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Position in reciprocal lattice (for Triangular real lattice) to find photonic gapmap

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susovan0010

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Hi,
To find Gap-Map, using FDTD, for square lattice of dielectric coulumns in air, I choose the 'X' position in reciprocal lattice, while varying the radius of the rods. The result is good.

But while considering the triangular lattice, I am a bit confused to choose the point in reciprocal lattice. Is it the 'M' or 'K'. Where the gap opens?
 

Wikipedia has a good article in Brillouin zones. You are correct that M and K are the other two lattice points (aside from the center Γ -- in two dimensions). Which one you choose, is of course up to you.

Normally one needs to show that a bandgap exists in both directions in order to have a gap in any direction along the surface.
 
Thank you. Your valuable comment goes with my intuition.:smile:

Is there any specific direction (either ΓM or MK) along which the gap will be maximum for a given radius?
 

susovan0010 said:
Is there any specific direction (either ΓM or MK) along which the gap will be maximum for a given radius?
Click to expand...

I don't know anything about triangular unit cells, but I would guess that they're nearly identical for smaller radii.

Good luck figuring it out!
 

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