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Advanced photonic bandgap (triangular lattice)
Posted Apr 22, 2015, 10:41 a.m. EDT Wave Optics, Studies & Solvers Version 5.1 2 Replies
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I'm trying to expand the photonic bandgap model (www.comsol.com/model/bandgap-analysis-of-a-photonic-crystal-798) to a slightly different structure, but since I'm new to photonic crystals, I'm struggling with this.
In the model, a square lattice is simulated, with lattice constants a1, a2 = a. The primitive cell is a square with the circular column in the centre. I want to simulate a triangular lattice. The cell changes into a parallelogram, and
. Now, if I just want to sweep from k=0 to 
(M point in the Brillouin Zone), it works fine out of the box. I don't know how to proceed from here, in order to calculate the whole bandgap (Gamma -> M -> K -> Gamma). I thought I'd simply redo the initial eigenfrequency step for M point, and then move on to the k sweep. K values are defined as follows:kk1*(k1*b1x+k2*b2x)
kk2*(k1*b1y+k2*b2y)
Where b1, b2 are reciprocal lattice vectors and kk1/k1/k2 are my parameters. For the initial eigenfrequency sweep at Gamma I set:
kk1=kk2=k1=k2=0
For the subsequent sweep kk2=1 and I'm sweeping k1=0...1.
Now, to get from M
to K 
, I set kk2=k1=1 for the initial eigenfrequency study, and I'm getting eigenfrequencies corresponding to those obtained from the first sweep (at the end of the sweep, kk2=1). However, if I now want to sweep from kk1=0...1/3, I get the following error:Failed to find a solution for the initial parameter.
Maximum number of Newton iterations reached.
There was an error message from the linear solver.
The relative error (1.7e+003) is greater than the relative tolerance.
Returned solution is not converged.
Where might this be coming from? There must be a difference between starting at k=0 and k!=0 that I'm missing.
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Hello Adam Klimont
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One way to accomplish the Gamma-M-K-Gamma sweep is to define a parameter "a", such that when it changes from 0 to 3, k follows the path:
a=0...1: k=0...b1
a=1..2: k=b1...b2
a=2..3: k=b2...0
I created two interpolations in Global Definitions -> Parameters (see attached screenshots). Then I defined two variables, kx and ky, in the following way:
kx = (k1(k)*b1x+k2(k)*b2x)
ky = (k1(k)*b1y+k2(k)*b2y)
Then I set Floquet Periodic Conditions in the Physics tab and set the periodicity to kx and ky.
With this set up, you should be able to sweep k from 0 to 3, and this will correspond to the 1st Brillouin Zone of the triangular lattice.
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