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A three-focal-point method is introduced for an optimal design of a planar waveguide demultiplexer with a flattened spectral response. The grating in an etched diffraction grating demultiplexer is divided into three interleaved subgratings with some appropriate ratio of the facet numbers of the subgratings. With a Gaussian approximation, an analytical formula is derived for the optimal condition for minimal ripple in the flat-top spectral response. A required passband width determines the separation between the peaks of the two outmost subimages, which then determines the optimal ratio of the facet numbers of the subgratings according to the derived analytical formula. The present method is illustrated and verified with a design example. The ripple for the designed flat-top demultiplexer is suppressed greatly by controlling appropriately the facet numbers of the three subgratings according to the present analytical formula.
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Shi et al. (2002) studied this question.
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