Abstract

A simple and rigorous analytical expression of the propagating field behind an axicon illuminated by an azimuthally polarized beam has been deduced by use of the vector interference theory. This analytical expression can easily be used to calculate accurately the propagation field distribution of azimuthally polarized beams throughout the whole space behind an axicon with any size base angle, not just restricted inside the geometric focal region as does the Fresnel diffraction integral. The numerical results show that the pattern of the beam produced by the azimuthally polarized Gaussian beam that passes through an axicon is a multiring, almost-equal-intensity, and propagation-invariant interference beam in the geometric focal region. The number of bright rings increases with the propagation distance, reaching its maximum at half of the geometric focal length and then decreasing. The intensity of bright rings gradually decreases with the propagation distance in the geometric focal region. However, in the far-field (noninterference) region, only one single-ring pattern is produced and the dark spot size expands rapidly with propagation distance.

© 2007 Optical Society of America

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References

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2006 (1)

C. Zheng, Y. Zhang, and D. Zhao, "Calculation of the vectorial field distribution of an axicon illuminated by a linearly polarized Gaussian beam," Optik 117, 118-122 (2006).
[CrossRef]

2005 (1)

2004 (1)

M. Lei and B. Yao, "Characteristics of beam profile of Gaussian beam passing through an axicon," Opt. Commun. 239, 367-372 (2004).
[CrossRef]

2003 (2)

C. Zhou, J. Jia, and L. Liu, "Circular Dammann grating," Opt. Lett. 28, 2174-2176 (2003).
[CrossRef] [PubMed]

M. de Angelis, L. Cacciapuoti, G. Pierattini, and G. M. Tino, "Axially symmetric hollow beams using refractive conical lenses," Opt. Lasers Eng. 39, 283-291 (2003).
[CrossRef]

2002 (2)

B. Dépret, P. Verkerk, and D. Hennequin, "Characterization and modeling of the hollow beam produced by a real conical lens," Opt. Commun. 211, 31-38 (2002).
[CrossRef]

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, "Transfer of orbital angular momentum to an optically trapped low-index particle," Phys. Rev. A 66, 063402 (2002).
[CrossRef]

2000 (2)

V. Jarutis, R. Paskauskas, and A. Stabinis, "Focusing of Laguerre-Gaussian beams by axicon," Opt. Commun. 184, 105-112 (2000).
[CrossRef]

J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297-301 (2000).
[CrossRef]

1999 (1)

1998 (1)

I. Manek, Y. B. Ovchinnikov, and R. Grimm, "Generation of a hollow laser beam for atom trapping using an axicon," Opt. Commun. 147, 67-70 (1998).
[CrossRef]

1996 (1)

C. Paterson and R. Smith, "Higher-order Bessel waves produced by axicon-type computer-generated holograms," Opt. Commun. 124, 121-130 (1996).
[CrossRef]

1991 (1)

1989 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

1954 (1)

J. Opt. Soc. Am. (1)

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

Opt. Commun. (6)

C. Paterson and R. Smith, "Higher-order Bessel waves produced by axicon-type computer-generated holograms," Opt. Commun. 124, 121-130 (1996).
[CrossRef]

J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297-301 (2000).
[CrossRef]

B. Dépret, P. Verkerk, and D. Hennequin, "Characterization and modeling of the hollow beam produced by a real conical lens," Opt. Commun. 211, 31-38 (2002).
[CrossRef]

V. Jarutis, R. Paskauskas, and A. Stabinis, "Focusing of Laguerre-Gaussian beams by axicon," Opt. Commun. 184, 105-112 (2000).
[CrossRef]

M. Lei and B. Yao, "Characteristics of beam profile of Gaussian beam passing through an axicon," Opt. Commun. 239, 367-372 (2004).
[CrossRef]

I. Manek, Y. B. Ovchinnikov, and R. Grimm, "Generation of a hollow laser beam for atom trapping using an axicon," Opt. Commun. 147, 67-70 (1998).
[CrossRef]

Opt. Lasers Eng. (1)

M. de Angelis, L. Cacciapuoti, G. Pierattini, and G. M. Tino, "Axially symmetric hollow beams using refractive conical lenses," Opt. Lasers Eng. 39, 283-291 (2003).
[CrossRef]

Opt. Lett. (2)

Optik (1)

C. Zheng, Y. Zhang, and D. Zhao, "Calculation of the vectorial field distribution of an axicon illuminated by a linearly polarized Gaussian beam," Optik 117, 118-122 (2006).
[CrossRef]

Phys. Rev. A (1)

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, "Transfer of orbital angular momentum to an optically trapped low-index particle," Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Ray tracing model and geometric scheme of a Gaussian beam that passes through an axicon illuminated by an azimuthally polarized incoming beam.

Fig. 2
Fig. 2

Intensity distribution at the XZ plane behind the axicon with n = 2 and a = 2 ° when the azimuthally polarized incident beam is used. Z m ( w 0 / tan σ ) is the length of the interference zone in the direction of the Z axis.

Fig. 3
Fig. 3

Beam patterns behind the axicon: (a) z = 0.01 Z m , (b) z = 0.05 Z m , (c) z = 0.1 Z m , (d) z = 0.5 Z m .

Fig. 4
Fig. 4

Beam patterns behind the axicon: (a) z = 0.95 Z m , (b) z = 1.0 Z m , (c) z = 1.2 Z m , (d) z = 2 Z m .

Fig. 5
Fig. 5

Intensity of the bright rings versus the propagation distance z.

Equations (12)

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p 0 = [ a ( φ ) b ( φ ) 0 ] .
E = E 1 + E 2 .
I φ ( ρ , φ , z ) = t s 2 [ E 1 2 + E 2 2 2 E 1 E 2 cos ( k Δ ) ] ,
E 1 = exp ( w 1 2 / w 0 2 ) ,
E 2 = exp ( w 2 2 / w 0 2 ) ,
Δ = n ( d 1 d 2 ) + ( r 1 r 2 ) ,
  w 1 = z tan σ + ρ 1 tan α tan σ ,
w 2 = z tan σ ρ 1 tan α tan σ ,
r 1 = 1 cos σ z + ρ tan α 1 tan α tan σ ,
r 2 = 1 cos σ z ρ tan α 1 tan α tan σ ,
d 1 = d ( 1 tan α tan σ ) tan α ( z + ρ tan α ) 1 tan α tan σ ,
d 2 = d ( 1 tan α tan σ ) + tan α ( z ρ tan α ) 1 tan α tan σ .

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