Gap position vs effective index

Hello everyone,
 
Is it *necessarily* true that all the bands move to lower frequency values 
as the effective index of the photonic crystal is increased ? I thought 
this was, in general, true. But now I have some calculations that show 
otherwise, and am a little confused.
 
I calculated the the first 8 bands of a 3D hexagonal lattice (from Gamma 
to A only) for different values of r/a, which means that the calculations 
were done for the same crystal with different filling fractions, or 
different effective refractive indices. The mean epsilon values were
indicated in the output files.

For silica spheres in air background, the bands move up (down) as the average 
index decreases (increases), as expected. But for air spheres in polymer 
background, the opposite is observed. Any idea why that could be ? Thanks for 
any suggestions.

Tushar
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ps: I'm very sure of the correctness of the ctl file since I have 
reproduced some previously published results with that.