Abstract

An optical beam is said to be self-healing when, distorted by an obstacle, the beam corrects itself upon propagation. In this Letter we show, through experiments supported by numerical simulations, that Helico-conical optical beams self-heal. We observe the strong resilience of these beams with different types of obstructions, and relate this to the characteristics of their transverse energy flow.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Broky, G. Siviloglou, A. Dogariu, and D. Christodoulides, Opt. Express 16, 12880 (2008).
    [CrossRef]
  2. J. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, and M. Dennis, Opt. Express 20, 18955 (2012).
    [CrossRef]
  3. P. Vaity and R. P. Singh, Opt. Lett. 36, 2994 (2011).
    [CrossRef]
  4. M. Anguiano-Morales, A. Martínez, M. Iturbe-Castillo, S. Chávez-Cerda, and N. Alcalá-Ochoa, Appl. Opt. 46, 8284 (2007).
    [CrossRef]
  5. Z. Bouchal, Opt. Commun. 210, 155 (2002).
    [CrossRef]
  6. S. Vyas, Y. Kozawa, and S. Sata, J. Opt. Soc. Am. A 28, 837 (2011).
    [CrossRef]
  7. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
    [CrossRef]
  8. J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
    [CrossRef]
  9. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  10. P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901(2012).
    [CrossRef]
  11. C. Alonzo, P. Rodrigo, and J. Glückstad, Opt. Express 13, 1749 (2005).
    [CrossRef]
  12. V. R. Daria, D. Z. Palima, and J. Glückstad, Opt. Express 19, 476 (2011).
    [CrossRef]
  13. V. R. Daria, D. Z. Palima, and J. Glückstad, in The Angular Momentum of Light, D. L. Andrew and M. Babiker, eds. (Cambridge University, 2012), Chap. 14.
  14. M. Padgett and R. Bowman, Nat. Photonics 5, 343(2011).
    [CrossRef]
  15. S. H. Tao, W. M. Lee, and X. Yuan, Appl. Opt. 43, 122(2004).
    [CrossRef]
  16. N. Hermosa and C. O. Manaois, Opt. Commun. 271, 178 (2007).
    [CrossRef]
  17. L. C. Thomson and J. Courtial, Opt. Commun. 281, 1217 (2008).
    [CrossRef]
  18. A. Vasara, J. Turunen, and A. Friberg, J. Opt. Soc. Am. A 6, 1748 (1989).
    [CrossRef]
  19. N. Chattrapiban, E. Rogers, D. Cofield, W. Hill, and R. Roy, Opt. Lett. 28, 2183 (2003).
    [CrossRef]
  20. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).
  21. N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, J. Opt. Soc. Am. A 25, 1642 (2008).
    [CrossRef]
  22. This formula comes from the maximum propagation distance of a BB [18]. For HCOBs, the slope of the cone depends on ℓ, and the smallest value of the propagation distance is at its steepest slope. The steepest slope thus defines the propagation distance of the HCOBs.
  23. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  24. A. Bekshaev and M. Soskin, Opt. Lett. 31, 2199 (2006).
    [CrossRef]

2012

J. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, and M. Dennis, Opt. Express 20, 18955 (2012).
[CrossRef]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901(2012).
[CrossRef]

2011

2008

2007

2006

2005

2004

2003

2002

Z. Bouchal, Opt. Commun. 210, 155 (2002).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

1992

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

1989

1987

Alcalá-Ochoa, N.

Allen, L.

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

Alonzo, C.

Ando, T.

Anguiano-Morales, M.

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Beijersbergen, M. W.

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

Bekshaev, A.

Bouchal, Z.

Z. Bouchal, Opt. Commun. 210, 155 (2002).
[CrossRef]

Bowman, R.

M. Padgett and R. Bowman, Nat. Photonics 5, 343(2011).
[CrossRef]

Broky, J.

Cannan, D.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901(2012).
[CrossRef]

Chattrapiban, N.

Chávez-Cerda, S.

Chen, Z.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901(2012).
[CrossRef]

Christodoulides, D.

Cofield, D.

Courtial, J.

L. C. Thomson and J. Courtial, Opt. Commun. 281, 1217 (2008).
[CrossRef]

Daria, V. R.

V. R. Daria, D. Z. Palima, and J. Glückstad, Opt. Express 19, 476 (2011).
[CrossRef]

V. R. Daria, D. Z. Palima, and J. Glückstad, in The Angular Momentum of Light, D. L. Andrew and M. Babiker, eds. (Cambridge University, 2012), Chap. 14.

Dennis, M.

Dholakia, K.

J. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, and M. Dennis, Opt. Express 20, 18955 (2012).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Dogariu, A.

Durnin, J.

Friberg, A.

Fukuchi, N.

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Glückstad, J.

V. R. Daria, D. Z. Palima, and J. Glückstad, Opt. Express 19, 476 (2011).
[CrossRef]

C. Alonzo, P. Rodrigo, and J. Glückstad, Opt. Express 13, 1749 (2005).
[CrossRef]

V. R. Daria, D. Z. Palima, and J. Glückstad, in The Angular Momentum of Light, D. L. Andrew and M. Babiker, eds. (Cambridge University, 2012), Chap. 14.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

Hara, T.

Hermosa, N.

N. Hermosa and C. O. Manaois, Opt. Commun. 271, 178 (2007).
[CrossRef]

Hill, W.

Hu, Y.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901(2012).
[CrossRef]

Inoue, T.

Iturbe-Castillo, M.

Kozawa, Y.

Lee, W. M.

Li, T.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901(2012).
[CrossRef]

Lindberg, J.

Manaois, C. O.

N. Hermosa and C. O. Manaois, Opt. Commun. 271, 178 (2007).
[CrossRef]

Martínez, A.

Matsumoto, N.

Mazilu, M.

McGloin, D.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Morandotti, R.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901(2012).
[CrossRef]

Mourka, A.

Ohtake, Y.

Padgett, M.

M. Padgett and R. Bowman, Nat. Photonics 5, 343(2011).
[CrossRef]

Palima, D. Z.

V. R. Daria, D. Z. Palima, and J. Glückstad, Opt. Express 19, 476 (2011).
[CrossRef]

V. R. Daria, D. Z. Palima, and J. Glückstad, in The Angular Momentum of Light, D. L. Andrew and M. Babiker, eds. (Cambridge University, 2012), Chap. 14.

Ring, J.

Rodrigo, P.

Rogers, E.

Roy, R.

Sata, S.

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Singh, R. P.

Siviloglou, G.

Soskin, M.

Spreeuw, R. J. C.

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

Tao, S. H.

Thomson, L. C.

L. C. Thomson and J. Courtial, Opt. Commun. 281, 1217 (2008).
[CrossRef]

Turunen, J.

Vaity, P.

Vasara, A.

Vyas, S.

Woerdman, J. P.

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

Yin, X.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901(2012).
[CrossRef]

Yuan, X.

Zhang, P.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901(2012).
[CrossRef]

Zhang, X.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901(2012).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Nat. Photonics

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

M. Padgett and R. Bowman, Nat. Photonics 5, 343(2011).
[CrossRef]

Nature

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Opt. Commun.

Z. Bouchal, Opt. Commun. 210, 155 (2002).
[CrossRef]

N. Hermosa and C. O. Manaois, Opt. Commun. 271, 178 (2007).
[CrossRef]

L. C. Thomson and J. Courtial, Opt. Commun. 281, 1217 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

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

Phys. Rev. Lett.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901(2012).
[CrossRef]

Other

V. R. Daria, D. Z. Palima, and J. Glückstad, in The Angular Momentum of Light, D. L. Andrew and M. Babiker, eds. (Cambridge University, 2012), Chap. 14.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

This formula comes from the maximum propagation distance of a BB [18]. For HCOBs, the slope of the cone depends on ℓ, and the smallest value of the propagation distance is at its steepest slope. The steepest slope thus defines the propagation distance of the HCOBs.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) Experimental setup. Holograms are encoded onto a SLM. (b) Samples of unblocked (above) and blocked (below) holograms are shown. L1 and L2 are collimating lenses while M1 and M2 are mirrors for alignment. BS is beam splitter.

Fig. 2.
Fig. 2.

Intensity profiles comparing reconstruction of blocked (b), (d) =50 HCOBs after 14 cm propagation with beams that are not blocked (a), (c). (a) and (b) are obtained from experiments while (c) and (d) are from numerical simulations. The top images are for K=0 while the bottom ones are for K=1. The block size is Δθ=π/3.

Fig. 3.
Fig. 3.

(a) Correlation for different values of . (b) Correlation with different block sizes. (c) Correlation for different block orientations. Numerical simulation results are placed as inset. K=0 uses circles, while K=1 uses squares.

Fig. 4.
Fig. 4.

A 0.38 mm strip is placed at the path of a =40 HCOB, 16 cm after the SLM. (a) and (c) are experimental results while (b) and (d) are numerical simulations. Top images are obtained right after the block while the bottom images are after 8 cm of propagation. (a), (b) and (c), (d) are K=0 and K=1 HCOBs, respectively.

Fig. 5.
Fig. 5.

Transverse energy flow for K=0 HCOBs with =30 for (a) no block and (b) blocked located 16 cm after the SLM. Both beams propagate a total distance of 20 cm. Arrow direction is the direction of the energy flow while its length is the magnitude. Dashed lines denote the original position of the block.

Metrics