Abstract

Optical intensity distributions in the focal region play an important role in many optical systems. In this paper, the tunable focusing properties of linearly polarized hyperbolic-cosine-Gaussian beams with sine-azimuthal variation wavefront were investigated by adding a spiral optical vortex. It was found that the focal patterns can be altered very considerably by changing the charge number of the optical vortex under a different phase parameter that indicates the phase change frequency upon increasing the azimuthal angle. The symmetry of focal patterns also changes remarkably upon increasing the charge number. And some novel focal patterns may appear, including a multiple-peak array, wheel focal pattern, or swallow-tailed focal pattern.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  30. X. Lian and B. Lü, “Phase singularities of nonparaxial cosh-Gaussian vortex beams diffracted by a rectangular aperture,” Opt. Laser Technol. 43, 1264–1269 (2011).
    [CrossRef]
  31. X. Gao, Q. Wang, Q. Zhan, M. Yun, H. Guo, and S. Zhuang, “Focal patterns of higher order hyperbolic-cosine-Gaussian beam with one optical vortex,” Opt. Quantum Electron. 42, 369–380 (2011).
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2013 (1)

C.-F. Kuo and S.-C. Chu, “Calculation of the force acting on a micro-sized particle with optical vortex array laser beam tweezers,” Proc. SPIE 8637, 86370A (2013).
[CrossRef]

2012 (5)

R. Talebzadeh, “Optical vortex bullets in inhomogeneous dispersive nonlinear fibers,” Opt. Eng. 51, 055003 (2012).
[CrossRef]

A. Popiołek-Masajada, J. Masajada, and I. Augustyniak, “New scanning technique for optical vortex microscopy,” Proc. SPIE 8697, 86970Z (2012).
[CrossRef]

H. Wang, C. Ding, Z. Zhao, Y. Zhang, and L. Pan, “Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic cosh-Gaussian pulse beams,” Opt. Laser Technol. 44, 1800–1807 (2012).
[CrossRef]

S. D. Patil, M. V. Takale, S. T. Navare, V. J. Fulari, and M. B. Dongare, “Relativistic self-focusing of cosh-Gaussian laser beams in a plasma,” Opt. Laser Technol. 44, 314–317 (2012).
[CrossRef]

H. T. Eyyuboğlu, “Scintillation behavior of cos, cosh and annular Gaussian beams in non-Kolmogorov turbulence,” Appl. Phys. B 108, 335–343 (2012).
[CrossRef]

2011 (5)

T. S. Gill, R. Mahajan, and R. Kaur, “Self-focusing of cosh-Gaussian laser beam in a plasma with weakly relativistic ponderomotive regime,” Phys. Plasmas 18, 033110 (2011).
[CrossRef]

G. Zhou, “Propagation of a higher-order cosh-Gaussian beam in turbulent atmosphere,” Opt. Express 19, 3945–3951 (2011).
[CrossRef]

F. S. Roux, “Evolution of optical vortex distributions in stochastic vortex fields,” Proc. SPIE 7950, 79500T (2011).
[CrossRef]

X. Lian and B. Lü, “Phase singularities of nonparaxial cosh-Gaussian vortex beams diffracted by a rectangular aperture,” Opt. Laser Technol. 43, 1264–1269 (2011).
[CrossRef]

X. Gao, Q. Wang, Q. Zhan, M. Yun, H. Guo, and S. Zhuang, “Focal patterns of higher order hyperbolic-cosine-Gaussian beam with one optical vortex,” Opt. Quantum Electron. 42, 369–380 (2011).

2010 (2)

X. Gao, Z. Li, J. Wang, L. Sun, and S. Zhuang, “Tunable gradient force of hyperbolic-cosine-Gaussian beam with vortices,” Opt. Lasers Eng. 48, 766–773 (2010).
[CrossRef]

X. Gao, Q. Zhan, J. Li, S. Hu, J. Wang, and S. Zhuang, “Dark focal spot shaping of hyperbolic-cosine-Gaussian beam,” J. Opt. Soc. Am. B 27, 696–702 (2010).
[CrossRef]

2009 (2)

X. Gao, J. Wang, H. Gu, and S. Hu, “Focusing of hyperbolic-cosine-Gaussian beam with a non-spiral vortex,” Optik 120, 201–206 (2009).
[CrossRef]

S. D. Patil, S. T. Navare, M. V. Takale, and M. B. Dongare, “Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption,” Opt. Lasers Eng. 47, 604–606 (2009).
[CrossRef]

2007 (4)

X. Gao and J. Li, “Focal shift of apodized truncated hyperbolic-cosine-Gaussian beam,” Opt. Commun. 273, 21–27 (2007).
[CrossRef]

X. Chu, Y. Ni, and G. Zhou, “Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere,” Appl. Phys. B 87, 547–552 (2007).
[CrossRef]

Y. C. Zhang, Y. J. Song, Z. R. Chen, J. H. Ji, and Z. X. Shi, “Virtual sources for a cosh-Gaussian beam,” Opt. Lett. 32, 292–294 (2007).
[CrossRef]

Q. Tang, Y. Yu, and Q. Hu, “A new method to generate flattened Gaussian beam by incoherent combination of cosh Gaussian beams,” Chin. Opt. Lett. 05, 46–48 (2007).

2006 (1)

X. Gao, “Focusing properties of the hyperbolic-cosine-Gaussian beam induced by phase plate,” Phys. Lett. A 360, 330–335 (2006).
[CrossRef]

2005 (2)

Z. Hricha and A. Belafhal, “Focusing properties and focal shift in hyperbolic-cosine-Gaussian beams,” Opt. Commun. 253, 242–249 (2005).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere,” Appl. Opt. 44, 976–983 (2005).
[CrossRef]

2003 (1)

2001 (1)

D. Neshev, A. Nepomnyashchy, and Y. Kivshar, “Nonlinear Aharonov–Bohm scattering by optical vortices,” Phys. Rev. Lett. 87, 043901 (2001).
[CrossRef]

2000 (1)

P. D. Trapani, W. Chinaglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef]

1999 (2)

1998 (2)

1997 (2)

L. W. Casperson, D. G. Hall, and A. A. Tovar, “Sinusoidal-Gaussian beams in complex optical systems,” J. Opt. Soc. Am. A 14, 3341–3348 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

Augustyniak, I.

A. Popiołek-Masajada, J. Masajada, and I. Augustyniak, “New scanning technique for optical vortex microscopy,” Proc. SPIE 8697, 86970Z (2012).
[CrossRef]

Baykal, Y.

Belafhal, A.

Z. Hricha and A. Belafhal, “Focusing properties and focal shift in hyperbolic-cosine-Gaussian beams,” Opt. Commun. 253, 242–249 (2005).
[CrossRef]

Casperson, L. W.

Chen, Z. R.

Chinaglia, W.

P. D. Trapani, W. Chinaglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef]

Chu, S.-C.

C.-F. Kuo and S.-C. Chu, “Calculation of the force acting on a micro-sized particle with optical vortex array laser beam tweezers,” Proc. SPIE 8637, 86370A (2013).
[CrossRef]

Chu, X.

X. Chu, Y. Ni, and G. Zhou, “Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere,” Appl. Phys. B 87, 547–552 (2007).
[CrossRef]

Ding, C.

H. Wang, C. Ding, Z. Zhao, Y. Zhang, and L. Pan, “Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic cosh-Gaussian pulse beams,” Opt. Laser Technol. 44, 1800–1807 (2012).
[CrossRef]

Dongare, M. B.

S. D. Patil, M. V. Takale, S. T. Navare, V. J. Fulari, and M. B. Dongare, “Relativistic self-focusing of cosh-Gaussian laser beams in a plasma,” Opt. Laser Technol. 44, 314–317 (2012).
[CrossRef]

S. D. Patil, S. T. Navare, M. V. Takale, and M. B. Dongare, “Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption,” Opt. Lasers Eng. 47, 604–606 (2009).
[CrossRef]

Eyyuboglu, H. T.

H. T. Eyyuboğlu, “Scintillation behavior of cos, cosh and annular Gaussian beams in non-Kolmogorov turbulence,” Appl. Phys. B 108, 335–343 (2012).
[CrossRef]

H. T. Eyyuboğlu and Y. Baykal, “Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere,” Appl. Opt. 44, 976–983 (2005).
[CrossRef]

Fulari, V. J.

S. D. Patil, M. V. Takale, S. T. Navare, V. J. Fulari, and M. B. Dongare, “Relativistic self-focusing of cosh-Gaussian laser beams in a plasma,” Opt. Laser Technol. 44, 314–317 (2012).
[CrossRef]

Gan, X.

Ganic, D.

Gao, X.

X. Gao, Q. Wang, Q. Zhan, M. Yun, H. Guo, and S. Zhuang, “Focal patterns of higher order hyperbolic-cosine-Gaussian beam with one optical vortex,” Opt. Quantum Electron. 42, 369–380 (2011).

X. Gao, Z. Li, J. Wang, L. Sun, and S. Zhuang, “Tunable gradient force of hyperbolic-cosine-Gaussian beam with vortices,” Opt. Lasers Eng. 48, 766–773 (2010).
[CrossRef]

X. Gao, Q. Zhan, J. Li, S. Hu, J. Wang, and S. Zhuang, “Dark focal spot shaping of hyperbolic-cosine-Gaussian beam,” J. Opt. Soc. Am. B 27, 696–702 (2010).
[CrossRef]

X. Gao, J. Wang, H. Gu, and S. Hu, “Focusing of hyperbolic-cosine-Gaussian beam with a non-spiral vortex,” Optik 120, 201–206 (2009).
[CrossRef]

X. Gao and J. Li, “Focal shift of apodized truncated hyperbolic-cosine-Gaussian beam,” Opt. Commun. 273, 21–27 (2007).
[CrossRef]

X. Gao, “Focusing properties of the hyperbolic-cosine-Gaussian beam induced by phase plate,” Phys. Lett. A 360, 330–335 (2006).
[CrossRef]

Gill, T. S.

T. S. Gill, R. Mahajan, and R. Kaur, “Self-focusing of cosh-Gaussian laser beam in a plasma with weakly relativistic ponderomotive regime,” Phys. Plasmas 18, 033110 (2011).
[CrossRef]

Gu, H.

X. Gao, J. Wang, H. Gu, and S. Hu, “Focusing of hyperbolic-cosine-Gaussian beam with a non-spiral vortex,” Optik 120, 201–206 (2009).
[CrossRef]

Gu, M.

Guo, H.

X. Gao, Q. Wang, Q. Zhan, M. Yun, H. Guo, and S. Zhuang, “Focal patterns of higher order hyperbolic-cosine-Gaussian beam with one optical vortex,” Opt. Quantum Electron. 42, 369–380 (2011).

Hall, D. G.

Hricha, Z.

Z. Hricha and A. Belafhal, “Focusing properties and focal shift in hyperbolic-cosine-Gaussian beams,” Opt. Commun. 253, 242–249 (2005).
[CrossRef]

Hu, Q.

Q. Tang, Y. Yu, and Q. Hu, “A new method to generate flattened Gaussian beam by incoherent combination of cosh Gaussian beams,” Chin. Opt. Lett. 05, 46–48 (2007).

Hu, S.

X. Gao, Q. Zhan, J. Li, S. Hu, J. Wang, and S. Zhuang, “Dark focal spot shaping of hyperbolic-cosine-Gaussian beam,” J. Opt. Soc. Am. B 27, 696–702 (2010).
[CrossRef]

X. Gao, J. Wang, H. Gu, and S. Hu, “Focusing of hyperbolic-cosine-Gaussian beam with a non-spiral vortex,” Optik 120, 201–206 (2009).
[CrossRef]

Ji, J. H.

Kaur, R.

T. S. Gill, R. Mahajan, and R. Kaur, “Self-focusing of cosh-Gaussian laser beam in a plasma with weakly relativistic ponderomotive regime,” Phys. Plasmas 18, 033110 (2011).
[CrossRef]

Kivshar, Y.

D. Neshev, A. Nepomnyashchy, and Y. Kivshar, “Nonlinear Aharonov–Bohm scattering by optical vortices,” Phys. Rev. Lett. 87, 043901 (2001).
[CrossRef]

Kuo, C.-F.

C.-F. Kuo and S.-C. Chu, “Calculation of the force acting on a micro-sized particle with optical vortex array laser beam tweezers,” Proc. SPIE 8637, 86370A (2013).
[CrossRef]

Li, J.

X. Gao, Q. Zhan, J. Li, S. Hu, J. Wang, and S. Zhuang, “Dark focal spot shaping of hyperbolic-cosine-Gaussian beam,” J. Opt. Soc. Am. B 27, 696–702 (2010).
[CrossRef]

X. Gao and J. Li, “Focal shift of apodized truncated hyperbolic-cosine-Gaussian beam,” Opt. Commun. 273, 21–27 (2007).
[CrossRef]

Li, Z.

X. Gao, Z. Li, J. Wang, L. Sun, and S. Zhuang, “Tunable gradient force of hyperbolic-cosine-Gaussian beam with vortices,” Opt. Lasers Eng. 48, 766–773 (2010).
[CrossRef]

Lian, X.

X. Lian and B. Lü, “Phase singularities of nonparaxial cosh-Gaussian vortex beams diffracted by a rectangular aperture,” Opt. Laser Technol. 43, 1264–1269 (2011).
[CrossRef]

Lü, B.

X. Lian and B. Lü, “Phase singularities of nonparaxial cosh-Gaussian vortex beams diffracted by a rectangular aperture,” Opt. Laser Technol. 43, 1264–1269 (2011).
[CrossRef]

B. Lü, B. Zhang, and H. Ma, “Beam-propagation factor and mode-coherence coefficients of hyperbolic-cosine-Gaussian beams,” Opt. Lett. 24, 640–642 (1999).
[CrossRef]

B. Lü, H. Ma, and B. Zhang, “Propagation properties of cosh-Gaussian beams,” Opt. Commun. 164, 165–170 (1999).
[CrossRef]

Ma, H.

Mahajan, R.

T. S. Gill, R. Mahajan, and R. Kaur, “Self-focusing of cosh-Gaussian laser beam in a plasma with weakly relativistic ponderomotive regime,” Phys. Plasmas 18, 033110 (2011).
[CrossRef]

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

Masajada, J.

A. Popiołek-Masajada, J. Masajada, and I. Augustyniak, “New scanning technique for optical vortex microscopy,” Proc. SPIE 8697, 86970Z (2012).
[CrossRef]

Minardi, S.

P. D. Trapani, W. Chinaglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef]

Morita, R.

K. Yamane, Y. Toda, and R. Morita, “Generation of ultrashort optical vortex pulses using optical parametric amplification,” in CLEO Technical Digest (IEEE, 2012), paper JTu1K.4.

Navare, S. T.

S. D. Patil, M. V. Takale, S. T. Navare, V. J. Fulari, and M. B. Dongare, “Relativistic self-focusing of cosh-Gaussian laser beams in a plasma,” Opt. Laser Technol. 44, 314–317 (2012).
[CrossRef]

S. D. Patil, S. T. Navare, M. V. Takale, and M. B. Dongare, “Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption,” Opt. Lasers Eng. 47, 604–606 (2009).
[CrossRef]

Nepomnyashchy, A.

D. Neshev, A. Nepomnyashchy, and Y. Kivshar, “Nonlinear Aharonov–Bohm scattering by optical vortices,” Phys. Rev. Lett. 87, 043901 (2001).
[CrossRef]

Neshev, D.

D. Neshev, A. Nepomnyashchy, and Y. Kivshar, “Nonlinear Aharonov–Bohm scattering by optical vortices,” Phys. Rev. Lett. 87, 043901 (2001).
[CrossRef]

Ni, Y.

X. Chu, Y. Ni, and G. Zhou, “Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere,” Appl. Phys. B 87, 547–552 (2007).
[CrossRef]

Pan, L.

H. Wang, C. Ding, Z. Zhao, Y. Zhang, and L. Pan, “Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic cosh-Gaussian pulse beams,” Opt. Laser Technol. 44, 1800–1807 (2012).
[CrossRef]

Patil, S. D.

S. D. Patil, M. V. Takale, S. T. Navare, V. J. Fulari, and M. B. Dongare, “Relativistic self-focusing of cosh-Gaussian laser beams in a plasma,” Opt. Laser Technol. 44, 314–317 (2012).
[CrossRef]

S. D. Patil, S. T. Navare, M. V. Takale, and M. B. Dongare, “Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption,” Opt. Lasers Eng. 47, 604–606 (2009).
[CrossRef]

Piskarskas, A.

P. D. Trapani, W. Chinaglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef]

Popiolek-Masajada, A.

A. Popiołek-Masajada, J. Masajada, and I. Augustyniak, “New scanning technique for optical vortex microscopy,” Proc. SPIE 8697, 86970Z (2012).
[CrossRef]

Roux, F. S.

F. S. Roux, “Evolution of optical vortex distributions in stochastic vortex fields,” Proc. SPIE 7950, 79500T (2011).
[CrossRef]

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

Shi, Z. X.

Song, Y. J.

Sun, L.

X. Gao, Z. Li, J. Wang, L. Sun, and S. Zhuang, “Tunable gradient force of hyperbolic-cosine-Gaussian beam with vortices,” Opt. Lasers Eng. 48, 766–773 (2010).
[CrossRef]

Takale, M. V.

S. D. Patil, M. V. Takale, S. T. Navare, V. J. Fulari, and M. B. Dongare, “Relativistic self-focusing of cosh-Gaussian laser beams in a plasma,” Opt. Laser Technol. 44, 314–317 (2012).
[CrossRef]

S. D. Patil, S. T. Navare, M. V. Takale, and M. B. Dongare, “Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption,” Opt. Lasers Eng. 47, 604–606 (2009).
[CrossRef]

Talebzadeh, R.

R. Talebzadeh, “Optical vortex bullets in inhomogeneous dispersive nonlinear fibers,” Opt. Eng. 51, 055003 (2012).
[CrossRef]

Tang, Q.

Q. Tang, Y. Yu, and Q. Hu, “A new method to generate flattened Gaussian beam by incoherent combination of cosh Gaussian beams,” Chin. Opt. Lett. 05, 46–48 (2007).

Toda, Y.

K. Yamane, Y. Toda, and R. Morita, “Generation of ultrashort optical vortex pulses using optical parametric amplification,” in CLEO Technical Digest (IEEE, 2012), paper JTu1K.4.

Tovar, A. A.

Trapani, P. D.

P. D. Trapani, W. Chinaglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef]

Valiulis, G.

P. D. Trapani, W. Chinaglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef]

Wang, H.

H. Wang, C. Ding, Z. Zhao, Y. Zhang, and L. Pan, “Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic cosh-Gaussian pulse beams,” Opt. Laser Technol. 44, 1800–1807 (2012).
[CrossRef]

Wang, J.

X. Gao, Z. Li, J. Wang, L. Sun, and S. Zhuang, “Tunable gradient force of hyperbolic-cosine-Gaussian beam with vortices,” Opt. Lasers Eng. 48, 766–773 (2010).
[CrossRef]

X. Gao, Q. Zhan, J. Li, S. Hu, J. Wang, and S. Zhuang, “Dark focal spot shaping of hyperbolic-cosine-Gaussian beam,” J. Opt. Soc. Am. B 27, 696–702 (2010).
[CrossRef]

X. Gao, J. Wang, H. Gu, and S. Hu, “Focusing of hyperbolic-cosine-Gaussian beam with a non-spiral vortex,” Optik 120, 201–206 (2009).
[CrossRef]

Wang, Q.

X. Gao, Q. Wang, Q. Zhan, M. Yun, H. Guo, and S. Zhuang, “Focal patterns of higher order hyperbolic-cosine-Gaussian beam with one optical vortex,” Opt. Quantum Electron. 42, 369–380 (2011).

Yamane, K.

K. Yamane, Y. Toda, and R. Morita, “Generation of ultrashort optical vortex pulses using optical parametric amplification,” in CLEO Technical Digest (IEEE, 2012), paper JTu1K.4.

Yu, Y.

Q. Tang, Y. Yu, and Q. Hu, “A new method to generate flattened Gaussian beam by incoherent combination of cosh Gaussian beams,” Chin. Opt. Lett. 05, 46–48 (2007).

Yun, M.

X. Gao, Q. Wang, Q. Zhan, M. Yun, H. Guo, and S. Zhuang, “Focal patterns of higher order hyperbolic-cosine-Gaussian beam with one optical vortex,” Opt. Quantum Electron. 42, 369–380 (2011).

Zhan, Q.

X. Gao, Q. Wang, Q. Zhan, M. Yun, H. Guo, and S. Zhuang, “Focal patterns of higher order hyperbolic-cosine-Gaussian beam with one optical vortex,” Opt. Quantum Electron. 42, 369–380 (2011).

X. Gao, Q. Zhan, J. Li, S. Hu, J. Wang, and S. Zhuang, “Dark focal spot shaping of hyperbolic-cosine-Gaussian beam,” J. Opt. Soc. Am. B 27, 696–702 (2010).
[CrossRef]

Zhang, B.

Zhang, Y.

H. Wang, C. Ding, Z. Zhao, Y. Zhang, and L. Pan, “Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic cosh-Gaussian pulse beams,” Opt. Laser Technol. 44, 1800–1807 (2012).
[CrossRef]

Zhang, Y. C.

Zhao, Z.

H. Wang, C. Ding, Z. Zhao, Y. Zhang, and L. Pan, “Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic cosh-Gaussian pulse beams,” Opt. Laser Technol. 44, 1800–1807 (2012).
[CrossRef]

Zhou, G.

G. Zhou, “Propagation of a higher-order cosh-Gaussian beam in turbulent atmosphere,” Opt. Express 19, 3945–3951 (2011).
[CrossRef]

X. Chu, Y. Ni, and G. Zhou, “Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere,” Appl. Phys. B 87, 547–552 (2007).
[CrossRef]

Zhuang, S.

X. Gao, Q. Wang, Q. Zhan, M. Yun, H. Guo, and S. Zhuang, “Focal patterns of higher order hyperbolic-cosine-Gaussian beam with one optical vortex,” Opt. Quantum Electron. 42, 369–380 (2011).

X. Gao, Q. Zhan, J. Li, S. Hu, J. Wang, and S. Zhuang, “Dark focal spot shaping of hyperbolic-cosine-Gaussian beam,” J. Opt. Soc. Am. B 27, 696–702 (2010).
[CrossRef]

X. Gao, Z. Li, J. Wang, L. Sun, and S. Zhuang, “Tunable gradient force of hyperbolic-cosine-Gaussian beam with vortices,” Opt. Lasers Eng. 48, 766–773 (2010).
[CrossRef]

Zozulya, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (2)

X. Chu, Y. Ni, and G. Zhou, “Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere,” Appl. Phys. B 87, 547–552 (2007).
[CrossRef]

H. T. Eyyuboğlu, “Scintillation behavior of cos, cosh and annular Gaussian beams in non-Kolmogorov turbulence,” Appl. Phys. B 108, 335–343 (2012).
[CrossRef]

Chin. Opt. Lett. (1)

Q. Tang, Y. Yu, and Q. Hu, “A new method to generate flattened Gaussian beam by incoherent combination of cosh Gaussian beams,” Chin. Opt. Lett. 05, 46–48 (2007).

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

Opt. Commun. (3)

B. Lü, H. Ma, and B. Zhang, “Propagation properties of cosh-Gaussian beams,” Opt. Commun. 164, 165–170 (1999).
[CrossRef]

Z. Hricha and A. Belafhal, “Focusing properties and focal shift in hyperbolic-cosine-Gaussian beams,” Opt. Commun. 253, 242–249 (2005).
[CrossRef]

X. Gao and J. Li, “Focal shift of apodized truncated hyperbolic-cosine-Gaussian beam,” Opt. Commun. 273, 21–27 (2007).
[CrossRef]

Opt. Eng. (1)

R. Talebzadeh, “Optical vortex bullets in inhomogeneous dispersive nonlinear fibers,” Opt. Eng. 51, 055003 (2012).
[CrossRef]

Opt. Express (2)

Opt. Laser Technol. (3)

S. D. Patil, M. V. Takale, S. T. Navare, V. J. Fulari, and M. B. Dongare, “Relativistic self-focusing of cosh-Gaussian laser beams in a plasma,” Opt. Laser Technol. 44, 314–317 (2012).
[CrossRef]

H. Wang, C. Ding, Z. Zhao, Y. Zhang, and L. Pan, “Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic cosh-Gaussian pulse beams,” Opt. Laser Technol. 44, 1800–1807 (2012).
[CrossRef]

X. Lian and B. Lü, “Phase singularities of nonparaxial cosh-Gaussian vortex beams diffracted by a rectangular aperture,” Opt. Laser Technol. 43, 1264–1269 (2011).
[CrossRef]

Opt. Lasers Eng. (2)

X. Gao, Z. Li, J. Wang, L. Sun, and S. Zhuang, “Tunable gradient force of hyperbolic-cosine-Gaussian beam with vortices,” Opt. Lasers Eng. 48, 766–773 (2010).
[CrossRef]

S. D. Patil, S. T. Navare, M. V. Takale, and M. B. Dongare, “Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption,” Opt. Lasers Eng. 47, 604–606 (2009).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

X. Gao, Q. Wang, Q. Zhan, M. Yun, H. Guo, and S. Zhuang, “Focal patterns of higher order hyperbolic-cosine-Gaussian beam with one optical vortex,” Opt. Quantum Electron. 42, 369–380 (2011).

Optik (1)

X. Gao, J. Wang, H. Gu, and S. Hu, “Focusing of hyperbolic-cosine-Gaussian beam with a non-spiral vortex,” Optik 120, 201–206 (2009).
[CrossRef]

Phys. Lett. A (1)

X. Gao, “Focusing properties of the hyperbolic-cosine-Gaussian beam induced by phase plate,” Phys. Lett. A 360, 330–335 (2006).
[CrossRef]

Phys. Plasmas (1)

T. S. Gill, R. Mahajan, and R. Kaur, “Self-focusing of cosh-Gaussian laser beam in a plasma with weakly relativistic ponderomotive regime,” Phys. Plasmas 18, 033110 (2011).
[CrossRef]

Phys. Rev. Lett. (3)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

P. D. Trapani, W. Chinaglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843–3846 (2000).
[CrossRef]

D. Neshev, A. Nepomnyashchy, and Y. Kivshar, “Nonlinear Aharonov–Bohm scattering by optical vortices,” Phys. Rev. Lett. 87, 043901 (2001).
[CrossRef]

Proc. SPIE (3)

F. S. Roux, “Evolution of optical vortex distributions in stochastic vortex fields,” Proc. SPIE 7950, 79500T (2011).
[CrossRef]

C.-F. Kuo and S.-C. Chu, “Calculation of the force acting on a micro-sized particle with optical vortex array laser beam tweezers,” Proc. SPIE 8637, 86370A (2013).
[CrossRef]

A. Popiołek-Masajada, J. Masajada, and I. Augustyniak, “New scanning technique for optical vortex microscopy,” Proc. SPIE 8697, 86970Z (2012).
[CrossRef]

Other (2)

K. Yamane, Y. Toda, and R. Morita, “Generation of ultrashort optical vortex pulses using optical parametric amplification,” in CLEO Technical Digest (IEEE, 2012), paper JTu1K.4.

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

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Figures (14)

Fig. 1.
Fig. 1.

Intensity distributions for NA=0.4, β=1, m1=1, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 2.
Fig. 2.

Intensity distributions for NA=0.4, β=1, m1=2, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 3.
Fig. 3.

Intensity distributions for NA=0.4, β=1, m1=3, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 4.
Fig. 4.

Intensity distributions for NA=0.4, β=1, m1=4, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 5.
Fig. 5.

Intensity distributions for NA=0.4, β=1, m1=5, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 6.
Fig. 6.

Intensity distributions for NA=0.4, β=4, m1=1, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 7.
Fig. 7.

Intensity distributions for NA=0.4, β=4, m1=2, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 8.
Fig. 8.

Intensity distributions for NA=0.4, β=4, m1=3, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 9.
Fig. 9.

Intensity distributions for NA=0.4, β=4, m1=4, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 10.
Fig. 10.

Intensity distributions for NA=0.4, β=4, m1=5, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 11.
Fig. 11.

Intensity distributions for NA=0.9, β=1, m1=3, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 12.
Fig. 12.

Intensity distributions for NA=0.9, β=1, m1=4, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 13.
Fig. 13.

Intensity distributions for NA=0.9, β=4, m1=3, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Fig. 14.
Fig. 14.

Intensity distributions for NA=0.9, β=4, m1=4, and (a) m2=0, (b) m2=1, (c) m2=2, (d) m2=3, (e) m2=4, and (f) m2=5, respectively.

Equations (3)

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E(θ,φ)=A0·cosh[NA1·βx·sin(θ)·cos(φ)]·cosh[NA1·βy·sin(θ)·sin(φ)]·exp[sin2(θ)NA2·w2]·exp[iπsin(m1ϕ)im2ϕ],
E⃗(ρ,ψ,z)=1λθ1θ202πE(θ,φ)·{[cosθ+sin2φ(1cosθ)]x+cosφsinφ(cosθ1)ycosφsinθz}·exp[ikρsinθcos(φψ)]·exp(ikzcosθ)sinθdθdφ,
E⃗(ρ,ψ,z)=A0λ0θ02π{cosh[NA1·βx·sinθ·cosφ]·cosh[NA1·βy·sin(θ)·sin(φ)]·exp[sin2(θ)NA2·w2]·exp[iπsin(m1ϕ)im2ϕ]}·{[cosθ+sin2φ(1cosθ)]x+cosφsinφ(cosθ1)ycosφsinθz}·exp[ikρsinθcos(φψ)]·exp(ikzcosθ)sinθdθdφ.

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