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A rigorous unidirectional method for designing finite aperture diffractive optical elements

Jianhua Jiang and Gregory P. Nordin

Open Access Open Access

Abstract

We have developed a rigorous unidirectional method for designing finite-aperture diffractive optical elements (DOE’s) that employs a micro-genetic algorithm (µGA) for global optimization in conjunction with a 2-D Finite-Difference Time-Domain (FDTD) method for rigorous electromagnetic computation. The theory and implementation of this µGA-FDTD design method for normally incident TE illumination are briefly discussed. Design examples are presented, including a micro-lens, a 1-to-2 beam-fanner and a 1-to-3 beam-fanner.

©2000 Optical Society of America

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Figures (5)
Fig. 1.
Fig. 1. Schematic diagram of the 2-D FDTD geometry showing TE polarization definition

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Fig. 2.
Fig. 2. Design geometry for the numerical design examples

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Fig. 3.
Fig. 3. Microlens test case for µGA-FDTD Design tool with field distribution of analytical profile as target function (a) µGA convergence curve, (b) field distributions of both analytical and optimized profiles, and (c) the analytical and optimized microlens profiles.

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Fig. 4.
Fig. 4. Two µGA-FDTD optimized DOE profiles for 1-to-2 beamfanner with 25µm peak separation (a) Optimized DOE profiles and (b) their corresponding field distribution.

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Fig. 5.
Fig. 5. Optimized wide-angle 1-to-3 beamfanner with 50um peak separartions (a) Optimized DOE profile and (b) its field distribution

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Equations (2)

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f = ∑ i = 1 L ∣ ∣ E ( x i ) ∣ 2 − ∣ E analy ( x i ) ∣ 2 ∣ ,
f = ∑ i = 1 L ∣ E ( x i ) ∣ · [ exp ( − ( x i − 12.5 ) 2 2 σ 2 ) + exp ( − ( x i + 12.5 ) 2 2 σ 2 ) − 5 ( 1 − rect ( x i 40 ) ) ]
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