Abstract

We show that, contrary to popular belief, diffraction-free beams may not only reconstruct themselves after hitting an opaque obstacle but also, for example, Gaussian beams. We unravel the mathematics and the physics underlying the self-reconstruction mechanism and we provide for a novel definition for the minimum reconstruction distance beyond geometric optics, which is in principle applicable to any optical beam that admits an angular spectrum representation. Moreover, we propose to quantify the self-reconstruction ability of a beam via a newly established degree of self-healing. This is defined via a comparison between the amplitudes, as opposite to intensities, of the original beam and the obstructed one. Such comparison is experimentally accomplished by tailoring an innovative experimental technique based upon Shack-Hartmann wave front reconstruction. We believe that these results can open new avenues in this field.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Self-healing property of a caustic optical beam

Marcelino Anguiano-Morales, Amalia Martínez, M. David Iturbe-Castillo, Sabino Chávez-Cerda, and N. Alcalá-Ochoa
Appl. Opt. 46(34) 8284-8290 (2007)

Quantitative description of the self-healing ability of a beam

Xiuxiang Chu and Wei Wen
Opt. Express 22(6) 6899-6904 (2014)

Self-healing properties of Hermite-Gaussian correlated Schell-model beams

Zhiheng Xu, Xianlong Liu, Yahong Chen, Fei Wang, Lin Liu, Yashar E. Monfared, Sergey A. Ponomarenko, Yangjian Cai, and Chunhao Liang
Opt. Express 28(3) 2828-2837 (2020)

References

  • View by:
  • |
  • |
  • |

  1. Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
    [Crossref]
  2. M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” JETP Lett. 71, 130–133 (2000).
    [Crossref]
  3. V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Splading, G. Cristobal, and K. Dholakia, “The reconstruction of optical angular momentum after distortion in amplitude, phase and polarization,” J. Opt. A: Pure Appl. Opt. 6, S235–S238 (2004).
    [Crossref]
  4. J. Arlt, V. Garcés-Chávez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
    [Crossref]
  5. 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]
  6. F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Phot. 4, 780–785 (2010).
    [Crossref]
  7. F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat. Commun. 3, 632 (2012).
    [Crossref] [PubMed]
  8. M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
    [Crossref]
  9. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref] [PubMed]
  10. Z. Bouchal, “Resistance of nondiffracting vortex beams to amplitude and phase perturbations,” Opt. Commun. 210, 155–164 (2002).
    [Crossref]
  11. S. H. Tao and X. Yuan, “Self-reconstruction property of fractional Bessel beams,” J. Opt. Soc. Am. A 21, 1192–1197 (2004).
    [Crossref]
  12. P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8, 477–482 (2006).
    [Crossref]
  13. X. Chu, “Analytical study on the self-healing property of Bessel beam,” Eur. Phys. J. D 66, 259 (2012).
    [Crossref]
  14. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
    [Crossref]
  15. M. Anguiano-Morales, A. Martínez, M. D. Iturbe-Castillo, S. Chávez-Cerda, and N. Alcalá-Ochoa, “Self-healing property of a caustic optical beam,” Appl. Opt. 46, 8284–8290 (2007).
    [Crossref] [PubMed]
  16. P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
    [Crossref] [PubMed]
  17. V. Arrizón, D. Aguirre-Olivas, G. Mellado-Villaseñor, and S. Chávez-Cerda, “Self-healing in scaled propagation invariant beams,” arXiv:1503.03125 (2015).
  18. P. Vainty and R. P. Singh, “Self-healing property of optical ring lattice,” Opt. Lett. 36, 2994–2996 (2011).
    [Crossref]
  19. J. D. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, and M. R. Dennis, “Autofocusing and self-healing of Pearcey beams,” Opt. Express 20, 18955–18966 (2012).
    [Crossref] [PubMed]
  20. S. Vyas, Y. Kozawa, and S. Sato, “Self-healing of tightly focused scalar and vector Bessel-Gauss beams at the focal plane,” J. Opt. Soc. Am. A 28, 837–843 (2011).
    [Crossref]
  21. G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89, 043807 (2014).
    [Crossref]
  22. F. Wang, Y. Chen, X. Liu, Y. Cai, and S. A. Ponomarenko, “Self-reconstruction of partially coherent light beams scattered by opaque obstacles,” Opt. Express 24, 23735–23746 (2016).
    [Crossref] [PubMed]
  23. A. Aiello and G. S. Agarwal, “Wave-optics description of self-healing mechanism in Bessel beams,” Opt. Lett. 39, 6819–6822 (2014).
    [Crossref] [PubMed]
  24. D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
    [Crossref]
  25. I. A. Litvin, M. G. Mclaren, and A. Forbes, “A conical wave approach to calculating suggBessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
    [Crossref]
  26. D. L. Andrews, ed., Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic, 2008).
  27. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
    [Crossref]
  28. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
    [Crossref]
  29. R. Kress, Linear Integral Equations (Springer, 1999).
    [Crossref]
  30. K. Ball, “Ellipsoids of maximal volume in convex bodies,” Geom. Dedic. 41, 241–250 (1992).
    [Crossref]
  31. M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information,” (Cambridge University, 2000).
  32. X. Chu and W. Wen, “Quantitative description of the self-healing ability of a beam,” Opt. Express 22, 6899–6904 (2012).
    [Crossref]
  33. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Dover, 1999).
  34. M. Hillery, “Nonclassical distance in quantum optics,” Phys. Rev. A 35, 725–732 (1987).
    [Crossref]
  35. V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78, 2275–2278 (1997).
    [Crossref]
  36. A. B. Klimov, L. L. Sánchez-Soto, E. C. Yustas, J. Söderholm, and G. Björk, “Distance-based degrees of polarization for a quantum field,” Phys. Rev. A 72, 033813 (2005).
    [Crossref]
  37. S. Gnutzmann and K. Życzkowski, “Rényi–Wehrl entropies as measures of localization in phase space,” J. Phys. A 34, 10123 (2001).
    [Crossref]

2016 (1)

2014 (3)

A. Aiello and G. S. Agarwal, “Wave-optics description of self-healing mechanism in Bessel beams,” Opt. Lett. 39, 6819–6822 (2014).
[Crossref] [PubMed]

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89, 043807 (2014).
[Crossref]

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref]

2012 (5)

F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat. Commun. 3, 632 (2012).
[Crossref] [PubMed]

X. Chu, “Analytical study on the self-healing property of Bessel beam,” Eur. Phys. J. D 66, 259 (2012).
[Crossref]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

J. D. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, and M. R. Dennis, “Autofocusing and self-healing of Pearcey beams,” Opt. Express 20, 18955–18966 (2012).
[Crossref] [PubMed]

X. Chu and W. Wen, “Quantitative description of the self-healing ability of a beam,” Opt. Express 22, 6899–6904 (2012).
[Crossref]

2011 (2)

2010 (1)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Phot. 4, 780–785 (2010).
[Crossref]

2009 (1)

I. A. Litvin, M. G. Mclaren, and A. Forbes, “A conical wave approach to calculating suggBessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
[Crossref]

2008 (1)

2007 (1)

2006 (1)

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8, 477–482 (2006).
[Crossref]

2005 (2)

D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

A. B. Klimov, L. L. Sánchez-Soto, E. C. Yustas, J. Söderholm, and G. Björk, “Distance-based degrees of polarization for a quantum field,” Phys. Rev. A 72, 033813 (2005).
[Crossref]

2004 (2)

S. H. Tao and X. Yuan, “Self-reconstruction property of fractional Bessel beams,” J. Opt. Soc. Am. A 21, 1192–1197 (2004).
[Crossref]

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Splading, G. Cristobal, and K. Dholakia, “The reconstruction of optical angular momentum after distortion in amplitude, phase and polarization,” J. Opt. A: Pure Appl. Opt. 6, S235–S238 (2004).
[Crossref]

2002 (2)

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]

Z. Bouchal, “Resistance of nondiffracting vortex beams to amplitude and phase perturbations,” Opt. Commun. 210, 155–164 (2002).
[Crossref]

2001 (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]

S. Gnutzmann and K. Życzkowski, “Rényi–Wehrl entropies as measures of localization in phase space,” J. Phys. A 34, 10123 (2001).
[Crossref]

2000 (1)

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” JETP Lett. 71, 130–133 (2000).
[Crossref]

1998 (1)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

1997 (1)

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78, 2275–2278 (1997).
[Crossref]

1992 (1)

K. Ball, “Ellipsoids of maximal volume in convex bodies,” Geom. Dedic. 41, 241–250 (1992).
[Crossref]

1987 (2)

M. Hillery, “Nonclassical distance in quantum optics,” Phys. Rev. A 35, 725–732 (1987).
[Crossref]

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

Agarwal, G. S.

Aguirre-Olivas, D.

V. Arrizón, D. Aguirre-Olivas, G. Mellado-Villaseñor, and S. Chávez-Cerda, “Self-healing in scaled propagation invariant beams,” arXiv:1503.03125 (2015).

Aiello, A.

Alcalá-Ochoa, N.

Anguiano-Morales, M.

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]

Arrizón, V.

V. Arrizón, D. Aguirre-Olivas, G. Mellado-Villaseñor, and S. Chávez-Cerda, “Self-healing in scaled propagation invariant beams,” arXiv:1503.03125 (2015).

Ball, K.

K. Ball, “Ellipsoids of maximal volume in convex bodies,” Geom. Dedic. 41, 241–250 (1992).
[Crossref]

Björk, G.

A. B. Klimov, L. L. Sánchez-Soto, E. C. Yustas, J. Söderholm, and G. Björk, “Distance-based degrees of polarization for a quantum field,” Phys. Rev. A 72, 033813 (2005).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

Bouchal, Z.

Z. Bouchal, “Resistance of nondiffracting vortex beams to amplitude and phase perturbations,” Opt. Commun. 210, 155–164 (2002).
[Crossref]

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

Broky, J.

Brown, C. T. A.

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8, 477–482 (2006).
[Crossref]

Cai, Y.

Cannan, D.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Chávez-Cerda, S.

M. Anguiano-Morales, A. Martínez, M. D. Iturbe-Castillo, S. Chávez-Cerda, and N. Alcalá-Ochoa, “Self-healing property of a caustic optical beam,” Appl. Opt. 46, 8284–8290 (2007).
[Crossref] [PubMed]

V. Arrizón, D. Aguirre-Olivas, G. Mellado-Villaseñor, and S. Chávez-Cerda, “Self-healing in scaled propagation invariant beams,” arXiv:1503.03125 (2015).

Chen, Y.

Chen, Z.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

Christodoulides, D. N.

Chu, X.

X. Chu, “Analytical study on the self-healing property of Bessel beam,” Eur. Phys. J. D 66, 259 (2012).
[Crossref]

X. Chu and W. Wen, “Quantitative description of the self-healing ability of a beam,” Opt. Express 22, 6899–6904 (2012).
[Crossref]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information,” (Cambridge University, 2000).

Cristobal, G.

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Splading, G. Cristobal, and K. Dholakia, “The reconstruction of optical angular momentum after distortion in amplitude, phase and polarization,” J. Opt. A: Pure Appl. Opt. 6, S235–S238 (2004).
[Crossref]

Dennis, M. R.

Dholakia, K.

J. D. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, and M. R. Dennis, “Autofocusing and self-healing of Pearcey beams,” Opt. Express 20, 18955–18966 (2012).
[Crossref] [PubMed]

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8, 477–482 (2006).
[Crossref]

D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Splading, G. Cristobal, and K. Dholakia, “The reconstruction of optical angular momentum after distortion in amplitude, phase and polarization,” J. Opt. A: Pure Appl. Opt. 6, S235–S238 (2004).
[Crossref]

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]

Dogariu, A.

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]

Fahrbach, F. O.

F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat. Commun. 3, 632 (2012).
[Crossref] [PubMed]

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Phot. 4, 780–785 (2010).
[Crossref]

Fernandez-Nieves, A.

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Splading, G. Cristobal, and K. Dholakia, “The reconstruction of optical angular momentum after distortion in amplitude, phase and polarization,” J. Opt. A: Pure Appl. Opt. 6, S235–S238 (2004).
[Crossref]

Fischer, P.

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8, 477–482 (2006).
[Crossref]

Fomin, S. V.

A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Dover, 1999).

Forbes, A.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref]

I. A. Litvin, M. G. Mclaren, and A. Forbes, “A conical wave approach to calculating suggBessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
[Crossref]

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Splading, G. Cristobal, and K. Dholakia, “The reconstruction of optical angular momentum after distortion in amplitude, phase and polarization,” J. Opt. A: Pure Appl. Opt. 6, S235–S238 (2004).
[Crossref]

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]

Gnutzmann, S.

S. Gnutzmann and K. Życzkowski, “Rényi–Wehrl entropies as measures of localization in phase space,” J. Phys. A 34, 10123 (2001).
[Crossref]

Hillery, M.

M. Hillery, “Nonclassical distance in quantum optics,” Phys. Rev. A 35, 725–732 (1987).
[Crossref]

Hu, Y.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Iturbe-Castillo, M. D.

Klimov, A. B.

A. B. Klimov, L. L. Sánchez-Soto, E. C. Yustas, J. Söderholm, and G. Björk, “Distance-based degrees of polarization for a quantum field,” Phys. Rev. A 72, 033813 (2005).
[Crossref]

Knight, P. L.

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78, 2275–2278 (1997).
[Crossref]

Kolmogorov, A. N.

A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Dover, 1999).

Kozawa, Y.

Kress, R.

R. Kress, Linear Integral Equations (Springer, 1999).
[Crossref]

Li, T.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Lindberg, J.

Little, H.

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8, 477–482 (2006).
[Crossref]

Litvin, I. A.

I. A. Litvin, M. G. Mclaren, and A. Forbes, “A conical wave approach to calculating suggBessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
[Crossref]

Liu, X.

Lopez-Mariscal, C.

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8, 477–482 (2006).
[Crossref]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
[Crossref]

Marienko, I. G.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” JETP Lett. 71, 130–133 (2000).
[Crossref]

Martínez, A.

Mazilu, M.

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Splading, G. Cristobal, and K. Dholakia, “The reconstruction of optical angular momentum after distortion in amplitude, phase and polarization,” J. Opt. A: Pure Appl. Opt. 6, S235–S238 (2004).
[Crossref]

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]

McLaren, M.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref]

Mclaren, M. G.

I. A. Litvin, M. G. Mclaren, and A. Forbes, “A conical wave approach to calculating suggBessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
[Crossref]

Mellado-Villaseñor, G.

V. Arrizón, D. Aguirre-Olivas, G. Mellado-Villaseñor, and S. Chávez-Cerda, “Self-healing in scaled propagation invariant beams,” arXiv:1503.03125 (2015).

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]

Mhlanga, T.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref]

Miceli, J. J.

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

Morandotti, R.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Mourka, A.

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information,” (Cambridge University, 2000).

Padgett, M. J.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref]

Plenio, M. B.

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78, 2275–2278 (1997).
[Crossref]

Ponomarenko, S. A.

Ring, J. D.

Rippin, M. A.

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78, 2275–2278 (1997).
[Crossref]

Rohrbach, A.

F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat. Commun. 3, 632 (2012).
[Crossref] [PubMed]

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Phot. 4, 780–785 (2010).
[Crossref]

Roux, F. S.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref]

Sánchez-Soto, L. L.

A. B. Klimov, L. L. Sánchez-Soto, E. C. Yustas, J. Söderholm, and G. Björk, “Distance-based degrees of polarization for a quantum field,” Phys. Rev. A 72, 033813 (2005).
[Crossref]

Sato, S.

Sibbett, W.

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8, 477–482 (2006).
[Crossref]

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]

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Phot. 4, 780–785 (2010).
[Crossref]

Singh, R. P.

Siviloglou, G. A.

Smith, R. L.

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8, 477–482 (2006).
[Crossref]

Söderholm, J.

A. B. Klimov, L. L. Sánchez-Soto, E. C. Yustas, J. Söderholm, and G. Björk, “Distance-based degrees of polarization for a quantum field,” Phys. Rev. A 72, 033813 (2005).
[Crossref]

Soskin, M. S.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” JETP Lett. 71, 130–133 (2000).
[Crossref]

Splading, G. C.

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Splading, G. Cristobal, and K. Dholakia, “The reconstruction of optical angular momentum after distortion in amplitude, phase and polarization,” J. Opt. A: Pure Appl. Opt. 6, S235–S238 (2004).
[Crossref]

Summers, M. D.

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Splading, G. Cristobal, and K. Dholakia, “The reconstruction of optical angular momentum after distortion in amplitude, phase and polarization,” J. Opt. A: Pure Appl. Opt. 6, S235–S238 (2004).
[Crossref]

Tao, S. H.

Vainty, P.

Vasnetsov, M. V.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” JETP Lett. 71, 130–133 (2000).
[Crossref]

Vedral, V.

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78, 2275–2278 (1997).
[Crossref]

Vyas, S.

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

Wang, F.

Wen, W.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
[Crossref]

Wu, G.

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89, 043807 (2014).
[Crossref]

Yin, X.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Yuan, X.

Yustas, E. C.

A. B. Klimov, L. L. Sánchez-Soto, E. C. Yustas, J. Söderholm, and G. Björk, “Distance-based degrees of polarization for a quantum field,” Phys. Rev. A 72, 033813 (2005).
[Crossref]

Zhang, P.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Zhang, X.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Zyczkowski, K.

S. Gnutzmann and K. Życzkowski, “Rényi–Wehrl entropies as measures of localization in phase space,” J. Phys. A 34, 10123 (2001).
[Crossref]

Appl. Opt. (1)

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

Eur. Phys. J. D (1)

X. Chu, “Analytical study on the self-healing property of Bessel beam,” Eur. Phys. J. D 66, 259 (2012).
[Crossref]

Geom. Dedic. (1)

K. Ball, “Ellipsoids of maximal volume in convex bodies,” Geom. Dedic. 41, 241–250 (1992).
[Crossref]

J. Opt. A (1)

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8, 477–482 (2006).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

V. Garcés-Chávez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Splading, G. Cristobal, and K. Dholakia, “The reconstruction of optical angular momentum after distortion in amplitude, phase and polarization,” J. Opt. A: Pure Appl. Opt. 6, S235–S238 (2004).
[Crossref]

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

J. Phys. A (1)

S. Gnutzmann and K. Życzkowski, “Rényi–Wehrl entropies as measures of localization in phase space,” J. Phys. A 34, 10123 (2001).
[Crossref]

JETP Lett. (1)

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” JETP Lett. 71, 130–133 (2000).
[Crossref]

Nat. Commun. (2)

F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat. Commun. 3, 632 (2012).
[Crossref] [PubMed]

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref]

Nat. Phot. (1)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Phot. 4, 780–785 (2010).
[Crossref]

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]

Opt. Commun. (4)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[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]

Z. Bouchal, “Resistance of nondiffracting vortex beams to amplitude and phase perturbations,” Opt. Commun. 210, 155–164 (2002).
[Crossref]

I. A. Litvin, M. G. Mclaren, and A. Forbes, “A conical wave approach to calculating suggBessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. A (3)

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89, 043807 (2014).
[Crossref]

A. B. Klimov, L. L. Sánchez-Soto, E. C. Yustas, J. Söderholm, and G. Björk, “Distance-based degrees of polarization for a quantum field,” Phys. Rev. A 72, 033813 (2005).
[Crossref]

M. Hillery, “Nonclassical distance in quantum optics,” Phys. Rev. A 35, 725–732 (1987).
[Crossref]

Phys. Rev. Lett. (3)

V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78, 2275–2278 (1997).
[Crossref]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

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

Other (7)

V. Arrizón, D. Aguirre-Olivas, G. Mellado-Villaseñor, and S. Chávez-Cerda, “Self-healing in scaled propagation invariant beams,” arXiv:1503.03125 (2015).

D. L. Andrews, ed., Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic, 2008).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
[Crossref]

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

R. Kress, Linear Integral Equations (Springer, 1999).
[Crossref]

M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information,” (Cambridge University, 2000).

A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Dover, 1999).

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 (7)

Fig. 1
Fig. 1 Obstruction of area O represented in red. This region is circumscribed by the blue circle of radius a (exradius) and it inscribes the yellow circle of radius b (inradius). Both circles are centered along the z-axis of the beam at x = y = 0.
Fig. 2
Fig. 2 Intensity distributions (evaluated at y = 0), of (from left to right): the incident field ψ(x, 0, z), the “virtual” field transmitted by the aperture complementary to the obstruction ψA(x, 0, z), and the field transmitted behind the obstacle ψO(x, 0, z). The plots correspond to a Gaussian beam w0 = 0.26 mm and a soft-edge Gaussian obstruction with full width a/w0 = 0.28. At z/zR = 2, the intensity profiles of ψ(x, 0, z) and ψO(x, 0, z) appear very similar.
Fig. 3
Fig. 3 Minimum reconstruction distance z0/a as a function of θ0 as well as the paraxial approximation. We also plot z0/zR, which shows a perfect linear behavior. The numerical factor 10−3 is introduced to fit both curves in the same scale.
Fig. 4
Fig. 4 (a) Plots of the degree of self-healing DSH(z) for a Gaussian field of waist w0 and different radii b of the integration region E. The continuous blue line represents the limit value for b → 0. (b) The limit value of DSH(z) for b → 0, given in (26), for several values of the width a of the soft-edge Gaussian obstruction.
Fig. 5
Fig. 5 (Left panel) Experimental setup used to check the self-healing of a fundamental Gaussian beam created by the He-Ne laser. (Right panel) Intensity scans recorded by the CCD camera at increasing distances ζ = 0, 0.5, 1.5, 4 and 6.5 (from left to the right). The beam has a waist w0 = 0.24 mm, divergence θ0 = 0.84 mrad, and Rayleigh range zR = 285 mm. The upper row corresponds to the obstructed beam (with α = 0.206), whereas the lower row is for the unobstructed beam. In the first two scans, the images are very small, so we have included insets (in white frames) with enlarged pictures to better appreciate the patterns.
Fig. 6
Fig. 6 Real and imaginary parts of the energy-normalized field amplitudes at the positions ζ = 0.05, 0.28, and 0.56 (from left to right). The obstructed field is represented in orange, while the unobstructed is in blue. The obstruction is characterized by α = 0.14.
Fig. 7
Fig. 7 Experimentally determined degree of self-healing DSH(ζ) obtained from the field measurements shown in Fig. 6. The integration region E is a dist of radius b = a = 0.07 mm. The error bars represent standard deviations.

Equations (27)

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

Ψ O ( x , y , 0 ) = t O ( x , y ) Ψ ( x , y , 0 ) .
Ψ O ( x , y , z ) = 1 ( 2 π ) 2 exp ( i ρ κ ) exp ( i z k z ) [ t O ^ ( κ κ ) Ψ ^ ( κ ) d 2 κ ] d 2 κ .
Ψ O ( x , y , 0 ) = [ 1 t A ( x , y ) ] Ψ ( x , y , 0 ) Ψ ( x , y , 0 ) Ψ A ( x , y , 0 ) .
[ Ψ O ] = [ Ψ ] + [ Ψ A ] 2 Re Ψ * ( x , y , 0 ) Ψ A ( x , y , 0 ) d x d y ,
Ψ O ( x , y , z ) λ 0 Ψ ( x , y , z ) , z z 0 ,
Ψ ( x , y , z ) = 1 2 π exp ( i ρ κ ) exp ( i z k z ) Ψ ^ ( κ ) d 2 κ .
Ψ ^ O ( κ ) λ 0 Ψ ^ ( κ ) .
1 2 π t O ^ ( κ κ ) Ψ ^ ( κ ) d 2 κ λ 0 Ψ ^ ( κ ) .
z 0 a tan θ ,
1 tan θ = k z ( k x 2 + k y 2 ) 1 / 2 = ( k 2 k x 2 k y 2 ) 1 / 2 ( k x 2 + k y 2 ) 1 / 2 ,
z 0 ~ a Z ( κ ) : = a ( k 2 κ 2 ) 1 / 2 κ .
z 0 a = Z ( κ ) = ( k 2 κ 2 ) 1 / 2 κ | Ψ ^ ( κ ) | 2 d 2 κ | Ψ ^ ( κ ) | 2 d 2 κ ,
Ψ ( x , y , z ) = exp ( i k z ) ψ ( x , y , z ) ,
ψ ( x , y , z ) = 1 z i z R exp [ i k 2 ( x 2 + y 2 z i z R ) ] ,
t O ( x , y ) = 1 exp ( | ρ ρ 0 | 2 2 a 2 ) ,
ψ A ( x , y , z ) = a R z R 1 z i a R exp [ i k 2 ( x 2 + y 2 z i a R ) ] ,
a R = z R 1 + z R k a 2 z R .
z 0 a = π 2 θ 0 2 I 0 ( 1 / θ 0 2 ) + I 1 ( 1 / θ 0 2 ) sinh ( 1 / θ 0 2 ) ,
z 0 a 2 π tan θ 0 ,
z 0 z R k a π 2 θ 0 .
Ψ O ( x , y , z ) | ( x , y ) E λ 0 Ψ ( x , y , z ) | ( x , y ) E z z 0 .
f | g : = E f * ( x , y , z ) g ( x , y , z ) d x d y .
𝔻 r ( Ψ , Ψ O ) = Ψ Ψ O Ψ + Ψ O = Ψ A | Ψ A 1 / 2 [ Ψ A | Ψ A + 4 Ψ | Ψ 4 Re Ψ | Ψ A ] 1 / 2 ,
𝔻 r ( Ψ , Ψ O ) 1 λ 0 1 + λ 0 .
D SH ( z ) = 1 𝔻 r 2 ( Ψ , Ψ O ) ,
D SH ( ζ ) = ζ 1 β 2 β 2 + ζ 2 ,
ζ = z z R , α = a w 0 ,

Metrics