extending field solutions with mpb-data

Hi all,

It seems like the program "mpb-data -m M" just tiles field solutions M
times, ignorning the plane-wave phase of the solutions as you move from one
unit cell to another.  It needs to know the k-vector of the solution to
extend the fields into neighboring unit cells.

As a concrete example, I'll use the 2-dimensional array of dielectric rods
in air from Chapter 5 of "Photonic Crystals: Molding the Flow of Light",
which is also the example "sq-rods.ctl" that comes with MPB.

Consider Figure 3 of chapter 5.  Specifically, consider the bottom-left
subfigure, which depicts the z-component of the D-field of the TM modes at
the M-point, for the 1st band.  By simply tiling the solution in the unit
cell, you DO NOT get the solution depicted in the figure; instead, you get
something that looks like a mode at the Gamma-point (see top-left or
top-right subfigure).  In fact, if all mpb-data does is tile the solutions
from the unit cell, then it will always tile those solutions out to look
like something at the Gamma-point, since simply tiling is equivalent to
assuming U(r+R) = U(r)e^0 (something with kx=ky=0).  This doesn't even make
sense if, for instance, the field is odd across the unit cell.

My question, then, is whether these figures were created using "mpb-data" on
the field solutions of the unit cell?  If so, how?  Can I tell mpb-data what
the k-vector of the solution is?  It seems to me that running "mpb-data" on
the unit cell field solutions just tiles them, rather than including the
plane-wave phase variation.  Is the only way to get the solution including
the proper periodicity to simulate multiple periods of the unit cell, or is
there some way to get mpb-data to do it correctly?  I know I can write a
script to do it myself because I know the unit-cell solution and the
k-vector, but I'd like to avoid this if there's already some functionality
built into mpb-data.

Thanks,
Matt Eichenfield
[email protected]

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