Abstract

We have developed iterative algorithms for the calculation of holograms for non-diffracting or self-imaging light beams. Our methods make use of the special Fourier-space properties of the target beams. We demonstrate experimentally the holographic generation of perhaps the most challenging type of beam: a self-imaging beam shaped in more than one plane. Potential applications include the generation of light “crystals” for optical trapping and atomic diffraction studies.

© 2006 Optical Society of America

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  1. J. Durnin, J. J. J. Miceli, and J. H. Eberly, "Diffraction-free Beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
    [CrossRef]
  2. J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
    [CrossRef]
  3. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
    [CrossRef]
  4. D. McGloin, V. Garcés-Chávez, and K. Dholakia, "Interfering Bessel beams for optical micromanipulation," Opt. Lett. 28, 657-659 (2003).
  5. E. Goldfain, "Optical biopsy with long-range nondiffracting beams," in Optical Biopsy III, R. R. Alfano, ed., Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), pp. 119-127 (2000).
  6. J. Durnin, "Exact solutions for nondiffracting beams. I. The scalar theory," J. Opt. Soc. Am. A 4, 651-654 (1987).
  7. S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclass. Opt. 4, S52-S57 (2002).
    [CrossRef]
  8. Z. Bouchal and J. Kyvalský, "Controllable 3D spatial localization of light fields synthesized by non-diffracting modes," J. Mod. Opt. 51, 157-176 (2004).
  9. K. Patorski, "The self-imaging phenomenon and its applications," Progr. Opt. XXVII, 3-108 (1989).
  10. E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, "3D interferometric optical tweezers using a single spatial light modulator," Opt. Express 13, 3777-3786 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3777.
    [CrossRef]
  11. R. Piestun and J. Shamir, "Control of wave-front propagation with diffractive elements," Opt. Lett. 19, 771-773 (1994).
  12. V. V. Kotlyar, S. N. Khonina, and V. A. Soifer, "Algorithm for the Generation of Non-diffracting Bessel Modes," J. Mod. Opt. 42, 1231-1239 (1995).
  13. V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
  14. M. R. Dennis, "Braided nodal lines in wave superpositions," New J. Phys. 5, 1341-1348 (2003).
  15. Z. Bouchal, "Controlled spatial shaping of nondiffracting patterns and arrays," Opt. Lett. 27, 1376-1378 (2002).
  16. G. Indebetouw, "Quasi-self-imaging using aperiodic sequences," J. Opt. Soc. Am. A 9, 549-558 (1992).
  17. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).
  18. M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, "Synthesis of digital holograms by direct binary search," Appl. Opt. 26, 2788-2798 (1987).
  19. V. Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis Ltd, London, 1997).
  20. T. Haist, M. Schönleber, and H. J. Tiziani, "Computer-generated holograms from 3D-objects written on twistednematic liquid crystal displays," Opt. Commun. 140, 299-308 (1997).
    [CrossRef]
  21. G. Shabtay, "Three-dimensional beam forming and Ewald’s surfaces," Opt. Commun. 226, 33-37 (2003).
    [CrossRef]
  22. G. Whyte and J. Courtial, "Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm," New J. Phys. 7, 117 (2005).
    [CrossRef]
  23. CRL Opto Ltd., 1024 × 768 pixels, 13.9mm × 8.5mm active area.
  24. L. Santos, "Introduction to Focus Issue: Cold Atomic Gases in Optical Lattices," Optics Express 12, 2-3 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-2.
    [CrossRef]

2005 (2)

2004 (2)

L. Santos, "Introduction to Focus Issue: Cold Atomic Gases in Optical Lattices," Optics Express 12, 2-3 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-2.
[CrossRef]

Z. Bouchal and J. Kyvalský, "Controllable 3D spatial localization of light fields synthesized by non-diffracting modes," J. Mod. Opt. 51, 157-176 (2004).

2003 (3)

M. R. Dennis, "Braided nodal lines in wave superpositions," New J. Phys. 5, 1341-1348 (2003).

G. Shabtay, "Three-dimensional beam forming and Ewald’s surfaces," Opt. Commun. 226, 33-37 (2003).
[CrossRef]

D. McGloin, V. Garcés-Chávez, and K. Dholakia, "Interfering Bessel beams for optical micromanipulation," Opt. Lett. 28, 657-659 (2003).

2002 (3)

Z. Bouchal, "Controlled spatial shaping of nondiffracting patterns and arrays," Opt. Lett. 27, 1376-1378 (2002).

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef]

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclass. Opt. 4, S52-S57 (2002).
[CrossRef]

2001 (1)

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

1997 (2)

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: rotating images," J. Mod. Opt. 44, 1409-1416 (1997).

T. Haist, M. Schönleber, and H. J. Tiziani, "Computer-generated holograms from 3D-objects written on twistednematic liquid crystal displays," Opt. Commun. 140, 299-308 (1997).
[CrossRef]

1995 (1)

V. V. Kotlyar, S. N. Khonina, and V. A. Soifer, "Algorithm for the Generation of Non-diffracting Bessel Modes," J. Mod. Opt. 42, 1231-1239 (1995).

1994 (1)

1992 (1)

1989 (1)

K. Patorski, "The self-imaging phenomenon and its applications," Progr. Opt. XXVII, 3-108 (1989).

1987 (3)

1972 (1)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

Allebach, J. P.

Allison, I.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclass. Opt. 4, S52-S57 (2002).
[CrossRef]

Arlt, J.

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Bouchal, Z.

Z. Bouchal and J. Kyvalský, "Controllable 3D spatial localization of light fields synthesized by non-diffracting modes," J. Mod. Opt. 51, 157-176 (2004).

Z. Bouchal, "Controlled spatial shaping of nondiffracting patterns and arrays," Opt. Lett. 27, 1376-1378 (2002).

Chávez-Cerda, S.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclass. Opt. 4, S52-S57 (2002).
[CrossRef]

Cooper, J.

Courtial, J.

E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, "3D interferometric optical tweezers using a single spatial light modulator," Opt. Express 13, 3777-3786 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3777.
[CrossRef]

G. Whyte and J. Courtial, "Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm," New J. Phys. 7, 117 (2005).
[CrossRef]

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclass. Opt. 4, S52-S57 (2002).
[CrossRef]

Dennis, M. R.

M. R. Dennis, "Braided nodal lines in wave superpositions," New J. Phys. 5, 1341-1348 (2003).

Dholakia, K.

D. McGloin, V. Garcés-Chávez, and K. Dholakia, "Interfering Bessel beams for optical micromanipulation," Opt. Lett. 28, 657-659 (2003).

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef]

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Durnin, J.

J. Durnin, "Exact solutions for nondiffracting beams. I. The scalar theory," J. Opt. Soc. Am. A 4, 651-654 (1987).

J. Durnin, J. 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. J. Miceli, and J. H. Eberly, "Diffraction-free Beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef]

Garcés-Chávez, V.

D. McGloin, V. Garcés-Chávez, and K. Dholakia, "Interfering Bessel beams for optical micromanipulation," Opt. Lett. 28, 657-659 (2003).

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef]

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

Gutiérrez-Vega, J.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclass. Opt. 4, S52-S57 (2002).
[CrossRef]

Haist, T.

T. Haist, M. Schönleber, and H. J. Tiziani, "Computer-generated holograms from 3D-objects written on twistednematic liquid crystal displays," Opt. Commun. 140, 299-308 (1997).
[CrossRef]

Indebetouw, G.

Jordan, P.

Khonina, S. N.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: rotating images," J. Mod. Opt. 44, 1409-1416 (1997).

V. V. Kotlyar, S. N. Khonina, and V. A. Soifer, "Algorithm for the Generation of Non-diffracting Bessel Modes," J. Mod. Opt. 42, 1231-1239 (1995).

Kotlyar, V. V.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: rotating images," J. Mod. Opt. 44, 1409-1416 (1997).

V. V. Kotlyar, S. N. Khonina, and V. A. Soifer, "Algorithm for the Generation of Non-diffracting Bessel Modes," J. Mod. Opt. 42, 1231-1239 (1995).

Kyvalský, J.

Z. Bouchal and J. Kyvalský, "Controllable 3D spatial localization of light fields synthesized by non-diffracting modes," J. Mod. Opt. 51, 157-176 (2004).

MacVicar, I.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclass. Opt. 4, S52-S57 (2002).
[CrossRef]

McGloin, D.

D. McGloin, V. Garcés-Chávez, and K. Dholakia, "Interfering Bessel beams for optical micromanipulation," Opt. Lett. 28, 657-659 (2003).

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef]

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef]

Miceli, J. J. J.

J. Durnin, J. J. J. Miceli, and J. H. Eberly, "Diffraction-free Beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef]

New, G.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclass. Opt. 4, S52-S57 (2002).
[CrossRef]

O’Neil, A.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclass. Opt. 4, S52-S57 (2002).
[CrossRef]

Padgett, M.

E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, "3D interferometric optical tweezers using a single spatial light modulator," Opt. Express 13, 3777-3786 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3777.
[CrossRef]

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclass. Opt. 4, S52-S57 (2002).
[CrossRef]

Patorski, K.

K. Patorski, "The self-imaging phenomenon and its applications," Progr. Opt. XXVII, 3-108 (1989).

Piestun, R.

Santos, L.

L. Santos, "Introduction to Focus Issue: Cold Atomic Gases in Optical Lattices," Optics Express 12, 2-3 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-2.
[CrossRef]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

Schonbrun, E.

Schönleber, M.

T. Haist, M. Schönleber, and H. J. Tiziani, "Computer-generated holograms from 3D-objects written on twistednematic liquid crystal displays," Opt. Commun. 140, 299-308 (1997).
[CrossRef]

Seldowitz, M. A.

Shabtay, G.

G. Shabtay, "Three-dimensional beam forming and Ewald’s surfaces," Opt. Commun. 226, 33-37 (2003).
[CrossRef]

Shamir, J.

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef]

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Soifer, V. A.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: rotating images," J. Mod. Opt. 44, 1409-1416 (1997).

V. V. Kotlyar, S. N. Khonina, and V. A. Soifer, "Algorithm for the Generation of Non-diffracting Bessel Modes," J. Mod. Opt. 42, 1231-1239 (1995).

Sweeney, D. W.

Tiziani, H. J.

T. Haist, M. Schönleber, and H. J. Tiziani, "Computer-generated holograms from 3D-objects written on twistednematic liquid crystal displays," Opt. Commun. 140, 299-308 (1997).
[CrossRef]

Whyte, G.

G. Whyte and J. Courtial, "Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm," New J. Phys. 7, 117 (2005).
[CrossRef]

Wulff, K. D.

Appl. Opt. (1)

J. Mod. Opt. (3)

V. V. Kotlyar, S. N. Khonina, and V. A. Soifer, "Algorithm for the Generation of Non-diffracting Bessel Modes," J. Mod. Opt. 42, 1231-1239 (1995).

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: rotating images," J. Mod. Opt. 44, 1409-1416 (1997).

Z. Bouchal and J. Kyvalský, "Controllable 3D spatial localization of light fields synthesized by non-diffracting modes," J. Mod. Opt. 51, 157-176 (2004).

J. Opt. B: Quantum Semiclass. Opt. (1)

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, "Holographic generation and orbital angular momentum of high-order Mathieu beams," J. Opt. B: Quantum Semiclass. Opt. 4, S52-S57 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef]

New J. Phys. (2)

M. R. Dennis, "Braided nodal lines in wave superpositions," New J. Phys. 5, 1341-1348 (2003).

G. Whyte and J. Courtial, "Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm," New J. Phys. 7, 117 (2005).
[CrossRef]

Opt. Commun. (3)

T. Haist, M. Schönleber, and H. J. Tiziani, "Computer-generated holograms from 3D-objects written on twistednematic liquid crystal displays," Opt. Commun. 140, 299-308 (1997).
[CrossRef]

G. Shabtay, "Three-dimensional beam forming and Ewald’s surfaces," Opt. Commun. 226, 33-37 (2003).
[CrossRef]

J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Optics Express (1)

L. Santos, "Introduction to Focus Issue: Cold Atomic Gases in Optical Lattices," Optics Express 12, 2-3 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-2.
[CrossRef]

Optik (1)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

Phys. Rev. Lett. (1)

J. Durnin, J. J. J. Miceli, and J. H. Eberly, "Diffraction-free Beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef]

Progr. Opt. (1)

K. Patorski, "The self-imaging phenomenon and its applications," Progr. Opt. XXVII, 3-108 (1989).

Other (3)

CRL Opto Ltd., 1024 × 768 pixels, 13.9mm × 8.5mm active area.

E. Goldfain, "Optical biopsy with long-range nondiffracting beams," in Optical Biopsy III, R. R. Alfano, ed., Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), pp. 119-127 (2000).

V. Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis Ltd, London, 1997).

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