Abstract

We generate and investigate a self-healing pillar array with a specific phase function comprised of four engineered cubic phase plates with encoded amplitude and phase. This array shows an enhanced self-healing effect at arbitrary obstructed positions in transverse as well as longitudinal locations along propagation where its symmetrical pattern with uniform intensity distribution can be maintained. The transverse power flow in terms of Poynting vector is studied for better interpretation of the self-healing property.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011

R. Cao, Y. Yang, J. Wang, J. Bu, M. Wang, and X. C. Yuan, Appl. Phys. Lett. 99, 261106 (2011).
[CrossRef]

C.-Y. Hwang, K.-Y. Kim, and B. Lee, Opt. Express 19, 7356 (2011).
[CrossRef]

2010

2008

2007

I. M. Besieris and A. M. Shaarawi, Opt. Lett. 32, 2447 (2007).
[CrossRef]

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

Y. Sun, J. Bu, L. Ong, and X. C. Yuan, Appl. Phys. Lett. 91, 051101 (2007).
[CrossRef]

2004

J. M. Tam, I. Biran, and D. R. Walt, Appl. Phys. Lett. 84, 4289 (2004).
[CrossRef]

C. H. Sow, A. A. Bettiol, Y. Y. G. Lee, F. C. Cheong, C. T. Lim, and F. Watt, Appl. Phys. B 78, 705 (2004).
[CrossRef]

2003

M. P. MacDonald, G. C. Spalding, and K. Dholakia, Nature 426, 421 (2003).
[CrossRef]

2002

A. Terray, J. Oakey, and D. W. M. Marr, Science 296, 1841 (2002).
[CrossRef]

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

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

2001

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and P. E. Bryant, Opt. Lett. 26, 863 (2001).
[CrossRef]

1999

1998

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

1987

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Alfano, R. R.

Arlt, J.

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

Bandres, M.

Besieris, I. M.

Bettiol, A. A.

C. H. Sow, A. A. Bettiol, Y. Y. G. Lee, F. C. Cheong, C. T. Lim, and F. Watt, Appl. Phys. B 78, 705 (2004).
[CrossRef]

Biran, I.

J. M. Tam, I. Biran, and D. R. Walt, Appl. Phys. Lett. 84, 4289 (2004).
[CrossRef]

Bouchal, Z.

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

Broky, J.

Bryant, P. E.

Bu, J.

R. Cao, Y. Yang, J. Wang, J. Bu, M. Wang, and X. C. Yuan, Appl. Phys. Lett. 99, 261106 (2011).
[CrossRef]

Y. Sun, J. Bu, L. Ong, and X. C. Yuan, Appl. Phys. Lett. 91, 051101 (2007).
[CrossRef]

Campos, J.

Cao, R.

R. Cao, Y. Yang, J. Wang, J. Bu, M. Wang, and X. C. Yuan, Appl. Phys. Lett. 99, 261106 (2011).
[CrossRef]

Cheong, F. C.

C. H. Sow, A. A. Bettiol, Y. Y. G. Lee, F. C. Cheong, C. T. Lim, and F. Watt, Appl. Phys. B 78, 705 (2004).
[CrossRef]

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

Choi, D.

Christodoulides, D.

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, Opt. Lett. 33, 207 (2008).
[CrossRef]

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Christodoulides, D. N.

Cottrell, D.

Cottrell, D. M.

Davis, J.

Davis, J. A.

Dearing, M. T.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Dholakia, K.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, Nature 426, 421 (2003).
[CrossRef]

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

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

M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and P. E. Bryant, Opt. Lett. 26, 863 (2001).
[CrossRef]

Dogariu, A.

Dufresne, E. R.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Durnin, J.

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Garces-Chavez, V.

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

Grier, D. G.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Hwang, C.-Y.

Kim, K. Y.

Kim, K.-Y.

Lee, B.

Lee, Y. Y. G.

C. H. Sow, A. A. Bettiol, Y. Y. G. Lee, F. C. Cheong, C. T. Lim, and F. Watt, Appl. Phys. B 78, 705 (2004).
[CrossRef]

Lim, C. T.

C. H. Sow, A. A. Bettiol, Y. Y. G. Lee, F. C. Cheong, C. T. Lim, and F. Watt, Appl. Phys. B 78, 705 (2004).
[CrossRef]

MacDonald, M.

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

MacDonald, M. P.

Marr, D. W. M.

A. Terray, J. Oakey, and D. W. M. Marr, Science 296, 1841 (2002).
[CrossRef]

McGloin, D.

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

Melville, H.

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

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Mintry, M.

Moreno, I.

Oakey, J.

A. Terray, J. Oakey, and D. W. M. Marr, Science 296, 1841 (2002).
[CrossRef]

Ong, L.

Y. Sun, J. Bu, L. Ong, and X. C. Yuan, Appl. Phys. Lett. 91, 051101 (2007).
[CrossRef]

Paterson, L.

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and P. E. Bryant, Opt. Lett. 26, 863 (2001).
[CrossRef]

Shaarawi, A. M.

Sheets, S. A.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Sibbett, W.

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

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and P. E. Bryant, Opt. Lett. 26, 863 (2001).
[CrossRef]

Siviloglou, G.

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, Opt. Lett. 33, 207 (2008).
[CrossRef]

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Siviloglou, G. A.

Sow, C. H.

C. H. Sow, A. A. Bettiol, Y. Y. G. Lee, F. C. Cheong, C. T. Lim, and F. Watt, Appl. Phys. B 78, 705 (2004).
[CrossRef]

Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, Nature 426, 421 (2003).
[CrossRef]

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Sun, Y.

Y. Sun, J. Bu, L. Ong, and X. C. Yuan, Appl. Phys. Lett. 91, 051101 (2007).
[CrossRef]

Sztul, H. I.

Tam, J. M.

J. M. Tam, I. Biran, and D. R. Walt, Appl. Phys. Lett. 84, 4289 (2004).
[CrossRef]

Terray, A.

A. Terray, J. Oakey, and D. W. M. Marr, Science 296, 1841 (2002).
[CrossRef]

Volke-Sepulveda, K.

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

Walt, D. R.

J. M. Tam, I. Biran, and D. R. Walt, Appl. Phys. Lett. 84, 4289 (2004).
[CrossRef]

Wang, J.

R. Cao, Y. Yang, J. Wang, J. Bu, M. Wang, and X. C. Yuan, Appl. Phys. Lett. 99, 261106 (2011).
[CrossRef]

Wang, M.

R. Cao, Y. Yang, J. Wang, J. Bu, M. Wang, and X. C. Yuan, Appl. Phys. Lett. 99, 261106 (2011).
[CrossRef]

Watt, F.

C. H. Sow, A. A. Bettiol, Y. Y. G. Lee, F. C. Cheong, C. T. Lim, and F. Watt, Appl. Phys. B 78, 705 (2004).
[CrossRef]

Yang, Y.

R. Cao, Y. Yang, J. Wang, J. Bu, M. Wang, and X. C. Yuan, Appl. Phys. Lett. 99, 261106 (2011).
[CrossRef]

Yuan, X. C.

R. Cao, Y. Yang, J. Wang, J. Bu, M. Wang, and X. C. Yuan, Appl. Phys. Lett. 99, 261106 (2011).
[CrossRef]

Y. Sun, J. Bu, L. Ong, and X. C. Yuan, Appl. Phys. Lett. 91, 051101 (2007).
[CrossRef]

Yzuel, M. J.

Appl. Opt.

Appl. Phys. B

C. H. Sow, A. A. Bettiol, Y. Y. G. Lee, F. C. Cheong, C. T. Lim, and F. Watt, Appl. Phys. B 78, 705 (2004).
[CrossRef]

Appl. Phys. Lett.

R. Cao, Y. Yang, J. Wang, J. Bu, M. Wang, and X. C. Yuan, Appl. Phys. Lett. 99, 261106 (2011).
[CrossRef]

J. M. Tam, I. Biran, and D. R. Walt, Appl. Phys. Lett. 84, 4289 (2004).
[CrossRef]

Y. Sun, J. Bu, L. Ong, and X. C. Yuan, Appl. Phys. Lett. 91, 051101 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Nature

M. P. MacDonald, G. C. Spalding, and K. Dholakia, Nature 426, 421 (2003).
[CrossRef]

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

Opt. Commun.

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Rev. Sci. Instrum.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Science

A. Terray, J. Oakey, and D. W. M. Marr, Science 296, 1841 (2002).
[CrossRef]

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the experimental setup. The laser wavelength is 532 nm and the focal length of Fourier lens is 30 cm. Inset (a) is the phase distribution imposed on SLM; inset (b) is the pattern recorded by CCD.

Fig. 2.
Fig. 2.

Obstacles in different planes and their self-reconstructions of (a) and (b) pillar array and (c) Airy beam. Locations of the obstacle along propagation direction are (a) 2.25 cm, (b) 3.25 cm, and (c) 2.25 cm.

Fig. 3.
Fig. 3.

Patterns with different obstructed positions are compared in (a) and (b). Patterns with different sizes of obstacles are compared between (a) and (c); the corresponding self-healing simulation of (a), (b), and (c) are shown in (d), (e), and (f). (a) through (c) have the same propagation distance of 4.5 cm; (d) through (f) have the same propagation distance of 15 cm.

Fig. 4.
Fig. 4.

(a) The white arrows indicate energy flow. (b) and (d) Distorted pattern obstructed by opaque obstacle indicated by a red dotted circle. (c) and (e) Self-reconstructed pattern after a distance of 13 cm in propagation.

Equations (6)

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

u ( s x , s y , ξ ) = Ai ( s x ( ξ / 2 ) 2 + i a ξ ) Ai ( s y ( ξ / 2 ) 2 + i a ξ ) × exp ( a s x + a s y ( a ξ 2 / 2 ) i ( ξ 3 / 6 ) + i ( a 2 ξ / 2 ) + i ξ ( s x + s y ) / 2 ) ,
P 1 ( k x , k y ) = exp ( i Q ( k x 3 + k y 3 ) 3 ) exp ( i 2 π d x k x + i 2 π d y k y ) ,
P c ( k x , k y ) = P 1 + P 2 + P 3 + P 4 = A ( k x , k y ) exp [ i ϕ ( k x , k y ) ] ,
A ( k x , k y ) = | cos ( k x 3 3 Q 2 π d x k x ) × cos ( k y 3 3 Q 2 π d y k y ) | ,
P ( k x , k y ) = { 0 ( A > 0 ) π ( A < 0 ) .
S⃗ = S⃗ z + S⃗ = 1 2 η o [ | μ | 2 z ^ + i 2 k [ μ * μ μ μ * ] ] ,

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