Dear Prof. Johnson I was reading your paper " guided modes in photonic crystal slabs" that I encountered this problem . I myself tried to find gap-midgap ratio for some structures like square lattice of square air holes and 45 degrees rotated square air holes .When I tried to compare the results that I found with GME package of Prof.Andreani with the formula wich is an estimation of the height of the slab in your paper I understood that when I enter the average dielectic constant like a conventional avrage in a unit cell I found that my results from your formula is by a factor of 2 smaller than the ones I've found by calculating the band structures for different heights . I looked again at your paper and I found that you've defined the average dielecric constant two times , one for TE and one for TM polarizations. maybe the problem is just the average dielectric constant . I didn't get how to define different average dielectric constant for different polarizations .
Regards Mina Esmaeelpour
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