On Jan 16, 2009, at 11:39 PM, Ian D. Hosein wrote:
I'm calculating the band structure of a 3D opal crystal structure in MPB and its theoretical reflection spectra in MEEP. Ideally the gap center and reflection peak center should match. I am finding my reflection peak center
There are slight differences between MPB and Meep due to discretization errors and the differences in numerical schemes, but these go away in the limit of high resolution. But I think your mistake is more fundamental.
It is not true that the gap center and reflection peak should always match. This happens in 1d quarter-wave stacks, but in general the decay rate of the fields does not necessarily peak exactly at mid-gap.
One way to see this is to look at the decay rate of the fields near the band edge: you can show by analytic continuation that the decay rate depends on the distance from the band edge and the curvature of the band edge. (See e.g. the very brief discussion in chapter 4 of our book, ab-initio.mit.edu/book) But the curvature of the upper and lower band edges are not generally the same, so the decay rate does not change symmetrically as you approach the upper and lower band edges...hence the decay rate does not peak exactly at mid-gap.
Steven _______________________________________________ meep-discuss mailing list [email protected] http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
