Abstract

We introduce the concept of the perfect optical vortex whose dark hollow radius does not depend on the topological charge. It is shown analytically and experimentally that such a vortex can be approximately generated in the Fourier transforming optical system with a computer-controlled liquid-crystal spatial light modulator.

© 2013 Optical Society of America

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References

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2012 (3)

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, Appl. Phys. B 106, 915(2012).
[CrossRef]

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

A. Dudley and A. Forbes, J. Opt. Soc. Am. A 29, 567(2012).
[CrossRef]

2011 (1)

2010 (1)

2009 (3)

2007 (1)

2006 (1)

2005 (1)

2004 (1)

1990 (1)

K. Lu and B. E. A. Saleh, Opt. Eng. 29, 240 (1990).
[CrossRef]

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Harcourt/Academic, 2001).

Arrizón, V.

Belyi, V.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

Burge, R. E.

Calatayud, A.

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, Appl. Phys. B 106, 915(2012).
[CrossRef]

Carrada, R.

Chavez-Cerda, S.

Chen, J.

Cristóbal, G.

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, Appl. Phys. B 106, 915(2012).
[CrossRef]

Dudley, A.

Fang, Z.

Fang, Z. L.

Forbes, A.

Furlan, W. D.

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, Appl. Phys. B 106, 915(2012).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Guo, C.-S.

He, J.-L.

Khilo, N.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, Opt. Express 17, 23389 (2009).
[CrossRef]

Lin, J.

Liu, X.

Lu, K.

K. Lu and B. E. A. Saleh, Opt. Eng. 29, 240 (1990).
[CrossRef]

Méndez, G.

Monsoriu, J. A.

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, Appl. Phys. B 106, 915(2012).
[CrossRef]

Remón, L.

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, Appl. Phys. B 106, 915(2012).
[CrossRef]

Ren, X.-Y.

Rodrigo, J. A.

A. Calatayud, J. A. Rodrigo, L. Remón, W. D. Furlan, G. Cristóbal, and J. A. Monsoriu, Appl. Phys. B 106, 915(2012).
[CrossRef]

Ropot, P.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

Ruiz, U.

Saleh, B. E. A.

K. Lu and B. E. A. Saleh, Opt. Eng. 29, 240 (1990).
[CrossRef]

Sánchez-de-la-Llave, D.

Tao, S. H.

Vasilyeu, R.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, Opt. Express 17, 23389 (2009).
[CrossRef]

Wang, F.

Wang, H.-T.

Weber, H. J.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Harcourt/Academic, 2001).

Yu, Y.

Yuan, X.-C.

Zhao, X.

Zhu, S. W.

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Figures (6)

Fig. 1.
Fig. 1.

Simulated intensity profiles and corresponding 2D patterns of the “perfect” vortex for truncating parameter N=40, vortex radius ρ0=0.5a, and topological vortex charges ν=1 (a) and ν=10 (b).

Fig. 2.
Fig. 2.

Optical system for generating the “perfect” vortex: 1, laser; 2 and 3, beam expander; 4 and 6, polarizers; 5, twisted nematic LC-SLM; 7, spherical lens with focal distance f; 8, computer.

Fig. 3.
Fig. 3.

Simulated intensity profiles and corresponding 2D patterns of the vortex generated in the setup in Fig. 2: (a) for ν=1 and (b) for ν=10.

Fig. 4.
Fig. 4.

Control video signal (a) and interference pattern registered at the output of the LC-SLM (b) in the first experiment.

Fig. 5.
Fig. 5.

Example of control signal used in the second experiment.

Fig. 6.
Fig. 6.

Experimentally generated vortices: (a) ν=5, (b) ν=8, (c) ν=10, and (d) ν=13.

Equations (12)

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gν(ρ,θ)δ(ρρ0)exp(iνθ),ν=1,2,3,,
g(ρ)=n=1cν,nJν(αν,nρa),0ρa,ν1,
cν,n=2a2[Jν+1(αν,n)]20ag(ρ)Jν(αν,nρa)ρdρ,
gν(ρ,θ)circ(ρa)exp(iνθ)n=1Jν(αν,nρ0/a)[Jν+1(αν,n)]2Jν(αν,nρa).
tν(r,φ)n=1Nαν,nβν,nexp[iν(φφν,n)]δ(rrν,n),
Uν(ρ,θ)002πtν(r,φ)exp(i2πλfrρcos(φθ))rdrdφ,
Jν(x)=iν2π02πexp(iνϕ)exp(ixcosϕ)dϕ,
Uν(ρ,θ)exp(iνθ)n=1Nαν,n2βν,nexp(iνφν,n)Jν(2πRαν,nρλfαν,N).
λfαν,N/2πRaν
βν,n|Jν(αν,nρ0/aν)|αν,n2[Jν+1(αν,n)]2,
φν,n={0forJν(αν,nρ0/aν)0π/νforJν(αν,nρ0/aν)<0,
Uν(ρ,θ)exp(iνθ)n=1NJν(αν,nρ0/aν)[Jν+1(αν,n)]2Jν(αν,nρaν).

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