In the first chapter (WDM Devices — AWG with Flat Response), the reasons for the Flat Response required, cause for Gaussian Passband, and three main passband optimization proposals are introduced in brief. This chapter is about two other passband optimization proposals.
4) Shaping of Phase Transfer Function
Let’s review the proposals of adding MMI at the input and taper at the output. The core feature is to flatten the focused optical field 
or the eigen mode 
of the output waveguide. Thus the correlation function 
between the two optical fields is flattened. Anyway, the correlation between two mismatched optical fields will introduce excess power loss. The more is the mismatch, the more is the power loss. The AWG designers need to balance the passband width and the loss penalty.
Optical Passive Components 