Abstract

Lens axicons, i.e., lenses or lens systems designed to work like axicons, can be a simple and inexpensive way of generating the characteristic axicon focal line. In the design of most lens axicons, only on-axis properties have been considered. We present the design of a lens axicon with improved off-axis characteristics. It is constructed from a singlet lens but with a double-pass feature that allows for a line of uniform width and a stop positioned to minimize aberrations. We perform off-axis analysis and experiments for this system and for another lens axicon, one designed for its on-axis characteristics. We conclude that the off-axis performance of the double-pass axicon is better than both that of an ordinary cone axicon and that of the other lens axicon.

© 2007 Optical Society of America

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References

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  1. J. H. McLeod, "The axicon: a new type of optical element," J. Opt. Soc. Am. 18, 592-597 (1954).
    [CrossRef]
  2. Z. Jaroszewicz, Axicons: Design and Propagation Properties, Vol. 5 of Research and Development Treatises (SPIE Polish Chapter, Warsaw, 1997).
  3. X. Zhang, B. Zhao, and Z. Li, "Measurement method of spatial straightness error using nondiffracting beam and moiré-fringe technology," J. Opt. A , Pure Appl. Opt. 6, 121-126 (2004).
    [CrossRef]
  4. J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-554 (2000).
    [CrossRef]
  5. Y. F. Xiao, H. H. Chu, H. E. Tsai, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, "Efficient generation of extended plasma waveguides with the axicon ignitor-heater scheme," Phys. Plasmas 11, L21-L23 (2004).
    [CrossRef]
  6. Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, "High-resolution optical coherence tomography over a large depth range with an axicon lens," Opt. Lett. 27, 243-245 (2002).
    [CrossRef]
  7. G. Haüsler and W. Heckel, "Light sectioning with a large depth and high resolution," Appl. Opt. 27, 5165-5169 (1988).
    [CrossRef] [PubMed]
  8. W. Chi and N. George, "Electronic imaging using a logarithmic asphere," Opt. Lett. 26, 875-877 (2001).
    [CrossRef]
  9. J. Pu, H. Zhang, and S. Nemoto, "Uniform-intensity axicon: a lens coded with a symetrically cubic phase plate," Opt. Quantum Electron. 33, 653-660 (2001).
    [CrossRef]
  10. A. A. S. Awwal and J. U. Ahmed, "Refractive system for generation of high-power diffraction-free laser beams," Opt. Laser Technol. 33, 97-102 (2001).
    [CrossRef]
  11. K. M. Iftekharuddin, A. A. S. Awwal, and M. A. Karim, "Gaussian-to-Bessel beam transformation using a split refractive system," Appl. Opt. 32, 2252-2256 (1993).
    [CrossRef]
  12. R. M. Herman and T. A. Wiggins, "Production and uses of diffractionless beams," J. Opt. Soc. Am. A 8, 932-942 (1991).
    [CrossRef]
  13. R. M. Herman and T. A. Wiggins, "High-efficiency diffractionless beams of constant size and intensity," Appl. Opt. 33, 7297-7306 (1994).
    [CrossRef] [PubMed]
  14. T. Aruga, "Generation of long-range nondiffracting narrow light beams," Appl. Opt. 36, 3762-3768 (1997).
    [CrossRef] [PubMed]
  15. T. Aruga and S. W. Li, "Super high resolution for long-range imaging," Appl. Opt. 38, 2795-2799 (1999).
    [CrossRef]
  16. Z. Jaroszewicz and J. Morales, "Lens axicons: systems composed of a diverging aberrated lens and a perfect converging lens," J. Opt. Soc. Am. A 15, 2383-2390 (1998).
    [CrossRef]
  17. Z. Jaroszewicz and J. Morales, "Lens axicons: systems composed of a diverging aberrated lens and a converging aberrated lens," J. Opt. Soc. Am. A 16, 191-197 (1999).
    [CrossRef]
  18. J. Pu, H. Zhang, and S. Nemoto, "Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields," Opt. Eng. 39, 803-807 (2000).
    [CrossRef]
  19. A. Burvall, K. Kolacz, Z. Jaroszewicz, and A. T. Friberg, "A simple lens axicon," Appl. Opt. 43, 4838-4844 (2004).
    [CrossRef] [PubMed]
  20. J. Rayces, "Formation of axicon images," J. Opt. Soc. Am. 48, 576-578 (1958).
    [CrossRef]
  21. W. H. Steel, "Axicons with spherical surfaces," in Colloquia of the International Commission for Optics: Optics in Metrology, P. Mollet, ed. (Pergamon Press, 1960), pp. 181-192.
  22. We refer to positive spherical aberration when the wavefront aberration is positive, i.e., when the transverse and longitudinal aberrations are negative, and vice versa for negative spherical aberration. See, e.g., W. T. Welford, Aberrations of the Symmetrical Optical System (Academic Press, 1974).
  23. J. Sochacki, Z. Jaroszewicz, L. R. Staronski, and A. Kolodziejczyk, "Annular-aperture logarithmic axicon," J. Opt. Soc. Am. A 10, 1765-1768 (1993).
    [CrossRef]
  24. A. G. Sedukhin, "Beam-preshaping axicon focusing," J. Opt. Soc. Am. A 15, 3057-3066 (1998).
    [CrossRef]
  25. R. Arimoto, C. Saloma, T. Tanaka, and S. Kawata, "Imaging properties of an axicon in a scanning optical system," Appl. Opt. 31, 6653-6657 (1992).
    [CrossRef] [PubMed]
  26. Z. Bin and Z. Zhu, "Diffraction property of an axicon in oblique illumination," Appl. Opt. 37, 2563-2568 (1998).
    [CrossRef]
  27. T. Tanaka and S. Yamamoto, "Comparison of aberration between axicon and lens," Opt. Commun. 184, 113-118 (2000).
    [CrossRef]
  28. A. Thaning, Z. Jaroszewicz, and A. T. Friberg, "Diffractive axicons in oblique illumination: analysis and experiments and comparison with elliptical axicons," Appl. Opt. 42, 9-17 (2003).
    [CrossRef] [PubMed]
  29. G. E. Sommargren and H. J. Weaver, "Diffraction of light by an opaque sphere. I: Description and properties of the diffraction pattern," Appl. Opt. 29, 4646-4657 (1990).
    [CrossRef] [PubMed]
  30. J. J. Stamnes, Waves in Focal Regions (Adam Hilger, 1986).

2004 (3)

Y. F. Xiao, H. H. Chu, H. E. Tsai, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, "Efficient generation of extended plasma waveguides with the axicon ignitor-heater scheme," Phys. Plasmas 11, L21-L23 (2004).
[CrossRef]

X. Zhang, B. Zhao, and Z. Li, "Measurement method of spatial straightness error using nondiffracting beam and moiré-fringe technology," J. Opt. A , Pure Appl. Opt. 6, 121-126 (2004).
[CrossRef]

A. Burvall, K. Kolacz, Z. Jaroszewicz, and A. T. Friberg, "A simple lens axicon," Appl. Opt. 43, 4838-4844 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

2001 (3)

W. Chi and N. George, "Electronic imaging using a logarithmic asphere," Opt. Lett. 26, 875-877 (2001).
[CrossRef]

J. Pu, H. Zhang, and S. Nemoto, "Uniform-intensity axicon: a lens coded with a symetrically cubic phase plate," Opt. Quantum Electron. 33, 653-660 (2001).
[CrossRef]

A. A. S. Awwal and J. U. Ahmed, "Refractive system for generation of high-power diffraction-free laser beams," Opt. Laser Technol. 33, 97-102 (2001).
[CrossRef]

2000 (3)

J. Pu, H. Zhang, and S. Nemoto, "Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields," Opt. Eng. 39, 803-807 (2000).
[CrossRef]

T. Tanaka and S. Yamamoto, "Comparison of aberration between axicon and lens," Opt. Commun. 184, 113-118 (2000).
[CrossRef]

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

1999 (2)

1998 (3)

1997 (1)

1994 (1)

1993 (2)

1992 (1)

1991 (1)

1990 (1)

1988 (1)

1958 (1)

1954 (1)

J. H. McLeod, "The axicon: a new type of optical element," J. Opt. Soc. Am. 18, 592-597 (1954).
[CrossRef]

Ahmed, J. U.

A. A. S. Awwal and J. U. Ahmed, "Refractive system for generation of high-power diffraction-free laser beams," Opt. Laser Technol. 33, 97-102 (2001).
[CrossRef]

Arimoto, R.

Arlt, J.

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

Aruga, T.

Awwal, A. A. S.

A. A. S. Awwal and J. U. Ahmed, "Refractive system for generation of high-power diffraction-free laser beams," Opt. Laser Technol. 33, 97-102 (2001).
[CrossRef]

K. M. Iftekharuddin, A. A. S. Awwal, and M. A. Karim, "Gaussian-to-Bessel beam transformation using a split refractive system," Appl. Opt. 32, 2252-2256 (1993).
[CrossRef]

Bin, Z.

Burvall, A.

Chen, S. Y.

Y. F. Xiao, H. H. Chu, H. E. Tsai, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, "Efficient generation of extended plasma waveguides with the axicon ignitor-heater scheme," Phys. Plasmas 11, L21-L23 (2004).
[CrossRef]

Chen, Z.

Chi, W.

Chu, H. H.

Y. F. Xiao, H. H. Chu, H. E. Tsai, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, "Efficient generation of extended plasma waveguides with the axicon ignitor-heater scheme," Phys. Plasmas 11, L21-L23 (2004).
[CrossRef]

Dholakia, K.

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

Ding, Z.

Friberg, A. T.

George, N.

Haüsler, G.

Heckel, W.

Herman, R. M.

Hitomi, T.

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

Iftekharuddin, K. M.

Jaroszewicz, Z.

Karim, M. A.

Kawata, S.

Kolacz, K.

Kolodziejczyk, A.

Lee, C. H.

Y. F. Xiao, H. H. Chu, H. E. Tsai, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, "Efficient generation of extended plasma waveguides with the axicon ignitor-heater scheme," Phys. Plasmas 11, L21-L23 (2004).
[CrossRef]

Li, S. W.

Li, Z.

X. Zhang, B. Zhao, and Z. Li, "Measurement method of spatial straightness error using nondiffracting beam and moiré-fringe technology," J. Opt. A , Pure Appl. Opt. 6, 121-126 (2004).
[CrossRef]

Lin, J. Y.

Y. F. Xiao, H. H. Chu, H. E. Tsai, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, "Efficient generation of extended plasma waveguides with the axicon ignitor-heater scheme," Phys. Plasmas 11, L21-L23 (2004).
[CrossRef]

McLeod, J. H.

J. H. McLeod, "The axicon: a new type of optical element," J. Opt. Soc. Am. 18, 592-597 (1954).
[CrossRef]

Morales, J.

Nelson, J. S.

Nemoto, S.

J. Pu, H. Zhang, and S. Nemoto, "Uniform-intensity axicon: a lens coded with a symetrically cubic phase plate," Opt. Quantum Electron. 33, 653-660 (2001).
[CrossRef]

J. Pu, H. Zhang, and S. Nemoto, "Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields," Opt. Eng. 39, 803-807 (2000).
[CrossRef]

Pu, J.

J. Pu, H. Zhang, and S. Nemoto, "Uniform-intensity axicon: a lens coded with a symetrically cubic phase plate," Opt. Quantum Electron. 33, 653-660 (2001).
[CrossRef]

J. Pu, H. Zhang, and S. Nemoto, "Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields," Opt. Eng. 39, 803-807 (2000).
[CrossRef]

Rayces, J.

Ren, H.

Saloma, C.

Sedukhin, A. G.

Sochacki, J.

Sommargren, G. E.

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Adam Hilger, 1986).

Staronski, L. R.

Steel, W. H.

W. H. Steel, "Axicons with spherical surfaces," in Colloquia of the International Commission for Optics: Optics in Metrology, P. Mollet, ed. (Pergamon Press, 1960), pp. 181-192.

Tanaka, T.

Thaning, A.

Tsai, H. E.

Y. F. Xiao, H. H. Chu, H. E. Tsai, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, "Efficient generation of extended plasma waveguides with the axicon ignitor-heater scheme," Phys. Plasmas 11, L21-L23 (2004).
[CrossRef]

Wang, J.

Y. F. Xiao, H. H. Chu, H. E. Tsai, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, "Efficient generation of extended plasma waveguides with the axicon ignitor-heater scheme," Phys. Plasmas 11, L21-L23 (2004).
[CrossRef]

Weaver, H. J.

Wiggins, T. A.

Xiao, Y. F.

Y. F. Xiao, H. H. Chu, H. E. Tsai, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, "Efficient generation of extended plasma waveguides with the axicon ignitor-heater scheme," Phys. Plasmas 11, L21-L23 (2004).
[CrossRef]

Yamamoto, S.

T. Tanaka and S. Yamamoto, "Comparison of aberration between axicon and lens," Opt. Commun. 184, 113-118 (2000).
[CrossRef]

Zhang, H.

J. Pu, H. Zhang, and S. Nemoto, "Uniform-intensity axicon: a lens coded with a symetrically cubic phase plate," Opt. Quantum Electron. 33, 653-660 (2001).
[CrossRef]

J. Pu, H. Zhang, and S. Nemoto, "Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields," Opt. Eng. 39, 803-807 (2000).
[CrossRef]

Zhang, X.

X. Zhang, B. Zhao, and Z. Li, "Measurement method of spatial straightness error using nondiffracting beam and moiré-fringe technology," J. Opt. A , Pure Appl. Opt. 6, 121-126 (2004).
[CrossRef]

Zhao, B.

X. Zhang, B. Zhao, and Z. Li, "Measurement method of spatial straightness error using nondiffracting beam and moiré-fringe technology," J. Opt. A , Pure Appl. Opt. 6, 121-126 (2004).
[CrossRef]

Zhao, Y.

Zhu, Z.

Appl. Opt. (10)

G. E. Sommargren and H. J. Weaver, "Diffraction of light by an opaque sphere. I: Description and properties of the diffraction pattern," Appl. Opt. 29, 4646-4657 (1990).
[CrossRef] [PubMed]

R. Arimoto, C. Saloma, T. Tanaka, and S. Kawata, "Imaging properties of an axicon in a scanning optical system," Appl. Opt. 31, 6653-6657 (1992).
[CrossRef] [PubMed]

K. M. Iftekharuddin, A. A. S. Awwal, and M. A. Karim, "Gaussian-to-Bessel beam transformation using a split refractive system," Appl. Opt. 32, 2252-2256 (1993).
[CrossRef]

R. M. Herman and T. A. Wiggins, "High-efficiency diffractionless beams of constant size and intensity," Appl. Opt. 33, 7297-7306 (1994).
[CrossRef] [PubMed]

T. Aruga, "Generation of long-range nondiffracting narrow light beams," Appl. Opt. 36, 3762-3768 (1997).
[CrossRef] [PubMed]

Z. Bin and Z. Zhu, "Diffraction property of an axicon in oblique illumination," Appl. Opt. 37, 2563-2568 (1998).
[CrossRef]

T. Aruga and S. W. Li, "Super high resolution for long-range imaging," Appl. Opt. 38, 2795-2799 (1999).
[CrossRef]

G. Haüsler and W. Heckel, "Light sectioning with a large depth and high resolution," Appl. Opt. 27, 5165-5169 (1988).
[CrossRef] [PubMed]

A. Thaning, Z. Jaroszewicz, and A. T. Friberg, "Diffractive axicons in oblique illumination: analysis and experiments and comparison with elliptical axicons," Appl. Opt. 42, 9-17 (2003).
[CrossRef] [PubMed]

A. Burvall, K. Kolacz, Z. Jaroszewicz, and A. T. Friberg, "A simple lens axicon," Appl. Opt. 43, 4838-4844 (2004).
[CrossRef] [PubMed]

Appl. Phys. B (1)

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

J. Opt. A (1)

X. Zhang, B. Zhao, and Z. Li, "Measurement method of spatial straightness error using nondiffracting beam and moiré-fringe technology," J. Opt. A , Pure Appl. Opt. 6, 121-126 (2004).
[CrossRef]

J. Opt. Soc. Am. (2)

J. H. McLeod, "The axicon: a new type of optical element," J. Opt. Soc. Am. 18, 592-597 (1954).
[CrossRef]

J. Rayces, "Formation of axicon images," J. Opt. Soc. Am. 48, 576-578 (1958).
[CrossRef]

J. Opt. Soc. Am. A (5)

Opt. Commun. (1)

T. Tanaka and S. Yamamoto, "Comparison of aberration between axicon and lens," Opt. Commun. 184, 113-118 (2000).
[CrossRef]

Opt. Eng. (1)

J. Pu, H. Zhang, and S. Nemoto, "Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields," Opt. Eng. 39, 803-807 (2000).
[CrossRef]

Opt. Laser Technol. (1)

A. A. S. Awwal and J. U. Ahmed, "Refractive system for generation of high-power diffraction-free laser beams," Opt. Laser Technol. 33, 97-102 (2001).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

J. Pu, H. Zhang, and S. Nemoto, "Uniform-intensity axicon: a lens coded with a symetrically cubic phase plate," Opt. Quantum Electron. 33, 653-660 (2001).
[CrossRef]

Phys. Plasmas (1)

Y. F. Xiao, H. H. Chu, H. E. Tsai, C. H. Lee, J. Y. Lin, J. Wang, and S. Y. Chen, "Efficient generation of extended plasma waveguides with the axicon ignitor-heater scheme," Phys. Plasmas 11, L21-L23 (2004).
[CrossRef]

Other (4)

Z. Jaroszewicz, Axicons: Design and Propagation Properties, Vol. 5 of Research and Development Treatises (SPIE Polish Chapter, Warsaw, 1997).

W. H. Steel, "Axicons with spherical surfaces," in Colloquia of the International Commission for Optics: Optics in Metrology, P. Mollet, ed. (Pergamon Press, 1960), pp. 181-192.

We refer to positive spherical aberration when the wavefront aberration is positive, i.e., when the transverse and longitudinal aberrations are negative, and vice versa for negative spherical aberration. See, e.g., W. T. Welford, Aberrations of the Symmetrical Optical System (Academic Press, 1974).

J. J. Stamnes, Waves in Focal Regions (Adam Hilger, 1986).

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Figures (8)

Fig. 1
Fig. 1

Principle and notation for the suggested double-pass axicon. Parameter values are given in Table 1.

Fig. 2
Fig. 2

On-axis intensity for the BK7 double-pass lens axicon in Fig. 1. The line indicates values obtained from numerical evaluation of the Fresnel diffraction integral, normalized to 1. The dots indicate experimental values, rescaled from arbitrary units to fit the numerical values.

Fig. 3
Fig. 3

Half-width of the focal line for the BK7 double-pass lens axicon in Fig. 1. The solid curve was obtained numerically from the stationary-phase approximation in Eq. (1). The solid dots indicate experimental measurements. The dotted curves show the width of the weak Arago spot that can be seen before and after the focal line.

Fig. 4
Fig. 4

Experimental arrangement to test the axicon performance.

Fig. 5
Fig. 5

Numerically obtained transverse intensity pattern of the double-pass axicon in Fig. 1, at z = 90 mm and at an oblique illumination angle of (a) ω = 0 ° , (b) ω = 2 ° , and (c) ω = 4 ° . For comparison, numerical calculations of the transverse intensity of a corresponding linear cone axicon ( α = 0.05 , z = 120   mm ) at (c) ω = 0 ° , (d) ω = 2 ° , and (e) ω = 4 ° are also shown.

Fig. 6
Fig. 6

Numerically obtained transverse intensity patterns for the doublet-lens axicon in Ref. 19, at z = 220   mm for an oblique illumination angle of (a) ω = 0 ° , (b) ω = 2 ° , and (c) ω = 4 ° . For comparison, numerical calculations of the transverse intensity pattern of a corresponding linear cone axicon ( α = 0.025 , z = 220   mm ) at (d) ω = 0 ° , (e) ω = 2 ° , and (f) ω = 3 ° are also shown. Note the change of scale in (c) and (f).

Fig. 7
Fig. 7

Experimental results for the double-pass axicon in Fig. 1, at z = 70   mm and (a) ω = 0 ° , (b) ω = 2 ° , and (c) ω = 4 ° . Similarly, at z = 90   mm and (d) ω = 0 ° , (e) ω = 2 ° , and (f) ω = 4°.

Fig. 8
Fig. 8

Experimental results for the doublet-lens axicon in Ref. 19, at z = 220   mm for an oblique illumination angle of (a) ω = 0 ° , (b) ω = 2 ° , and (c) ω = 4 ° . Note the change of scale in (c).

Tables (1)

Tables Icon

Table 1 Parameters of the Tested Double-Pass Lens Axicon

Equations (1)

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w ( z ) = 2.4048 λ 2 π 1 ϕ [ ρ c ( z ) ] ,

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