Abstract

The propagation of polarized Hermite-cosine-Gaussian (HCosG) beams in uniaxial crystals orthogonal to the optical axis is investigated. Analytical formulas for a HCosG beam propagating in uniaxial crystals orthogonal to the optical axis are derived, and the propagation properties of the beam are illustrated numerically. The results show that the HCosG beam can keep its initial beam profile almost invariant for a short propagation distance. However, the initial symmetry and the linear polarization of an incident HCosG beam cannot be preserved during propagation in uniaxial crystals. In addition, the distributions of optical fields are closely related to the decentered parameter.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  33. D. Liu and Z. Zhou, “Propagation properties of anomalous hollow beam in uniaxial crystals orthogonal to the optical axis,” Opt. Laser Technol. 41, 877-884 (2009).
    [CrossRef]
  34. 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]
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2009

A. Yang, E. Zhang, X. Ji, and B. Lü, “Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence,” Opt. Laser Technol. 41, 714-722 (2009).
[CrossRef]

B. Tang and M. Jiang, “Propagation properties of vectorial Hermite-cosine-Gaussian beams beyond the paraxial approximation,” J. Mod. Opt. 56, 955-962 (2009).
[CrossRef]

D. Liu and Z. Zhou, “Propagation properties of anomalous hollow beam in uniaxial crystals orthogonal to the optical axis,” Opt. Laser Technol. 41, 877-884 (2009).
[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, “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

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]

A. Yang, E. Zhang, X. Ji, and B. Lü, “Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence,” Opt. Express 16, 8366-8380 (2008).
[CrossRef] [PubMed]

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]

2007

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

2006

B. Tang, H. Tang, K. Zhu, H. Yang, and W. Wen, “Propagation properties of Hermite-Cosh-Gaussian beams in uniaxially anisotropic crystals,” J. Optoelectron., Laser 17, 365-368 (2006). (in Chinese)

D. Deng, “Propagation of elegant Hermite cosine Gaussian laser beams,” Opt. Commun. 259, 409-414 (2006).
[CrossRef]

2005

2004

N. R. Zhou and G. H. Zeng, “Propagation properties of Hermite-cosine-Gaussian beams through a paraxial optical ABCD system with hard-edge aperture,” Opt. Commun. 232, 49-59 (2004).
[CrossRef]

Y. L. Qiu, H. Guo, X. Z. Chen, and H. J. Kong, “Propagation properties of an elegant Hermite-cosh-Gaussian beam through a finite aperture,” J. Opt. A, Pure Appl. Opt. 6, 210-215 (2004).
[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]

A. Ciattoni and C. Palma, “Anisotropic beam spreading in uniaxial crystal,” Opt. Commun. 231, 79-92 (2004).
[CrossRef]

2003

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

A. Ciattoni and C. Palma, “Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis,” Opt. Commun. 224, 175-183 (2003).
[CrossRef]

D. M. Zhao, H. D. Mao, and D. Sun, “Approximate analytical expression for the kurtosis parameter of off-axial Hermite-cosine-Gaussian beams propagating through apertured and misaligned ABCD optical systems,” Optik (Stuttgart) 114, 535-538 (2003).
[CrossRef]

D. M. Zhao, H. D. Mao, W. C. Zhang, and S. Wang, “Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5-12 (2003).
[CrossRef]

D. M. Zhao, W. C. Zhang, S. M. Wang, H. J. Liu, Q. H. Zhu, and X. F. Wei, “Propagation of one-dimensional off-axial Hermite-cosine-Gaussian beams through an apertured paraxial ABCD optical system” Optik (Stuttgart) 114, 49-51 (2003).
[CrossRef]

2002

2001

X. Wang and B. Lü, “The M2 factor of Hermite-cosh-Gaussian beams,” J. Mod. Opt. 48, 2097-2103 (2001).

A. Ciattoni, B. Crosignani, and C. Palma, “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, “Ordinary and extraordinary beams characterization in uniaxially anisotropic crystals,” Opt. Commun. 195, 55-61 (2001).
[CrossRef]

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

2000

A. Belafhal and M. Ibnchaikh, “Propagation properties of Hermite-cosh-Gaussian laser beams,” Opt. Commun. 186, 269-276 (2000).
[CrossRef]

1998

1983

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1970).

Baykal, Y.

Belafhal, A.

A. Belafhal and M. Ibnchaikh, “Propagation properties of Hermite-cosh-Gaussian laser beams,” Opt. Commun. 186, 269-276 (2000).
[CrossRef]

Casperson, L. W

Casperson, L. W.

Chen, X. Z.

Y. L. Qiu, H. Guo, X. Z. Chen, and H. J. Kong, “Propagation properties of an elegant Hermite-cosh-Gaussian beam through a finite aperture,” J. Opt. A, Pure Appl. Opt. 6, 210-215 (2004).
[CrossRef]

Ciattoni, A.

A. Ciattoni and C. Palma, “Anisotropic beam spreading in uniaxial crystal,” Opt. Commun. 231, 79-92 (2004).
[CrossRef]

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

A. Ciattoni and C. Palma, “Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis,” Opt. Commun. 224, 175-183 (2003).
[CrossRef]

A. Ciattoni, G. Cincotti, and C. Palma, “Propagation of cylindrically symmetric fields in uniaxial crystals” J. Opt. Soc. Am. A 19, 792-796 (2002).
[CrossRef]

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

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

A. Ciattoni, B. Crosignani, and C. Palma, “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, “Ordinary and extraordinary beams characterization in uniaxially anisotropic crystals,” Opt. Commun. 195, 55-61 (2001).
[CrossRef]

Cincotti, G.

A. Ciattoni, G. Cincotti, and C. Palma, “Propagation of cylindrically symmetric fields in uniaxial crystals” J. Opt. Soc. Am. A 19, 792-796 (2002).
[CrossRef]

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

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

A. Ciattoni, G. Cincotti, and C. Palma, “Ordinary and extraordinary beams characterization in uniaxially anisotropic crystals,” Opt. Commun. 195, 55-61 (2001).
[CrossRef]

Crosignani, B.

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 (Stuttgart) 118, 547-551 (2007).
[CrossRef]

D. Deng, “Propagation of elegant Hermite cosine Gaussian laser beams,” Opt. Commun. 259, 409-414 (2006).
[CrossRef]

Eyyuboglu, H. T.

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 (Stuttgart) 118, 547-551 (2007).
[CrossRef]

Feit, M. D.

Fleck, J. A.

Fu, X. Q.

S. Yu, H. Guo, X. Q. Fu, and W. Hu, “Propagation properties of elegant Hermite-cosh-Gaussian laser beams,” Opt. Commun. 204, 59-66 (2002).

Guo, H.

Y. L. Qiu, H. Guo, X. Z. Chen, and H. J. Kong, “Propagation properties of an elegant Hermite-cosh-Gaussian beam through a finite aperture,” J. Opt. A, Pure Appl. Opt. 6, 210-215 (2004).
[CrossRef]

S. Yu, H. Guo, X. Q. Fu, and W. Hu, “Propagation properties of elegant Hermite-cosh-Gaussian laser beams,” Opt. Commun. 204, 59-66 (2002).

Hu, W.

S. Yu, H. Guo, X. Q. Fu, and W. Hu, “Propagation properties of elegant Hermite-cosh-Gaussian laser beams,” Opt. Commun. 204, 59-66 (2002).

Ibnchaikh, M.

A. Belafhal and M. Ibnchaikh, “Propagation properties of Hermite-cosh-Gaussian laser beams,” Opt. Commun. 186, 269-276 (2000).
[CrossRef]

Ji, X.

A. Yang, E. Zhang, X. Ji, and B. Lü, “Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence,” Opt. Laser Technol. 41, 714-722 (2009).
[CrossRef]

A. Yang, E. Zhang, X. Ji, and B. Lü, “Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence,” Opt. Express 16, 8366-8380 (2008).
[CrossRef] [PubMed]

Jiang, M.

B. Tang and M. Jiang, “Propagation properties of vectorial Hermite-cosine-Gaussian beams beyond the paraxial approximation,” J. Mod. Opt. 56, 955-962 (2009).
[CrossRef]

Kong, H. J.

Y. L. Qiu, H. Guo, X. Z. Chen, and H. J. Kong, “Propagation properties of an elegant Hermite-cosh-Gaussian beam through a finite aperture,” J. Opt. A, Pure Appl. Opt. 6, 210-215 (2004).
[CrossRef]

Liu, D.

D. Liu and Z. 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 and Z. Zhou, “Propagation properties of anomalous hollow beam in uniaxial crystals orthogonal to the optical axis,” Opt. Laser Technol. 41, 877-884 (2009).
[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. J.

D. M. Zhao, W. C. Zhang, S. M. Wang, H. J. Liu, Q. H. Zhu, and X. F. Wei, “Propagation of one-dimensional off-axial Hermite-cosine-Gaussian beams through an apertured paraxial ABCD optical system” Optik (Stuttgart) 114, 49-51 (2003).
[CrossRef]

Lü, B.

A. Yang, E. Zhang, X. Ji, and B. Lü, “Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence,” Opt. Laser Technol. 41, 714-722 (2009).
[CrossRef]

A. Yang, E. Zhang, X. Ji, and B. Lü, “Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence,” Opt. Express 16, 8366-8380 (2008).
[CrossRef] [PubMed]

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]

X. Wang and B. Lü, “The M2 factor of Hermite-cosh-Gaussian beams,” J. Mod. Opt. 48, 2097-2103 (2001).

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]

Mao, H. D.

D. M. Zhao, H. D. Mao, and D. Sun, “Approximate analytical expression for the kurtosis parameter of off-axial Hermite-cosine-Gaussian beams propagating through apertured and misaligned ABCD optical systems,” Optik (Stuttgart) 114, 535-538 (2003).
[CrossRef]

D. M. Zhao, H. D. Mao, W. C. Zhang, and S. Wang, “Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5-12 (2003).
[CrossRef]

Palma, C.

A. Ciattoni and C. Palma, “Anisotropic beam spreading in uniaxial crystal,” Opt. Commun. 231, 79-92 (2004).
[CrossRef]

A. Ciattoni and C. Palma, “Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis,” Opt. Commun. 224, 175-183 (2003).
[CrossRef]

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

A. Ciattoni, G. Cincotti, and C. Palma, “Propagation of cylindrically symmetric fields in uniaxial crystals” J. Opt. Soc. Am. A 19, 792-796 (2002).
[CrossRef]

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

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

A. Ciattoni, B. Crosignani, and C. Palma, “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, “Ordinary and extraordinary beams characterization in uniaxially anisotropic crystals,” Opt. Commun. 195, 55-61 (2001).
[CrossRef]

Qiu, Y. L.

Y. L. Qiu, H. Guo, X. Z. Chen, and H. J. Kong, “Propagation properties of an elegant Hermite-cosh-Gaussian beam through a finite aperture,” J. Opt. A, Pure Appl. Opt. 6, 210-215 (2004).
[CrossRef]

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 (Stuttgart) 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 (Stuttgart) 118, 547-551 (2007).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1970).

Sun, D.

D. Sun and D. M. Zhao, “Wigner distribution function of Hermite-cosine-Gaussian beams through an apertured optical system,” J. Opt. Soc. Am. A 22, 1683-1690 (2005).
[CrossRef]

D. M. Zhao, H. D. Mao, and D. Sun, “Approximate analytical expression for the kurtosis parameter of off-axial Hermite-cosine-Gaussian beams propagating through apertured and misaligned ABCD optical systems,” Optik (Stuttgart) 114, 535-538 (2003).
[CrossRef]

Tang, B.

B. Tang and M. Jiang, “Propagation properties of vectorial Hermite-cosine-Gaussian beams beyond the paraxial approximation,” J. Mod. Opt. 56, 955-962 (2009).
[CrossRef]

B. Tang, H. Tang, K. Zhu, H. Yang, and W. Wen, “Propagation properties of Hermite-Cosh-Gaussian beams in uniaxially anisotropic crystals,” J. Optoelectron., Laser 17, 365-368 (2006). (in Chinese)

Tang, H.

B. Tang, H. Tang, K. Zhu, H. Yang, and W. Wen, “Propagation properties of Hermite-Cosh-Gaussian beams in uniaxially anisotropic crystals,” J. Optoelectron., Laser 17, 365-368 (2006). (in Chinese)

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 (Stuttgart) 118, 547-551 (2007).
[CrossRef]

Tovar, A. A.

Wang, S.

D. M. Zhao, H. D. Mao, W. C. Zhang, and S. Wang, “Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5-12 (2003).
[CrossRef]

Wang, S. M.

D. M. Zhao, W. C. Zhang, S. M. Wang, H. J. Liu, Q. H. Zhu, and X. F. Wei, “Propagation of one-dimensional off-axial Hermite-cosine-Gaussian beams through an apertured paraxial ABCD optical system” Optik (Stuttgart) 114, 49-51 (2003).
[CrossRef]

Wang, X.

X. Wang and B. Lü, “The M2 factor of Hermite-cosh-Gaussian beams,” J. Mod. Opt. 48, 2097-2103 (2001).

Wei, X. F.

D. M. Zhao, W. C. Zhang, S. M. Wang, H. J. Liu, Q. H. Zhu, and X. F. Wei, “Propagation of one-dimensional off-axial Hermite-cosine-Gaussian beams through an apertured paraxial ABCD optical system” Optik (Stuttgart) 114, 49-51 (2003).
[CrossRef]

Wen, W.

B. Tang, H. Tang, K. Zhu, H. Yang, and W. Wen, “Propagation properties of Hermite-Cosh-Gaussian beams in uniaxially anisotropic crystals,” J. Optoelectron., Laser 17, 365-368 (2006). (in Chinese)

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]

Yang, A.

A. Yang, E. Zhang, X. Ji, and B. Lü, “Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence,” Opt. Laser Technol. 41, 714-722 (2009).
[CrossRef]

A. Yang, E. Zhang, X. Ji, and B. Lü, “Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence,” Opt. Express 16, 8366-8380 (2008).
[CrossRef] [PubMed]

Yang, H.

B. Tang, H. Tang, K. Zhu, H. Yang, and W. Wen, “Propagation properties of Hermite-Cosh-Gaussian beams in uniaxially anisotropic crystals,” J. Optoelectron., Laser 17, 365-368 (2006). (in Chinese)

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]

Yu, S.

S. Yu, H. Guo, X. Q. Fu, and W. Hu, “Propagation properties of elegant Hermite-cosh-Gaussian laser beams,” Opt. Commun. 204, 59-66 (2002).

Zeng, G. H.

N. R. Zhou and G. H. Zeng, “Propagation properties of Hermite-cosine-Gaussian beams through a paraxial optical ABCD system with hard-edge aperture,” Opt. Commun. 232, 49-59 (2004).
[CrossRef]

Zhang, E.

A. Yang, E. Zhang, X. Ji, and B. Lü, “Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence,” Opt. Laser Technol. 41, 714-722 (2009).
[CrossRef]

A. Yang, E. Zhang, X. Ji, and B. Lü, “Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence,” Opt. Express 16, 8366-8380 (2008).
[CrossRef] [PubMed]

Zhang, W. C.

D. M. Zhao, W. C. Zhang, S. M. Wang, H. J. Liu, Q. H. Zhu, and X. F. Wei, “Propagation of one-dimensional off-axial Hermite-cosine-Gaussian beams through an apertured paraxial ABCD optical system” Optik (Stuttgart) 114, 49-51 (2003).
[CrossRef]

D. M. Zhao, H. D. Mao, W. C. Zhang, and S. Wang, “Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5-12 (2003).
[CrossRef]

Zhao, D. M.

D. Sun and D. M. Zhao, “Wigner distribution function of Hermite-cosine-Gaussian beams through an apertured optical system,” J. Opt. Soc. Am. A 22, 1683-1690 (2005).
[CrossRef]

D. M. Zhao, H. D. Mao, and D. Sun, “Approximate analytical expression for the kurtosis parameter of off-axial Hermite-cosine-Gaussian beams propagating through apertured and misaligned ABCD optical systems,” Optik (Stuttgart) 114, 535-538 (2003).
[CrossRef]

D. M. Zhao, H. D. Mao, W. C. Zhang, and S. Wang, “Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5-12 (2003).
[CrossRef]

D. M. Zhao, W. C. Zhang, S. M. Wang, H. J. Liu, Q. H. Zhu, and X. F. Wei, “Propagation of one-dimensional off-axial Hermite-cosine-Gaussian beams through an apertured paraxial ABCD optical system” Optik (Stuttgart) 114, 49-51 (2003).
[CrossRef]

Zhou, N. R.

N. R. Zhou and G. H. Zeng, “Propagation properties of Hermite-cosine-Gaussian beams through a paraxial optical ABCD system with hard-edge aperture,” Opt. Commun. 232, 49-59 (2004).
[CrossRef]

Zhou, Z.

D. Liu and Z. 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 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, “Propagation properties of anomalous hollow beam in uniaxial crystals orthogonal to the optical axis,” Opt. Laser Technol. 41, 877-884 (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]

Zhu, K.

B. Tang, H. Tang, K. Zhu, H. Yang, and W. Wen, “Propagation properties of Hermite-Cosh-Gaussian beams in uniaxially anisotropic crystals,” J. Optoelectron., Laser 17, 365-368 (2006). (in Chinese)

Zhu, Q. H.

D. M. Zhao, W. C. Zhang, S. M. Wang, H. J. Liu, Q. H. Zhu, and X. F. Wei, “Propagation of one-dimensional off-axial Hermite-cosine-Gaussian beams through an apertured paraxial ABCD optical system” Optik (Stuttgart) 114, 49-51 (2003).
[CrossRef]

Eur. Phys. J. D

D. Liu and Z. 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]

IEEE J. Quantum Electron.

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

J. Mod. Opt.

X. Wang and B. Lü, “The M2 factor of Hermite-cosh-Gaussian beams,” J. Mod. Opt. 48, 2097-2103 (2001).

B. Tang and M. Jiang, “Propagation properties of vectorial Hermite-cosine-Gaussian beams beyond the paraxial approximation,” J. Mod. Opt. 56, 955-962 (2009).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

Y. L. Qiu, H. Guo, X. Z. Chen, and H. J. Kong, “Propagation properties of an elegant Hermite-cosh-Gaussian beam through a finite aperture,” J. Opt. A, Pure Appl. Opt. 6, 210-215 (2004).
[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]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

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

H. T. Eyyuboğlu and Y. Baykal, “Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulent atmosphere,” J. Opt. Soc. Am. A 22, 2709-2718 (2005).
[CrossRef]

H. T. Eyyuboğlu, “Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere,” J. Opt. Soc. Am. A 22, 1527-1535 (2005).
[CrossRef]

D. Sun and D. M. Zhao, “Wigner distribution function of Hermite-cosine-Gaussian beams through an apertured optical system,” J. Opt. Soc. Am. A 22, 1683-1690 (2005).
[CrossRef]

L. W. Casperson and A. A. Tovar, “Hermite-sinusoidal-Gaussian beams in complex optical systems,” J. Opt. Soc. Am. A 15, 954-961 (1998).
[CrossRef]

A. A. Tovar and L. W Casperson, “Production and propagation of Hermite-sinusoidal-Gaussian beams,” J. Opt. Soc. Am. A 15, 2425-2432 (1998).
[CrossRef]

A. Ciattoni and C. Palma, “Optical propagation in uniaxial crystal 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]

A. Ciattoni, G. Cincotti, and C. Palma, “Propagation of cylindrically symmetric fields in uniaxial crystals” J. Opt. Soc. Am. A 19, 792-796 (2002).
[CrossRef]

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

J. Optoelectron., Laser

B. Tang, H. Tang, K. Zhu, H. Yang, and W. Wen, “Propagation properties of Hermite-Cosh-Gaussian beams in uniaxially anisotropic crystals,” J. Optoelectron., Laser 17, 365-368 (2006). (in Chinese)

Opt. Commun.

N. R. Zhou and G. H. Zeng, “Propagation properties of Hermite-cosine-Gaussian beams through a paraxial optical ABCD system with hard-edge aperture,” Opt. Commun. 232, 49-59 (2004).
[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]

A. Ciattoni and C. Palma, “Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis,” Opt. Commun. 224, 175-183 (2003).
[CrossRef]

A. Ciattoni and C. Palma, “Anisotropic beam spreading in uniaxial crystal,” Opt. Commun. 231, 79-92 (2004).
[CrossRef]

A. Belafhal and M. Ibnchaikh, “Propagation properties of Hermite-cosh-Gaussian laser beams,” Opt. Commun. 186, 269-276 (2000).
[CrossRef]

S. Yu, H. Guo, X. Q. Fu, and W. Hu, “Propagation properties of elegant Hermite-cosh-Gaussian laser beams,” Opt. Commun. 204, 59-66 (2002).

D. Deng, “Propagation of elegant Hermite cosine Gaussian laser beams,” Opt. Commun. 259, 409-414 (2006).
[CrossRef]

D. M. Zhao, H. D. Mao, W. C. Zhang, and S. Wang, “Propagation of off-axial Hermite-cosine-Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5-12 (2003).
[CrossRef]

H. T. Eyyuboğlu, “Propagation of Hermite-cosh-Gaussian laser beams in turbulent atmosphere,” Opt. Commun. 245, 37-47 (2005).
[CrossRef]

A. Ciattoni, G. Cincotti, and C. Palma, “Ordinary and extraordinary beams characterization in uniaxially anisotropic crystals,” Opt. Commun. 195, 55-61 (2001).
[CrossRef]

Opt. Express

Opt. Laser Technol.

A. Yang, E. Zhang, X. Ji, and B. Lü, “Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence,” Opt. Laser Technol. 41, 714-722 (2009).
[CrossRef]

D. Liu and Z. Zhou, “Propagation properties of anomalous hollow beam in uniaxial crystals orthogonal to the optical axis,” Opt. Laser Technol. 41, 877-884 (2009).
[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]

Optik (Stuttgart)

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

D. M. Zhao, H. D. Mao, and D. Sun, “Approximate analytical expression for the kurtosis parameter of off-axial Hermite-cosine-Gaussian beams propagating through apertured and misaligned ABCD optical systems,” Optik (Stuttgart) 114, 535-538 (2003).
[CrossRef]

D. M. Zhao, W. C. Zhang, S. M. Wang, H. J. Liu, Q. H. Zhu, and X. F. Wei, “Propagation of one-dimensional off-axial Hermite-cosine-Gaussian beams through an apertured paraxial ABCD optical system” Optik (Stuttgart) 114, 49-51 (2003).
[CrossRef]

Other

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1970).

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Figures (5)

Fig. 1
Fig. 1

Profiles of transverse field | A e x | of a HCosG beam propagating in a uniaxial crystal orthogonal to the optical axis at different planes with b = 2.5 : (a) z = 0 , (b) z = 400 μ m , (c) z = 2000 μ m , (d) z = 6000 μ m .

Fig. 2
Fig. 2

Profiles of transverse field | A e x | of a HCosG beam propagating in a uniaxial crystal orthogonal to the optical axis for different decentered parameters b at the z = 4000 μ m plane: (a) b = 0.5 , (b) b = 2.5 , (c) b = 5 , (d) b = 10 .

Fig. 3
Fig. 3

Profiles of transverse field | E y | of a HCosG beam propagating in a uniaxial crystal orthogonal to the optical axis at different planes with b = 2.5 : (a) z = 0 , (b) z = 400 μ m , (c) z = 2000 μ m , (d) z = 6000 μ m .

Fig. 4
Fig. 4

Profiles of field | A e z | of a HCosG beam propagating in a uniaxial crystal orthogonal to the optical axis at different planes with b = 2.5 : (a) z = 0 μ m , (b) z = 400 μ m , (c) z = 2000 μ m , (d) z = 6000 μ m .

Fig. 5
Fig. 5

Intensity distributions of a HCosG beam propagating in a uniaxial crystal orthogonal to the optical axis at different planes: (a) z = 400 μ m , b = 2.5 ; (b) z = 400 μ m , b = 5 ; (c) z = 4000 μ m , b = 2.5 ; (d) z = 4000 μ m , b = 5 .

Equations (39)

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ε = ( n e 2 0 0 0 n o 2 0 0 0 n o 2 ) ,
E ( r , 0 ) = E 0 H m ( 2 x w 0 ) H n ( 2 y w 0 ) exp ( x 2 + y 2 w 0 2 ) cos ( Ω 0 x ) cos ( Ω 0 y ) ,
E ( r ) = E e ( r ) + E o ( r ) ,
E e ( r , z ) = d 2 k exp ( i k r ) exp ( i k e z z ) ( E ̃ x ( k ) k x k y k 0 2 n o 2 k x 2 E ̃ x ( k ) k e z k x k 0 2 n o 2 k x 2 E ̃ x ( k ) ) ,
E o ( r , z ) = d 2 k exp ( i k r ) exp ( i k o z z ) ( 0 k x k y k 0 2 n o 2 k x 2 E ̃ x ( k ) + E ̃ y ( k ) k y k o z [ k x k y k 0 2 n o 2 k x 2 E ̃ x ( k ) + E ̃ y ( k ) ] ) ,
E ̃ ( k ) = 1 ( 2 π ) 2 d 2 r exp ( i k r ) E ( r , 0 )
k o z ( k ) = ( k 0 2 n o 2 k 2 ) 1 2 ,
k e z ( k ) = [ k 0 2 n e 2 ( n e 2 n o 2 ) k x 2 k y 2 ] 1 2 .
E e x ( r , z ) = exp ( i k 0 n e z ) d 2 k exp ( i k r ) exp ( i n e 2 k x 2 + n o 2 k y 2 2 k 0 n e n o 2 z ) E ̃ x ( k ) = exp ( i k 0 n e z ) A e x ( r , z ) ,
E e y ( r , z ) = exp ( i k 0 n e z ) d 2 k exp ( i k r ) exp ( i n e 2 k x 2 + n o 2 k y 2 2 k 0 n e n o 2 z ) ( k x k y k 0 2 n o 2 ) E ̃ x ( k ) = exp ( i k 0 n e z ) A e y ( r , z ) ,
E e z ( r , z ) = exp ( i k 0 n e z ) d 2 k exp ( i k r ) exp ( i n e 2 k x 2 + n o 2 k y 2 2 k 0 n e n o 2 z ) ( n e k x k 0 n o 2 ) E ̃ x ( k ) = exp ( i k 0 n e z ) A e z ( r , z ) ,
E o x ( r , z ) = 0 ,
E o y ( r , z ) = exp ( i k 0 n o z ) d 2 k exp ( i k r ) exp ( i k x 2 + k y 2 2 k 0 n o z ) ( k x k y k 0 2 n o 2 E ̃ x ( k ) + E ̃ y ( k ) ) = exp ( i k 0 n o z ) A o y ( r , z ) ,
E o z ( r , z ) = exp ( i k 0 n o z ) d 2 k exp ( i k r ) exp ( i k x 2 + k y 2 2 k 0 n o z ) ( k y k 0 n o ) E ̃ y ( k ) = exp ( i k 0 n o z ) A o z ( r , z ) .
H m ( x ) = ( 1 ) m H m ( x ) ,
exp [ ( x y ) 2 ] H m ( α x ) d x = π ( 1 α 2 ) m 2 H m [ α y ( 1 α 2 ) 1 2 ]
E ̃ ( k ) = ( i ) m + n w 0 2 E 0 exp ( b 2 2 ) 16 π exp ( w 0 2 k 2 4 ) × [ H m , n , ( k x , k y ) + H m , n , + ( k x , k y ) + H m , n + , ( k x , k y ) + H m , n + , + ( k x , k y ) ] e ̂ x ,
H m , n , ( k x , k y ) = H m ( k x w 0 b 2 ) H n ( k y w 0 b 2 ) exp [ ( k x + k y ) b w 0 2 ] ,
H m , n , + ( k x , k y ) = H m ( k x w 0 b 2 ) H n ( k y w 0 + b 2 ) exp [ ( k x k y ) b w 0 2 ] ,
H m , n + , ( k x , k y ) = H m ( k x w 0 + b 2 ) H n ( k y w 0 b 2 ) exp [ ( k x k y ) b w 0 2 ] ,
H m , n + , + ( k x , k y ) = H m ( k x w 0 + b 2 ) H n ( k y w 0 + b 2 ) exp [ ( k x + k y ) b w 0 2 ] .
( k ξ ) n exp ( i k ξ ξ ) = ( i ξ ) n exp ( i k ξ ξ ) , ξ = x , y ,
H n ( t ) = k = 0 [ n 2 ] ( 1 ) k n ! k ! ( n 2 k ) ! ( 2 t ) n 2 k ,
H m ( x + y ) = ν = 0 m 1 2 m 2 ( m ν ) H ν ( x 2 ) H m ν ( y 2 ) ,
( m ν ) = m ( m 1 ) ( m ν + 1 ) ν ! ,
A e x ( r , z ) = w 0 2 E 0 4 exp ( b 2 2 ) μ = 1 4 ν 1 = 0 m ν 2 = 0 n p = 0 [ ν 1 2 ] q = 0 [ ν 2 2 ] S ( m , n ) Q e x ( z ) Q e y ( z ) F μ ( x , y ) x ( ν 1 2 p ) y ( ν 2 2 q ) exp ( x 2 Q ex ( z ) y 2 Q e y ( z ) ) ,
A e y ( r , z ) = w 0 2 E 0 4 k 0 2 n o 2 exp ( b 2 2 ) μ = 1 4 ν 1 = 0 m ν 2 = 0 n p = 0 [ ν 1 2 ] q = 0 [ ν 2 2 ] S ( m , n ) Q ex ( z ) Q e y ( z ) F μ ( x , y ) x ( ν 1 2 p + 1 ) y ( ν 2 2 q + 1 ) exp ( x 2 Q ex ( z ) y 2 Q e y ( z ) ) ,
A e z ( r , z ) = w 0 2 E 0 n e 4 k 0 n o 2 exp ( b 2 2 ) μ = 1 4 ν 1 = 0 m ν 2 = 0 n p = 0 [ ν 1 2 ] q = 0 [ ν 2 2 ] S ( m , n ) i Q ex ( z ) Q e y ( z ) F μ ( x , y ) x ( ν 1 2 p + 1 ) y ( ν 2 2 q ) exp ( x 2 Q ex ( z ) y 2 Q e y ( z ) ) ,
S ( m , n ) = ( 1 ) p + q ( i ) m + n + ν 1 + ν 2 2 p 2 q ( 2 w 0 ) ν 1 + ν 2 2 p 2 q ν 1 ! ν 2 ! 2 ( m + n ) 2 p ! q ! ( ν 1 2 p ) ! ( ν 2 2 q ) ! ( m ν 1 ) ( n ν 2 ) ,
F 1 ( x , y ) = H m ν 1 ( b ) H n ν 2 ( b ) exp [ b w 0 i 2 ( x + y ) ] ,
F 2 ( x , y ) = H m ν 1 ( b ) H n ν 2 ( b ) exp [ b w 0 i 2 ( x y ) ] ,
F 3 ( x , y ) = H m ν 1 ( b ) H n ν 2 ( b ) exp [ b w 0 i 2 ( x y ) ] ,
F 4 ( x , y ) = H m ν 1 ( b ) H n ν 2 ( b ) exp [ b w 0 i 2 ( x + y ) ] ,
Q e x ( z ) = w 0 2 + 2 n e z i k 0 n o 2 ,
Q e y ( z ) = w 0 2 + 2 z i k 0 n e .
A o x ( r , z ) = 0 ,
A o y ( r , z ) = w 0 2 E 0 4 k 0 2 n o 2 exp ( b 2 2 ) μ = 1 4 ν 1 = 0 m ν 2 = 0 n p = 0 [ ν 1 2 ] q = 0 [ ν 2 2 ] S ( m , n ) Q o ( z ) F μ ( x , y ) x ( ν 1 2 p + 1 ) y ( ν 2 2 q + 1 ) exp ( x 2 + y 2 Q o ( z ) ) ,
A o z ( r , z ) = 0 ,
Q o ( z ) = w 0 2 + 2 z i k 0 n o .

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