Abstract

We calculated and measured the difference between focal positions of radially and azimuthally polarized beams after passing through a uniaxial crystal. Calculations were carried out on the basis of the ray optics and the vector diffraction theory. The results of the calculations were in good agreement with those of the experiment. In addition, we discussed the polarization selection in a hemispherical laser cavity that was used for the generation of a radially polarized beam by use of the birefringence of a c-cut Nd:YVO4 laser crystal [Opt. Lett. 31, 2151 (2006) ]. The stability range of the laser cavity length for the generation of a radially polarized beam was also in good agreement with the differences mentioned above.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. J. A. Fleck, Jr. and M. D. Feit, "Beam propagation in uniaxial anisotropic media," J. Opt. Soc. Am. 73, 920-926 (1983).
    [CrossRef]
  2. G. S. Sithambaranathan and J. J. Stamnes, "Transmission of a Gaussian beam into a biaxial crystal," J. Opt. Soc. Am. A 18, 1670-1677 (2001).
    [CrossRef]
  3. A. Caittoni, G. Cincotti, and C. Palma, "Propagation of cylindrically symmetric fields in uniaxial crystals," J. Opt. Soc. Am. A 19, 792-796 (2002).
    [CrossRef]
  4. B. E. Bernacki and M. Mansuripur, "Investigation of substrate birefringence effects on optical disk-performance," Appl. Opt. 32, 6547-6555 (1993).
    [CrossRef] [PubMed]
  5. S. Stallinga, "Axial birefringence in high-numerical-aperture optical systems and the light distribution close to focus," J. Opt. Soc. Am. A 18, 2846-2859 (2001).
    [CrossRef]
  6. M. Jain, J. K. Lotsberg, and J. J. Stamnes, "Comparisons of exact and paraxial intensities of electromagnetic waves focused into uniaxial crystals," J. Opt. A, Pure Appl. Opt. 8, 709-719 (2006).
    [CrossRef]
  7. I. Moshe and S. Jackel, "Influence of birefringence-induced bifocusing on optical beams," J. Opt. Soc. Am. B 22, 1228-1235 (2005).
    [CrossRef]
  8. K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical vector beams," Opt. Express 7, 77-87 (2000).
    [CrossRef] [PubMed]
  9. M. Erdélyi and Z. Bor, "Radial and azimuthal polarizers," J. Opt. A, Pure Appl. Opt. 8, 737-742 (2006).
    [CrossRef]
  10. 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]
  11. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
    [CrossRef]
  12. M. Avendaño-Alejo and M. Rosete-Aguilar, "Optical path difference in a plane-parallel uniaxial plate," J. Opt. Soc. Am. A 23, 926-932 (2006).
    [CrossRef]

2006 (4)

M. Jain, J. K. Lotsberg, and J. J. Stamnes, "Comparisons of exact and paraxial intensities of electromagnetic waves focused into uniaxial crystals," J. Opt. A, Pure Appl. Opt. 8, 709-719 (2006).
[CrossRef]

M. Erdélyi and Z. Bor, "Radial and azimuthal polarizers," J. Opt. A, Pure Appl. Opt. 8, 737-742 (2006).
[CrossRef]

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]

M. Avendaño-Alejo and M. Rosete-Aguilar, "Optical path difference in a plane-parallel uniaxial plate," J. Opt. Soc. Am. A 23, 926-932 (2006).
[CrossRef]

2005 (1)

2002 (1)

2001 (2)

2000 (1)

1993 (1)

1983 (1)

1959 (1)

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

Appl. Opt. (1)

J. Opt. A, Pure Appl. Opt. (2)

M. Jain, J. K. Lotsberg, and J. J. Stamnes, "Comparisons of exact and paraxial intensities of electromagnetic waves focused into uniaxial crystals," J. Opt. A, Pure Appl. Opt. 8, 709-719 (2006).
[CrossRef]

M. Erdélyi and Z. Bor, "Radial and azimuthal polarizers," J. Opt. A, Pure Appl. Opt. 8, 737-742 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

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

Opt. Express (1)

Opt. Lett. (1)

Proc. R. Soc. London, Ser. A (1)

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Schematic of the propagation of rays passing through a birefringent slab whose c axis is perpendicular to the slab surface. Dashed–dotted lines correspond to the path of an ordinary ray. Dotted lines and dashed lines correspond to the wave normal and the Poynting vector, respectively. The thickness of the slab is D. The polarization directions of the ordinary and the extraordinary rays are perpendicular and parallel to the paper, respectively.

Fig. 2
Fig. 2

Calculated intensity distributions near the focus for beams (upper) with azimuthal polarization and (lower) with radial polarization after passing through an Y V O 4 slab 15 mm long. The horizontal axis indicates the distance from the point corresponding to the focal point without the crystal.

Fig. 3
Fig. 3

Schematic of a setup for measurement of variation of the beam diameter along with the propagation of radially and azimuthally polarized beams after passing through a birefringent Y V O 4 slab whose c axis is parallel to the beam axis.

Fig. 4
Fig. 4

Measured beam diameter as a function of the position of the CCD camera. Rectangles and circles show the results for radially and azimuthally polarized beams, respectively.

Fig. 5
Fig. 5

Measured output power of a radially polarized Nd : Y V O 4 laser as a function of the cavity length.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E r ( r , z ) = A 0 α cos 1 2 ( θ ) sin ( 2 θ ) l 0 ( θ ) J 1 ( k r sin θ ) exp ( i k z cos θ ) d θ ,
E a ( r , z ) = 2 A 0 α cos 1 2 ( θ ) sin θ l 0 ( θ ) J 1 ( k r sin θ ) exp ( i k z cos θ ) d θ ,
l 0 ( θ ) = exp ( i k Φ ( θ ) ) ,
Φ o ( θ ) = ( n o a b ¯ + b c ¯ ) a d ¯ = D { n o cos θ o + sin θ ( tan θ tan θ o ) 1 cos θ } = D ( n o cos θ o cos θ ) ,
Φ e ( θ ) = D ( ( cos 2 θ e n o 2 + sin 2 θ e n e 2 ) 1 2 cos θ e cos θ ) .

Metrics