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Hi Oleg,

do you want to calculate the band structure of a superlattice, where one lattice site is periodically changed according to the shape of your defect?

Or do you actually want to calculate the modes of the defect within the extended perfect crystal (which actually don't have a real bandstructure since they are localized)?

Or do you aim to calculate how the field structure of a crystal mode is changed in vicinity of the defect (their shape will just be affected close to the defect the field shape and bandstructure in the remaining perfect crystal won't change much since you could look on some spot arbitrarily far from the defect)?

Best,

I have calculated the band structure (picture 1) for a photonic crystal wihtout any defects. Picture 2 is a unit cell.

So, I want to calculate the band structure of another photonic crystal with a central defect. Crystal is shown on the picture 3.

Hi Oleg,

what I wanted to say is, that, if you would like to calculate a bandstructure, you will need a periodic system, so simply a larger unit cell, where your defect sits in the center.
This will give you the bandstructure of a crystal where the defect is repeated with the same lattice constant and symmetry of the larger unit cell you set. But I am not sure, whether this is what you want to have.
The bandstructure of a single defect in an infinite crystal on the other hand does not really make a lot of sense, since the term bandstructure refers to a periodic system (so the 'defect' (it is not a defect any more) is repeated within one lattice constant).
Around the defect the shape of the eigenmodes of the lattice may be a little bit deformed, but in an infinite crystal this deformation is arbitrarily small compared to the remaining field and will hence not change the bandstructure of this modes (although you change the k distribution in this limited area a bit what will lead to scattering (into, out of and between different modes)).
What one usually wants to do with a defect in a photonic crystal is to create some localized modes (best with energies inside a bandgap of the surrounding crystal). For that, take your defect and add some undisturbed lattice sites around (as you did in picture 3). Make sure to have quite a few lattice constants between the defect and the boundary of your simulation volume (the later fields should better not touch it significantly). Then add scattering boundaries around (with that you get even a Q for the defect modes) and simulate the eigenfrequencies. This will give you the modes of the defect, the eigenfrequencies and their approximate Q factor, BUT not a bandstructure (since they are localized, the modes do not have one single k value).
You could in the latter case also make a half or quarter or so of your structure and include symmetries.
I hope this helps you a bit.

Cheers,
Hannes