An analytic method of spatial phase modulation based on Fourier analysis is introduced for the design of a planar waveguide demultiplexer with a flat-top spectral response. An analytic formula for an etched diffraction grating demultiplexer is derived using the scalar diffraction theory. The spatial phase modulation is realized by slightly adjusting each grating facet's position according to the analytic formula to obtain a spectral response with a flat top and sharp transitions as well as a good dispersion characteristic. The analytic formula is characterized by two parameters: a transverse shift distance and a profile exponent for the phase modulation. A linear relation between the passband width and the transverse shift distance is given, and an optimal figure of merit of the spectral response is obtained by choosing an appropriate profile exponent. A numerical example of a typical SiO 2 etched diffraction grating demultiplexer is used to demonstrate the advantages of this method.
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