Abstract

We present a design method based on the Gerchberg-Saxton algorithm for the design of high-performance diffractive optical elements. Results from this algorithm are compared with results from simulated annealing and the iterative Fourier-transform algorithm. The element performance is comparable with those designed by simulated annealing, whereas the design time is similar to the iterative Fourier-transform method. Finally, we present results for a demanding beam-shaping task that was beyond the capabilities of either of the traditional algorithms. The element performances demonstrate greater than 85% efficiency and less than 2% uniformity error.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2003 (1)

M. J. Thomson, M. R. Taghizadeh, “Diffractive elements for high power fibre coupling applications,” J. Mod. Opt. 50, 1691–1699 (2003).

2002 (1)

2000 (1)

P. Birch, R. Young, M. Farsari, C. Chatwin, S. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

1999 (1)

1995 (1)

1993 (1)

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

1992 (1)

1990 (1)

1989 (1)

1988 (1)

1983 (1)

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

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Abushagar, M. A. G.

Birch, P.

P. Birch, R. Young, M. Farsari, C. Chatwin, S. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

Brigham, E. O.

E. O. Brigham, Fast Fourier Transform and Its Applications (Prentice-Hall, Englewood Cliffs, N.J., 1988).

Bryngdahl, O.

Budgett, S.

P. Birch, R. Young, M. Farsari, C. Chatwin, S. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

Chatwin, C.

P. Birch, R. Young, M. Farsari, C. Chatwin, S. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

Dandliker, R.

Farsari, M.

P. Birch, R. Young, M. Farsari, C. Chatwin, S. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

Gale, M. T.

Gelatt, C. D.

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

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

Herzig, H. P.

Johnson, E. G.

Kirkpatrick, S.

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

Liu, J. S.

Miller, J. M.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

Noponen, E.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

Prongué, D.

Ross, N.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Taghizadeh, M. R.

M. J. Thomson, M. R. Taghizadeh, “Diffractive elements for high power fibre coupling applications,” J. Mod. Opt. 50, 1691–1699 (2003).

J. S. Liu, M. R. Taghizadeh, “Iterative algorithm for the design of diffractive phase elements for laser beam shaping,” Opt. Lett. 27, 1463–1465 (2002).
[CrossRef]

A. J. Waddie, M. R. Taghizadeh, “Interference effects in far-field diffractive optical elements,” Appl. Opt. 38, 5915–5919 (1999).
[CrossRef]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

Thomson, M. J.

M. J. Thomson, M. R. Taghizadeh, “Diffractive elements for high power fibre coupling applications,” J. Mod. Opt. 50, 1691–1699 (2003).

Turunen, J.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

Vasara, A.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

Vecchi, M. P.

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

Waddie, A. J.

Wyrowski, F.

Young, R.

P. Birch, R. Young, M. Farsari, C. Chatwin, S. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

Appl. Opt. (3)

J. Mod. Opt. (2)

M. J. Thomson, M. R. Taghizadeh, “Diffractive elements for high power fibre coupling applications,” J. Mod. Opt. 50, 1691–1699 (2003).

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Lasers Eng. (1)

P. Birch, R. Young, M. Farsari, C. Chatwin, S. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33, 439–448 (2000).
[CrossRef]

Opt. Lett. (1)

Optik (Stuttgart) (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Science (1)

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

Other (2)

E. O. Brigham, Fast Fourier Transform and Its Applications (Prentice-Hall, Englewood Cliffs, N.J., 1988).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the GS algorithm.

Fig. 2
Fig. 2

Illustration of the principle of the modification: (a) shows G(u, v), the output from the previous iteration; (b) shows F(u, v), the modified constraint; (c) shows T(u, v), the desired output. It can clearly be seen that the modified constraint is a mirror image of the output from the previous iteration about the desired output.

Fig. 3
Fig. 3

White on black image of the Heriot-Watt University crest. In the design, the white areas are the desired on diffraction orders.

Fig. 4
Fig. 4

Geometry of the connector used for the eight- and ten-way fan-outs. Situated at the center of each connector site are 400-μm core fibers.

Fig. 5
Fig. 5

Simulated performance of the eight-way fan-out.

Fig. 6
Fig. 6

Simulated performance of the ten-way fan-out.

Tables (1)

Tables Icon

Table 1 Comparison of Design Algorithms

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

P=exp-ΔET,
Fmodu, v=Tu, v+c1Tu, v-Gu, v
Fmodu, v=Tu, vTu, vGu, vc2,
η= Gu, v.
ΔR=max1-Gu, vTu, v.

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