Abstract

The focusing of a light beam with radial polarization has substantial advantages as the irradiance distribution in the focal plane is symmetric and there is maximum absorption at the focus. Using half wave plates cut into four quadrants with each quadrant having a linear polarization directed outwards gives a total field that approximates radial polarization, called pseudoradial polarization. The irradiance distributions in the focal region for different polarizations and beam profiles are compared. The irradiance is calculated by the numerical integration of the two-dimensional Rayleigh-Sommerfeld diffraction integral of the first kind using the 2DSC method for both circular and annular apertures.

© 2005 Optical Society of America

Full Article  |  PDF Article
Related Articles
Focusing of doughnut laser beams by a high numerical-aperture objective in free space

Djenan Ganic, Xiaosong Gan, and Min Gu
Opt. Express 11(21) 2747-2752 (2003)

Annular pupils, radial polarization, and superresolution

Colin J. R. Sheppard and Amarjyoti Choudhury
Appl. Opt. 43(22) 4322-4327 (2004)

The structure of focused, radially polarized fields

D. W. Diehl, R. W. Schoonover, and T. D. Visser
Opt. Express 14(7) 3030-3038 (2006)

References

  • View by:
  • |
  • |
  • |

  1. I. J. Cooper and C.J.R. Sheppard, “A matrix method for calculating the three-dimensional irradiance distribution in the focal region of a convergent beam,” Optik,  113, 298–304 (2003).
    [Crossref]
  2. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
    [Crossref]
  3. K.S. Youngsworth and T.G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-2-77
    [Crossref]
  4. Q. Zhan and J.R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10, 324–331 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-7-324
    [PubMed]
  5. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179, 1–7 (2000).
    [Crossref]
  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. N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhance Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
    [Crossref]
  8. D. P. Biss and T.G. Brown, “Cylindrical vector beam focusing through a dielectric interface,” Opt. Express 9, 490–497 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-10-490
    [Crossref] [PubMed]
  9. A.S. van de Nes, P.R.T. Munro, S.F. Pereira, J.J.M. Braat, and P. Török, “Cylindrical vector beam focusing through a dielectric interface: comment,” Opt. Express 12, 967–969 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-967
    [Crossref] [PubMed]
  10. D. P. Biss and T.G. Brown, “Cylindrical vector beam focusing through a dielectric interface: reply to comment,” Opt. Express 92, 970–971 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-970
    [Crossref]

2004 (3)

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhance Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

A.S. van de Nes, P.R.T. Munro, S.F. Pereira, J.J.M. Braat, and P. Török, “Cylindrical vector beam focusing through a dielectric interface: comment,” Opt. Express 12, 967–969 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-967
[Crossref] [PubMed]

D. P. Biss and T.G. Brown, “Cylindrical vector beam focusing through a dielectric interface: reply to comment,” Opt. Express 92, 970–971 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-970
[Crossref]

2003 (2)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper Focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

I. J. Cooper and C.J.R. Sheppard, “A matrix method for calculating the three-dimensional irradiance distribution in the focal region of a convergent beam,” Optik,  113, 298–304 (2003).
[Crossref]

2002 (1)

2001 (1)

2000 (2)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[Crossref]

Biss, D. P.

D. P. Biss and T.G. Brown, “Cylindrical vector beam focusing through a dielectric interface: reply to comment,” Opt. Express 92, 970–971 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-970
[Crossref]

D. P. Biss and T.G. Brown, “Cylindrical vector beam focusing through a dielectric interface,” Opt. Express 9, 490–497 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-10-490
[Crossref] [PubMed]

Braat, J.J.M.

Brown, T.G.

Cooper, I. J.

I. J. Cooper and C.J.R. Sheppard, “A matrix method for calculating the three-dimensional irradiance distribution in the focal region of a convergent beam,” Optik,  113, 298–304 (2003).
[Crossref]

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]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Hayazawa, N.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhance Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

Kawata, S.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhance Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

Leger, J.R.

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]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Munro, P.R.T.

Pereira, S.F.

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]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[Crossref]

Saito, Y.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhance Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

Sheppard, C.J.R.

I. J. Cooper and C.J.R. Sheppard, “A matrix method for calculating the three-dimensional irradiance distribution in the focal region of a convergent beam,” Optik,  113, 298–304 (2003).
[Crossref]

Török, P.

van de Nes, A.S.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[Crossref]

Youngsworth, K.S.

Zhan, Q.

Appl. Phys. Lett. (1)

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhance Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

Opt. Commun. (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Opt. Express (5)

Optik (1)

I. J. Cooper and C.J.R. Sheppard, “A matrix method for calculating the three-dimensional irradiance distribution in the focal region of a convergent beam,” Optik,  113, 298–304 (2003).
[Crossref]

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]

Proc. Roy. Soc. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. 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.

Irradiance distribution (dB) in the focal (XY) plane for a beam linearly polarized in the X direction. (a) X component, (b) Y component, (c) Z component and (d) total irradiance.

Fig. 2.
Fig. 2.

The irradiance (dB) in the focal plane for a pseudoradial polarized beam. (a) Circular aperture and (b) Annular aperture.

Fig. 3.
Fig. 3.

Uniform four quadrant pseudoradial polarizated beam. The total irradiance W and its X, Y and Z components, W x, W y and W z in the radial X direction (a) and axial Z direction (b). The total irradiance W (dB) along a discontinuity (at 45° to the X axis) and along either the X or Y axis (c).

Fig. 4.
Fig. 4.

The full width at half maximum of the total average electric energy density and the longitudinal component (L) measured in wavelength units for circular and annular (A) apertures for the different beams.

Fig. 5.
Fig. 5.

The strength of the first side lobes along the coordinate axes measured in decibels for the circular and annular apertures (A) for the different beams

Metrics