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 .

Mina Esmaeelpour
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