Abstract

The effects of interference between closely packed diffraction orders in the far field are studied for a number of different scalar-domain diffractive optical elements (DOE’s). We demonstrate that there are specific order separations that minimize the observed degradation in the far-field output uniformity. Finally, a DOE that is designed to ensure that the order separation lies near one of these minima is compared with a more general design that produces an equivalent far-field output.

© 1999 Optical Society of America

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References

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  7. A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
    [CrossRef] [PubMed]
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1998 (1)

1997 (1)

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

1996 (2)

1994 (1)

M. R. Taghizadeh, J. M. Miller, P. Blair, F. A. P. Tooley, “Developing diffractive optics for optical computing,” IEEE Micro 14, 10–19 (1994).
[CrossRef]

1992 (2)

1990 (1)

1989 (1)

1972 (1)

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

Baillie, D. A.

Baker, H. J.

P. Blair, D. R. Jones, F. Villareal, A. J. Waddie, N. Ross, M. R. Taghizadeh, H. J. Baker, D. R. Hall, “Transmissive ZnSe diffractive optical elements for high power CO2 material processing applications,” in Technical Digest Conference on Lasers and Electro-Optics/Europe ’98 (IEEE, New York, 1998), p. 318.

Barton, I. M.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

I. M. Barton, “Diffractive optical elements in the scalar domain,” Ph.D. dissertation (Department of Physics, Heriot-Watt University, Edinburgh, UK, 1998).

Beyerlein, M.

Blair, P.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

M. R. Taghizadeh, J. M. Miller, P. Blair, F. A. P. Tooley, “Developing diffractive optics for optical computing,” IEEE Micro 14, 10–19 (1994).
[CrossRef]

P. Blair, D. R. Jones, F. Villareal, A. J. Waddie, N. Ross, M. R. Taghizadeh, H. J. Baker, D. R. Hall, “Transmissive ZnSe diffractive optical elements for high power CO2 material processing applications,” in Technical Digest Conference on Lasers and Electro-Optics/Europe ’98 (IEEE, New York, 1998), p. 318.

P. Blair, “Diffractive optical elements, design and fabrication issues,” Ph.D. dissertation, (Department of Physics, Heriot-Watt University, Edinburgh, UK, 1995).

Buller, G. S.

Desmulliez, M. P. Y.

Dines, J. A. B.

Dresel, T.

Forbes, M. G.

Gerchberg, R. W.

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

Goodman, J. W.

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

Gourlay, J.

Hall, D. R.

P. Blair, D. R. Jones, F. Villareal, A. J. Waddie, N. Ross, M. R. Taghizadeh, H. J. Baker, D. R. Hall, “Transmissive ZnSe diffractive optical elements for high power CO2 material processing applications,” in Technical Digest Conference on Lasers and Electro-Optics/Europe ’98 (IEEE, New York, 1998), p. 318.

Ichikawa, H.

Jaakkola, T.

Jones, D. R.

P. Blair, D. R. Jones, F. Villareal, A. J. Waddie, N. Ross, M. R. Taghizadeh, H. J. Baker, D. R. Hall, “Transmissive ZnSe diffractive optical elements for high power CO2 material processing applications,” in Technical Digest Conference on Lasers and Electro-Optics/Europe ’98 (IEEE, New York, 1998), p. 318.

Kuisma, S.

Layet, B.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

B. Layet, M. R. Taghizadeh, “Analysis of gratings with large periods and small feature sizes by stitching of the electromagnetic field,” Opt. Lett. 21, 1508–1510 (1996).
[CrossRef] [PubMed]

Mait, J. N.

Miller, J. M.

Neilson, D. T.

Noponen, E.

Pottier, F.

Prince, S. M.

Ross, N.

P. Blair, D. R. Jones, F. Villareal, A. J. Waddie, N. Ross, M. R. Taghizadeh, H. J. Baker, D. R. Hall, “Transmissive ZnSe diffractive optical elements for high power CO2 material processing applications,” in Technical Digest Conference on Lasers and Electro-Optics/Europe ’98 (IEEE, New York, 1998), p. 318.

Saxton, W. O.

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

Schwider, J.

Sibbett, W.

Smith, G. R.

Stanley, C. R.

Taghizadeh, M. R.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

B. Layet, M. R. Taghizadeh, “Analysis of gratings with large periods and small feature sizes by stitching of the electromagnetic field,” Opt. Lett. 21, 1508–1510 (1996).
[CrossRef] [PubMed]

M. R. Taghizadeh, J. M. Miller, P. Blair, F. A. P. Tooley, “Developing diffractive optics for optical computing,” IEEE Micro 14, 10–19 (1994).
[CrossRef]

M. R. Taghizadeh, J. Turunen, “Synthetic diffractive elements for optical interconnection,” Opt. Comput. Process. 2, 221–242 (1992).

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
[CrossRef] [PubMed]

P. Blair, D. R. Jones, F. Villareal, A. J. Waddie, N. Ross, M. R. Taghizadeh, H. J. Baker, D. R. Hall, “Transmissive ZnSe diffractive optical elements for high power CO2 material processing applications,” in Technical Digest Conference on Lasers and Electro-Optics/Europe ’98 (IEEE, New York, 1998), p. 318.

Tagizadeh, M. R.

Tooley, F. A. P.

M. R. Taghizadeh, J. M. Miller, P. Blair, F. A. P. Tooley, “Developing diffractive optics for optical computing,” IEEE Micro 14, 10–19 (1994).
[CrossRef]

Turunen, J.

Underwood, I.

Vasara, A.

Villareal, F.

P. Blair, D. R. Jones, F. Villareal, A. J. Waddie, N. Ross, M. R. Taghizadeh, H. J. Baker, D. R. Hall, “Transmissive ZnSe diffractive optical elements for high power CO2 material processing applications,” in Technical Digest Conference on Lasers and Electro-Optics/Europe ’98 (IEEE, New York, 1998), p. 318.

Vögele, B.

Waddie, A.

Waddie, A. J.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

P. Blair, D. R. Jones, F. Villareal, A. J. Waddie, N. Ross, M. R. Taghizadeh, H. J. Baker, D. R. Hall, “Transmissive ZnSe diffractive optical elements for high power CO2 material processing applications,” in Technical Digest Conference on Lasers and Electro-Optics/Europe ’98 (IEEE, New York, 1998), p. 318.

Walker, A. C.

Westerholm, J.

Wilkinson, L. C.

Williams, R.

Wyrowski, F.

Yang, T.-Y.

Appl. Opt. (4)

IEEE Micro (1)

M. R. Taghizadeh, J. M. Miller, P. Blair, F. A. P. Tooley, “Developing diffractive optics for optical computing,” IEEE Micro 14, 10–19 (1994).
[CrossRef]

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

Microelectron. Eng. (1)

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

Opt. Comput. Process. (1)

M. R. Taghizadeh, J. Turunen, “Synthetic diffractive elements for optical interconnection,” Opt. Comput. Process. 2, 221–242 (1992).

Opt. Lett. (1)

Optik (1)

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

Other (4)

P. Blair, D. R. Jones, F. Villareal, A. J. Waddie, N. Ross, M. R. Taghizadeh, H. J. Baker, D. R. Hall, “Transmissive ZnSe diffractive optical elements for high power CO2 material processing applications,” in Technical Digest Conference on Lasers and Electro-Optics/Europe ’98 (IEEE, New York, 1998), p. 318.

P. Blair, “Diffractive optical elements, design and fabrication issues,” Ph.D. dissertation, (Department of Physics, Heriot-Watt University, Edinburgh, UK, 1995).

I. M. Barton, “Diffractive optical elements in the scalar domain,” Ph.D. dissertation (Department of Physics, Heriot-Watt University, Edinburgh, UK, 1998).

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

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of the DOE imaging system showing the parameters used throughout this paper. (b) Far-field intensity distribution of a single diffracted spot. σ is the diffraction-limited spot size.

Fig. 2
Fig. 2

Section of output from a 1 × 100 fan-out element of period 8.4 mm. The beam diameters used were 10, 12.5, and 15 mm, yielding spot separations of 0.97σ, 1.22σ, and 1.47σ, respectively.

Fig. 3
Fig. 3

Interference between two equally bright spots for different relative phases.

Fig. 4
Fig. 4

Maximum variation in beam intensity with relative order separation for the 2-D nearest-neighbor and 1-D three-order cases.

Fig. 5
Fig. 5

Variation in DOE nonuniformity with relative order separation for three different beam-shaping elements.

Fig. 6
Fig. 6

Comparison between annular flattop beam-shaping elements with output from the grating when interference effects are ignored and output when they are included.

Tables (1)

Tables Icon

Table 1 DOE used in the Uniformity Study

Equations (10)

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px, y=A expj πx2+y2λfjλf-  Pu, v × exp-j 2πλfux+yvdudv,
Pu, v=expj2πndu, v/λ,
ΔR=maxm,n1-ImnaImnt,
Sab=fλaT2-aλ21/2-bT2-bλ21/2,
Sab=fλTa-b.
Smanb=fλTm-a2+n-b21/2.
σR=fλ/T1.22fλ/D=D1.22T.
Ix=2 J1πx-x0/σπx-x0/σ+expjϕ2 J1πx-x1/σπx-x1/σ2,
Imn=j=m-1m+1k=n-1n+1 2ηjkJ1πm-j2+n-k21/2σRπm-j2+n-k21/2σR×expjθjk-θmn2,
σRj=j+0.229,

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