Abstract

Spatial engineering of polarization is proposed as a novel method of beam shaping. It is shown that a flat-top-shaped focus can be obtained in the far field by changing the polarization in the pupil plane in a spatially inhomogeneous manner. Experiments have been carried out to verify the validity of this method in one dimension. By comparison with traditional beam shaping methods, polarization beam shaping yields the smallest flat-top focus while maintaining high efficiency.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [PubMed]
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    [CrossRef] [PubMed]
  10. 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]
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    [CrossRef]
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  14. L. A. Romero and F. M. Dickey, "Lossless laser beam shaping," Appl. Opt. 13, 751-760 (1996).

2002

2000

S. Quabis, R. Dorn, M. Eberler, O. Glckl, 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]

1996

L. A. Romero and F. M. Dickey, "Lossless laser beam shaping," Appl. Opt. 13, 751-760 (1996).

1995

1983

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

1981

1978

W. Lee, "Computer-generated holograms: techniques and applications," Prog. Opt. 16, 119-232 (1978).
[CrossRef]

1959

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.

Opt. Commun.

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

Opt. Express

Proc. R. Soc. London Ser. A

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]

Prog. Opt.

W. Lee, "Computer-generated holograms: techniques and applications," Prog. Opt. 16, 119-232 (1978).
[CrossRef]

Science

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Other

A. K. Spilman and T. G. Brown, "Stress birefringent, space-variant wave plates for vortex illumination," Appl. Opt. 46, 61-66 (2007).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2004).

F. M. Dickey and S. C. Holswade, eds., Laser Beam Shaping-Theory and Techniques (Marcel Dekker, 2000).
[CrossRef]

D. Shealy, "Geometrical methods," Chap. 4, in Ref.[1].

D. M. Brown, F. M. Dickey, and L. S. Weichman, "Multi-aperture beam integration systems," Chap. 7, in Ref. [1].

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Figures (11)

Fig. 1
Fig. 1

(Color online) Simulated annealing result for a one-dimensional polarization plate. The inset shows a visualization of the one-dimensional polarization plate.

Fig. 2
Fig. 2

(Color online) Intensity distribution in the focal plane for the one-dimensional polarization plate.

Fig. 3
Fig. 3

Computer generated hologram for x and y channels. The two channels need to be illuminated by orthogonally polarized light.

Fig. 4
Fig. 4

(Color online) Experimental setup for beam shaping using a one-dimensional polarization plate.

Fig. 5
Fig. 5

(Color online) Experimental result of beam shaping using a one-dimensional polarization plate. The polarization plate is realized using computer generated holograms. (a) Intensity distribution along the beam shaping direction, compared with theory. (b) Intensity distribution along orthogonal direction, with no beam shaping.

Fig. 6
Fig. 6

(Color online) Three-segment polarization plate.

Fig. 7
Fig. 7

(Color online) Comparison of focal pattern from the three-segment polarization plate and the continuous polarization plate.

Fig. 8
Fig. 8

(Color online) Experimental result of beam shaping using a three-segment one-dimensional polarization plate. (a) Experimental intensity distribution measured along the beam shaping direction, compared with theory. (b) Experimental intensity distribution measured along orthogonal direction, no beam shaping.

Fig. 9
Fig. 9

(Color online) Strehl ratio degradation versus defocusing. Solid curve shows linearly polarized plane wave incidence, the dashed curve shows polarization beam shaping.

Fig. 10
Fig. 10

(Color online) Polarization state along the flat-top pattern in the focal plane: (a) flat-top pattern obtained using the one-dimensional polarization plate and the five sample points; (b) the polarization state of the five points.

Fig. 11
Fig. 11

(Color online) Beam shaping on a Gaussian laser beam using a one-dimensional polarization plate: (a) the designed polarization plate and comparison with that for uniform illumination; (b) the flat-top focal spot. The inset shows the profile of the Gaussian incident beam.

Equations (1)

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β = 2 2 π r 0 y 0 λ f ,

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