Abstract

We propose a promising and practical scheme to generate a vectorial Mathieu-like hollow beam (vMHB) by using an axicon optical system including a dual-mode elliptic hollow fiber (EHF), and calculate the intensity and polarization distributions of the beam and its fractional orbital angular momentum (OAM). We also fit its intensity profile and obtain suitable theoretical expressions to describe three-dimensional (3D) propagation characteristics of such a Mathieu-like hollow beam. Our study shows that the generated beam is a vMHB within the propagation distance 1.22.2m, which has an unchanged (diffraction-free) intensity profile and periodically rotated polarization properties as well as an unchanged fractional OAM within 1.22.2m.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, Opt. Lett. 25, 1493 (2000).
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2011

2010

H. Li and J. Yin, Chin. Phys. B 19, 083204 (2010).
[CrossRef]

2008

2006

2002

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

2001

S. Chávez-Cerda, J. C. Gutiérrez-Vega, and G. H. C. New, Opt. Lett. 26, 1803 (2001).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

2000

1997

J. Yin, H. R. Noh, K. Lee, K. H. Kim, Y. Wang, and W. Jhe, Opt. Commun. 138, 287 (1997).
[CrossRef]

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

1970

1962

C. Yeh, J. Appl. Phys. 33, 3235 (1962).
[CrossRef]

Ahluwalia, B. P. S.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Allison, I.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

Alvarez-Elizondo, M. B.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Bu, J.

Chávez-Cerda, S.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

S. Chávez-Cerda, J. C. Gutiérrez-Vega, and G. H. C. New, Opt. Lett. 26, 1803 (2001).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, Opt. Lett. 25, 1493 (2000).
[CrossRef]

Cheong, W. C.

Collins, J. S. A.

Courtial, J.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

Gao, W.

J. Yin, W. Gao, and Y. Zhu, in Progress in Optics, E.Wolf, ed. (Elsevier, 2003), pp. 119–204.
[CrossRef]

Gutiérrez-Vega, J. C.

M. B. Alvarez-Elizondo, R. Rodriguez-Masegosa, and J. C. Gutiérrez-Vega, Opt. Express 16, 18770 (2008).
[CrossRef]

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

S. Chávez-Cerda, J. C. Gutiérrez-Vega, and G. H. C. New, Opt. Lett. 26, 1803 (2001).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, Opt. Lett. 25, 1493 (2000).
[CrossRef]

Iturbe-Castillo, M. D.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, Opt. Lett. 25, 1493 (2000).
[CrossRef]

Jáuregui, R.

B. M. Rodríguez-Lara and R. Jáuregui, Phys. Rev. A 78, 033813 (2008).
[CrossRef]

Jhe, W.

J. Yin, H. R. Noh, K. Lee, K. H. Kim, Y. Wang, and W. Jhe, Opt. Commun. 138, 287 (1997).
[CrossRef]

Kim, K. H.

J. Yin, H. R. Noh, K. Lee, K. H. Kim, Y. Wang, and W. Jhe, Opt. Commun. 138, 287 (1997).
[CrossRef]

Lee, K.

J. Yin, H. R. Noh, K. Lee, K. H. Kim, Y. Wang, and W. Jhe, Opt. Commun. 138, 287 (1997).
[CrossRef]

Li, H.

H. Li and J. Yin, Opt. Lett. 36, 457 (2011).
[CrossRef] [PubMed]

H. Li and J. Yin, Chin. Phys. B 19, 083204 (2010).
[CrossRef]

Luneberg, R. K.

R. K. Luneberg, Mathematical Theory of Optics (University of California Berkeley, 1964).

MacVicar, I.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

New, G. H. C.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

S. Chávez-Cerda, J. C. Gutiérrez-Vega, and G. H. C. New, Opt. Lett. 26, 1803 (2001).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

Noh, H. R.

J. Yin, H. R. Noh, K. Lee, K. H. Kim, Y. Wang, and W. Jhe, Opt. Commun. 138, 287 (1997).
[CrossRef]

O’Neil, A. T.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

Padgett, M. J.

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

Ramirez, G. A.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

Rodriguez-Dagnino, R. M.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

Rodríguez-Lara, B. M.

B. M. Rodríguez-Lara and R. Jáuregui, Phys. Rev. A 78, 033813 (2008).
[CrossRef]

Rodriguez-Masegosa, R.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Tao, S. H.

Tepichin, E.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

Wang, H.

Wang, Y.

J. Yin, H. R. Noh, K. Lee, K. H. Kim, Y. Wang, and W. Jhe, Opt. Commun. 138, 287 (1997).
[CrossRef]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Yeh, C.

C. Yeh, J. Appl. Phys. 33, 3235 (1962).
[CrossRef]

Yin, J.

H. Li and J. Yin, Opt. Lett. 36, 457 (2011).
[CrossRef] [PubMed]

H. Li and J. Yin, Chin. Phys. B 19, 083204 (2010).
[CrossRef]

J. Yin, H. R. Noh, K. Lee, K. H. Kim, Y. Wang, and W. Jhe, Opt. Commun. 138, 287 (1997).
[CrossRef]

J. Yin, W. Gao, and Y. Zhu, in Progress in Optics, E.Wolf, ed. (Elsevier, 2003), pp. 119–204.
[CrossRef]

Yuan, X. C.

Zhang, L. S.

Zhu, Y.

J. Yin, W. Gao, and Y. Zhu, in Progress in Optics, E.Wolf, ed. (Elsevier, 2003), pp. 119–204.
[CrossRef]

Chin. Phys. B

H. Li and J. Yin, Chin. Phys. B 19, 083204 (2010).
[CrossRef]

J. Appl. Phys.

C. Yeh, J. Appl. Phys. 33, 3235 (1962).
[CrossRef]

J. Opt. B

S. Chávez-Cerda, M. J. Padgett, I. Allison, G. H. C. New, J. C. Gutiérrez-Vega, A. T. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

J. Yin, H. R. Noh, K. Lee, K. H. Kim, Y. Wang, and W. Jhe, Opt. Commun. 138, 287 (1997).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

B. M. Rodríguez-Lara and R. Jáuregui, Phys. Rev. A 78, 033813 (2008).
[CrossRef]

Other

J. Yin, W. Gao, and Y. Zhu, in Progress in Optics, E.Wolf, ed. (Elsevier, 2003), pp. 119–204.
[CrossRef]

R. K. Luneberg, Mathematical Theory of Optics (University of California Berkeley, 1964).

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Figures (4)

Fig. 1
Fig. 1

(a) Generation scheme of vMHB. (b) Cross section of the EHF. (c) Elliptic coordinate system.

Fig. 2
Fig. 2

(a) Longitudinal and transverse intensity distributions after the axicon within z 3 = 1.2 m 2.2 m . Bright areas indicate the relative intensity, and the arrows in panels (b)–(d) show the polarization states of the beam in each z 3 plane.

Fig. 3
Fig. 3

(a) Elliptic coordinate system adopted in fitting the intensity distribution. (b)–(e) The calculated results of the generated beam and its fitting ones, in which (b) and (c) are the results of the intensity distributions in the y and x directions; (d) is one of the circumferential intensity distributions; (e) shows the dependences of the maximum intensity in the y direction on z 3 .

Fig. 4
Fig. 4

OAM per photon of the vMHB. Dots with dashed curve show the OAM per photon in the entire cross section. Squares with solid curve are the numerically calculated results of the OAM per photon in the central elliptic ring of the vMHB.

Equations (6)

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E ˜ j ( ξ 2 , η 2 , z 1 + z 2 ) = i λ B 0 2 π 0 E ˜ j ( ξ 1 , η 1 , z 1 ) × exp [ i k z 2 + i k 2 B ( A ( x 1 2 + y 1 2 ) 2 ( x 1 x 2 + y 1 y 2 ) + D ( x 2 2 + y 2 2 ) ) ] × exp [ k α ( n 1 ) h sin h 2 ξ 1 + cos 2 η 1 ] h 2 ( cos h 2 ξ 1 cos 2 η 1 ) d ξ 1 d η 1 ,
( A B C D ) = ( [ f 1 ( f 2 L 2 z 3 ) + L 1 ( L 2 + z 3 ) f 2 z 2 ] / f 1 f 2 L 2 + z 3 + L 1 [ 1 ( L 2 + z 3 ) / f 2 ] ( f 1 + f 2 L 1 ) / f 1 f 2 1 L 1 / f 2 ) ;
Δ z = ρ 2 ρ 1 ( n 1 ) α + β .
I ( ζ , υ ; q ) = [ P J e 1 ( ζ ; q ) S e 1 ( υ ; q ) ] 2 + [ Q J o 1 ( ζ ; q ) S o 1 ( υ ; q ) ] 2 .
I ( ζ , υ , z 3 ; q ) = I ( ζ , υ ; q ) · [ 149603.35 + 150676.86 exp ( exp ( ε ) ε + 1 ) ] ,
x = h sinh ζ sin υ , y = h cosh ζ cos υ , z = z 3 ,

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