Abstract

In this work we apply the Dammann grating concept to generate an equal-intensity square array of Bessel quasi-free diffraction beams that diverge from a common center. We generate a binary phase mask that combines the axicon phase with the phase of a Dammann grating. The procedure can be extended to include vortex spiral phases that generate an array of optical pipes. Experimental results are provided by means of a twisted nematic liquid crystal display operating as a binary π phase spatial light modulator.

© 2012 Optical Society of America

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  1. J. Durnin, “Exact solutions for nondiffracting beams I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  2. D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
    [CrossRef]
  3. D. Li, K. Imasaki, S. Miyamoto, S. Amano, and T. Mochizuki, “Conceptual design of Bessel beam cavity for free-electron laser,” Int. J. Infrared Millim. Waves 27, 165–171 (2006).
    [CrossRef]
  4. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef]
  5. J. H. McLeod, “The axicon: a new type of element,” J. Opt. Soc. Am. 44, 592–597 (1954).
    [CrossRef]
  6. G. Scott and M. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
    [CrossRef]
  7. A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
  8. J. A. Davis, J. Guertin, and D. M. Cottrell, “Diffraction-free beams generated with programmable spatial light modulators,” Appl. Opt. 32, 6368–6370 (1993).
    [CrossRef]
  9. J. A. Davis, E. Carcole, and D. M. Cottrell, “Nondiffractive interference patterns generated with programmable spatial light modulators,” Appl. Opt. 35, 599–602 (1996).
    [CrossRef]
  10. J. A. Davis, E. Carcole, and D. M. Cottrell, “Intensity and phase measurements of nondiffracting beams generated with a magneto optical spatial light modulator,” Appl. Opt. 35, 593–598 (1996).
    [CrossRef]
  11. J. A. Davis, E. Carcole, and D. M. Cottrell, “Range-finding by triangulation of nondiffracting beams,” Appl. Opt. 35, 2159–2161, (1996).
    [CrossRef]
  12. Z. Jaroszewicz, V. Climent, V. Durán, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, “Programmable axicon for variable inclination of the focal segment,” J. Mod. Opt. 51, 2185–2190 (2004).
    [CrossRef]
  13. H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
    [CrossRef]
  14. C. Zhou and L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34, 5961–5969 (1995).
    [CrossRef]
  15. I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35, 1536–1538 (2010).
    [CrossRef]
  16. J. A. Davis, I. Moreno, J. L. Martínez, T. J. Hernández, and D. M. Cottrell, “Creating three-dimensional lattice patterns using programmable Dammann gratings,” Appl. Opt. 50, 3653–3657 (2011).
    [CrossRef]
  17. I. Moreno, J. L. Martínez, and J. A. Davis, “Two-dimensional polarization rotator using a twisted-nematic liquid crystal display,” Appl. Opt. 46, 881–887 (2007).
    [CrossRef]

2011

2010

2007

2006

D. Li, K. Imasaki, S. Miyamoto, S. Amano, and T. Mochizuki, “Conceptual design of Bessel beam cavity for free-electron laser,” Int. J. Infrared Millim. Waves 27, 165–171 (2006).
[CrossRef]

2005

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

2004

Z. Jaroszewicz, V. Climent, V. Durán, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, “Programmable axicon for variable inclination of the focal segment,” J. Mod. Opt. 51, 2185–2190 (2004).
[CrossRef]

1996

1995

1993

1992

G. Scott and M. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[CrossRef]

1989

1987

J. Durnin, “Exact solutions for nondiffracting beams I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

1977

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

1954

Amano, S.

D. Li, K. Imasaki, S. Miyamoto, S. Amano, and T. Mochizuki, “Conceptual design of Bessel beam cavity for free-electron laser,” Int. J. Infrared Millim. Waves 27, 165–171 (2006).
[CrossRef]

Burvall, A.

Z. Jaroszewicz, V. Climent, V. Durán, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, “Programmable axicon for variable inclination of the focal segment,” J. Mod. Opt. 51, 2185–2190 (2004).
[CrossRef]

Carcole, E.

Climent, V.

Z. Jaroszewicz, V. Climent, V. Durán, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, “Programmable axicon for variable inclination of the focal segment,” J. Mod. Opt. 51, 2185–2190 (2004).
[CrossRef]

Cottrell, D. M.

Dammann, H.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Davis, J. A.

Dholakia, K.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Durán, V.

Z. Jaroszewicz, V. Climent, V. Durán, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, “Programmable axicon for variable inclination of the focal segment,” J. Mod. Opt. 51, 2185–2190 (2004).
[CrossRef]

Durnin, J.

J. Durnin, “Exact solutions for nondiffracting beams I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Friberg, A. T.

Z. Jaroszewicz, V. Climent, V. Durán, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, “Programmable axicon for variable inclination of the focal segment,” J. Mod. Opt. 51, 2185–2190 (2004).
[CrossRef]

A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).

Guertin, J.

Hernández, T. J.

Imasaki, K.

D. Li, K. Imasaki, S. Miyamoto, S. Amano, and T. Mochizuki, “Conceptual design of Bessel beam cavity for free-electron laser,” Int. J. Infrared Millim. Waves 27, 165–171 (2006).
[CrossRef]

Jaroszewicz, Z.

Z. Jaroszewicz, V. Climent, V. Durán, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, “Programmable axicon for variable inclination of the focal segment,” J. Mod. Opt. 51, 2185–2190 (2004).
[CrossRef]

Klotz, E.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Kolodziejczyk, A.

Z. Jaroszewicz, V. Climent, V. Durán, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, “Programmable axicon for variable inclination of the focal segment,” J. Mod. Opt. 51, 2185–2190 (2004).
[CrossRef]

Lancis, J.

Z. Jaroszewicz, V. Climent, V. Durán, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, “Programmable axicon for variable inclination of the focal segment,” J. Mod. Opt. 51, 2185–2190 (2004).
[CrossRef]

Li, D.

D. Li, K. Imasaki, S. Miyamoto, S. Amano, and T. Mochizuki, “Conceptual design of Bessel beam cavity for free-electron laser,” Int. J. Infrared Millim. Waves 27, 165–171 (2006).
[CrossRef]

Liu, L.

Martínez, J. L.

McArdle, M.

G. Scott and M. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[CrossRef]

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

McLeod, J. H.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Miyamoto, S.

D. Li, K. Imasaki, S. Miyamoto, S. Amano, and T. Mochizuki, “Conceptual design of Bessel beam cavity for free-electron laser,” Int. J. Infrared Millim. Waves 27, 165–171 (2006).
[CrossRef]

Mochizuki, T.

D. Li, K. Imasaki, S. Miyamoto, S. Amano, and T. Mochizuki, “Conceptual design of Bessel beam cavity for free-electron laser,” Int. J. Infrared Millim. Waves 27, 165–171 (2006).
[CrossRef]

Moreno, I.

Scott, G.

G. Scott and M. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[CrossRef]

Turunen, J.

Vasara, A.

Yuan, X.-C.

Zhang, N.

Zhou, C.

Appl. Opt.

Contemp. Phys.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Int. J. Infrared Millim. Waves

D. Li, K. Imasaki, S. Miyamoto, S. Amano, and T. Mochizuki, “Conceptual design of Bessel beam cavity for free-electron laser,” Int. J. Infrared Millim. Waves 27, 165–171 (2006).
[CrossRef]

J. Mod. Opt.

Z. Jaroszewicz, V. Climent, V. Durán, J. Lancis, A. Kolodziejczyk, A. Burvall, and A. T. Friberg, “Programmable axicon for variable inclination of the focal segment,” J. Mod. Opt. 51, 2185–2190 (2004).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Acta

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Opt. Eng.

G. Scott and M. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the effects due to the binarization of the axicon phase profile. Multiple orders generate multiple axicon terms.

Fig. 2.
Fig. 2.

Two dimensional (2D) binary phase patterns for (a) Linear axicon, (b) Binary axicon, (c) Binary vortex axicon, (d) 2D Dammann grating, (e) 2D Dammann axicon and (f) 2D Dammann vortex axicon.

Fig. 3.
Fig. 3.

Experimental patterns at various distances from the SLM for (a) the binary axicon [using the binary phase pattern from Fig. 2(b)], (b) the binary vortex axicon with charge =16 [using the binary phase pattern from Fig. 2(c)].

Fig. 4.
Fig. 4.

Experimental patterns at distance of z=175cm for various Dammann vortex axicons with different values of the topological charge .

Fig. 5.
Fig. 5.

Experimental patterns at various distances from the SLM for the (a) Dammann axicon using the binary phase pattern from Fig. 2(e), (b) Dammann vortex (=16) axicon using the binary phase pattern from Fig. 2(f).

Equations (9)

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g(r)=exp[iϕ(r)]=exp(i2πr/r0),
zmax=pMΔ22λ.
g(r)=m=+cmexp(i2πmr/r0),
cm=0r0g(r)exp(+i2πmr/r0)dr.
zmax(m)=1mpMΔ22λ.
g(r,θ)=exp[i(2πrr0+θ)],
g(r,θ)=m=+cmexp(i2πmr/r0)exp(imθ).
g(r,θ)=exp(i2πr/r0)exp(iθ)exp(i2πx/d0).
g(r,θ)=[m=+cmexp(i2πmr/r0)exp(imθ)]×[n=+cnexp(i2πnx/d0)].

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