Poonam,

Before I get into the other stuff I would question your units of c/a for a BG definition. Band gaps should should be in terms of frequency or normalized frequency not in terms of wave vector. Not only this but units of wavevectors are 1/m not 1/s as would be the case with c/a.

My previous comment specifically discussed the design of your base crystal. Your r/a ratio determines if you have a band gap given the materials in use. You either set a constant and scan r, calculating the band structure at each point, or you look up a band map from a reference in order to determine the r/a that gives you the largest band gap for your polarization.

With r/a set you set a = 1 and then set your r to give your r/a previously calculated. Now calculated your band structure diagram which should plot normalized frequency (wa/2pic, note we plot w/2pic) versus the wave vector. A band gap should ideally span the entire k space, otherwise your structures performance will be highly dependent on direction of propagation within the crystal. What you do is you find the primary gap (this would be the one at the lowest wa/2pic) and pick off the two values that correspond to the edges these are in wa/2pic and determine the center of these two. You then use this wa/2pic number with your operating wavelength (this should give you w) in order to solve for the a you need to use for your operating wavelength.

I will be honest this is fundamental design basics for work in photonic crystals and should be well understood before proceeding with any design work. I strongly recommend you read either the 1st or 2nd edition of “Molding the Flow of Light” by Joannopoulos, Meade, and Winn.

Scott