glass laser amplifier,” IEEE J. Quantum. Electron. 14(5), 353–363 (1978).

[Crossref]

C. A. Palla, C. Pacheco, and M. E. Carrín, “Production of structured lipids by acidolysis with immobilized Rhizomucor miehei lipases: selection of suitable reaction conditions,” J. Mol. Catal., B Enzym. 76, 106–115 (2012).

[Crossref]

C. A. Palla, C. Pacheco, and M. E. Carrín, “Production of structured lipids by acidolysis with immobilized Rhizomucor miehei lipases: selection of suitable reaction conditions,” J. Mol. Catal., B Enzym. 76, 106–115 (2012).

[Crossref]

S. N. Vlasov, V. A. Petrishev, and V. I. Talanov, “Average description of wave beams in linear and nonlinear media,” Radiophys Quant. El. 14(9), 1062–1070 (1974).

[Crossref]

S. Gladysz, J. C. Christou, L. W. Bradford, and L. C. Roberts, “Temporal Variability and Statistics of the Strehl Ratio in Adaptive-Optics,” Publ. Astron. Soc. Pac. 120(872), 1132–1143 (2008).

[Crossref]

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, “Compensation of nonlinear self-focusing in high-power lasers,” IEEE J. Quantum Electron. 36(6), 687–691 (2000).

[Crossref]

A. M. Rubenchik, S. K. Turitsyn, and M. P. Fedoruk, “Modulation instability in high power laser amplifiers,” Opt. Express 18(2), 1380–1388 (2010).

[Crossref]
[PubMed]

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Laser beam self-focusing in the atmosphere,” Phys. Rev. Lett. 102(23), 233902 (2009).

[Crossref]
[PubMed]

A. E. Siegman, “How to (maybe) measure laser beam quality,” OSA Trends Opt. Phonotic Ser. 17, 184–199 (1998).

S. N. Vlasov, V. A. Petrishev, and V. I. Talanov, “Average description of wave beams in linear and nonlinear media,” Radiophys Quant. El. 14(9), 1062–1070 (1974).

[Crossref]

R. H. Hardin and F. D. Tappert, “Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equation,” SIAM Rev. Chronicles 15(2), 805–809 (1973).

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, “Compensation of nonlinear self-focusing in high-power lasers,” IEEE J. Quantum Electron. 36(6), 687–691 (2000).

[Crossref]

A. M. Rubenchik, S. K. Turitsyn, and M. P. Fedoruk, “Modulation instability in high power laser amplifiers,” Opt. Express 18(2), 1380–1388 (2010).

[Crossref]
[PubMed]

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Laser beam self-focusing in the atmosphere,” Phys. Rev. Lett. 102(23), 233902 (2009).

[Crossref]
[PubMed]

F. E. S. Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE 5160, 86–97 (2004).

[Crossref]

S. N. Vlasov, V. A. Petrishev, and V. I. Talanov, “Average description of wave beams in linear and nonlinear media,” Radiophys Quant. El. 14(9), 1062–1070 (1974).

[Crossref]

H. Deng, X. Ji, X. Li, H. Zhang, X. Wang, and Y. Zhang, “Effect of spatial coherence on laser beam self-focusing from orbit to the ground in the atmosphere,” Opt. Express 24(13), 14429–14437 (2016).

[Crossref]
[PubMed]

H. Deng, X. Ji, X. Li, and X. Wang, “Effect of spherical aberration on laser beam self-focusing in the atmosphere,” Opt. Lett. 40(16), 3881–3884 (2015).

[Crossref]
[PubMed]

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, “Compensation of nonlinear self-focusing in high-power lasers,” IEEE J. Quantum Electron. 36(6), 687–691 (2000).

[Crossref]

X. Ji, H. Chen, and G. Ji, “Characteristics of annular beams propagating through atmospheric turbulence along a downlink path and an uplink path,” Appl. Phys. B 122(8), 221 (2016).

[Crossref]

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, “Compensation of nonlinear self-focusing in high-power lasers,” IEEE J. Quantum Electron. 36(6), 687–691 (2000).

[Crossref]

J. A. Fleck, J. R. Morris, and E. S. Bliss, “Small-scale self-focusing effects in a high-power glass laser amplifier,” IEEE J. Quantum. Electron. 14(5), 353–363 (1978).

[Crossref]

C. A. Palla, C. Pacheco, and M. E. Carrín, “Production of structured lipids by acidolysis with immobilized Rhizomucor miehei lipases: selection of suitable reaction conditions,” J. Mol. Catal., B Enzym. 76, 106–115 (2012).

[Crossref]

Y. Cai and S. He, “Propagation of various dark hollow beams in a turbulent atmosphere,” Opt. Express 14(4), 1353–1367 (2006).

[Crossref]
[PubMed]

L. Dou, X. Ji, and P. Li, “Propagation of partially coherent annular beams with decentered field in turbulence along a slant path,” Opt. Express 20(8), 8417–8430 (2012).

[Crossref]
[PubMed]

H. Deng, X. Ji, X. Li, H. Zhang, X. Wang, and Y. Zhang, “Effect of spatial coherence on laser beam self-focusing from orbit to the ground in the atmosphere,” Opt. Express 24(13), 14429–14437 (2016).

[Crossref]
[PubMed]

A. M. Rubenchik, S. K. Turitsyn, and M. P. Fedoruk, “Modulation instability in high power laser amplifiers,” Opt. Express 18(2), 1380–1388 (2010).

[Crossref]
[PubMed]

A. E. Siegman, “How to (maybe) measure laser beam quality,” OSA Trends Opt. Phonotic Ser. 17, 184–199 (1998).

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).

[Crossref]

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Laser beam self-focusing in the atmosphere,” Phys. Rev. Lett. 102(23), 233902 (2009).

[Crossref]
[PubMed]

S. V. Chekalin and V. P. Kandidov, “From self-focusing light beams to femtosecond laser pulse filamentation,” Phys. Uspekhi 56(2), 123–140 (2013).

[Crossref]

F. E. S. Vetelino and L. C. Andrews, “Annular Gaussian beams in turbulent media,” Proc. SPIE 5160, 86–97 (2004).

[Crossref]

S. Gladysz, J. C. Christou, L. W. Bradford, and L. C. Roberts, “Temporal Variability and Statistics of the Strehl Ratio in Adaptive-Optics,” Publ. Astron. Soc. Pac. 120(872), 1132–1143 (2008).

[Crossref]

S. N. Vlasov, V. A. Petrishev, and V. I. Talanov, “Average description of wave beams in linear and nonlinear media,” Radiophys Quant. El. 14(9), 1062–1070 (1974).

[Crossref]

R. H. Hardin and F. D. Tappert, “Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equation,” SIAM Rev. Chronicles 15(2), 805–809 (1973).

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995), Chap. 2.