Abstract

The intensity distributions near the focal point for radially polarized laser beams including higher-order transverse modes are calculated based on vector diffraction theory. For higher-order radially polarized mode beams as well as a fundamental mode (R-TEM01*) beam, the strong longitudinal component forms a sharper spot at the focal point under a high-NA focusing condition. In particular, double-ring-shaped radially polarized mode (R-TEM11*) beams can effectively reduce the focal spot size because of destructive interference between the inner and the outer rings with π phase shift. Compared with an R-TEM01* beam focusing in a limit of NA=1, the full width at half-maximum values of the focal spot for an R-TEM11* beam are decreased by 13.6% for the longitudinal component and 25.8% for the total intensity.

© 2007 Optical Society of America

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2006 (4)

2005 (2)

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

Y. Kozawa and S. Sato, "Generation of a radially polarized laser beam by use of a conical Brewster prism," Opt. Lett. 30, 3063-3065 (2005).
[CrossRef] [PubMed]

2004 (2)

2003 (1)

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

2001 (1)

L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens systems," Opt. Commun. 191, 161-172 (2001).
[CrossRef]

2000 (4)

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

J. Arlt and M. J. Padgett, "Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam," Opt. Lett. 25, 191-193 (2000).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöcke, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

1999 (1)

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

1998 (1)

1997 (1)

1993 (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 253, 358-379 (1959).
[CrossRef]

Ahmed, M. A.

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

Arlt, J.

Brown, T. G.

Chang, R. S.

Choudhury, A.

Clark, G. H.

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. Glöcke, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöcke, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Glöcke, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöcke, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Glur, H.

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

Graf, T.

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

Helseth, L. E.

L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens systems," Opt. Commun. 191, 161-172 (2001).
[CrossRef]

Kim, G. H.

Kimura, W. D.

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]

S. Quabis, R. Dorn, M. Eberler, O. Glöcke, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Moser, T.

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

Nesterov, A. V.

V. G. Niziev, R. S. Chang, and A. V. Nesterov, "Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer," Appl. Opt. 45, 8393-8399 (2006).
[CrossRef] [PubMed]

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

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

Niziev, V. G.

V. G. Niziev, R. S. Chang, and A. V. Nesterov, "Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer," Appl. Opt. 45, 8393-8399 (2006).
[CrossRef] [PubMed]

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

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

Padgett, M. J.

Parriaux, O.

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

Pigeon, F.

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

S. Quabis, R. Dorn, M. Eberler, O. Glöcke, and G. Leuchs, "Focusing light to 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. R. Soc. London 253, 358-379 (1959).
[CrossRef]

Romano, V.

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

Sato, S.

Sheppard, C. J. R.

Tidwell, S. C.

Tovar, A. A.

Wolf, E.

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

Yonezawa, K.

Youngworth, K. S.

Zhan, Q.

Appl. Opt. (3)

Appl. Phys. B (1)

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

J. Opt. Soc. Am. A (2)

J. Phys. D (2)

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

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

Opt. Commun. (2)

L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens systems," Opt. Commun. 191, 161-172 (2001).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöcke, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

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. R. Soc. London (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 253, 358-379 (1959).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Bottom, theoretical intensity distributions of radially polarized TEM 01 * , TEM 11 * , TEM 21 * modes. Top, corresponding instantaneous polarization states.

Fig. 2
Fig. 2

Calculated intensity profiles near the focal point ( z = 0 ) for the focusing of (a) R - TEM 01 * , (b) R - TEM 11 * , (c) R - TEM 21 * , (d) R - TEM 51 * modes, with a NA of 1. The total intensity (solid curves), the longitudinal component (dashed curves), and the radial component (dotted curves) are drawn in each figure. Every profile is normalized to the peak intensity in (a). The horizontal axis is in units of wavelength.

Fig. 3
Fig. 3

Intensity profiles of (a) longitudinal components and (b) total intensity in the focal plane for different transverse modes. The peak intensity for each mode is normalized to 1.

Fig. 4
Fig. 4

Calculated intensity profiles of the longitudinal component along the z axis for R - TEM 01 * , R - TEM 11 * , R - TEM 21 * , R - TEM 51 * mode focusing. The peak intensity for each mode is normalized to 1.

Fig. 5
Fig. 5

Peak intensity of the longitudinal component ( E z 2 ) at the focal point plotted against the beam width parameter β 0 for R - TEM 01 * (dashed curve) and R - TEM 11 * (solid curve) mode focusing. (b) FWHM variation of the focal spot corresponding to (a). The FWHM value is in units of wavelength.

Fig. 6
Fig. 6

Calculated intensity profiles near the focal point ( z = 0 ) of R - TEM 11 * mode focusing for β 0 = (a) 4.0, (b) 3.0, (c) 1.926, (d) 1.5, (e) 1.258, (f) 1.2 with a NA = 1 . The total intensity (solid curves), the longitudinal component (dashed curves), and the radial component (dotted curves) are drawn in each figure. Every profile is normalized to the peak intensity in (c). The horizontal axis is in units of wavelength.

Tables (1)

Tables Icon

Table 1 FWHM ( λ 1 ) of the Focal Spot for High-NA Focusing a

Equations (3)

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E r ( r , ϕ , z ) = A 0 θ max 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 z ( r , ϕ , z ) = 2 i A 0 θ max cos 1 2 ( θ ) sin 2 ( θ ) l 0 ( θ ) J 0 ( k r sin θ ) exp ( i k z cos θ ) d θ ,
l 0 ( θ ) = β 0 2 sin θ sin 2 θ max exp ( β 0 2 sin 2 θ sin 2 θ max ) L p 1 ( 2 β 0 2 sin 2 θ sin 2 θ max ) ,

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