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Limits of scalar diffraction theory and an iterative angular spectrum algorithm for finite aperture diffractive optical element design

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Abstract

We have designed high-efficiency finite-aperture diffractive optical elements (DOE’s) with features on the order of or smaller than the wavelength of the incident illumination. The use of scalar diffraction theory is generally not considered valid for the design of DOE’s with such features. However, we have found several cases in which the use of a scalar-based design is, in fact, quite accurate. We also present a modified scalar-based iterative design method that incorporates the angular spectrum approach to design diffractive optical elements that operate in the near-field and have sub-wavelength features. We call this design method the iterative angular spectrum approach (IASA). Upon comparison with a rigorous electromagnetic analysis technique, specifically, the finite difference time-domain method (FDTD), we find that our scalar-based design method is surprisingly valid for DOE’s having sub-wavelength features.

©2001 Optical Society of America

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Figures (11)

Fig. 1.
Fig. 1. Diffractive optic geometry
Fig. 2.
Fig. 2. Heuristically designed DOE profiles
Fig. 3.
Fig. 3. Irradiance profiles for heuristically designed DOE profiles
Fig. 4.
Fig. 4. Total field amplitudes for heuristic gratings
Fig. 5.
Fig. 5. Total field phases for heuristic gratings
Fig. 6.
Fig. 6. Angular spectrum magnitudes for heuristic gratings just past DOE
Fig. 7.
Fig. 7. Propagating field amplitudes for heuristic gratings just past DOE
Fig. 8.
Fig. 8. Propagating field phases for heuristic gratings just past DOE
Fig. 9.
Fig. 9. IASA DOE profiles
Fig. 10.
Fig. 10. Irradiances for IASA profiles
Fig. 11.
Fig. 11. IASA: multiple peak beamfanners

Tables (3)

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Table 1. Diffraction efficiencies and errors for heuristically designed 1–2 beamfanners

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Table 2. Diffraction efficiencies and errors for 1-2 beamfanners designed via IASA

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Table 3. Diffraction efficiencies and errors for 1–3 and 1–4 beamfanners

Equations (3)

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η = apertures Idx all space Idx
Error s = η TE or TM η scalar η scalar
TE / TM difference = η TM η TE η TE
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