Abstract

The self-reconstruction of superpositions of Laguerre–Gaussian (LG) beams has been observed experimentally, but the results appear anomalous and without a means to predict under what conditions this take place. In this Letter, we offer a simple equation for predicting the self-reconstruction distance of superpositions of LG beams, which we confirm by numerical propagation as well as by experiment. We explain that the self-reconstruction process is not guaranteed and predict its dependence on the obstacle location and obstacle size.

© 2013 Optical Society of America

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References

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    [CrossRef]

2013

N. Hermosa, C. Rosales-Guzmán, and J. P. Torres, Opt. Lett. 38, 383 (2013).
[CrossRef]

S. Ngcobo, I. A. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
[CrossRef]

2012

D. Naidoo, K. Ait-Ameur, M. Brunel, and A. Forbes, Appl. Phys. B 106, 683 (2012).
[CrossRef]

R. Rop, I. A. Litvin, and A. Forbes, J. Opt. 14, 035702 (2012).
[CrossRef]

2011

2009

I. A. Litvin, M. G. McLaren, and A. Forbes, Opt. Commun. 282, 1078 (2009).
[CrossRef]

2007

2003

J. Arlt, J. Mod. Opt. 50, 1573 (2003).

2000

L. Allen and M. J. Padgett, Opt. Commun. 184, 67 (2000).
[CrossRef]

1998

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

Ait-Ameur, K.

D. Naidoo, K. Ait-Ameur, M. Brunel, and A. Forbes, Appl. Phys. B 106, 683 (2012).
[CrossRef]

Allen, L.

L. Allen and M. J. Padgett, Opt. Commun. 184, 67 (2000).
[CrossRef]

Arlt, J.

J. Arlt, J. Mod. Opt. 50, 1573 (2003).

Arnold, A. S.

Bouchal, Z.

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

Brunel, M.

D. Naidoo, K. Ait-Ameur, M. Brunel, and A. Forbes, Appl. Phys. B 106, 683 (2012).
[CrossRef]

Burger, L.

S. Ngcobo, I. A. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
[CrossRef]

I. A. Litvin, L. Burger, and A. Forbes, Opt. Express 15, 14065 (2007).
[CrossRef]

Chlup, M.

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

Ellinas, D.

Forbes, A.

S. Ngcobo, I. A. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
[CrossRef]

R. Rop, I. A. Litvin, and A. Forbes, J. Opt. 14, 035702 (2012).
[CrossRef]

D. Naidoo, K. Ait-Ameur, M. Brunel, and A. Forbes, Appl. Phys. B 106, 683 (2012).
[CrossRef]

I. A. Litvin, M. G. McLaren, and A. Forbes, Opt. Commun. 282, 1078 (2009).
[CrossRef]

I. A. Litvin, L. Burger, and A. Forbes, Opt. Express 15, 14065 (2007).
[CrossRef]

Franke-Arnold, S.

Girkin, J. M.

Hermosa, N.

Leach, J.

Lembessis, V. E.

Litvin, I. A.

S. Ngcobo, I. A. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
[CrossRef]

R. Rop, I. A. Litvin, and A. Forbes, J. Opt. 14, 035702 (2012).
[CrossRef]

I. A. Litvin, M. G. McLaren, and A. Forbes, Opt. Commun. 282, 1078 (2009).
[CrossRef]

I. A. Litvin, L. Burger, and A. Forbes, Opt. Express 15, 14065 (2007).
[CrossRef]

McLaren, M. G.

I. A. Litvin, M. G. McLaren, and A. Forbes, Opt. Commun. 282, 1078 (2009).
[CrossRef]

Naidoo, D.

D. Naidoo, K. Ait-Ameur, M. Brunel, and A. Forbes, Appl. Phys. B 106, 683 (2012).
[CrossRef]

Ngcobo, S.

S. Ngcobo, I. A. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
[CrossRef]

Ohberg, P.

Padgett, M. J.

Rop, R.

R. Rop, I. A. Litvin, and A. Forbes, J. Opt. 14, 035702 (2012).
[CrossRef]

Rosales-Guzmán, C.

Singh, R. P.

Torres, J. P.

Vaity, P.

Wagner, J.

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

Wright, A. J.

Appl. Phys. B

D. Naidoo, K. Ait-Ameur, M. Brunel, and A. Forbes, Appl. Phys. B 106, 683 (2012).
[CrossRef]

J. Mod. Opt.

J. Arlt, J. Mod. Opt. 50, 1573 (2003).

J. Opt.

R. Rop, I. A. Litvin, and A. Forbes, J. Opt. 14, 035702 (2012).
[CrossRef]

Nat. Commun.

S. Ngcobo, I. A. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
[CrossRef]

Opt. Commun.

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

I. A. Litvin, M. G. McLaren, and A. Forbes, Opt. Commun. 282, 1078 (2009).
[CrossRef]

L. Allen and M. J. Padgett, Opt. Commun. 184, 67 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic representation of the rotation of the shadow region in an obstructed LG beam with different signs of the angular momentum. (b) Schematic for the derivation of the self-reconstruction distance zr and (c) dependence of the reconstruction distance on the initial position (zI) and angular size (θI) of the obstacle. (d) Dependence of the maximum angular size obstruction θ(zI)max on the initial position of the obstacle zI for the different Rayleigh range of the beam.

Fig. 2.
Fig. 2.

Modal decomposition of eight-petal beam.

Fig. 3.
Fig. 3.

(a) Simulation of the free space propagation of obstructed LG04 and LG04 beams. (b) Simulation and corresponding experimental verification of the reconstruction of the superposition beam (LG04 and LG04).

Equations (3)

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

u(r,ϕ)=A(r)[exp(ilϕ)+exp(ilϕ)],
zmin=zRTan(θI+arctan(zIzR))zI.
θ(zI)max=12(π2arctan(zIzR)).

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