Abstract

The analytical expressions for a partially coherent flat-topped vortex hollow beam propagating in uniaxial crystals orthogonal to the optical axis are derived, and the intensity and coherent vortex properties of partially coherent flat-topped vortex hollow beam propagation in uniaxial crystals orthogonal to the optical axis are analyzed by numerical examples. The influence of beam order parameter N, topological charge M, the coherence length and the ratio of refractive indices ne/no of uniaxial crystals on the normalized intensity distribution and coherent vortex of a partially coherent flat-topped vortex hollow beam propagating in uniaxial crystals are discussed in detail.

© 2016 Optical Society of Korea

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  1. M. Born and E. Wolf, Principle of Optics (Cambridge University Press, Cambridge, UK, 1999).
  2. A. Ciattoni, B. Crosignani, and P. Di Porto, “Vectorial theory of propagation in uniaxially anisotropic media,” J. Opt. Soc. Am. A 18, 1656-1661 (2001).
    [Crossref]
  3. A. Ciattoni, G. Cincotti, and C. Palma, “Nonparaxial description of reflection and transmission at the interface between an isotropic media and a uniaxial crystal,” J. Opt. Soc. Am. A 19, 1422-1431 (2002).
    [Crossref]
  4. A. Ciattoni and C. Palma, “Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond,” J. Opt. Soc. Am. A 20, 2163-2171 (2003).
    [Crossref]
  5. G. Cincotti, A. Ciattoni, and C. Palma, “Laguerre-Gauss and Bessel-Gauss beams in uniaxial crystals,” J. Opt. Soc. Am. A 19, 1680-1688 (2002).
    [Crossref]
  6. G. Cincotti, A. Ciattoni, and C. Palma, “Hermite-Gauss beams in uniaxially anisotropic crystals,” IEEE J. Quantum Electron. 37, 1517-1524 (2001).
    [Crossref]
  7. D. Deng, H. Yu, S. Xu, J. Shao, and Z. Fan, “Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals,” Opt. Commun. 281, 202-209 (2008).
    [Crossref]
  8. D. Liu and Z. Zhou, “Various dark hollow beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. A: Pure Appl. Opt. 10, 095005 (2008).
    [Crossref]
  9. B. Lü and S. Luo, “Propagation properties of three-dimensional flattened Gaussian beams in uniaxially anisotropic crystals,” Opt. Laser Technol. 36, 51-56 (2004).
    [Crossref]
  10. D. Liu and Z. Zhou, “Propagation and the kurtosis parameter of Gaussian flat-topped beams in uniaxial crystals orthogonal to the optical axis,” Opt. Laser Eng. 48, 58-63 (2010).
    [Crossref]
  11. D. Liu, H. Wang, Y. Wang, and Y. Yin, “Propagation properties of elliptical Gaussian beam in uniaxial crystals along the optical axis,” Opt. Laser Technol. 73, 12-18 (2015).
    [Crossref]
  12. X. Wang, Z. Liu, and D. Zhao, “Nonparaxial propagation of elliptical Gaussian vortex beams in uniaxial crystal orthogonal to the optical axis,” J. Opt. Soc. Am. A 31, 2268-2274 (2014).
    [Crossref]
  13. D. Deng, J. Shen, Y. Tian, J. Shao, and Z. Fan, “Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals,” Optik 118, 547-551 (2007).
    [Crossref]
  14. D. Liu and Z. Zhou, “Propagation of Partially Coherent Flat-topped Beams in Uniaxial Crystals Orthogonal to the Optical Axis,” J. Opt. Soc. Am. A 26, 924-930 (2009).
    [Crossref]
  15. D. J. Liua and Z. X. Zhou, “Propagation of Partially Polarized, Partially Coherent Beams in Uniaxial Crystals Orthogonal to the Optical Axis,” Eur. Phys. J. D 54, 95-101 (2009).
    [Crossref]
  16. Z. Zhu, L. Liu, F. Wang, and Y. Cai, “Evolution properties of a Laguerre-Gaussian correlated Schell-model beam propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. Soc. Am. A 32, 374-380 (2015).
    [Crossref]
  17. D. Liu, H. Wang, Y. Wang, and H. Yin, “Evolution properties of four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” Eur. Phys. J. D 69, 218 (2015).
    [Crossref]
  18. D. Liu, Y. Wang, and H. Yin, “Evolution properties of partially coherent four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. Soc. Am. A 32: 1683-1690 (2015).
    [Crossref]
  19. L. Guo, Z. and Tang, W. Wan, “Propagation of four-petal Gaussian vortex beam through a paraxial ABCD optical system,” Optik 125, 5542-5545 (2014).
    [Crossref]
  20. H. Dai, Y. Liu, D. Luo, and X. Sun, “Propagation properties of an optical vortex carried by an Airy beam: experimental implementation,” Opt. Lett. 36, 1617-1619 (2011).
    [Crossref]
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    [Crossref]
  22. G. Zhou, Y. Cai, and X. Chu, “Propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere,” Opt. Express 20, 9897-9910 (2012).
    [Crossref]
  23. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263-267 (2003).
    [Crossref]
  24. H. Liu, Y. Lü, J. Xia, X. Pu, and L. Zhang, “Flat-topped vortex hollow beam and its propagation properties,” J. Opt. 17, 075606(7pp) (2015).
    [Crossref]
  25. A. Jeffrey and H. Dai, Handbook of Mathematical Formulas and Integrals, 4th ed. (Academic Press Inc, Amsterdam, Netherlands, 2008).
  26. G. Gbur and T. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222, 117-125 (2003).
    [Crossref]

2015 (5)

D. Liu, H. Wang, Y. Wang, and Y. Yin, “Propagation properties of elliptical Gaussian beam in uniaxial crystals along the optical axis,” Opt. Laser Technol. 73, 12-18 (2015).
[Crossref]

Z. Zhu, L. Liu, F. Wang, and Y. Cai, “Evolution properties of a Laguerre-Gaussian correlated Schell-model beam propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. Soc. Am. A 32, 374-380 (2015).
[Crossref]

D. Liu, H. Wang, Y. Wang, and H. Yin, “Evolution properties of four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” Eur. Phys. J. D 69, 218 (2015).
[Crossref]

D. Liu, Y. Wang, and H. Yin, “Evolution properties of partially coherent four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. Soc. Am. A 32: 1683-1690 (2015).
[Crossref]

H. Liu, Y. Lü, J. Xia, X. Pu, and L. Zhang, “Flat-topped vortex hollow beam and its propagation properties,” J. Opt. 17, 075606(7pp) (2015).
[Crossref]

2014 (2)

L. Guo, Z. and Tang, W. Wan, “Propagation of four-petal Gaussian vortex beam through a paraxial ABCD optical system,” Optik 125, 5542-5545 (2014).
[Crossref]

X. Wang, Z. Liu, and D. Zhao, “Nonparaxial propagation of elliptical Gaussian vortex beams in uniaxial crystal orthogonal to the optical axis,” J. Opt. Soc. Am. A 31, 2268-2274 (2014).
[Crossref]

2012 (2)

2011 (1)

2010 (1)

D. Liu and Z. Zhou, “Propagation and the kurtosis parameter of Gaussian flat-topped beams in uniaxial crystals orthogonal to the optical axis,” Opt. Laser Eng. 48, 58-63 (2010).
[Crossref]

2009 (2)

D. Liu and Z. Zhou, “Propagation of Partially Coherent Flat-topped Beams in Uniaxial Crystals Orthogonal to the Optical Axis,” J. Opt. Soc. Am. A 26, 924-930 (2009).
[Crossref]

D. J. Liua and Z. X. Zhou, “Propagation of Partially Polarized, Partially Coherent Beams in Uniaxial Crystals Orthogonal to the Optical Axis,” Eur. Phys. J. D 54, 95-101 (2009).
[Crossref]

2008 (2)

D. Deng, H. Yu, S. Xu, J. Shao, and Z. Fan, “Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals,” Opt. Commun. 281, 202-209 (2008).
[Crossref]

D. Liu and Z. Zhou, “Various dark hollow beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. A: Pure Appl. Opt. 10, 095005 (2008).
[Crossref]

2007 (1)

D. Deng, J. Shen, Y. Tian, J. Shao, and Z. Fan, “Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals,” Optik 118, 547-551 (2007).
[Crossref]

2004 (1)

B. Lü and S. Luo, “Propagation properties of three-dimensional flattened Gaussian beams in uniaxially anisotropic crystals,” Opt. Laser Technol. 36, 51-56 (2004).
[Crossref]

2003 (3)

A. Ciattoni and C. Palma, “Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond,” J. Opt. Soc. Am. A 20, 2163-2171 (2003).
[Crossref]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263-267 (2003).
[Crossref]

G. Gbur and T. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222, 117-125 (2003).
[Crossref]

2002 (2)

2001 (2)

A. Ciattoni, B. Crosignani, and P. Di Porto, “Vectorial theory of propagation in uniaxially anisotropic media,” J. Opt. Soc. Am. A 18, 1656-1661 (2001).
[Crossref]

G. Cincotti, A. Ciattoni, and C. Palma, “Hermite-Gauss beams in uniaxially anisotropic crystals,” IEEE J. Quantum Electron. 37, 1517-1524 (2001).
[Crossref]

Born, M.

M. Born and E. Wolf, Principle of Optics (Cambridge University Press, Cambridge, UK, 1999).

Cai, Y.

Chu, X.

Ciattoni, A.

Cincotti, G.

Crosignani, B.

Dai, H.

H. Dai, Y. Liu, D. Luo, and X. Sun, “Propagation properties of an optical vortex carried by an Airy beam: experimental implementation,” Opt. Lett. 36, 1617-1619 (2011).
[Crossref]

A. Jeffrey and H. Dai, Handbook of Mathematical Formulas and Integrals, 4th ed. (Academic Press Inc, Amsterdam, Netherlands, 2008).

Deng, D.

D. Deng, H. Yu, S. Xu, J. Shao, and Z. Fan, “Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals,” Opt. Commun. 281, 202-209 (2008).
[Crossref]

D. Deng, J. Shen, Y. Tian, J. Shao, and Z. Fan, “Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals,” Optik 118, 547-551 (2007).
[Crossref]

Di Porto, P.

Fan, Z.

D. Deng, H. Yu, S. Xu, J. Shao, and Z. Fan, “Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals,” Opt. Commun. 281, 202-209 (2008).
[Crossref]

D. Deng, J. Shen, Y. Tian, J. Shao, and Z. Fan, “Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals,” Optik 118, 547-551 (2007).
[Crossref]

Gbur, G.

G. Gbur and T. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222, 117-125 (2003).
[Crossref]

Guo, L.

L. Guo, Z. and Tang, W. Wan, “Propagation of four-petal Gaussian vortex beam through a paraxial ABCD optical system,” Optik 125, 5542-5545 (2014).
[Crossref]

Jeffrey, A.

A. Jeffrey and H. Dai, Handbook of Mathematical Formulas and Integrals, 4th ed. (Academic Press Inc, Amsterdam, Netherlands, 2008).

Konyaev, P.

Liu, D.

D. Liu, Y. Wang, and H. Yin, “Evolution properties of partially coherent four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. Soc. Am. A 32: 1683-1690 (2015).
[Crossref]

D. Liu, H. Wang, Y. Wang, and H. Yin, “Evolution properties of four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” Eur. Phys. J. D 69, 218 (2015).
[Crossref]

D. Liu, H. Wang, Y. Wang, and Y. Yin, “Propagation properties of elliptical Gaussian beam in uniaxial crystals along the optical axis,” Opt. Laser Technol. 73, 12-18 (2015).
[Crossref]

D. Liu and Z. Zhou, “Propagation and the kurtosis parameter of Gaussian flat-topped beams in uniaxial crystals orthogonal to the optical axis,” Opt. Laser Eng. 48, 58-63 (2010).
[Crossref]

D. Liu and Z. Zhou, “Propagation of Partially Coherent Flat-topped Beams in Uniaxial Crystals Orthogonal to the Optical Axis,” J. Opt. Soc. Am. A 26, 924-930 (2009).
[Crossref]

D. Liu and Z. Zhou, “Various dark hollow beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. A: Pure Appl. Opt. 10, 095005 (2008).
[Crossref]

Liu, H.

H. Liu, Y. Lü, J. Xia, X. Pu, and L. Zhang, “Flat-topped vortex hollow beam and its propagation properties,” J. Opt. 17, 075606(7pp) (2015).
[Crossref]

Liu, L.

Liu, Y.

Liu, Z.

Liua, D. J.

D. J. Liua and Z. X. Zhou, “Propagation of Partially Polarized, Partially Coherent Beams in Uniaxial Crystals Orthogonal to the Optical Axis,” Eur. Phys. J. D 54, 95-101 (2009).
[Crossref]

Lü, B.

B. Lü and S. Luo, “Propagation properties of three-dimensional flattened Gaussian beams in uniaxially anisotropic crystals,” Opt. Laser Technol. 36, 51-56 (2004).
[Crossref]

Lü, Y.

H. Liu, Y. Lü, J. Xia, X. Pu, and L. Zhang, “Flat-topped vortex hollow beam and its propagation properties,” J. Opt. 17, 075606(7pp) (2015).
[Crossref]

Lukin, V.

Luo, D.

Luo, S.

B. Lü and S. Luo, “Propagation properties of three-dimensional flattened Gaussian beams in uniaxially anisotropic crystals,” Opt. Laser Technol. 36, 51-56 (2004).
[Crossref]

Palma, C.

Pu, X.

H. Liu, Y. Lü, J. Xia, X. Pu, and L. Zhang, “Flat-topped vortex hollow beam and its propagation properties,” J. Opt. 17, 075606(7pp) (2015).
[Crossref]

Sennikov, V.

Shao, J.

D. Deng, H. Yu, S. Xu, J. Shao, and Z. Fan, “Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals,” Opt. Commun. 281, 202-209 (2008).
[Crossref]

D. Deng, J. Shen, Y. Tian, J. Shao, and Z. Fan, “Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals,” Optik 118, 547-551 (2007).
[Crossref]

Shen, J.

D. Deng, J. Shen, Y. Tian, J. Shao, and Z. Fan, “Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals,” Optik 118, 547-551 (2007).
[Crossref]

Sun, X.

Tang, Z.

L. Guo, Z. and Tang, W. Wan, “Propagation of four-petal Gaussian vortex beam through a paraxial ABCD optical system,” Optik 125, 5542-5545 (2014).
[Crossref]

Tian, Y.

D. Deng, J. Shen, Y. Tian, J. Shao, and Z. Fan, “Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals,” Optik 118, 547-551 (2007).
[Crossref]

Visser, T.

G. Gbur and T. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222, 117-125 (2003).
[Crossref]

Wan, W.

L. Guo, Z. and Tang, W. Wan, “Propagation of four-petal Gaussian vortex beam through a paraxial ABCD optical system,” Optik 125, 5542-5545 (2014).
[Crossref]

Wang, F.

Wang, H.

D. Liu, H. Wang, Y. Wang, and Y. Yin, “Propagation properties of elliptical Gaussian beam in uniaxial crystals along the optical axis,” Opt. Laser Technol. 73, 12-18 (2015).
[Crossref]

D. Liu, H. Wang, Y. Wang, and H. Yin, “Evolution properties of four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” Eur. Phys. J. D 69, 218 (2015).
[Crossref]

Wang, X.

Wang, Y.

D. Liu, Y. Wang, and H. Yin, “Evolution properties of partially coherent four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. Soc. Am. A 32: 1683-1690 (2015).
[Crossref]

D. Liu, H. Wang, Y. Wang, and H. Yin, “Evolution properties of four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” Eur. Phys. J. D 69, 218 (2015).
[Crossref]

D. Liu, H. Wang, Y. Wang, and Y. Yin, “Propagation properties of elliptical Gaussian beam in uniaxial crystals along the optical axis,” Opt. Laser Technol. 73, 12-18 (2015).
[Crossref]

Wolf, E.

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263-267 (2003).
[Crossref]

M. Born and E. Wolf, Principle of Optics (Cambridge University Press, Cambridge, UK, 1999).

Xia, J.

H. Liu, Y. Lü, J. Xia, X. Pu, and L. Zhang, “Flat-topped vortex hollow beam and its propagation properties,” J. Opt. 17, 075606(7pp) (2015).
[Crossref]

Xu, S.

D. Deng, H. Yu, S. Xu, J. Shao, and Z. Fan, “Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals,” Opt. Commun. 281, 202-209 (2008).
[Crossref]

Yin, H.

D. Liu, H. Wang, Y. Wang, and H. Yin, “Evolution properties of four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” Eur. Phys. J. D 69, 218 (2015).
[Crossref]

D. Liu, Y. Wang, and H. Yin, “Evolution properties of partially coherent four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. Soc. Am. A 32: 1683-1690 (2015).
[Crossref]

Yin, Y.

D. Liu, H. Wang, Y. Wang, and Y. Yin, “Propagation properties of elliptical Gaussian beam in uniaxial crystals along the optical axis,” Opt. Laser Technol. 73, 12-18 (2015).
[Crossref]

Yu, H.

D. Deng, H. Yu, S. Xu, J. Shao, and Z. Fan, “Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals,” Opt. Commun. 281, 202-209 (2008).
[Crossref]

Zhang, L.

H. Liu, Y. Lü, J. Xia, X. Pu, and L. Zhang, “Flat-topped vortex hollow beam and its propagation properties,” J. Opt. 17, 075606(7pp) (2015).
[Crossref]

Zhao, D.

Zhou, G.

Zhou, Z.

D. Liu and Z. Zhou, “Propagation and the kurtosis parameter of Gaussian flat-topped beams in uniaxial crystals orthogonal to the optical axis,” Opt. Laser Eng. 48, 58-63 (2010).
[Crossref]

D. Liu and Z. Zhou, “Propagation of Partially Coherent Flat-topped Beams in Uniaxial Crystals Orthogonal to the Optical Axis,” J. Opt. Soc. Am. A 26, 924-930 (2009).
[Crossref]

D. Liu and Z. Zhou, “Various dark hollow beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. A: Pure Appl. Opt. 10, 095005 (2008).
[Crossref]

Zhou, Z. X.

D. J. Liua and Z. X. Zhou, “Propagation of Partially Polarized, Partially Coherent Beams in Uniaxial Crystals Orthogonal to the Optical Axis,” Eur. Phys. J. D 54, 95-101 (2009).
[Crossref]

Zhu, Z.

Appl. Opt. (1)

Eur. Phys. J. D (2)

D. J. Liua and Z. X. Zhou, “Propagation of Partially Polarized, Partially Coherent Beams in Uniaxial Crystals Orthogonal to the Optical Axis,” Eur. Phys. J. D 54, 95-101 (2009).
[Crossref]

D. Liu, H. Wang, Y. Wang, and H. Yin, “Evolution properties of four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” Eur. Phys. J. D 69, 218 (2015).
[Crossref]

IEEE J. Quantum Electron. (1)

G. Cincotti, A. Ciattoni, and C. Palma, “Hermite-Gauss beams in uniaxially anisotropic crystals,” IEEE J. Quantum Electron. 37, 1517-1524 (2001).
[Crossref]

J. Opt, (1)

H. Liu, Y. Lü, J. Xia, X. Pu, and L. Zhang, “Flat-topped vortex hollow beam and its propagation properties,” J. Opt. 17, 075606(7pp) (2015).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

D. Liu and Z. Zhou, “Various dark hollow beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. A: Pure Appl. Opt. 10, 095005 (2008).
[Crossref]

J. Opt. Soc. Am. A (8)

A. Ciattoni, B. Crosignani, and P. Di Porto, “Vectorial theory of propagation in uniaxially anisotropic media,” J. Opt. Soc. Am. A 18, 1656-1661 (2001).
[Crossref]

A. Ciattoni, G. Cincotti, and C. Palma, “Nonparaxial description of reflection and transmission at the interface between an isotropic media and a uniaxial crystal,” J. Opt. Soc. Am. A 19, 1422-1431 (2002).
[Crossref]

G. Cincotti, A. Ciattoni, and C. Palma, “Laguerre-Gauss and Bessel-Gauss beams in uniaxial crystals,” J. Opt. Soc. Am. A 19, 1680-1688 (2002).
[Crossref]

A. Ciattoni and C. Palma, “Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond,” J. Opt. Soc. Am. A 20, 2163-2171 (2003).
[Crossref]

D. Liu and Z. Zhou, “Propagation of Partially Coherent Flat-topped Beams in Uniaxial Crystals Orthogonal to the Optical Axis,” J. Opt. Soc. Am. A 26, 924-930 (2009).
[Crossref]

X. Wang, Z. Liu, and D. Zhao, “Nonparaxial propagation of elliptical Gaussian vortex beams in uniaxial crystal orthogonal to the optical axis,” J. Opt. Soc. Am. A 31, 2268-2274 (2014).
[Crossref]

Z. Zhu, L. Liu, F. Wang, and Y. Cai, “Evolution properties of a Laguerre-Gaussian correlated Schell-model beam propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. Soc. Am. A 32, 374-380 (2015).
[Crossref]

D. Liu, Y. Wang, and H. Yin, “Evolution properties of partially coherent four-petal Gaussian vortex beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. Soc. Am. A 32: 1683-1690 (2015).
[Crossref]

Opt. Commun. (2)

G. Gbur and T. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222, 117-125 (2003).
[Crossref]

D. Deng, H. Yu, S. Xu, J. Shao, and Z. Fan, “Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals,” Opt. Commun. 281, 202-209 (2008).
[Crossref]

Opt. Express (1)

Opt. Laser Eng. (1)

D. Liu and Z. Zhou, “Propagation and the kurtosis parameter of Gaussian flat-topped beams in uniaxial crystals orthogonal to the optical axis,” Opt. Laser Eng. 48, 58-63 (2010).
[Crossref]

Opt. Laser Technol. (2)

D. Liu, H. Wang, Y. Wang, and Y. Yin, “Propagation properties of elliptical Gaussian beam in uniaxial crystals along the optical axis,” Opt. Laser Technol. 73, 12-18 (2015).
[Crossref]

B. Lü and S. Luo, “Propagation properties of three-dimensional flattened Gaussian beams in uniaxially anisotropic crystals,” Opt. Laser Technol. 36, 51-56 (2004).
[Crossref]

Opt. Lett. (1)

Optik (2)

D. Deng, J. Shen, Y. Tian, J. Shao, and Z. Fan, “Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals,” Optik 118, 547-551 (2007).
[Crossref]

L. Guo, Z. and Tang, W. Wan, “Propagation of four-petal Gaussian vortex beam through a paraxial ABCD optical system,” Optik 125, 5542-5545 (2014).
[Crossref]

Phys. Lett. A (1)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263-267 (2003).
[Crossref]

Other (2)

M. Born and E. Wolf, Principle of Optics (Cambridge University Press, Cambridge, UK, 1999).

A. Jeffrey and H. Dai, Handbook of Mathematical Formulas and Integrals, 4th ed. (Academic Press Inc, Amsterdam, Netherlands, 2008).

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