Design scheme for Mach-Zehnder interferometric coarse wavelength division multiplexing splitters and combiners

I propose an analytical approach to design flattened wavelength splitters with cascaded Mach-Zehnder interferometers when wavelength dependence of the directional couplers cannot be neglected. I start from a geometrical representation of the action of a doubly point-symmetrical filter, assuming no wavelength dependence of the couplers. Next I derive the analytical formulas behind its working principle and extend them to the wavelength-dependent case. I also show how the geometrical representation allows one to broaden the class of working structures.