Here is link to an online course on advanced electromagnetics that includes videos, notes, and other resources:
http://emlab.utep.edu/ee5390em21.htm
Lectures 7 and 8 cover periodic structures, theory of band diagrams, and how to construct them. For more detail on the specifics of the numerical methods, see the Computational Electromagnetics course at http://emlab.utep.edu/ee5390cem.htm. This is specifically discussed in the Plane Wave Expansion Method lectures. There is also Lecture 14 on photonic crystals in the first course. From all of this, you should be on your way to calculating band diagrams.
To reduce mutual coupling, I am not completely sure what mechanism you are using. Assuming you are using the band gap, you simply would design a lattice to have a band gap that covers the bandwidth of your problem. Lecture 14 does a pretty good job explaining band gaps and what you have to do to control this in photonic crystals.