Abstract

The propagation of a circularly symmetric laser beam along the optical axis of a c-cut uniaxial crystal is described through the angular plane wave analysis. We show that radial and azimuthal polarization states appear as polarization eigenstates in a c-cut uniaxial crystal. As a consequence, no cross-talk occurs between these eigenstates during beam propagation.

© 2007 Optical Society of America

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References

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  1. A. Ciattoni, G. Cincotta, and C. Palma, "Propagation of cylindrically symmetric fields in a uniaxial crystal," J. Opt. Soc. Am. A 19, 792-796 (2002).
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  2. D. Pohl, "Operation of a ruby laser in the purely transverse electric mode TE01," Appl. Phys. Lett. 20, 266-267 (1972).
    [CrossRef]
  3. K. Yonezawa, Y. Kozawa, and S. Sato, "Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal," Opt. Lett. 31, 2151-2153 (2006).
    [CrossRef] [PubMed]
  4. V. Niziev and A. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D 32, 1455-1461 (1999).
    [CrossRef]
  5. I. Moshe, S. Jackel, and A. Meir, "Production of radially and azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects," Opt. Lett. 28, 807-809 (2003).
    [CrossRef] [PubMed]
  6. R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  7. T. Moser, H. Glur, V. Romano, M. A. Ahmed, F. Pigeon, O. Parriaux, and Th. Graf, "Polarization-selective grating mirrors used in the generation of radial polarization," Appl. Phys. B: Photophys. Laser Chem. 80, 707-713 (2005).
    [CrossRef]
  8. Y. Kozawa and S. Sato, "Focusing property of a double-shaped radially polarized beam," Opt. Lett. 31, 820-822 (2006).
    [CrossRef] [PubMed]
  9. T. Moser, J. Balmer, D. Delbeke, P. Muys, S. Verstuyft, and R. Baets, "Intracavity generation of radially polarized CO2 laser beams based on a simple binary dielectric diffraction grating," Appl. Opt. 45, 8517-8522 (2006).
    [CrossRef] [PubMed]
  10. M. Meier, V. Romano, and T. Feurer, "Material processing with pulsed radially and azimuthally polarized laser radiation," Appl. Phys. A: Solids Surf. 86, 329-334 (2007).
    [CrossRef]
  11. A. Nesterov and V. Niziev, "Laser beams with axially symmetric polarization," J. Phys. D 33, 1817-1822 (2000).
    [CrossRef]
  12. P. Pääkkönen, J. Tervo, P. Vahimaa, and J. Turunen, "General vectorial decomposition of electromagnetic fields with application to propagation-invariant and rotating fields," Opt. Express 10, 949-959 (2002).
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  13. A. Ciattoni, G. Cincotti, C. Palma, and H. Weber, "Energy exchange between Cartesian components of a paraxial beam in a uniaxial crystal," J. Opt. Soc. Am. A 19, 1894-1900 (2002).
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    [CrossRef]

2007 (1)

M. Meier, V. Romano, and T. Feurer, "Material processing with pulsed radially and azimuthally polarized laser radiation," Appl. Phys. A: Solids Surf. 86, 329-334 (2007).
[CrossRef]

2006 (3)

2005 (1)

T. Moser, H. Glur, V. Romano, M. A. Ahmed, F. Pigeon, O. Parriaux, and Th. Graf, "Polarization-selective grating mirrors used in the generation of radial polarization," Appl. Phys. B: Photophys. Laser Chem. 80, 707-713 (2005).
[CrossRef]

2003 (2)

2002 (3)

2001 (1)

2000 (1)

A. Nesterov and V. Niziev, "Laser beams with axially symmetric polarization," J. Phys. D 33, 1817-1822 (2000).
[CrossRef]

1999 (1)

V. Niziev and A. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D 32, 1455-1461 (1999).
[CrossRef]

1972 (1)

D. Pohl, "Operation of a ruby laser in the purely transverse electric mode TE01," Appl. Phys. Lett. 20, 266-267 (1972).
[CrossRef]

Ahmed, M. A.

T. Moser, H. Glur, V. Romano, M. A. Ahmed, F. Pigeon, O. Parriaux, and Th. Graf, "Polarization-selective grating mirrors used in the generation of radial polarization," Appl. Phys. B: Photophys. Laser Chem. 80, 707-713 (2005).
[CrossRef]

Baets, R.

Balmer, J.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Ciattoni, A.

Cincotta, G.

Cincotti, G.

Delbeke, D.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Feurer, T.

M. Meier, V. Romano, and T. Feurer, "Material processing with pulsed radially and azimuthally polarized laser radiation," Appl. Phys. A: Solids Surf. 86, 329-334 (2007).
[CrossRef]

Glur, H.

T. Moser, H. Glur, V. Romano, M. A. Ahmed, F. Pigeon, O. Parriaux, and Th. Graf, "Polarization-selective grating mirrors used in the generation of radial polarization," Appl. Phys. B: Photophys. Laser Chem. 80, 707-713 (2005).
[CrossRef]

Gori, F.

Graf, Th.

T. Moser, H. Glur, V. Romano, M. A. Ahmed, F. Pigeon, O. Parriaux, and Th. Graf, "Polarization-selective grating mirrors used in the generation of radial polarization," Appl. Phys. B: Photophys. Laser Chem. 80, 707-713 (2005).
[CrossRef]

Jackel, S.

Kozawa, Y.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Meier, M.

M. Meier, V. Romano, and T. Feurer, "Material processing with pulsed radially and azimuthally polarized laser radiation," Appl. Phys. A: Solids Surf. 86, 329-334 (2007).
[CrossRef]

Meir, A.

Moser, T.

T. Moser, J. Balmer, D. Delbeke, P. Muys, S. Verstuyft, and R. Baets, "Intracavity generation of radially polarized CO2 laser beams based on a simple binary dielectric diffraction grating," Appl. Opt. 45, 8517-8522 (2006).
[CrossRef] [PubMed]

T. Moser, H. Glur, V. Romano, M. A. Ahmed, F. Pigeon, O. Parriaux, and Th. Graf, "Polarization-selective grating mirrors used in the generation of radial polarization," Appl. Phys. B: Photophys. Laser Chem. 80, 707-713 (2005).
[CrossRef]

Moshe, I.

Muys, P.

Nesterov, A.

A. Nesterov and V. Niziev, "Laser beams with axially symmetric polarization," J. Phys. D 33, 1817-1822 (2000).
[CrossRef]

V. Niziev and A. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D 32, 1455-1461 (1999).
[CrossRef]

Niziev, V.

A. Nesterov and V. Niziev, "Laser beams with axially symmetric polarization," J. Phys. D 33, 1817-1822 (2000).
[CrossRef]

V. Niziev and A. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D 32, 1455-1461 (1999).
[CrossRef]

Pääkkönen, P.

Palma, C.

Parriaux, O.

T. Moser, H. Glur, V. Romano, M. A. Ahmed, F. Pigeon, O. Parriaux, and Th. Graf, "Polarization-selective grating mirrors used in the generation of radial polarization," Appl. Phys. B: Photophys. Laser Chem. 80, 707-713 (2005).
[CrossRef]

Pigeon, F.

T. Moser, H. Glur, V. Romano, M. A. Ahmed, F. Pigeon, O. Parriaux, and Th. Graf, "Polarization-selective grating mirrors used in the generation of radial polarization," Appl. Phys. B: Photophys. Laser Chem. 80, 707-713 (2005).
[CrossRef]

Pohl, D.

D. Pohl, "Operation of a ruby laser in the purely transverse electric mode TE01," Appl. Phys. Lett. 20, 266-267 (1972).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Romano, V.

M. Meier, V. Romano, and T. Feurer, "Material processing with pulsed radially and azimuthally polarized laser radiation," Appl. Phys. A: Solids Surf. 86, 329-334 (2007).
[CrossRef]

T. Moser, H. Glur, V. Romano, M. A. Ahmed, F. Pigeon, O. Parriaux, and Th. Graf, "Polarization-selective grating mirrors used in the generation of radial polarization," Appl. Phys. B: Photophys. Laser Chem. 80, 707-713 (2005).
[CrossRef]

Sato, S.

Tervo, J.

Turunen, J.

Vahimaa, P.

Verstuyft, S.

Weber, H.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Yonezawa, K.

Appl. Opt. (1)

Appl. Phys. A: Solids Surf. (1)

M. Meier, V. Romano, and T. Feurer, "Material processing with pulsed radially and azimuthally polarized laser radiation," Appl. Phys. A: Solids Surf. 86, 329-334 (2007).
[CrossRef]

Appl. Phys. B: Photophys. Laser Chem. (1)

T. Moser, H. Glur, V. Romano, M. A. Ahmed, F. Pigeon, O. Parriaux, and Th. Graf, "Polarization-selective grating mirrors used in the generation of radial polarization," Appl. Phys. B: Photophys. Laser Chem. 80, 707-713 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

D. Pohl, "Operation of a ruby laser in the purely transverse electric mode TE01," Appl. Phys. Lett. 20, 266-267 (1972).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Phys. D (2)

V. Niziev and A. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D 32, 1455-1461 (1999).
[CrossRef]

A. Nesterov and V. Niziev, "Laser beams with axially symmetric polarization," J. Phys. D 33, 1817-1822 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Other (1)

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

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Figures (2)

Fig. 1
Fig. 1

Axially symmetric intensity distributions with (a) radial and (b) azimuthal polarization. The gray scale corresponds to the intensity. The arrows indicate the state of polarization, and their length is proportional to the electric field amplitude.

Fig. 2
Fig. 2

All plane waves with radial polarization are polarized along the extraordinary axis, and all plane waves with azimuthal polarization are ordinary waves. The normal to the interface (n), the direction of the wave vectors (k), and the ordinary and extraordinary polarization are indicated. The inset illustrates that irrespective of transverse position the radial polarization always coincides with the extraordinary polarization.

Equations (31)

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ϵ = [ n o 2 0 0 0 n o 2 0 0 0 n e 2 ] ,
E ( r , z ) = exp ( i k 0 n o ) [ A o ( r , z ) + A e ( r , z ) ] ,
r = x e x + y e y
k = k x e x + k y e y .
A o ( r , z ) = d k 1 k 2 [ k y 2 k x k y k x k y k x 2 ] E ( k , 0 ) exp ( i k r i k 2 2 k 0 n o z ) ,
A e ( r , z ) = d k 1 k 2 [ k x 2 k x k y k x k y k y 2 ] E ( k , 0 ) exp ( i k r i n o k 2 2 k 0 n e 2 z ) .
E ( k , 0 ) = 1 ( 2 π ) 2 d r E ( r , 0 ) exp ( i k r )
E z ( r , z ) = 0 z d ζ [ E x ( r , ζ ) x + E y ( r , ζ ) y ] .
E ( r , 0 ) = E ( r , 0 ) .
E ( k , 0 ) = 1 2 π 0 d r r J 0 ( k r ) E ( r , 0 ) ,
r = r ( cos ϕ e x + sin ϕ e y ) ,
k = k ( cos θ e x + sin θ e y ) .
A o ( r , ϕ , z ) = A o ( 0 ) ( r , z ) + R ( ϕ ) A o ( 2 ) ( r , z ) ,
A e ( r , ϕ , z ) = A e ( 0 ) ( r , z ) R ( ϕ ) A e ( 2 ) ( r , z ) ,
R ( ϕ ) = [ cos ( 2 ϕ ) sin ( 2 ϕ ) sin ( 2 ϕ ) cos ( 2 ϕ ) ] .
A o ( n ) ( r , z ) = π 0 d k E ( k , 0 ) k J n ( k r ) exp ( i z k 2 2 k 0 n o ) ,
A e ( n ) ( r , z ) = π 0 d k E ( k , 0 ) k J n ( k r ) exp ( i n o z k 2 2 k 0 n e 2 ) ,
A o a E ( k , 0 ) + b R ( ϕ ) E ( k , 0 ) ,
A e c E ( k , 0 ) d R ( ϕ ) E ( k , 0 ) ,
E R ( r , 0 ) = E ( r , 0 ) e r ,
E A ( r , 0 ) = E ( r , 0 ) e ϕ ,
E R ( k , 0 ) = E ( k , 0 ) e r ,
E A ( k , 0 ) = E ( k , 0 ) e ϕ .
e r = cos ϕ e x + sin ϕ e y ,
e ϕ = sin ϕ e x + cos ϕ e y .
R ( ϕ ) e r = e r ,
R ( ϕ ) e ϕ = e ϕ .
A o a E ( k , 0 ) e ϕ + b E ( k , 0 ) R ( ϕ ) e ϕ ,
A e c E ( k , 0 ) e r d E ( k , 0 ) R ( ϕ ) e r .
A o [ a E ( k , 0 ) b E ( k , 0 ) ] e ϕ ,
A e [ c E ( k , 0 ) d E ( k , 0 ) ] e r .

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