Abstract

We generate helical Ince–Gaussian (HIG) beams by using complex amplitude and phase masks encoded onto a liquid-crystal display (LCD). These beams display an intensity pattern consisting of elliptic rings, whose number and ellipticity can be controlled, and a phase exhibiting a number of in-line vortices, each with a unitary topological charge. We show experimental results that display the properties of these elliptic dark hollow beams. We introduce a novel interference technique for generating the object and reference beams by using a single LCD and show the vortex interference patterns. We expect that these HIG beams will be useful in optical trapping applications.

© 2006 Optical Society of America

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References

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    [CrossRef]

2004 (4)

2001 (1)

2000 (1)

1999 (2)

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, Appl. Opt. 38, 5004 (1999).
[CrossRef]

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

1995 (1)

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Amako, J.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

Bandres, M. A.

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Campos, J.

Cottrell, D. M.

Crabtree, K.

Davis, J. A.

Gutiérrez-Vega, J. C.

He, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Heckenberg, N. R.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Mansuripur, M.

M. Mansuripur and E. M. Wright, Opt. Photon. News 10(2), 40.

McNamara, D. E.

Moreno, I.

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Rubinsztein-Dunlop, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Mod. Opt. 42, 217 (1995).
[CrossRef]

Schwarz, U. T.

Smith, D. A.

Sonehara, T.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

Tsai, P.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, Opt. Eng. 38, 1051 (1999).
[CrossRef]

Wright, E. M.

M. Mansuripur and E. M. Wright, Opt. Photon. News 10(2), 40.

Yzuel, M. J.

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Figures (3)

Fig. 1
Fig. 1

Computer masks for the HIG 6 , 6 , 3 + beam, showing (a) magnitude, (b) phase, (c) linear phase added to HIG phase, and (d) amplitude-modulated phase mask.

Fig. 2
Fig. 2

Experimental intensity results, showing (a) even IG 6 , 6 , 3 beam, (b) odd IG 6 , 6 , 3 beam, (c) HIG 6 , 6 , 3 + beam, (d) one intensity ring for the HIG 8 , 8 , 2 + beam, (e) two intensity rings for the HIG 10 , 8 , 2 + beam, (f) three intensity rings for the HIG 12 , 8 , 2 + beam, (g) zero-ellipticity HIG 12 , 12 , 0 + beam, (h) higher ellipticity HIG 12 , 12 , 6 + beam, (i) high ellipticity HIG 12 , 12 , 12 + beam; intensity for the HIG 4 , 4 , 2 + beam at (j) the focal plane, (k) 0.8 m , and (l) 1.0 m . Photographs show 600 × 600 camera pixels with sizes of 6.7 μ m square.

Fig. 3
Fig. 3

Experimental interference pattern, showing positions of vortices as the ellipticity parameter decreases: (a) ϵ = 3 , (b) ϵ = 0.5 , (c) ϵ = 0 .

Equations (5)

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IG p , m , ϵ e ( r ) = A C p m ( i ξ , ϵ ) C p m ( η , ϵ ) exp ( r 2 w 0 2 ) ,
IG p , m , ϵ o ( r ) = B S p m ( i ξ , ϵ ) S p m ( η , ϵ ) exp ( r 2 w 0 2 ) ,
HIG p , m , ϵ ± ( ξ , η ) = IG p , m , ϵ e ( ξ , η , ϵ ) ± i IG p , m , ϵ o ( ξ , η , ϵ ) = M ( x , y ) exp [ i ϕ ( x , y ) ] ,
M ( x , y ) exp { i [ ϕ ( x , y ) + 2 π x d ] } .
exp { i M ( x , y ) [ ϕ ( x , y ) + 2 π x d ] } ,

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