On Jun 25, 2009, at 5:56 PM, Ian D. Hosein wrote:
Is there a quantitative way to determine if the fields of the
different
calculated bands overlap in the unit cell, especially for
consecutive bands
at which a complete bandgap occurs?
Sure, but you have to be more specific about what you mean by "overlap".
Usually, when one talks about "overlap" between modes, one is
referring to some integral involving the two field patterns. MPB has
built-in field-integration routines (see the manual) that can compute
any user-defined integral you want.
For example, if your magnetic fields are H1 and H2, you could
integrate H1* H2. But this gives zero for two modes at the same k
point, because the Hermitian nature of the eigenproblem guarantees
orthogonality.
Typically, overlap integrals are relevant when you have some
perturbation in the system that couples the eigenmodes of the
unperturbed system. The precise overlap integral that is relevant,
however, depends upon the nature of the perturbation.
For example, we have a recent paper that includes (among other
results) the correct overlap integrals for two modes at different
frequencies that are coupled by nonlinear harmonic generation: http://math.mit.edu/~stevenj/papers/RodriguezSo07.pdf
(Optics Express 15, 7303-7318, May 2007). Many other examples can
be found in the literature.
Regards,
Steven G. Johnson
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