Abstract

We report a focus shaping technique using generalized cylindrical vector beams. A generalized cylindrical vector beam can be decomposed into radially polarized and azimuthally polarized components. Such a generalized cylindrical beam can be generated from a radially polarized or an azimuthally polarized light using a two-half-wave-plate polarization rotator. The intensity pattern at the focus can be tailored by appropriately adjusting the rotation angle. Peak-centered, donut and flattop focal shapes can be obtained using this technique.

© 2002 Optical Society of America

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References

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Appl. Opt. (1)

Qiwen Zhan and James R. Leger, �Microellipsometer with radial symmetry,� submitted to Appl. Opt.

Appl. Phys. B (1)

S. Quabis, R. Dorn, M. Eberler, O. Gl�ckl and G. Leuchs, �The focus of light- theoretical calculation and experimental tomographic reconstruction,� Appl. Phys. B 72, 109-113 (2001).
[CrossRef]

Appl. Phys. Lett. (2)

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

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon and E. Hasman, �The formation of laser beams with pure azimuthal or radial polarization,� Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

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

J. Phys. D (1)

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. (6)

Y. Harada, T. Asakura, �Radiation forces on a dielectric sphere in the Rayleigh scattering regime,� Opt. Commun. 124, 529-541 (1996).

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

R. Oron, N. Davidson, A. A. Friesem and E. Hasman, �Efficient formation of pure helical laser beams,� Opt. Commun. 182, 205-208 (2000).
[CrossRef]

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

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen and J. P. Woerdman, �Astignmatic laser mode converters and transfer of orbital angular momentum,� Opt. Commun. 96, 123-132 (1993).
[CrossRef]

M. W. Beijerbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, �Helical-wavefront laser beam produced with a spiral phaseplate,� Opt. Commun. 112. 321-327 (1994).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. E (1)

B. Hafizi, E. Esarey and P. Sprangle, �Laser-driven acceleration with Bessel beams,� Phys. Rev. E 55, 3539-3545 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu and H. Sasada, �Novel optical trap of atoms with a doughnut beam,� Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg and H. Rubinsztein-Dunlop, �Direct observation of transfer of angular momentum to absorptive particle from a laser beam with a phase singularity,� Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen and M. J. Padgett, �Rotational frequency shift of a light beam,� Phys. Rev. Lett. 81, 4828-4830 (1998).
[CrossRef]

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]

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

E. Wolf, �Electromagnetic diffraction in optical systems I. An integral representation of the image field,� Proc. R. Soc. Ser. A 253, pp. 349-357 (1959).
[CrossRef]

Other (2)

Min Gu (editor), Advanced optical imaging theory, 75 (Springer-Verlag, New York, 1999

K. Schuster, �Radial polarization-rotating optical arrangement and microlithographic projection exposure system incorporating said arrangement,� US patent 6191880 B1 (2001).

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Figures (9)

Fig. 1
Fig. 1

Generalized cylindrical vector beam with ϕ0 rotation from the purely radially polarization.

Fig. 2.
Fig. 2.

A polarization rotator consisting of two half-wave plates. ∆ϕ is the angle between the fast axes of the two half-wave plates.

Fig. 3
Fig. 3

Focusing of a cylindrical vector beam. In the diagram, f is the focal length of the objective lens. Q(r, φ) is an observation point in the focal plane.

Fig.4
Fig.4

Intensity distribution at focal plane for radially polarized beam.

Fig.5
Fig.5

Intensity distribution in the vicinity of focus for radially polarized beam.

Fig.6
Fig.6

Intensity distribution at the focal plane for an azimuthally polarized beam. The focal field only has an azimuthal component. The radial and longitudinal components are zero.

Fig. 7
Fig. 7

Total intensity distributions in the vicinity of focus for azimuthally polarized beam.

Fig.8
Fig.8

Intensity distribution at focal plane for ϕ0=24°. Flattop focus is obtained.

Fig. 9
Fig. 9

Total intensity distribution in the vicinity of focus for ϕ0=24°.

Equations (8)

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E ( r , φ ) = P [ cos ϕ 0 e r + sin ϕ 0 e φ ]
T = ( cos ( 2 Δ ϕ ) sin ( 2 Δ ϕ ) sin ( 2 Δ ϕ ) cos ( 2 Δ ϕ ) ) = R ( 2 Δ ϕ )
E ( r , φ , z ) = E r e r + E z e z + E φ e φ
E r ( r , φ , z ) = A cos ϕ 0 0 θ max cos 1 / 2 ( θ ) P ( θ ) sin θ cos θ J 1 ( k r sin θ ) e i k z cos θ d θ
E z ( r , φ , z ) = i A cos ϕ 0 0 θ max cos 1 / 2 ( θ ) P ( θ ) sin 2 θ J 0 ( k r sin θ ) e i k z cos θ d θ
E φ ( r , φ , z ) = A sin ϕ 0 0 θ max cos 1 / 2 ( θ ) P ( θ ) J 1 ( k r sin θ ) e i k z cos θ d θ
P ( θ ) = { 1 if sin 1 ( 0.1 ) θ sin 1 ( NA ) 0 otherwise
F = 2 π R 3 ε 1 c ( ε 2 ε 1 ε 2 + 2 ε 1 ) I

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