Abstract

A multi-element design scheme is proposed to produce optical vortices of large spectrum width. The key component within the approach is a radially modulated spiral phase plate. Apart from a conventional spiral phase plate having an azimuthal phase function, the proposed element possesses an additional change of phase in the radial direction.

©2008 Optical Society of America

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References

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
  2. M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66 (2002).
    [Crossref]
  3. M. V. Berry, “Exploring the colours of dark light,” New J. Phys. 4, 74 (2002).
    [Crossref]
  4. J. Leach and M. J. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 154 (2003).
    [Crossref]
  5. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [Crossref]
  6. G. A. Swartzlander, “Achromatic optical vortex lens,” Opt. Lett. 31, 2042–2044 (2006).
    [Crossref] [PubMed]
  7. J. Lin, X.-C. Yuan, S. H. Tao, and R. E. Burge, “Variable-radius focused optical vortex with suppressed sidelobes,” Opt. Lett. 31, 1600–1602 (2006).
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  8. V. V. Kotlyar, A. A. Kovalev, V. A. Soifer, C. S. Tuvey, and J. A. Davis, “Sidelobe contrast reduction for optical vortex beams using a helical axicon,” Opt. Lett. 32, 921–923 (2007).
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  9. 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).
    [Crossref]
  10. S. H. Tao, W. M. Lee, and X.-C. Yuan, “Dynamic optical manipulation using higher order fractional Bessel beam generated from a spatial light modulator,” Opt. Lett. 28, 1867–1869 (2003).
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  11. M. Rioux, R. Tremblay, and P. A. Belanger, “Linear, annular, and radial focusing with axicons and applications to laser machining,” Appl. Opt. 17, 1532–1536 (1978).
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  12. T. Shiina, K. Yoshida, M. Ito, and Y. Okamura, “In-line type micropulse lidar with an annular beam: theoretical approach,” Appl. Opt. 44, 7467–7474 (2005).
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  13. C. Alonzo, P. J. Rodrigo, and J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13, 1749–1760 (2005).
  14. G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2002).
    [Crossref] [PubMed]
  15. J. Lin, X.-C. Yuan, J. Bu, H. L. Chen, Y. Y. Sun, and R. E. Burge, “Generalized model for orbital angular momentum states generated by parallel aligned phase wedges,” Opt. Lett. 32, 2170–2172 (2007).
    [Crossref] [PubMed]
  16. J. Lin, X.-C. Yuan, J. Bu, B. P. S. Ahluwalia, Y. Y. Sun, and R. E. Burge, “Selective generation of high order optical vortices from a single phase wedge,” Opt. Lett. 32, 2927–2929 (2007).
    [Crossref] [PubMed]
  17. J. W. Goodman, Introduction to Fourier optics, 2nd ed. (McGraw-Hill, Singapore, 1996).
  18. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref] [PubMed]
  19. W. C. Cheong, W. M. Lee, X.-C. Yuan, L.-S. Zhang, H. Wang, and K. Dholakia, “Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation,” Appl. Phys. Lett. 85, 5784–5786 (2004).
    [Crossref]
  20. G. Foo, D. M. Palacios, and G. A. Swartzlander, “Optical Vortex Coronagraph,” Opt. Lett. 30, 3308–3310 (2005).
    [Crossref]
  21. G. A. Swartzlander, “Broadband nulling of a vortex phase mask,” Opt. Lett. 30, 2876–2878 (2005).
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2007 (3)

2006 (2)

2005 (3)

2004 (1)

W. C. Cheong, W. M. Lee, X.-C. Yuan, L.-S. Zhang, H. Wang, and K. Dholakia, “Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation,” Appl. Phys. Lett. 85, 5784–5786 (2004).
[Crossref]

2003 (2)

2002 (3)

M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66 (2002).
[Crossref]

M. V. Berry, “Exploring the colours of dark light,” New J. Phys. 4, 74 (2002).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2002).
[Crossref] [PubMed]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

1989 (1)

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).
[Crossref]

1987 (1)

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

1978 (1)

Ahluwalia, B. P. S.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

Alonzo, C.

C. Alonzo, P. J. Rodrigo, and J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13, 1749–1760 (2005).

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

Belanger, P. A.

Berry, M. V.

M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66 (2002).
[Crossref]

M. V. Berry, “Exploring the colours of dark light,” New J. Phys. 4, 74 (2002).
[Crossref]

Bu, J.

Burge, R. E.

Chen, H. L.

Cheong, W. C.

W. C. Cheong, W. M. Lee, X.-C. Yuan, L.-S. Zhang, H. Wang, and K. Dholakia, “Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation,” Appl. Phys. Lett. 85, 5784–5786 (2004).
[Crossref]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Davis, J. A.

Dholakia, K.

W. C. Cheong, W. M. Lee, X.-C. Yuan, L.-S. Zhang, H. Wang, and K. Dholakia, “Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation,” Appl. Phys. Lett. 85, 5784–5786 (2004).
[Crossref]

Durnin, J.

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

Eberly, J. H.

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

Foo, G.

Friberg, A. T.

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).
[Crossref]

Glückstad, J.

C. Alonzo, P. J. Rodrigo, and J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13, 1749–1760 (2005).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier optics, 2nd ed. (McGraw-Hill, Singapore, 1996).

Ito, M.

Kotlyar, V. V.

Kovalev, A. A.

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Leach, J.

J. Leach and M. J. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 154 (2003).
[Crossref]

Lee, W. M.

W. C. Cheong, W. M. Lee, X.-C. Yuan, L.-S. Zhang, H. Wang, and K. Dholakia, “Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation,” Appl. Phys. Lett. 85, 5784–5786 (2004).
[Crossref]

S. H. Tao, W. M. Lee, and X.-C. Yuan, “Dynamic optical manipulation using higher order fractional Bessel beam generated from a spatial light modulator,” Opt. Lett. 28, 1867–1869 (2003).
[Crossref] [PubMed]

Lin, J.

Miceli, J. J.

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

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2002).
[Crossref] [PubMed]

Okamura, Y.

Padgett, M. J.

J. Leach and M. J. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 154 (2003).
[Crossref]

Palacios, D. M.

Rioux, M.

Rodrigo, P. J.

C. Alonzo, P. J. Rodrigo, and J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13, 1749–1760 (2005).

Shiina, T.

Soifer, V. A.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

Sun, Y. Y.

Swartzlander, G. A.

Tao, S. H.

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2002).
[Crossref] [PubMed]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2002).
[Crossref] [PubMed]

Tremblay, R.

Turunen, J.

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).
[Crossref]

Tuvey, C. S.

Vasara, A.

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).
[Crossref]

Wang, H.

W. C. Cheong, W. M. Lee, X.-C. Yuan, L.-S. Zhang, H. Wang, and K. Dholakia, “Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation,” Appl. Phys. Lett. 85, 5784–5786 (2004).
[Crossref]

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

Yoshida, K.

Yuan, X.-C.

Zhang, L.-S.

W. C. Cheong, W. M. Lee, X.-C. Yuan, L.-S. Zhang, H. Wang, and K. Dholakia, “Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation,” Appl. Phys. Lett. 85, 5784–5786 (2004).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

W. C. Cheong, W. M. Lee, X.-C. Yuan, L.-S. Zhang, H. Wang, and K. Dholakia, “Direct electron-beam writing of continuous spiral phase plates in negative resist with high power efficiency for optical manipulation,” Appl. Phys. Lett. 85, 5784–5786 (2004).
[Crossref]

J. Opt. Soc. Am. (1)

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).
[Crossref]

New J. Phys. (3)

M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66 (2002).
[Crossref]

M. V. Berry, “Exploring the colours of dark light,” New J. Phys. 4, 74 (2002).
[Crossref]

J. Leach and M. J. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 154 (2003).
[Crossref]

Opt. Commun. (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Opt. Express (1)

C. Alonzo, P. J. Rodrigo, and J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13, 1749–1760 (2005).

Opt. Lett. (8)

Phys. Rev. (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

Phys. Rev. Lett. (2)

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

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2002).
[Crossref] [PubMed]

Other (1)

J. W. Goodman, Introduction to Fourier optics, 2nd ed. (McGraw-Hill, Singapore, 1996).

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Figures (8)

Fig. 1.
Fig. 1. The achromatic design scheme for the generation of optical vortices under the illumination of a broadband source.

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Fig. 2.
Fig. 2. (a) Phase distribution of a conventional SPP exp(iℓθ) with ℓ>0, (b) Phase distribution of an RSPP exp(ikrθ) with k>0.

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Fig. 3.
Fig. 3. Analysis of the RSPP with the annular aperture of mean radius r ο : (a) the weight of the major optical vortex with topological charge ℓ0 as a function of the dimensionless width y=ℓ0πw/r ο ; (b) The weight distribution over topological charges (with a logarithmic ordinate) when r ο=1.54, ℓ0=2, and w=0.25.

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Fig. 4.
Fig. 4. Fraunhofer diffraction patterns calculated numerically under the condition of y=1 (specifically, r ο=1.54, ℓο=2, and w=0.25) for the mean radius of aperture (a) r=r ο ; (b) r=2r ο.

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Fig. 5.
Fig. 5. Experimental setup for the dynamic switching of the topological charge of an optical vortex generated by the RSPP. Axicon AX2 can be moved along the beam propagating direction in order to change the distance between the axicons.

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Fig. 6.
Fig. 6. The intensity profile of the annular beam. (a) Two-dimensional distribution, (b) The intensity plot along the horizontal line passing through the beam central in (a).

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Fig. 7.
Fig. 7. The far-field intensity distribution of various optical vortices produced by the same RSPP. (a) ℓ=2, (b) ℓ=3, (c) ℓ=4, (d) ℓ=5.

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Fig. 8.
Fig. 8. The interferometric measurement of topological charges of optical vortices. (a) ℓ=2, (b) ℓ=3, (c) ℓ=4, (d) ℓ=5.

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Equations (7)

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Φ ( r , θ ) = 2 π Δ n × h ( r , θ ) λ ,
t ( r , θ ) = { exp ( i k r θ ) 0 ≤ r ≤ R 1 else
A n ( w ) = ∫ r 0 − w 2 r 0 + w 2 ∣ ∫ 0 2 π t ( r , θ ) exp ( − i n θ ) d θ ∣ 2 r d r 2 π 2 [ ( r 0 + w 2 ) 2 − ( r 0 − w 2 ) 2 ] , ( w < 2 r 0 )
A n ( w ) = r 0 2 π 2 ℓ 0 2 w [ Ci ( 2 ℓ 0 π − 2 n π − ℓ 0 π w r 0 ) − Ci ( 2 ℓ 0 π − 2 n π + ℓ 0 π w r 0 )
+ In ( 2 ℓ 0 − 2 n + ℓ 0 w r 0 ) − In ( 2 ℓ 0 − 2 n − ℓ 0 w r 0 ) + 2 n π Si ( 2 ℓ 0 π − 2 n π + ℓ 0 π w r 0 )
− 2 n π Si ( 2 ℓ 0 π − 2 n π − ℓ 0 π w r 0 ) + 8 ℓ 0 n r 0 w 4 r 0 2 ( n − ℓ 0 ) 2 − ℓ 0 2 w 2 sin ⁡ 2 ( ℓ 0 π w 2 r 0 ) ] ,
A ℓ 0 ( y ) = 2 Si ( y ) y − sin ⁡ c 2 ( y 2 )

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