Abstract

We show that the complex-amplitude cross-correlation function between two beams can be obtained by the global Stokes parameters. We apply this approach to determine the topological charge of a Laguerre–Gaussian (LG) beam by performing power measurements only. Additionally, we study the connection of the cross-correlation function with the degree of polarization for nonuniformly polarized beams, and we obtain closed-form expressions of the cross correlation for LG vector modes and the generalized full Poincaré beams.

© 2014 Optical Society of America

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References

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  1. M. Harris, C. A. Hill, P. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
    [CrossRef]
  2. M. Harris, C. A. Hill, and J. M. Vaughan, Opt. Commun. 106, 161 (1994).
    [CrossRef]
  3. H. I. Sztul and R. R. Alfano, Opt. Lett. 31, 999 (2006).
    [CrossRef]
  4. G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
    [CrossRef]
  5. J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
    [CrossRef]
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    [CrossRef]
  10. R. Martínez-Herrero, P. M. Mejías, and G. Piquero, Opt. Commun. 265, 6 (2006).
    [CrossRef]
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    [CrossRef]
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2012 (2)

2011 (3)

2010 (2)

A. M. Beckley, T. G. Brown, and M. A. Alonso, Opt. Express 18, 10777 (2010).
[CrossRef]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

2009 (1)

2008 (1)

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

2006 (2)

R. Martínez-Herrero, P. M. Mejías, and G. Piquero, Opt. Commun. 265, 6 (2006).
[CrossRef]

H. I. Sztul and R. R. Alfano, Opt. Lett. 31, 999 (2006).
[CrossRef]

1999 (1)

G. Piquero, J. M. Movilla, P. M. Mejías, and R. Martínez-Herrero, Opt. Quantum Electron. 31, 223 (1999).
[CrossRef]

1994 (2)

M. Harris, C. A. Hill, P. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
[CrossRef]

M. Harris, C. A. Hill, and J. M. Vaughan, Opt. Commun. 106, 161 (1994).
[CrossRef]

Alfano, R. R.

Alonso, M. A.

Anderson, M. E.

Beckley, A. M.

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

Brown, T. G.

Chávez-Cerda, S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Cheng, W.

de Araujo, L. E. E.

Fonseca, E. J. S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Galvez, E. J.

Guo, C.-S.

Han, W.

Han, Y.

Harris, M.

M. Harris, C. A. Hill, P. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
[CrossRef]

M. Harris, C. A. Hill, and J. M. Vaughan, Opt. Commun. 106, 161 (1994).
[CrossRef]

Hickmann, J. M.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Hill, C. A.

M. Harris, C. A. Hill, and J. M. Vaughan, Opt. Commun. 106, 161 (1994).
[CrossRef]

M. Harris, C. A. Hill, P. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
[CrossRef]

Khadka, S.

Lu, L.-L.

Martínez-Herrero, R.

R. Martínez-Herrero, P. M. Mejías, and G. Piquero, Opt. Commun. 265, 6 (2006).
[CrossRef]

G. Piquero, J. M. Movilla, P. M. Mejías, and R. Martínez-Herrero, Opt. Quantum Electron. 31, 223 (1999).
[CrossRef]

Mejías, P. M.

R. Martínez-Herrero, P. M. Mejías, and G. Piquero, Opt. Commun. 265, 6 (2006).
[CrossRef]

G. Piquero, J. M. Movilla, P. M. Mejías, and R. Martínez-Herrero, Opt. Quantum Electron. 31, 223 (1999).
[CrossRef]

Movilla, J. M.

G. Piquero, J. M. Movilla, P. M. Mejías, and R. Martínez-Herrero, Opt. Quantum Electron. 31, 223 (1999).
[CrossRef]

Nomoto, S.

Piquero, G.

R. Martínez-Herrero, P. M. Mejías, and G. Piquero, Opt. Commun. 265, 6 (2006).
[CrossRef]

G. Piquero, J. M. Movilla, P. M. Mejías, and R. Martínez-Herrero, Opt. Quantum Electron. 31, 223 (1999).
[CrossRef]

Schubert, W. H.

Soares, W. C.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Sztul, H. I.

Tapster, P.

M. Harris, C. A. Hill, P. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
[CrossRef]

Vaughan, J. M.

M. Harris, C. A. Hill, P. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
[CrossRef]

M. Harris, C. A. Hill, and J. M. Vaughan, Opt. Commun. 106, 161 (1994).
[CrossRef]

Wang, H.-T.

Wang, L.-G.

Zhan, Q.

Zhao, G.

Appl. Opt. (1)

Opt. Commun. (2)

M. Harris, C. A. Hill, and J. M. Vaughan, Opt. Commun. 106, 161 (1994).
[CrossRef]

R. Martínez-Herrero, P. M. Mejías, and G. Piquero, Opt. Commun. 265, 6 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Opt. Quantum Electron. (1)

G. Piquero, J. M. Movilla, P. M. Mejías, and R. Martínez-Herrero, Opt. Quantum Electron. 31, 223 (1999).
[CrossRef]

Phys. Rev. A (1)

M. Harris, C. A. Hill, P. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
[CrossRef]

Phys. Rev. Lett. (2)

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Other (1)

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, eds., NIST Handbook of Mathematical Functions (Cambridge University, 2010), Eq. (13.2.7).

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Figures (3)

Fig. 1.
Fig. 1.

Autocorrelation function of a LG beam for different azimuthal orders m.

Fig. 2.
Fig. 2.

Experimental setup to observe the autocorrelation function Am(a,0).

Fig. 3.
Fig. 3.

Global normalized Stokes parameter s¯1=S¯1/S¯0 as a function of the normalized separation a/w0 for a diagonally polarized LG beam with azimuthal orders (a) m=1 and (b) m=2, theoretical (solid line) and experimental (circles).

Equations (20)

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C(a,b)=f*(x,y)g(x+a,y+b)dr,
E(x,y)=E+(x,y)c^++E(x,y)c^,
E(x,y)=P[cosθf(x,y)c^++sinθg(x+a,y+b)c^],
S¯0=P,S¯1=2PsinθcosθRe{C(a,b)},S¯2=2PsinθcosθIm{C(a,b)},S¯3=P(cos2θsin2θ),
S¯i=Si(x,y)dr,
C(a,b)=S¯1(a,b)+iS¯2(a,b)(S¯02S¯32)1/2.
ψm(x,y)=Am(x+iy)mexp(x2y2),Am=(2m+1πm!)1/2,
Am(a,b)=exp(c22)j=0mDjmc2j,Djm1πm!(2)jk=jm(mk)(2k2j)×Γ(12+mk)Γ(12j+k),
S¯0=1,S¯1=Am(a,b),S¯2=S¯3=0.
S¯0=P,S¯1=2PxP,S¯2=2PuP,S¯3=2P+P,
EVM(x,y)=12ψm(x,y)c^++12ψm(x,y)c^,
CVM=(1)m2mm!(a+ib)2mexp(c22).
EFP(x,y)=12ψm(x,y)c^++12ψn(x,y)c^,
Cm,n=(1)mm!n!exp(c22)(a+ib2)nmU(m,1+(nm);c22),
Am=(1)mm!exp(c22)U(m,1;c22),
C0,1=12(a+ib)exp(c22).
ψm(x,y)=Am(w0μ)m+1(x+iy)mexp(x2+y2μw02),
CVM=(1)mm!α(a+ib2w0α)2mexp(c22w02α),
Cm,n=(1)mm!n!αm+1exp(c22w02α)×(a+ib2w0α)nmU(m,1+(nm);c22w02α),
Am=(1)mm!αm+1exp(c22w02α)×U(m,1;c22w02α).

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