Abstract

By analysis of the degree of cross-polarization of a stochastic electromagnetic vortex beam, we find that the number of bright ring dislocations is equal to the topological charge of the vortex beam. Based on this property, we suggest a method to access the measurement of the orbital angular momentum of vector vortex beams, which holds true for cases of high coherence or low coherence.

© 2014 Optical Society of America

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  2. H. I. Sztul and R. R. Alfano, Opt. Lett. 31, 999 (2006).
    [CrossRef]
  3. I. Moreno, J. A. Davis, B. M. L. Pascoguin, M. J. Mitry, and D. M. Cottrell, Opt. Lett. 34, 2927 (2009).
    [CrossRef]
  4. C. S. Guo, L. L. Lu, and H. T. Wang, Opt. Lett. 34, 3686 (2009).
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  5. L. E. E. de Araujo and M. E. Anderson, Opt. Lett. 36, 787 (2011).
    [CrossRef]
  6. D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
    [CrossRef]
  7. Y. J. Yang, M. Mazilu, and K. Dholakia, Opt. Lett. 37, 4949 (2012).
  8. C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
    [CrossRef]
  9. P. Ding and J. Pu, Opt. Express 22, 1350 (2014).
    [CrossRef]
  10. H. Garcia-Gracia, B. Perez-Garcia, D. Lopez-Mago, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, J. Opt. 16, 045702 (2014).
    [CrossRef]
  11. B. Perez-Garcia, D. Lopez-Mago, H. Garcia-Gracia, J. A. Garza-Alanis, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, Opt. Lett. 39, 1929 (2014).
    [CrossRef]
  12. T. Shirai and E. Wolf, Opt. Commun. 272, 289 (2007).
    [CrossRef]
  13. S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
    [CrossRef]
  14. J. Pu and O. Korotkova, Opt. Commun. 282, 1691 (2009).
    [CrossRef]
  15. S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
    [CrossRef]
  16. P. Ding and H. Ren, Opt. Eng. 51, 018002 (2012).
    [CrossRef]
  17. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  18. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  19. M. Luo, Q. Chen, L. Hua, and D. Zhao, Phys. Lett. A 378, 308 (2014).
    [CrossRef]
  20. H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
    [CrossRef]
  21. G. Basso, L. Oliveira, and I. Vidal, Opt. Lett. 39, 1220 (2014).
    [CrossRef]

2014 (5)

2012 (3)

Y. J. Yang, M. Mazilu, and K. Dholakia, Opt. Lett. 37, 4949 (2012).

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

P. Ding and H. Ren, Opt. Eng. 51, 018002 (2012).
[CrossRef]

2011 (1)

2009 (4)

I. Moreno, J. A. Davis, B. M. L. Pascoguin, M. J. Mitry, and D. M. Cottrell, Opt. Lett. 34, 2927 (2009).
[CrossRef]

C. S. Guo, L. L. Lu, and H. T. Wang, Opt. Lett. 34, 3686 (2009).
[CrossRef]

J. Pu and O. Korotkova, Opt. Commun. 282, 1691 (2009).
[CrossRef]

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
[CrossRef]

2008 (1)

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
[CrossRef]

2007 (1)

T. Shirai and E. Wolf, Opt. Commun. 272, 289 (2007).
[CrossRef]

2006 (1)

2004 (1)

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

2003 (1)

H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
[CrossRef]

1992 (1)

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

Alfano, R. R.

Allen, L.

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

Anderson, M. E.

Basso, G.

Beijersbergen, M. W.

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

Cai, Y.

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

Chen, Q.

M. Luo, Q. Chen, L. Hua, and D. Zhao, Phys. Lett. A 378, 308 (2014).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

de Araujo, L. E. E.

Dholakia, K.

Ding, P.

P. Ding and J. Pu, Opt. Express 22, 1350 (2014).
[CrossRef]

P. Ding and H. Ren, Opt. Eng. 51, 018002 (2012).
[CrossRef]

Dong, Y.

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

Garcia-Gracia, H.

B. Perez-Garcia, D. Lopez-Mago, H. Garcia-Gracia, J. A. Garza-Alanis, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, Opt. Lett. 39, 1929 (2014).
[CrossRef]

H. Garcia-Gracia, B. Perez-Garcia, D. Lopez-Mago, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, J. Opt. 16, 045702 (2014).
[CrossRef]

Garza-Alanis, J. A.

Guo, C. S.

Gutierrez-Vega, J. C.

B. Perez-Garcia, D. Lopez-Mago, H. Garcia-Gracia, J. A. Garza-Alanis, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, Opt. Lett. 39, 1929 (2014).
[CrossRef]

H. Garcia-Gracia, B. Perez-Garcia, D. Lopez-Mago, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, J. Opt. 16, 045702 (2014).
[CrossRef]

Han, Y.

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

Hernandez-Aranda, R. I.

H. Garcia-Gracia, B. Perez-Garcia, D. Lopez-Mago, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, J. Opt. 16, 045702 (2014).
[CrossRef]

B. Perez-Garcia, D. Lopez-Mago, H. Garcia-Gracia, J. A. Garza-Alanis, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, Opt. Lett. 39, 1929 (2014).
[CrossRef]

Hua, L.

M. Luo, Q. Chen, L. Hua, and D. Zhao, Phys. Lett. A 378, 308 (2014).
[CrossRef]

James, D. F. V.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
[CrossRef]

Korotkova, O.

J. Pu and O. Korotkova, Opt. Commun. 282, 1691 (2009).
[CrossRef]

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
[CrossRef]

Lopez-Mago, D.

H. Garcia-Gracia, B. Perez-Garcia, D. Lopez-Mago, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, J. Opt. 16, 045702 (2014).
[CrossRef]

B. Perez-Garcia, D. Lopez-Mago, H. Garcia-Gracia, J. A. Garza-Alanis, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, Opt. Lett. 39, 1929 (2014).
[CrossRef]

Lu, L. L.

Luo, M.

M. Luo, Q. Chen, L. Hua, and D. Zhao, Phys. Lett. A 378, 308 (2014).
[CrossRef]

Maleev, I. D.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Marathay, A. S.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Mazilu, M.

Mitry, M. J.

Moreno, I.

Oliveira, L.

Palacios, D. M.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Pascoguin, B. M. L.

Perez-Garcia, B.

H. Garcia-Gracia, B. Perez-Garcia, D. Lopez-Mago, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, J. Opt. 16, 045702 (2014).
[CrossRef]

B. Perez-Garcia, D. Lopez-Mago, H. Garcia-Gracia, J. A. Garza-Alanis, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, Opt. Lett. 39, 1929 (2014).
[CrossRef]

Pu, J.

P. Ding and J. Pu, Opt. Express 22, 1350 (2014).
[CrossRef]

J. Pu and O. Korotkova, Opt. Commun. 282, 1691 (2009).
[CrossRef]

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
[CrossRef]

Ren, H.

P. Ding and H. Ren, Opt. Eng. 51, 018002 (2012).
[CrossRef]

Roychowdhury, H.

H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
[CrossRef]

Sahin, S.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
[CrossRef]

Shirai, T.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
[CrossRef]

T. Shirai and E. Wolf, Opt. Commun. 272, 289 (2007).
[CrossRef]

Spreeuw, R. J. C.

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

Swartzlander, G. A.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Sztul, H. I.

Vidal, I.

Volkov, S. N.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
[CrossRef]

Wang, F.

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

Wang, H. T.

Woerdman, J. P.

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

Wolf, E.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
[CrossRef]

T. Shirai and E. Wolf, Opt. Commun. 272, 289 (2007).
[CrossRef]

H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Yang, Y. J.

Zhang, G.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
[CrossRef]

Zhao, C.

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

Zhao, D.

M. Luo, Q. Chen, L. Hua, and D. Zhao, Phys. Lett. A 378, 308 (2014).
[CrossRef]

Appl. Phys. Lett. (1)

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

J. Opt. (1)

H. Garcia-Gracia, B. Perez-Garcia, D. Lopez-Mago, R. I. Hernandez-Aranda, and J. C. Gutierrez-Vega, J. Opt. 16, 045702 (2014).
[CrossRef]

J. Opt. A (1)

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
[CrossRef]

Opt. Commun. (3)

J. Pu and O. Korotkova, Opt. Commun. 282, 1691 (2009).
[CrossRef]

T. Shirai and E. Wolf, Opt. Commun. 272, 289 (2007).
[CrossRef]

H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
[CrossRef]

Opt. Eng. (1)

P. Ding and H. Ren, Opt. Eng. 51, 018002 (2012).
[CrossRef]

Opt. Express (1)

Opt. Lett. (7)

Phys. Lett. A (1)

M. Luo, Q. Chen, L. Hua, and D. Zhao, Phys. Lett. A 378, 308 (2014).
[CrossRef]

Phys. Rev. A (1)

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

Phys. Rev. Lett. (1)

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Other (2)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

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Figures (3)

Fig. 1.
Fig. 1.

Degree of cross-polarization of stochastic electromagnetic vortex beams for different topological charges. (a) m=1, (b) m=2, (c) m=3, and (d) m=4, where δxx=0.5σ, δyy=0.3σ.

Fig. 2.
Fig. 2.

I(ρ,ρ) of stochastic electromagnetic vortex beams for different topological charges. The other parameters are the same as in Fig. 1.

Fig. 3.
Fig. 3.

(a)–(d) Distribution of intensity and (e)–(h) degree of cross-polarization for m=3 with varying coherence lengths. (a) and (e) δxx=2.5σ, δyy=2σ; (b) and (f) δxx=1.5σ, δyy=1σ; (c) and (g) δxx=1.2σ, δyy=0.8σ; (d) and (h) δxx=0.3σ, δyy=0.1σ.

Equations (8)

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Wij(0)(x1,y1,x2,y2;z=0)=AiAjBijσ2m(x1iy1)m(x2+iy2)m×exp(x12+y12+x22+y22σ2)×exp[(x1x2)2+(y1y2)2δij2],(i=x,y;j=x,y),
Bxx=Byy=1,|Bxy|=|Byx|.
Wij(ρ1,ρ2;z)=(k/2πz)2d2ρ1d2ρ2Wij(0)(ρ1,ρ1;z=0)×exp{ik2z[(ρ1ρ1)2(ρ2ρ2)2]},
Wij(x1,y1,x2,y2;z)=AiAjBijz2mΔijm+1k2mσ2mn=0m(Cmn)2n!4nδij2n×exp[αij*ρ12+αijρ222(x1x2+y1y2)/δij2Δijik2z(ρ12ρ22)]×[4(αij*ρ12+αijρ22)Δijδij2+ik2z2(x1y2x2y1)+(k2z2+8Δijδij4)(x1x2+y1y2)]mn,
ρ12=x12+y12,ρ22=x22+y22,αij=1σ2+1δij2+ik2z,Δij=1+4z2σ2k2(1σ2+2δij2).
Wij(ρ,ρ;z)=AiAjBijz2mΔijm+1k2mσ2mn=0m(Cmn)2n!4nδij2n×exp[(αij*+αij+2/δij2)Δijρ2]×{[4(αij*+αij)Δijδij2+k2z2+8Δijδij4]ρ2}mn.
P(ρ,ρ,z)=14DetW(ρ,ρ,z)[TrW(ρ,ρ,z)]2,
P(ρ,ρ,z)=|Wxx(ρ,ρ,z)Wyy(ρ,ρ,z)Wxx(ρ,ρ,z)+Wyy(ρ,ρ,z)|.

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