pbg patch antenna design

i am currently working on design of patch with photonic bang gap concept i have created clyindrical air gaps in my substrate to produce the PBG effect i am aware of the refrative index criteria of 2:1 for good design of pbg now can you please guide me
a) how to calculate and optimize a and r for pbg structures
b)use hfss to find that my desiged structure is producing the band gap at the desired frequancy
is possbile can you upload documents that can help me thanks