Abstract

Laguerre–Gaussian (LG) beams are used in many research fields, including microscopy, laser cavity modes, and optical tweezing. We developed a holographic method to generate pure LG modes (amplitude and phase) with a binary amplitude-only digital micromirror device (DMD) as an alternative to the commonly used phase-only spatial light modulator. The advantages of such a DMD include very high frame rates, low cost, and high damage thresholds. We have shown that the propagating shaped beams are self-similar and their phase fronts are of helical shape as demanded. We estimate the purity of the resultant beams to be above 94%.

© 2012 Optical Society of America

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  1. M. Padgett and L. Allen, Opt. Commun. 121, 36(1995).
    [CrossRef]
  2. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  3. A. T. O’Neill and M. J. Padgett, Opt. Commun. 193, 45 (2001).
    [CrossRef]
  4. J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
    [CrossRef]
  5. D. Petrov, Phys. Rev. A 82, 035801 (2010).
    [CrossRef]
  6. J. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
    [CrossRef]
  7. L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, Opt. Express 12, 6403 (2004).
    [CrossRef]
  8. N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, J. Opt. Soc. Am. A 25, 1642 (2008).
    [CrossRef]
  9. S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
    [CrossRef]
  10. J. Otona, M. S. Millana, P. Ambs, and E. Perez-Cabrea, Proc. SPIE 7000, 70001V (2008).
    [CrossRef]
  11. F. P. Martial and N. A. Hartell, PLoS ONE 7, e43942(2012).
    [CrossRef]
  12. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
    [CrossRef]
  13. J. Liyang, “High-precision laser beam shaping and image projection,” Ph.D. thesis (University of Texas, 2012).
  14. Y. X. Ren, M. Li, K. Huang, J. G. Wu, H. F. Gao, Z. Q. Wang, and Y. M. Li, Appl. Opt. 49, 1838 (2010).
    [CrossRef]
  15. G. Molina-Terriza and J. Torres, Nat. Phys. 3, 305(2007).
    [CrossRef]
  16. A. Bekshaev and O. Orlinska, Opt. Commun. 283, 1244 (2010).
    [CrossRef]
  17. F. Havermeyer, L. Ho, and C. Moser, Opt. Express 19, 14642 (2011).
    [CrossRef]
  18. L. A. Yoder, W. M. Duncan, E. M. Koontz, J. So, T. A. Bartlett, B. L. Lee, B. D. Sawyers, D. Powell, and P. Rancuret, Proc. SPIE 4457, 54 (2001).
  19. B. R. Brown and A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
    [CrossRef]
  20. A. Lohmann and D. P. Paris, Appl. Opt. 6, 1739 (1967).
    [CrossRef]
  21. D. Dudley, W. M. Duncan, and J. Slaughter, Proc. SPIE 4985, 14 (2003).
    [CrossRef]
  22. R. W. Floyd and L. Steinberg, in International Symposium Digest of Technical Papers, Society for Information Display (Academic, 1975), p. 36.
  23. The barely observable elipticity is due to small imperfections in our tilt angle adjustments, and input Gaussian beam. However, no splitting in l=2 and higher modes was observed, indicating that this imperfection is negligible.

2012

F. P. Martial and N. A. Hartell, PLoS ONE 7, e43942(2012).
[CrossRef]

2011

2010

D. Petrov, Phys. Rev. A 82, 035801 (2010).
[CrossRef]

Y. X. Ren, M. Li, K. Huang, J. G. Wu, H. F. Gao, Z. Q. Wang, and Y. M. Li, Appl. Opt. 49, 1838 (2010).
[CrossRef]

A. Bekshaev and O. Orlinska, Opt. Commun. 283, 1244 (2010).
[CrossRef]

2008

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, J. Opt. Soc. Am. A 25, 1642 (2008).
[CrossRef]

J. Otona, M. S. Millana, P. Ambs, and E. Perez-Cabrea, Proc. SPIE 7000, 70001V (2008).
[CrossRef]

2007

G. Molina-Terriza and J. Torres, Nat. Phys. 3, 305(2007).
[CrossRef]

2004

2003

J. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

D. Dudley, W. M. Duncan, and J. Slaughter, Proc. SPIE 4985, 14 (2003).
[CrossRef]

2002

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

2001

A. T. O’Neill and M. J. Padgett, Opt. Commun. 193, 45 (2001).
[CrossRef]

L. A. Yoder, W. M. Duncan, E. M. Koontz, J. So, T. A. Bartlett, B. L. Lee, B. D. Sawyers, D. Powell, and P. Rancuret, Proc. SPIE 4457, 54 (2001).

2000

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

1998

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

1995

M. Padgett and L. Allen, Opt. Commun. 121, 36(1995).
[CrossRef]

1992

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

1969

B. R. Brown and A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[CrossRef]

1967

Abraham, E. R. I.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

M. Padgett and L. Allen, Opt. Commun. 121, 36(1995).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Ambs, P.

J. Otona, M. S. Millana, P. Ambs, and E. Perez-Cabrea, Proc. SPIE 7000, 70001V (2008).
[CrossRef]

Ando, T.

Arlt, J.

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

Bartlett, T. A.

L. A. Yoder, W. M. Duncan, E. M. Koontz, J. So, T. A. Bartlett, B. L. Lee, B. D. Sawyers, D. Powell, and P. Rancuret, Proc. SPIE 4457, 54 (2001).

Beijersbergen, M.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Bekshaev, A.

A. Bekshaev and O. Orlinska, Opt. Commun. 283, 1244 (2010).
[CrossRef]

Brown, B. R.

B. R. Brown and A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[CrossRef]

Cao, Z.

Deyanova, Y.

J. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

Dholakia, K.

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

Dudley, D.

D. Dudley, W. M. Duncan, and J. Slaughter, Proc. SPIE 4985, 14 (2003).
[CrossRef]

Duncan, W. M.

D. Dudley, W. M. Duncan, and J. Slaughter, Proc. SPIE 4985, 14 (2003).
[CrossRef]

L. A. Yoder, W. M. Duncan, E. M. Koontz, J. So, T. A. Bartlett, B. L. Lee, B. D. Sawyers, D. Powell, and P. Rancuret, Proc. SPIE 4457, 54 (2001).

Floyd, R. W.

R. W. Floyd and L. Steinberg, in International Symposium Digest of Technical Papers, Society for Information Display (Academic, 1975), p. 36.

Fukuchi, N.

Gao, H. F.

Hara, T.

Hartell, N. A.

F. P. Martial and N. A. Hartell, PLoS ONE 7, e43942(2012).
[CrossRef]

Havermeyer, F.

Hitomi, T.

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

Ho, L.

Hu, L.

Huang, K.

Inoue, T.

Kennedy, S. A.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Koontz, E. M.

L. A. Yoder, W. M. Duncan, E. M. Koontz, J. So, T. A. Bartlett, B. L. Lee, B. D. Sawyers, D. Powell, and P. Rancuret, Proc. SPIE 4457, 54 (2001).

Lee, B. L.

L. A. Yoder, W. M. Duncan, E. M. Koontz, J. So, T. A. Bartlett, B. L. Lee, B. D. Sawyers, D. Powell, and P. Rancuret, Proc. SPIE 4457, 54 (2001).

Li, D.

Li, M.

Li, Y. M.

Liu, Y.

Liyang, J.

J. Liyang, “High-precision laser beam shaping and image projection,” Ph.D. thesis (University of Texas, 2012).

Lohmann, A.

Lohmann, A. W.

B. R. Brown and A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[CrossRef]

Martial, F. P.

F. P. Martial and N. A. Hartell, PLoS ONE 7, e43942(2012).
[CrossRef]

Matsumoto, N.

Millana, M. S.

J. Otona, M. S. Millana, P. Ambs, and E. Perez-Cabrea, Proc. SPIE 7000, 70001V (2008).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza and J. Torres, Nat. Phys. 3, 305(2007).
[CrossRef]

J. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

Moser, C.

Mu, Q.

O’Neill, A. T.

A. T. O’Neill and M. J. Padgett, Opt. Commun. 193, 45 (2001).
[CrossRef]

Ohtake, Y.

Orlinska, O.

A. Bekshaev and O. Orlinska, Opt. Commun. 283, 1244 (2010).
[CrossRef]

Otona, J.

J. Otona, M. S. Millana, P. Ambs, and E. Perez-Cabrea, Proc. SPIE 7000, 70001V (2008).
[CrossRef]

Padgett, M.

M. Padgett and L. Allen, Opt. Commun. 121, 36(1995).
[CrossRef]

Padgett, M. J.

A. T. O’Neill and M. J. Padgett, Opt. Commun. 193, 45 (2001).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

Paris, D. P.

Perez-Cabrea, E.

J. Otona, M. S. Millana, P. Ambs, and E. Perez-Cabrea, Proc. SPIE 7000, 70001V (2008).
[CrossRef]

Petrov, D.

D. Petrov, Phys. Rev. A 82, 035801 (2010).
[CrossRef]

Porterfield, J. Z.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Powell, D.

L. A. Yoder, W. M. Duncan, E. M. Koontz, J. So, T. A. Bartlett, B. L. Lee, B. D. Sawyers, D. Powell, and P. Rancuret, Proc. SPIE 4457, 54 (2001).

Rancuret, P.

L. A. Yoder, W. M. Duncan, E. M. Koontz, J. So, T. A. Bartlett, B. L. Lee, B. D. Sawyers, D. Powell, and P. Rancuret, Proc. SPIE 4457, 54 (2001).

Ren, Y. X.

Sawyers, B. D.

L. A. Yoder, W. M. Duncan, E. M. Koontz, J. So, T. A. Bartlett, B. L. Lee, B. D. Sawyers, D. Powell, and P. Rancuret, Proc. SPIE 4457, 54 (2001).

Slaughter, J.

D. Dudley, W. M. Duncan, and J. Slaughter, Proc. SPIE 4985, 14 (2003).
[CrossRef]

So, J.

L. A. Yoder, W. M. Duncan, E. M. Koontz, J. So, T. A. Bartlett, B. L. Lee, B. D. Sawyers, D. Powell, and P. Rancuret, Proc. SPIE 4457, 54 (2001).

Spreeuw, R.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Steinberg, L.

R. W. Floyd and L. Steinberg, in International Symposium Digest of Technical Papers, Society for Information Display (Academic, 1975), p. 36.

Szabo, M. J.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Teslow, H.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Torner, L.

J. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

Torres, J.

G. Molina-Terriza and J. Torres, Nat. Phys. 3, 305(2007).
[CrossRef]

J. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

Wang, Z. Q.

Woerdman, J.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Wu, J. G.

Xuan, L.

Yoder, L. A.

L. A. Yoder, W. M. Duncan, E. M. Koontz, J. So, T. A. Bartlett, B. L. Lee, B. D. Sawyers, D. Powell, and P. Rancuret, Proc. SPIE 4457, 54 (2001).

Appl. Opt.

Appl. Phys. B

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

IBM J. Res. Dev.

B. R. Brown and A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[CrossRef]

J. Mod. Opt.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Phys.

G. Molina-Terriza and J. Torres, Nat. Phys. 3, 305(2007).
[CrossRef]

Opt. Commun.

A. Bekshaev and O. Orlinska, Opt. Commun. 283, 1244 (2010).
[CrossRef]

A. T. O’Neill and M. J. Padgett, Opt. Commun. 193, 45 (2001).
[CrossRef]

M. Padgett and L. Allen, Opt. Commun. 121, 36(1995).
[CrossRef]

Opt. Express

Phys. Rev. A

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

D. Petrov, Phys. Rev. A 82, 035801 (2010).
[CrossRef]

J. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

PLoS ONE

F. P. Martial and N. A. Hartell, PLoS ONE 7, e43942(2012).
[CrossRef]

Proc. SPIE

L. A. Yoder, W. M. Duncan, E. M. Koontz, J. So, T. A. Bartlett, B. L. Lee, B. D. Sawyers, D. Powell, and P. Rancuret, Proc. SPIE 4457, 54 (2001).

J. Otona, M. S. Millana, P. Ambs, and E. Perez-Cabrea, Proc. SPIE 7000, 70001V (2008).
[CrossRef]

D. Dudley, W. M. Duncan, and J. Slaughter, Proc. SPIE 4985, 14 (2003).
[CrossRef]

Other

R. W. Floyd and L. Steinberg, in International Symposium Digest of Technical Papers, Society for Information Display (Academic, 1975), p. 36.

The barely observable elipticity is due to small imperfections in our tilt angle adjustments, and input Gaussian beam. However, no splitting in l=2 and higher modes was observed, indicating that this imperfection is negligible.

J. Liyang, “High-precision laser beam shaping and image projection,” Ph.D. thesis (University of Texas, 2012).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic of the experimental setup; (b)–(e) shaping amplitude and phase of LG22 mode (all patterns are 240×240px, corresponding to 1.8×1.8mm); (b) ideal amplitude; (c) fork-like hologram for l=2; (d) normalized multiplication of (b) by (c); and (e) dithered pattern loaded on the DMD. Note that the background corresponds to half filling to allow for negative amplitude of alternate rings in the LG pattern.

Fig. 2.
Fig. 2.

Intensities in the far field. The radius of the outer ring of the LG33 beam is 700 μm.

Fig. 3.
Fig. 3.

Radial profiles of intensity obtained from cross sections of Fig. 2 (dotted) versus ideal LG intensity profiles (solid).

Fig. 4.
Fig. 4.

Interference of an LG01 beam with an off-axis Gaussian beam in far field (Physical height: 100 μm).

Equations (6)

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

|upl(ρ,φ,ζ)|=(2ρ2R2(ζ))|l|Lp|l|(2ρ2R2(ζ))exp(ρ2R2(ζ))
Φ{upl(ρ,φ,ζ)}=lφ+ρ2R2(ζ)ζ.
Φl(ρ,φ)=lφ+2πλρcosφsinα.
Il(ρ,φ)=cos(Φl(ρ,φ)).
|uplcorr(r,φ,z=0)|=(2r2w2)lLpl(2r2w2)exp(p0·r2w2),
Ppl=|up,siml*·up,idl·rdrdφ|2.

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