Abstract

An experimental and theoretical investigation of laser beam shaping using a simple binary diffractive optic is presented. Beam tailoring has been characterized by the experimental determination of two relevant parameters: beam propagation factor M2 and the beam-shaping longitudinal range, which represents the propagating distance for which the tailored beam remains nearly unchanged.

© 2006 Optical Society of America

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References

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  1. W. B. Veldkamp, "Laser beam profile shaping with interlaced binary diffraction gratings," Appl. Opt. 21, 3209-3212 (1982).
    [CrossRef] [PubMed]
  2. J. Cordingley, "Application of a binary diffractive optics for beam shaping in semiconductor processing by lasers," Appl. Opt. 32, 2538-2542 (1993).
    [CrossRef] [PubMed]
  3. R. Bourouis, K. Aït-Ameur, and H. Ladjouze, "Optimisation of the Gaussian beam flattening using a phase-plate," J. Mod. Opt. 44, 1417-1427 (1997).
    [CrossRef]
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    [CrossRef] [PubMed]
  6. J. J. Kasinski and R. L. Burnham, "Near-diffraction-limited laser beam shaping with diamond-turned aspheric optic," Opt. Lett. 22, 1062-1064 (1997).
    [CrossRef] [PubMed]
  7. J. A. Hoffnagle and C. M. Jefferson, "Design and performance of a refractive optical system that converts a Gaussian to a flat-top beam," Appl. Opt. 39, 5488-5499 (2000).
    [CrossRef]
  8. S. Zhang, G. Neil, and M. Shinn, "Single-element laser beam shaper for uniform flat-top profiles," Opt. Express 11, 1942-1948 (2003).
    [CrossRef] [PubMed]
  9. P. J. Rodrigo, V. R. Daria, and J. Glückstad, "Real-time interactive optical micromanipulation of a mixture of high and low index particles," Opt. Express 12, 1417-1425 (2004).
    [CrossRef] [PubMed]
  10. D. Ganic, X. Gan, M. Gu, M. Hain, S. Somalingam, S. Stankovic, and T. Tschudi, "Generation of doughnut laser beams by use of a liquid-crystal cell with a conversion efficiency near 100%," Opt. Lett. 27, 1351-1353 (2002).
    [CrossRef]
  11. D. W. Zhang and X. C. Yuan, "Optical doughnut for optical tweezers," Opt. Lett. 28, 740-742 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. N. Passilly, R. de Saint Denis, K. Aït-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, "Simple interferometric technique for generation of a radially polarized light beam," J. Opt. Soc. Am. A 22, 984-991 (2005).
    [CrossRef]
  14. M. Fromager and K. Aït-Ameur, "Transformation of an elliptic into a circular beam using a diffractive binary optic," Opt. Commun. 190, 45-49 (2001).
    [CrossRef]
  15. U. D. Zeitner and F. Wyrowski, "High modal discrimination for laser resonators with Gaussian output beam," J. Mod. Opt. 46, 1309-1314 (1999).
    [CrossRef]
  16. A. A. Napartovich, N. N. Elkin, V. N. Troschieva, D. V. Vysotsky, and J. R. Leger, "Simplified intracavity phase plates for increasing laser-mode discrimination," Appl. Opt. 38, 3025-3029 (1999).
    [CrossRef]
  17. K. Aït-Ameur, F. Sanchez, and M. Brunel, "High transverse mode discrimination in apertured resonators using diffractive binary optics," Opt. Commun. 184, 73-78 (2000).
    [CrossRef]
  18. N. Passilly, M. Fromager, and K. Aït-Ameur, "Improvement of the self-Q-switching behavior of a Cr:LiSrAlF6 laser by use of a binary diffractive optics," Appl. Opt. 43, 5047-5059 (2004).
    [CrossRef] [PubMed]
  19. M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, "Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber," IEEE Photon. Technol. Lett. 18, 764-766 (2006).
    [CrossRef]
  20. D. W. Zhang and X. C. Yuan, "Optical doughnut for optical tweezers," Opt. Lett. 28, 740-742 (2003).
    [CrossRef] [PubMed]
  21. P. J. Rodrigo, V. R. Daria, and J. Glückstad, "Real-time interactive optical micromanipulation of a mixture of high and low-index particles," Opt. Express 12, 1417-1425 (2004).
    [CrossRef] [PubMed]
  22. D. McGloin, G. C. Spalding, H. Melville, W. Sibbet, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215-222 (2003).
    [CrossRef]
  23. R. Menzel, Photonics (Springer-Verlag, 2001), Chap. 2, p. 61.
  24. N. Passilly, G. Martel, and K. Aït-Ameur, "Beam propagation factor of truncated Laguerre-Gauss beams," J. Mod. Opt. 51, 2279-2286 (2004).
    [CrossRef]
  25. Y. Li and E. Wolf, "Focal shift in focused truncated Gaussian beams," Opt. Commun. 42, 151-156 (1982).
    [CrossRef]
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    [CrossRef] [PubMed]

2006

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, "Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber," IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

2005

2004

2003

2002

2001

M. Fromager and K. Aït-Ameur, "Transformation of an elliptic into a circular beam using a diffractive binary optic," Opt. Commun. 190, 45-49 (2001).
[CrossRef]

2000

J. A. Hoffnagle and C. M. Jefferson, "Design and performance of a refractive optical system that converts a Gaussian to a flat-top beam," Appl. Opt. 39, 5488-5499 (2000).
[CrossRef]

K. Aït-Ameur, F. Sanchez, and M. Brunel, "High transverse mode discrimination in apertured resonators using diffractive binary optics," Opt. Commun. 184, 73-78 (2000).
[CrossRef]

1999

1997

J. J. Kasinski and R. L. Burnham, "Near-diffraction-limited laser beam shaping with diamond-turned aspheric optic," Opt. Lett. 22, 1062-1064 (1997).
[CrossRef] [PubMed]

R. Bourouis, K. Aït-Ameur, and H. Ladjouze, "Optimisation of the Gaussian beam flattening using a phase-plate," J. Mod. Opt. 44, 1417-1427 (1997).
[CrossRef]

1995

1993

1987

1982

Y. Li and E. Wolf, "Focal shift in focused truncated Gaussian beams," Opt. Commun. 42, 151-156 (1982).
[CrossRef]

W. B. Veldkamp, "Laser beam profile shaping with interlaced binary diffraction gratings," Appl. Opt. 21, 3209-3212 (1982).
[CrossRef] [PubMed]

Aït-Ameur, K.

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, "Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber," IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

N. Passilly, R. de Saint Denis, K. Aït-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, "Simple interferometric technique for generation of a radially polarized light beam," J. Opt. Soc. Am. A 22, 984-991 (2005).
[CrossRef]

N. Passilly, M. Fromager, L. Méchin, C. Gunther, S. Eimer, T. Mohammed-Brahim, and K. Aït-Ameur, "1-D laser beam shaping using an adjustable binary diffractive optical element," Opt. Commun. 241, 465-473 (2004).
[CrossRef]

N. Passilly, M. Fromager, and K. Aït-Ameur, "Improvement of the self-Q-switching behavior of a Cr:LiSrAlF6 laser by use of a binary diffractive optics," Appl. Opt. 43, 5047-5059 (2004).
[CrossRef] [PubMed]

N. Passilly, G. Martel, and K. Aït-Ameur, "Beam propagation factor of truncated Laguerre-Gauss beams," J. Mod. Opt. 51, 2279-2286 (2004).
[CrossRef]

M. Fromager and K. Aït-Ameur, "Transformation of an elliptic into a circular beam using a diffractive binary optic," Opt. Commun. 190, 45-49 (2001).
[CrossRef]

K. Aït-Ameur, F. Sanchez, and M. Brunel, "High transverse mode discrimination in apertured resonators using diffractive binary optics," Opt. Commun. 184, 73-78 (2000).
[CrossRef]

R. Bourouis, K. Aït-Ameur, and H. Ladjouze, "Optimisation of the Gaussian beam flattening using a phase-plate," J. Mod. Opt. 44, 1417-1427 (1997).
[CrossRef]

Bourouis, R.

R. Bourouis, K. Aït-Ameur, and H. Ladjouze, "Optimisation of the Gaussian beam flattening using a phase-plate," J. Mod. Opt. 44, 1417-1427 (1997).
[CrossRef]

Brunel, M.

K. Aït-Ameur, F. Sanchez, and M. Brunel, "High transverse mode discrimination in apertured resonators using diffractive binary optics," Opt. Commun. 184, 73-78 (2000).
[CrossRef]

Burnham, R. L.

Cordingley, J.

Daria, V. R.

de Saint Denis, R.

Dholakia, K.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbet, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215-222 (2003).
[CrossRef]

Eimer, S.

N. Passilly, M. Fromager, L. Méchin, C. Gunther, S. Eimer, T. Mohammed-Brahim, and K. Aït-Ameur, "1-D laser beam shaping using an adjustable binary diffractive optical element," Opt. Commun. 241, 465-473 (2004).
[CrossRef]

Elkin, N. N.

Fromager, M.

N. Passilly, M. Fromager, and K. Aït-Ameur, "Improvement of the self-Q-switching behavior of a Cr:LiSrAlF6 laser by use of a binary diffractive optics," Appl. Opt. 43, 5047-5059 (2004).
[CrossRef] [PubMed]

N. Passilly, M. Fromager, L. Méchin, C. Gunther, S. Eimer, T. Mohammed-Brahim, and K. Aït-Ameur, "1-D laser beam shaping using an adjustable binary diffractive optical element," Opt. Commun. 241, 465-473 (2004).
[CrossRef]

M. Fromager and K. Aït-Ameur, "Transformation of an elliptic into a circular beam using a diffractive binary optic," Opt. Commun. 190, 45-49 (2001).
[CrossRef]

Gan, X.

Ganic, D.

Gilles, H.

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, "Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber," IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

Girard, S.

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, "Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber," IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

Glückstad, J.

Gu, M.

Gunther, C.

N. Passilly, M. Fromager, L. Méchin, C. Gunther, S. Eimer, T. Mohammed-Brahim, and K. Aït-Ameur, "1-D laser beam shaping using an adjustable binary diffractive optical element," Opt. Commun. 241, 465-473 (2004).
[CrossRef]

Hain, M.

Hierle, R.

Hoffnagle, J. A.

Jefferson, C. M.

Jin, G.

Kanzaki, O.

Kasinski, J. J.

Kessler, T. J.

Ladjouze, H.

R. Bourouis, K. Aït-Ameur, and H. Ladjouze, "Optimisation of the Gaussian beam flattening using a phase-plate," J. Mod. Opt. 44, 1417-1427 (1997).
[CrossRef]

Laroche, M.

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, "Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber," IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

Lawrence, G. N.

Leger, J. R.

Li, Y.

Y. Li and E. Wolf, "Focal shift in focused truncated Gaussian beams," Opt. Commun. 42, 151-156 (1982).
[CrossRef]

Lin, Y.

Martel, G.

N. Passilly, G. Martel, and K. Aït-Ameur, "Beam propagation factor of truncated Laguerre-Gauss beams," J. Mod. Opt. 51, 2279-2286 (2004).
[CrossRef]

McGloin, D.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbet, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215-222 (2003).
[CrossRef]

Méchin, L.

N. Passilly, M. Fromager, L. Méchin, C. Gunther, S. Eimer, T. Mohammed-Brahim, and K. Aït-Ameur, "1-D laser beam shaping using an adjustable binary diffractive optical element," Opt. Commun. 241, 465-473 (2004).
[CrossRef]

Melville, H.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbet, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215-222 (2003).
[CrossRef]

Menzel, R.

R. Menzel, Photonics (Springer-Verlag, 2001), Chap. 2, p. 61.

Mohammed-Brahim, T.

N. Passilly, M. Fromager, L. Méchin, C. Gunther, S. Eimer, T. Mohammed-Brahim, and K. Aït-Ameur, "1-D laser beam shaping using an adjustable binary diffractive optical element," Opt. Commun. 241, 465-473 (2004).
[CrossRef]

Napartovich, A. A.

Neil, G.

Passilly, N.

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, "Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber," IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

N. Passilly, R. de Saint Denis, K. Aït-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, "Simple interferometric technique for generation of a radially polarized light beam," J. Opt. Soc. Am. A 22, 984-991 (2005).
[CrossRef]

N. Passilly, M. Fromager, and K. Aït-Ameur, "Improvement of the self-Q-switching behavior of a Cr:LiSrAlF6 laser by use of a binary diffractive optics," Appl. Opt. 43, 5047-5059 (2004).
[CrossRef] [PubMed]

N. Passilly, M. Fromager, L. Méchin, C. Gunther, S. Eimer, T. Mohammed-Brahim, and K. Aït-Ameur, "1-D laser beam shaping using an adjustable binary diffractive optical element," Opt. Commun. 241, 465-473 (2004).
[CrossRef]

N. Passilly, G. Martel, and K. Aït-Ameur, "Beam propagation factor of truncated Laguerre-Gauss beams," J. Mod. Opt. 51, 2279-2286 (2004).
[CrossRef]

Roch, J.-F.

Rodrigo, P. J.

Sanchez, F.

K. Aït-Ameur, F. Sanchez, and M. Brunel, "High transverse mode discrimination in apertured resonators using diffractive binary optics," Opt. Commun. 184, 73-78 (2000).
[CrossRef]

Shinn, M.

Sibbet, W.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbet, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215-222 (2003).
[CrossRef]

Somalingam, S.

Spalding, G. C.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbet, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215-222 (2003).
[CrossRef]

Stankovic, S.

Tan, Q.

Tanaka, K.

Treussart, F.

Troschieva, V. N.

Tschudi, T.

Veldkamp, W. B.

Vysotsky, D. V.

Wolf, E.

Y. Li and E. Wolf, "Focal shift in focused truncated Gaussian beams," Opt. Commun. 42, 151-156 (1982).
[CrossRef]

Wyrowski, F.

U. D. Zeitner and F. Wyrowski, "High modal discrimination for laser resonators with Gaussian output beam," J. Mod. Opt. 46, 1309-1314 (1999).
[CrossRef]

Yan, Y.

Yuan, X. C.

Zeitner, U. D.

U. D. Zeitner and F. Wyrowski, "High modal discrimination for laser resonators with Gaussian output beam," J. Mod. Opt. 46, 1309-1314 (1999).
[CrossRef]

Zhang, D. W.

Zhang, S.

Appl. Opt.

IEEE Photon. Technol. Lett.

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, "Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber," IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

J. Mod. Opt.

N. Passilly, G. Martel, and K. Aït-Ameur, "Beam propagation factor of truncated Laguerre-Gauss beams," J. Mod. Opt. 51, 2279-2286 (2004).
[CrossRef]

U. D. Zeitner and F. Wyrowski, "High modal discrimination for laser resonators with Gaussian output beam," J. Mod. Opt. 46, 1309-1314 (1999).
[CrossRef]

R. Bourouis, K. Aït-Ameur, and H. Ladjouze, "Optimisation of the Gaussian beam flattening using a phase-plate," J. Mod. Opt. 44, 1417-1427 (1997).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

M. Fromager and K. Aït-Ameur, "Transformation of an elliptic into a circular beam using a diffractive binary optic," Opt. Commun. 190, 45-49 (2001).
[CrossRef]

N. Passilly, M. Fromager, L. Méchin, C. Gunther, S. Eimer, T. Mohammed-Brahim, and K. Aït-Ameur, "1-D laser beam shaping using an adjustable binary diffractive optical element," Opt. Commun. 241, 465-473 (2004).
[CrossRef]

K. Aït-Ameur, F. Sanchez, and M. Brunel, "High transverse mode discrimination in apertured resonators using diffractive binary optics," Opt. Commun. 184, 73-78 (2000).
[CrossRef]

Y. Li and E. Wolf, "Focal shift in focused truncated Gaussian beams," Opt. Commun. 42, 151-156 (1982).
[CrossRef]

D. McGloin, G. C. Spalding, H. Melville, W. Sibbet, and K. Dholakia, "Three-dimensional arrays of optical bottle beams," Opt. Commun. 225, 215-222 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Other

R. Menzel, Photonics (Springer-Verlag, 2001), Chap. 2, p. 61.

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Figures (10)

Fig. 1
Fig. 1

(Color online) Experimental setup for measuring, on both sides of the lens focal plane, the longitudinal evolution of intensity patterns of the beam tailored by the π plate.

Fig. 2
Fig. 2

Theoretical plots showing that the π plate is able to transform a Gaussian beam into a flat-top profile, a doughnut profile, or a TEM 10 -shaped profile, depending on the value of parameter Δ. r is the radial coordinate in the diffraction plane. Intensity patterns have been calculated in the focal plane of the imaging lens.

Fig. 3
Fig. 3

Experimental evolution of the tailored beam profile, for Δ = 1.25 , from z = f to z = f ± 4 z R . Note that, in plane z = f , the intensity distribution is a flat-top profile that can be fitted by a super Gaussian of the order of 6.

Fig. 4
Fig. 4

Evolution of the tailored beam profile for Δ = 1.25 from z = f to z = f ± 0.3 z R .

Fig. 5
Fig. 5

Evolution of the tailored beam profile for Δ = 0.5 from z = f to z = f ± 4 z R . This value of Δ is well adapted for the conversion of a TEM 00 into a TEM 10 beam.

Fig. 6
Fig. 6

Evolution of the tailored beam profile for Δ = 0.7 from z = f to z = f ± 4 z R .

Fig. 7
Fig. 7

(Color online) Evolution of M 2 , the beam-propagation factor of the beam emerging from the π plate, as a function of parameter Δ: solid curve, theoretical; squares, experimental.

Fig. 8
Fig. 8

(Color online) Variations of the on-axis intensity I d ( 0 , z ) as a function of the normalized propagation distance.

Fig. 9
Fig. 9

(Color online) Three-dimensional intensity distribution around the focal plane for Δ = 0.9 .

Fig. 10
Fig. 10

Theoretical variations of the diffraction efficiency η as a function of parameter Δ.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

τ ( ρ ) = { 1     f o r ρ ρ 0 + 1     f o r ρ > ρ 0 .
E in ( ρ ) = exp [ ρ 2 w 2 ] ,
z R = λ f 2 π W 2 ,
I 10 = ( 1 2 ρ 2 W 2 ) 2 exp [ 2 ρ 2 W 2 ] ,
B = π 2 P λ 2 ( M 2 ) 2 .

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