Abstract

A rigorous electromagnetic algorithm is presented for the analysis of electrically large diffractive optical elements (DOE's), i.e., those that contain small features and have large apertures compared with the wavelength of illumination. The technique uses a finite-sized analysis window within which a rigorous electromagnetic technique is used to solve the local boundary-value problem. To this end the boundary-element and finite-difference time-domain methods are used. The analysis window is translated over the entire surface of the DOE and stitches together the complete solution. We validate the techniques by comparing the stitched boundary fields with those of a complete analysis, in both magnitude and phase, for a binary lens. To illustrate the utility of our method we analyzed an eight-level diffractive lens with a 10,000-wavelength diameter sampled at 0.05 wavelength that required 8  Mbytes of memory on a desktop personal computer.

© 1999 Optical Society of America

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References

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    [CrossRef]
  4. S. Shi and D. W. Prather, “Application of an efficient FDTD-based algorithm to the analysis of diffractive optical elements,” submitted to Opt. Eng.
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    [CrossRef]
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    [CrossRef] [PubMed]
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1997

1996

1994

1993

Gallagher, N. C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Grann, E. B.

Gremaux, D. A.

Layet, B.

Mait, J. N.

Mirotznik, M. S.

Moharam, M. G.

Pommet, D. A.

Prather, D. W.

D. W. Prather, M. S. Mirotznik, and J. N. Mait, J. Opt. Soc. Am. A 14, 34 (1997).
[CrossRef]

S. Shi and D. W. Prather, “Application of an efficient FDTD-based algorithm to the analysis of diffractive optical elements,” submitted to Opt. Eng.

D. W. Prather and S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A (to be published).

Shi, S.

D. W. Prather and S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A (to be published).

S. Shi and D. W. Prather, “Application of an efficient FDTD-based algorithm to the analysis of diffractive optical elements,” submitted to Opt. Eng.

Taghizadeh, M. R.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Lett.

Other

S. Shi and D. W. Prather, “Application of an efficient FDTD-based algorithm to the analysis of diffractive optical elements,” submitted to Opt. Eng.

D. W. Prather and S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A (to be published).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (3)

Fig. 1
Fig. 1

Quantification of local coupling effects: (a) complete and segmented analysis of a binary diffractive lens, (b) error plots between complete and segmented boundary fields.

Fig. 2
Fig. 2

Illustration of the field stitching algorithm by translating an analysis window, which consists of a region of interest centered about two coupling regions, over the DOE surface.

Fig. 3
Fig. 3

Validation of the field stitching algorithm by overlaying the complete and stitched analysis for the electric-field (a) magnitude, (b) phase, and (c) line scans in the focal plane.

Tables (1)

Tables Icon

Table 1 Results from Analysis of Electrically Large Diffractive Lenses

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