Abstract

A new scheme for converting a Gaussian irradiance profile beam on the input plane into a uniform irradiance profile beam on the output plane is presented based on polarization-selective diffractive phase elements. The relevant elements were designed by use of the simulated annealing method. The simulation design shows that the shaping quality is substantially improved and is much better than that obtained with traditional diffractive phase elements.

© 2000 Optical Society of America

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References

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1999 (1)

J. Liu, B. Dong, B. Gu, G. Yang, “Generation of polarized patterns with the use of polarization-selective diffractive phase elements,” Optik 110, 335–339 (1999).

1998 (2)

1996 (2)

1995 (7)

1994 (1)

1993 (3)

J. E. Ford, F. Xu, K. Urquhart, Y. Fainman, “Polarization-selective computer-generated holograms,” Opt. Lett. 18, 456–458 (1993).
[CrossRef] [PubMed]

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Streibl, J. Lindolf, M. Collischon, A. Lang, J. Hutfless, “Polarizing reflection grating beamsplitter for the 10.6-µm wavelength,” Opt. Eng. 32, 1860–1865 (1993).
[CrossRef]

J. Cordingley, “Application of a binary diffractive optic for beam shaping in semiconductor processing by lasers,” Appl. Opt. 32, 2538–2542 (1993).
[CrossRef] [PubMed]

1991 (1)

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian into a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

1989 (1)

1983 (2)

1982 (1)

1981 (1)

Aleksoff, C. C.

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian into a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

Bräuer, R.

Bryngdahl, O.

Cederquist, J. N.

Chang, Y. H.

Chen, N.

Cheng, C. C.

Collischon, M.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Streibl, J. Lindolf, M. Collischon, A. Lang, J. Hutfless, “Polarizing reflection grating beamsplitter for the 10.6-µm wavelength,” Opt. Eng. 32, 1860–1865 (1993).
[CrossRef]

Cong, W.

Cordingley, J.

de Frutos, A. M.

Depine, R. A.

Dong, B.

Eismann, M. T.

Ellis, K. K.

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian into a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

Fainman, Y.

Ford, J. E.

Gelatt, C. D.

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

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), Chap. 4, pp. 57–61.

Gu, B.

Haidner, H.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Streibl, J. Lindolf, M. Collischon, A. Lang, J. Hutfless, “Polarizing reflection grating beamsplitter for the 10.6-µm wavelength,” Opt. Eng. 32, 1860–1865 (1993).
[CrossRef]

Harris, J. B.

Hutfless, J.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Streibl, J. Lindolf, M. Collischon, A. Lang, J. Hutfless, “Polarizing reflection grating beamsplitter for the 10.6-µm wavelength,” Opt. Eng. 32, 1860–1865 (1993).
[CrossRef]

Inchaussandague, M. E.

Kastner, C. J.

Kazumi, M.

Kipfer, P.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Streibl, J. Lindolf, M. Collischon, A. Lang, J. Hutfless, “Polarizing reflection grating beamsplitter for the 10.6-µm wavelength,” Opt. Eng. 32, 1860–1865 (1993).
[CrossRef]

Kirkpatrick, S.

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

Lang, A.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Streibl, J. Lindolf, M. Collischon, A. Lang, J. Hutfless, “Polarizing reflection grating beamsplitter for the 10.6-µm wavelength,” Opt. Eng. 32, 1860–1865 (1993).
[CrossRef]

Lindolf, J.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Streibl, J. Lindolf, M. Collischon, A. Lang, J. Hutfless, “Polarizing reflection grating beamsplitter for the 10.6-µm wavelength,” Opt. Eng. 32, 1860–1865 (1993).
[CrossRef]

Liu, J.

J. Liu, B. Dong, B. Gu, G. Yang, “Generation of polarized patterns with the use of polarization-selective diffractive phase elements,” Optik 110, 335–339 (1999).

Neagle, B. D.

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian into a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

Preist, T. W.

Quintanilla, M.

Richter, I.

Sambles, J. R.

Scherer, A.

Schmitz, M.

Schwider, J.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Streibl, J. Lindolf, M. Collischon, A. Lang, J. Hutfless, “Polarizing reflection grating beamsplitter for the 10.6-µm wavelength,” Opt. Eng. 32, 1860–1865 (1993).
[CrossRef]

Sheridan, J. T.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Streibl, J. Lindolf, M. Collischon, A. Lang, J. Hutfless, “Polarizing reflection grating beamsplitter for the 10.6-µm wavelength,” Opt. Eng. 32, 1860–1865 (1993).
[CrossRef]

Streibl, N.

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Streibl, J. Lindolf, M. Collischon, A. Lang, J. Hutfless, “Polarizing reflection grating beamsplitter for the 10.6-µm wavelength,” Opt. Eng. 32, 1860–1865 (1993).
[CrossRef]

Sun, P. C.

Tai, A. M.

Tan, X.

Tyan, R. C.

Urquhart, K.

Vecchi, M. P.

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

Veldkamp, W. B.

Xu, F.

Yang, G.

Yukihire, I.

Zhang, Y.

Appl. Opt. (9)

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

Opt. Eng. (2)

H. Haidner, P. Kipfer, J. T. Sheridan, J. Schwider, N. Streibl, J. Lindolf, M. Collischon, A. Lang, J. Hutfless, “Polarizing reflection grating beamsplitter for the 10.6-µm wavelength,” Opt. Eng. 32, 1860–1865 (1993).
[CrossRef]

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian into a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

Opt. Lett. (5)

Optik (1)

J. Liu, B. Dong, B. Gu, G. Yang, “Generation of polarized patterns with the use of polarization-selective diffractive phase elements,” Optik 110, 335–339 (1999).

Science (1)

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

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), Chap. 4, pp. 57–61.

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Figures (3)

Fig. 1
Fig. 1

Schematic view of a beam-shaping system composed of PDPE’s.

Fig. 2
Fig. 2

Distribution of the surface-relief depth for (a) PDPE1 to convert a Gaussian-profile beam into a uniform-profile beam and (b) PDPE2 to compensate the phase of the output beam into a constant phase.

Fig. 3
Fig. 3

Output intensity distribution of (a) the o ray and (b) the e ray. (c) The dashed curve represents the ideal intensity distribution of the desired beam, and the solid curve represents the output intensity distribution generated by our newly designed PDPE. (d) The dotted curve represents the intensity distribution of the incident beam with a one-dimensional Gaussian profile, and the solid curve represents the output intensity distribution generated by a conventional DPE.

Equations (9)

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U1αx1=ρ1 expiϕ1α,
U2αx2=ρ2α expiϕ2α.
U2αx2= Gx2, x1U1αx1dx1,
Gx2, x1=1iλl1/2 expi2πl/λexpiπx2-x12/λl.
Iout=|U2o|2+|U2e|2=I2o+I2e,
Iin=ρ12=ρ102 exp-x12/δ2,
ΔE=Iideal2-Iout22,
η=sigIoutdx2Iindx1,
Δξ=<|Iout-Iideal|>sig<Iideal>sig,

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