Abstract

Global invariant parameters are introduced to characterize the radial and azimuthal content of totally polarized beams. Such parameters are written in terms of the second moments of the optical beam and are invariant in propagation through symmetric first-order optical systems described by the ABCD matrix. Since it was proven in the past that the usual definition for radial polarization is not invariant, such invariance is novel in characterizing the radial and azimuthal polarizations content of optical beams. The possibility of obtaining a pure mode from a given beam using the proposed parameters is discussed.

© 2009 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  5. Y. Lumer, I. Moshe, A. Meir, Y. Paiken, G. Machavariani, and S. Jackel, J. Opt. Soc. Am. B 24, 2279 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. H. Weber, Opt. Quantum Electron. 24, S1027 (1992).
    [CrossRef]

2008 (1)

R. Martínez-Herrero, G. Piquero, and P. M. Mejías, Opt. Commun. 281, 1976 (2008).
[CrossRef]

2007 (4)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

1992 (1)

H. Weber, Opt. Quantum Electron. 24, S1027 (1992).
[CrossRef]

1991 (1)

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Freuer, T.

M. Meier, V. Romano, and T. Freuer, Appl. Phys. A 86, 329 (2007).
[CrossRef]

Jackel, S.

Leibush, E.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Lumer, Y.

Machavariani, G.

Martínez-Herrero, R.

R. Martínez-Herrero, G. Piquero, and P. M. Mejías, Opt. Commun. 281, 1976 (2008).
[CrossRef]

J. Serna, R. Martínez-Herrero, and P. M. Mejías, J. Opt. Soc. Am. A 8, 1094 (1991).
[CrossRef]

Meier, M.

M. Meier, V. Romano, and T. Freuer, Appl. Phys. A 86, 329 (2007).
[CrossRef]

Meir, A.

Mejías, P. M.

R. Martínez-Herrero, G. Piquero, and P. M. Mejías, Opt. Commun. 281, 1976 (2008).
[CrossRef]

J. Serna, R. Martínez-Herrero, and P. M. Mejías, J. Opt. Soc. Am. A 8, 1094 (1991).
[CrossRef]

Moshe, I.

Paiken, Y.

Piquero, G.

R. Martínez-Herrero, G. Piquero, and P. M. Mejías, Opt. Commun. 281, 1976 (2008).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Romano, V.

M. Meier, V. Romano, and T. Freuer, Appl. Phys. A 86, 329 (2007).
[CrossRef]

Salamin, Y. I.

Serna, J.

Weber, H.

H. Weber, Opt. Quantum Electron. 24, S1027 (1992).
[CrossRef]

Appl. Phys. A (1)

M. Meier, V. Romano, and T. Freuer, Appl. Phys. A 86, 329 (2007).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

R. Martínez-Herrero, G. Piquero, and P. M. Mejías, Opt. Commun. 281, 1976 (2008).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

H. Weber, Opt. Quantum Electron. 24, S1027 (1992).
[CrossRef]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

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Figures (1)

Fig. 1
Fig. 1

Radial beam parameter γ r as a function of the normalized astigmatism parameter.

Equations (33)

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E ( x , y , z ) = E s ( x , y , z ) s ̂ + E p ( x , y , z ) p ̂ ,
E ( r , θ , z ) = E r ( r , θ , z ) r ̂ + E θ ( r , θ , z ) θ ̂ ,
E r 2 = E s 2 cos 2 θ + E p 2 sin 2 θ + 2 sin θ cos θ Re ( E s E p * ) ,
E θ 2 = E s 2 sin 2 θ + E p 2 cos 2 θ 2 sin θ cos θ Re ( E s E p * ) .
χ r = E r 2 d r E 2 d r ,
χ θ = E θ 2 d r E 2 d r ,
r 2 r = x 2 s + y 2 p + 2 Re x y sp ,
η 2 r = u 2 s + v 2 p + 2 Re u v sp ,
r η r = x u s + y v p + Re ( x v sp + y u sp ) ,
r 2 θ = x 2 p + y 2 s 2 Re x y sp ,
η 2 θ = u 2 p + v 2 s 2 Re u v sp ,
r η θ = x u p + y v s Re ( x v sp + y u sp ) ,
α β i j = 1 I 0 k 2 4 π 2 α β E i * ( r + s 2 , z ) E j ( r s 2 , z ) exp ( i k s η ) d s d r d η ,
r 2 r + r 2 θ = r 2 ,
η 2 r + η 2 θ = η 2 ,
r η r + r η θ = r η ,
γ r = r 2 r η 2 r r η r 2 r 2 η 2 r η 2 ,
γ θ = r 2 θ η 2 θ r η θ 2 r 2 η 2 r η 2 .
x A x + B u ,
y A y + B v ,
u C x + D u ,
v C y + D v ,
r 2 r A 2 r 2 r + B 2 η 2 r + 2 A B r η r ,
η 2 r C 2 r 2 r + D 2 η 2 r + 2 C D r η r ,
r η r A C r 2 r + B D η 2 r + ( A D + B C ) r η r .
r 2 r η 2 r r η r 2 ABCD r 2 r η 2 r r η r 2 ,
r 2 r , θ = 0 χ r , θ = 0 .
γ r = r 2 r η 2 r r 2 r η 2 r + Q γ θ + r 2 r η 2 θ + r 2 θ η 2 r .
r 2 r ( z ) = r 2 r ( 0 ) + z 2 η 2 r + 2 z r η r ( 0 ) .
E ( r , θ ) = f ( r ) exp ( i k a R ( r ) cos ( m θ ) ) r ̂ ,
γ r = Q 0 + a 2 r 2 2 R 2 Q 0 + a 2 r 2 2 ( R 2 + m 2 ( R r ) 2 ) ,
E = E 0 r w exp ( r 2 w 2 + j k 2 R x ( x 2 y 2 ) ) r ̂ .
γ r = 8 R x 2 + k 2 w 4 8 R x 2 + 2 k 2 w 4 .

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