Abstract

A new class of vectorial vortex based on coherent addition of two orthogonal circularly polarized Bessel beams of identical order but with different propagation constants is presented. The transversely space-variant axially symmetric polarization distributions of these vectorial fields rotate as they propagate, while they maintain a propagation-invariant Bessel intensity distribution. These properties were demonstrated by use of discrete space-variant subwavelength gratings for 10.6μm CO2 laser radiation. The polarization properties were verified by both full space-variant polarization analysis and measurements. Rotating intensity patterns are also demonstrated by transmitting the vectorial vortices through a linear polarizer.

© 2005 Optical Society of America

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References

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  1. M. S. Soskin and M. V. Vanetsov, in Progress in Optics, E. Wolf, ed. (North-Holland, 2001), Vol. 42, pp. 219–276.
    [CrossRef]
  2. D. Palacios, D. Rozas, and G. A. Swartzlander, Phys. Rev. Lett. 88, 103902 (2002).
    [CrossRef]
  3. J. F. Nye, Proc. R. Soc. London Ser. A 387, 105 (1983).
    [CrossRef]
  4. J. F. Nye, Proc. R. Soc. London Ser. A 389, 279 (1983).
    [CrossRef]
  5. I. Freund, M. Soskin, and A. I. Mokhun, Opt. Commun. 208, 223 (2002).
    [CrossRef]
  6. O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
    [CrossRef]
  7. P. Pääkkönen, J. Tervo, P. Vahimaa, J. Turunen, and F. Gori, Opt. Express 10, 949 (2002).
    [CrossRef]
  8. A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
    [CrossRef] [PubMed]
  9. E. Collett, Polarized Light (Marcel Dekker, 1993).
  10. N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 88, 326 (1992).
    [CrossRef]
  11. A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
    [CrossRef]
  12. E. Hasman, G. Biener, A. Niv, and V. Kleiner, in Progress in Optics, E. Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 215–289.

2005

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
[CrossRef]

2004

2002

D. Palacios, D. Rozas, and G. A. Swartzlander, Phys. Rev. Lett. 88, 103902 (2002).
[CrossRef]

I. Freund, M. Soskin, and A. I. Mokhun, Opt. Commun. 208, 223 (2002).
[CrossRef]

O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
[CrossRef]

P. Pääkkönen, J. Tervo, P. Vahimaa, J. Turunen, and F. Gori, Opt. Express 10, 949 (2002).
[CrossRef]

1992

N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

1983

J. F. Nye, Proc. R. Soc. London Ser. A 387, 105 (1983).
[CrossRef]

J. F. Nye, Proc. R. Soc. London Ser. A 389, 279 (1983).
[CrossRef]

Angelsky, O.

O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
[CrossRef]

Biener, G.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
[CrossRef]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
[CrossRef] [PubMed]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, in Progress in Optics, E. Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 215–289.

Collett, E.

E. Collett, Polarized Light (Marcel Dekker, 1993).

Davidson, N.

N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

Freund, I.

I. Freund, M. Soskin, and A. I. Mokhun, Opt. Commun. 208, 223 (2002).
[CrossRef]

Friesem, A. A.

N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

Gori, F.

Hasman, E.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
[CrossRef]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
[CrossRef] [PubMed]

N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, in Progress in Optics, E. Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 215–289.

Kleiner, V.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
[CrossRef]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
[CrossRef] [PubMed]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, in Progress in Optics, E. Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 215–289.

Mokhun, A.

O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
[CrossRef]

Mokhun, A. I.

I. Freund, M. Soskin, and A. I. Mokhun, Opt. Commun. 208, 223 (2002).
[CrossRef]

Mokhun, I.

O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
[CrossRef]

Niv, A.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
[CrossRef]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
[CrossRef] [PubMed]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, in Progress in Optics, E. Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 215–289.

Nye, J. F.

J. F. Nye, Proc. R. Soc. London Ser. A 387, 105 (1983).
[CrossRef]

J. F. Nye, Proc. R. Soc. London Ser. A 389, 279 (1983).
[CrossRef]

Pääkkönen, P.

Palacios, D.

D. Palacios, D. Rozas, and G. A. Swartzlander, Phys. Rev. Lett. 88, 103902 (2002).
[CrossRef]

Rozas, D.

D. Palacios, D. Rozas, and G. A. Swartzlander, Phys. Rev. Lett. 88, 103902 (2002).
[CrossRef]

Soskin, M.

I. Freund, M. Soskin, and A. I. Mokhun, Opt. Commun. 208, 223 (2002).
[CrossRef]

O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
[CrossRef]

Soskin, M. S.

M. S. Soskin and M. V. Vanetsov, in Progress in Optics, E. Wolf, ed. (North-Holland, 2001), Vol. 42, pp. 219–276.
[CrossRef]

Swartzlander, G. A.

D. Palacios, D. Rozas, and G. A. Swartzlander, Phys. Rev. Lett. 88, 103902 (2002).
[CrossRef]

Tervo, J.

Turunen, J.

Vahimaa, P.

Vanetsov, M. V.

M. S. Soskin and M. V. Vanetsov, in Progress in Optics, E. Wolf, ed. (North-Holland, 2001), Vol. 42, pp. 219–276.
[CrossRef]

Opt. Commun.

I. Freund, M. Soskin, and A. I. Mokhun, Opt. Commun. 208, 223 (2002).
[CrossRef]

O. Angelsky, A. Mokhun, I. Mokhun, and M. Soskin, Opt. Commun. 207, 57 (2002).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Commun. 251, 306 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

D. Palacios, D. Rozas, and G. A. Swartzlander, Phys. Rev. Lett. 88, 103902 (2002).
[CrossRef]

Proc. R. Soc. London Ser. A

J. F. Nye, Proc. R. Soc. London Ser. A 387, 105 (1983).
[CrossRef]

J. F. Nye, Proc. R. Soc. London Ser. A 389, 279 (1983).
[CrossRef]

Other

E. Collett, Polarized Light (Marcel Dekker, 1993).

E. Hasman, G. Biener, A. Niv, and V. Kleiner, in Progress in Optics, E. Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 215–289.

M. S. Soskin and M. V. Vanetsov, in Progress in Optics, E. Wolf, ed. (North-Holland, 2001), Vol. 42, pp. 219–276.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Simulation results for m = 1 . (a) Normalized intensity pattern. (b) Radial dependence of the ellipticity angle; empty circle indicates singularity. (c), (d) Local polarization ellipses for propagation distances z z T = 0 , 0.5 , respectively. The domain size is shown by the dotted square in (a). The concentric solid and dashed circles indicate the locations of linear and circular polarization, respectively.

Fig. 2
Fig. 2

(a) Scanning electron microscope image of the element for m = 1 ; inset, grooves of the subwavelength grating. (b) Measured intensity distributions of linearly polarized illumination imaged through a linear polarizer immediately behind the elements for m = 1 , 2 , 3 .

Fig. 3
Fig. 3

(a), (c) Measured intensity distributions for m = 2 , 4 , respectively. (b) Measured azimuthal angle in the vicinity of the linear polarization circle at various distances behind the axicon for m = 2 . (d) Same as (b) but for m = 4 .

Fig. 4
Fig. 4

(a), (c) Calculated braided intensity for m = 1 , 3 , respectively. (b), (d) Corresponding measured intensity distributions at different location along the braid. Solid and dashed lines introduce the rotation of the patterns.

Equations (5)

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E = 1 2 { exp [ i m φ i k ( β α ) r ] R + exp [ i m φ i k ( β + α ) r ] L } .
E ( r , φ , z ) = A ( r , z ) { ( β α ) J m [ k ( β α ) r ] exp [ i ( m φ + k α β z ) ] R + ( β + α ) J m [ k ( β + α ) r ] exp [ i ( m φ + k α β z ) ] L } ,
sin ( 2 χ ) = ( β a ) 2 J m 2 [ k ( β a ) r ] ( β + a ) 2 J m 2 [ k ( β + a ) r ] ( β a ) 2 J m 2 [ k ( β a ) r ] + ( β + a ) 2 J m 2 [ k ( β + a ) r ] ,
ψ mod π = k α β z + m φ + π 2 ϑ { J m [ k ( β α ) r ] J m [ k ( β + α ) r ] } ,
I = z 8 λ { ( β + α ) 2 J m 2 [ k ( β + α ) r ] + ( β α ) 2 J m 2 [ k ( β α ) r ] + 2 ( β 2 α 2 ) J m [ k ( β + α ) r ] J m [ k ( β α ) r ] cos ( 2 m φ + 2 k α β z ) } .

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