Abstract

Quantitative description of the self-healing ability of a beam is very important for studying or comparing the self-healing ability of different beams. As describing the similarity by using the angle of two infinite-dimensional complex vectors in Hilbert space, the angle of two intensity profiles is proposed to quantitatively describe the self-healing ability of different beams. As a special case, quantitative description of the self-healing ability of a Bessel-Gaussian beam is studied. Results show that the angle of two intensity profiles can be used to describe the self-healing ability of arbitrary beams as the reconstruction distance for quantitatively describing the self-healing ability of Bessel beam. It offers a new method for studying or comparing the self-healing ability of different beams.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves: Theory and. Applications (John Wiley, 2008).
  2. V. Garcés-Chávez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85(18), 4001–4003 (2004).
    [CrossRef]
  3. X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, K. Dholakia, “Femtosecond cellular transfection using a nondiffracting light beam,” Appl. Phys. Lett. 91(5), 053902 (2007).
    [CrossRef]
  4. M. Boguslawski, P. Rose, C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 061111 (2011).
    [CrossRef]
  5. A. Chong, W. H. Renninger, D. N. Christodoulides, F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
    [CrossRef]
  6. M. V. Berry, N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
    [CrossRef]
  7. S. Vyas, Y. Kozawa, S. Sato, “Self-healing of tightly focused scalar and vector Bessel-Gauss beams at the focal plane,” J. Opt. Soc. Am. A 28(5), 837–843 (2011).
    [CrossRef] [PubMed]
  8. J. D. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, M. R. Dennis, “Auto-focusing and self-healing of Pearcey beams,” Opt. Express 20(17), 18955–18966 (2012).
    [CrossRef] [PubMed]
  9. R. Cao, Y. Hua, C. Min, S. Zhu, X. C. Yuan, “Self-healing optical pillar array,” Opt. Lett. 37(17), 3540–3542 (2012).
    [CrossRef] [PubMed]
  10. M. Anguiano-Morales, A. Martínez, M. D. Iturbe-Castillo, S. Chávez-Cerda, N. Alcalá-Ochoa, “Self-healing property of a caustic optical beam,” Appl. Opt. 46(34), 8284–8290 (2007).
    [CrossRef] [PubMed]
  11. P. Vaity, R. P. Singh, “Self-healing property of optical ring lattice,” Opt. Lett. 36(15), 2994–2996 (2011).
    [CrossRef] [PubMed]
  12. J. Broky, G. A. Siviloglou, A. Dogariu, D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
    [CrossRef] [PubMed]
  13. I. A. Litvin, M. G. Mclaren, A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
    [CrossRef]
  14. M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46(7), 078001 (2007).
    [CrossRef]
  15. E. Greenfield, M. Segev, W. Walasik, O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
    [CrossRef] [PubMed]
  16. Y. Kaganovsky, E. Heyman, “Wave analysis of Airy beams,” Opt. Express 18(8), 8440–8452 (2010).
    [CrossRef] [PubMed]
  17. R. Martínez-Herrero, I. Juvells, A. Carnicer, “On the physical realizability of highly focused electromagnetic field distributions,” Opt. Lett. 38(12), 2065–2067 (2013).
    [CrossRef] [PubMed]
  18. J. James, Mathematics Dictionary Mathematics Dictionary, 5th ed. (Springer, 1992).

2013

2012

2011

P. Vaity, R. P. Singh, “Self-healing property of optical ring lattice,” Opt. Lett. 36(15), 2994–2996 (2011).
[CrossRef] [PubMed]

M. Boguslawski, P. Rose, C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 061111 (2011).
[CrossRef]

S. Vyas, Y. Kozawa, S. Sato, “Self-healing of tightly focused scalar and vector Bessel-Gauss beams at the focal plane,” J. Opt. Soc. Am. A 28(5), 837–843 (2011).
[CrossRef] [PubMed]

E. Greenfield, M. Segev, W. Walasik, O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[CrossRef] [PubMed]

2010

Y. Kaganovsky, E. Heyman, “Wave analysis of Airy beams,” Opt. Express 18(8), 8440–8452 (2010).
[CrossRef] [PubMed]

A. Chong, W. H. Renninger, D. N. Christodoulides, F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

2009

I. A. Litvin, M. G. Mclaren, A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[CrossRef]

2008

2007

M. Anguiano-Morales, A. Martínez, M. D. Iturbe-Castillo, S. Chávez-Cerda, N. Alcalá-Ochoa, “Self-healing property of a caustic optical beam,” Appl. Opt. 46(34), 8284–8290 (2007).
[CrossRef] [PubMed]

X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, K. Dholakia, “Femtosecond cellular transfection using a nondiffracting light beam,” Appl. Phys. Lett. 91(5), 053902 (2007).
[CrossRef]

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46(7), 078001 (2007).
[CrossRef]

2004

V. Garcés-Chávez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85(18), 4001–4003 (2004).
[CrossRef]

1979

M. V. Berry, N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[CrossRef]

Agate, B.

X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, K. Dholakia, “Femtosecond cellular transfection using a nondiffracting light beam,” Appl. Phys. Lett. 91(5), 053902 (2007).
[CrossRef]

Alcalá-Ochoa, N.

Anguiano-Morales, M.

M. Anguiano-Morales, A. Martínez, M. D. Iturbe-Castillo, S. Chávez-Cerda, N. Alcalá-Ochoa, “Self-healing property of a caustic optical beam,” Appl. Opt. 46(34), 8284–8290 (2007).
[CrossRef] [PubMed]

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46(7), 078001 (2007).
[CrossRef]

Balazs, N. L.

M. V. Berry, N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[CrossRef]

Berry, M. V.

M. V. Berry, N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[CrossRef]

Boguslawski, M.

M. Boguslawski, P. Rose, C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 061111 (2011).
[CrossRef]

Broky, J.

Brown, C. T. A.

X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, K. Dholakia, “Femtosecond cellular transfection using a nondiffracting light beam,” Appl. Phys. Lett. 91(5), 053902 (2007).
[CrossRef]

Cao, R.

Carnicer, A.

Chávez-Cerda, S.

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46(7), 078001 (2007).
[CrossRef]

M. Anguiano-Morales, A. Martínez, M. D. Iturbe-Castillo, S. Chávez-Cerda, N. Alcalá-Ochoa, “Self-healing property of a caustic optical beam,” Appl. Opt. 46(34), 8284–8290 (2007).
[CrossRef] [PubMed]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

J. Broky, G. A. Siviloglou, A. Dogariu, D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[CrossRef] [PubMed]

Comrie, M.

X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, K. Dholakia, “Femtosecond cellular transfection using a nondiffracting light beam,” Appl. Phys. Lett. 91(5), 053902 (2007).
[CrossRef]

Dennis, M. R.

Denz, C.

M. Boguslawski, P. Rose, C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 061111 (2011).
[CrossRef]

Dholakia, K.

J. D. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, M. R. Dennis, “Auto-focusing and self-healing of Pearcey beams,” Opt. Express 20(17), 18955–18966 (2012).
[CrossRef] [PubMed]

X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, K. Dholakia, “Femtosecond cellular transfection using a nondiffracting light beam,” Appl. Phys. Lett. 91(5), 053902 (2007).
[CrossRef]

V. Garcés-Chávez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85(18), 4001–4003 (2004).
[CrossRef]

Dogariu, A.

Forbes, A.

I. A. Litvin, M. G. Mclaren, A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[CrossRef]

Garcés-Chávez, V.

X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, K. Dholakia, “Femtosecond cellular transfection using a nondiffracting light beam,” Appl. Phys. Lett. 91(5), 053902 (2007).
[CrossRef]

V. Garcés-Chávez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85(18), 4001–4003 (2004).
[CrossRef]

Greenfield, E.

E. Greenfield, M. Segev, W. Walasik, O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[CrossRef] [PubMed]

Gunn-Moore, F.

X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, K. Dholakia, “Femtosecond cellular transfection using a nondiffracting light beam,” Appl. Phys. Lett. 91(5), 053902 (2007).
[CrossRef]

Heyman, E.

Hua, Y.

Iturbe-Castillo, M. D.

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46(7), 078001 (2007).
[CrossRef]

M. Anguiano-Morales, A. Martínez, M. D. Iturbe-Castillo, S. Chávez-Cerda, N. Alcalá-Ochoa, “Self-healing property of a caustic optical beam,” Appl. Opt. 46(34), 8284–8290 (2007).
[CrossRef] [PubMed]

Juvells, I.

Kaganovsky, Y.

Kozawa, Y.

Lindberg, J.

Litvin, I. A.

I. A. Litvin, M. G. Mclaren, A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[CrossRef]

Martínez, A.

Martínez-Herrero, R.

Mazilu, M.

McGloin, D.

V. Garcés-Chávez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85(18), 4001–4003 (2004).
[CrossRef]

Mclaren, M. G.

I. A. Litvin, M. G. Mclaren, A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[CrossRef]

Melville, H.

V. Garcés-Chávez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85(18), 4001–4003 (2004).
[CrossRef]

Méndez-Otero, M. M.

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46(7), 078001 (2007).
[CrossRef]

Min, C.

Mourka, A.

Raz, O.

E. Greenfield, M. Segev, W. Walasik, O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[CrossRef] [PubMed]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

Ring, J. D.

Rose, P.

M. Boguslawski, P. Rose, C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 061111 (2011).
[CrossRef]

Roskey, D.

V. Garcés-Chávez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85(18), 4001–4003 (2004).
[CrossRef]

Sato, S.

Segev, M.

E. Greenfield, M. Segev, W. Walasik, O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[CrossRef] [PubMed]

Singh, R. P.

Siviloglou, G. A.

Stevenson, D. J.

X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, K. Dholakia, “Femtosecond cellular transfection using a nondiffracting light beam,” Appl. Phys. Lett. 91(5), 053902 (2007).
[CrossRef]

Summers, M. D.

V. Garcés-Chávez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85(18), 4001–4003 (2004).
[CrossRef]

Tsampoula, X.

X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, K. Dholakia, “Femtosecond cellular transfection using a nondiffracting light beam,” Appl. Phys. Lett. 91(5), 053902 (2007).
[CrossRef]

Vaity, P.

Vyas, S.

Walasik, W.

E. Greenfield, M. Segev, W. Walasik, O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[CrossRef] [PubMed]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

Wright, E. M.

V. Garcés-Chávez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85(18), 4001–4003 (2004).
[CrossRef]

Yuan, X. C.

Zhu, S.

Am. J. Phys.

M. V. Berry, N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

V. Garcés-Chávez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, K. Dholakia, “Optical levitation in a Bessel light beam,” Appl. Phys. Lett. 85(18), 4001–4003 (2004).
[CrossRef]

X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, K. Dholakia, “Femtosecond cellular transfection using a nondiffracting light beam,” Appl. Phys. Lett. 91(5), 053902 (2007).
[CrossRef]

M. Boguslawski, P. Rose, C. Denz, “Nondiffracting kagome lattice,” Appl. Phys. Lett. 98(6), 061111 (2011).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

A. Chong, W. H. Renninger, D. N. Christodoulides, F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

Opt. Commun.

I. A. Litvin, M. G. Mclaren, A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282(6), 1078–1082 (2009).
[CrossRef]

Opt. Eng.

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46(7), 078001 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

E. Greenfield, M. Segev, W. Walasik, O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[CrossRef] [PubMed]

Other

J. James, Mathematics Dictionary Mathematics Dictionary, 5th ed. (Springer, 1992).

H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves: Theory and. Applications (John Wiley, 2008).

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 (4)

Fig. 1
Fig. 1

Generation of a Bessel-Gaussian beam.

Fig. 2
Fig. 2

Intensity distribution of a Bessel-Gaussian beam at initial plane where w0 = 4μm (a) with an opaque obstacle (R = w0/5) (b) without opaque obstacle.

Fig. 3
Fig. 3

Intensity evolution of a Bessel-Gaussian beam propagating along z-axis where y = 0 and w0 = 4μm (a) with an opaque obstacle (R = w0/5) (b) without opaque obstacle.

Fig. 4
Fig. 4

One-dimensional similarity of the Bessel-Gaussian beam during propagation (a) with different w0 where R = 0.8μm and dmin = 3μm (b) with different R where w0 = 10μm, d1min = 1.5μm, d2min = 3μm and d3min = 4.5μm.

Equations (21)

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

cos ( E E ) = ( E , E ) E E
( E , E ) = E ( x , y , z ) E ¯ ( x , y , z ) d x d y .
f ( x , y , z ) = f ( x , y , z ) f ¯ ( x , y , z ) d x d y .
( E , E ) E E
E ( x , y , z ) E ¯ ( x , y , z ) d x d y = G ( u , v , z ) G ¯ ( u , v , z ) d u d v
E ( x , y , z ) E ¯ ( x , y , z ) d x d y = G ( u , v , z ) G ¯ ( u , v , z ) d u d v .
cos ( E E ) = cos ( G G ) = ( G , G ) G G
( G ( u , v , z ) G ( u , v , z ) ) = ( G ( u , v , 0 ) G ( u , v , 0 ) ) M ( u , v )
M ( u , v ) = exp ( i z k 2 u 2 v 2 )
| E E | | E | | E | ,
S = cos ( | E | | E | ) = ( | E | , | E | ) E E
d min = R / tan α
T ( κ ) = 1 κ δ ( κ k sin α )
G ( κ , z = 0 ) = 1 2 w 0 2 I 0 ( k 2 κ w 0 2 sin α ) exp { w 0 2 4 [ κ 2 + ( k sin α ) 2 ] }
M ( κ , z ) = exp ( i z k 2 κ 2 ) ,
G ( κ , z ) = 1 2 w 0 2 I 0 ( k 2 κ w 0 2 sin α ) exp { w 0 2 4 [ κ 2 + ( k sin α ) 2 ] } exp ( i z k 2 κ 2 ) .
E ( r , z ) = w 0 2 k w 0 2 k + 2 i z J 0 ( w 0 2 k 2 sin α w 0 2 k + 2 i z r ) exp [ k ( r 2 + 2 z 2 ) w 0 2 k + 2 i z + w 0 2 k 2 z i cos α w 0 2 k + 2 i z ]
E ( r , z = 0 ) = J 0 ( k r sin α ) exp ( r 2 w 0 2 )
E ( r , z ) = J 0 ( k r sin α ) exp ( i k z cos α ) .
g ( r , z = 0 ) = 1 exp ( r 2 R 2 )
E ( r , z ) = E ( r , z ) w 01 2 k w 01 2 k + 2 i z J 0 ( w 01 2 k 2 sin α w 01 2 k + 2 i z r ) exp [ k ( r 2 + 2 z 2 ) w 01 2 k + 2 i z + w 01 2 k 2 z i cos α w 01 2 k + 2 i z ]

Metrics