Hi folks,
I am going to find the band structure of a 1D photonic crystal waveguide by COMSOL. There is an example in application library for 2D photonic crystal with a 2D geometry. In the example the refractive index of materials are frequency dependent, and a nonlinear formulation is used to normalize the field in a unit cell and finding the frequency and so updating refractive indices. It is exactly the point that I need to understand completely, since material dispersion is important for me, too. However, I can not figure out how the nonlinear formulation for the field normalization works and how I can utilize the same principle for a 3D geometry. I would be really grateful if somebody can help me.
Thanks for your attention,
Zeinab
Hi Zeinab Jafari,
You can compute the photonic band structure of a 1D photonic crystal in 3D geometry in complete analogy with the example you mention from COMSOL's application library (Application ID:798). The main difference is in the normalization integral, which must be defined over volume instead of area and considering all components of the E field, instead of only the out-of-plane field Ez:
V = intop1(1)
nE = intop1(realdot(ewfd2.Ex,ewfd2.Ex) + realdot(ewfd2.Ey,ewfd2.Ey) + realdot(ewfd2.Ez,ewfd2.Ez))/V
In which case the ODE is still defined as:
1 [V^2/m^2] - nE
All the other instructions from the example should be relatively easy to extrapolate to 3D geometry. There is nevertheless one caveat as COMSOL Technical Support told me:
"What is less analogous however is how the solver defaults work. As it is a 3D model, you get a segregated solver. This is more suited for weakly coupled problems - in contrast, your global equation is only controlled by the coupling itself, making it singular when solved in its own step."
You must therefor us a fully coupled solver:
"Study 2 > Solver Configurations > Solution 2 > Stationary Solver 1, and select Fully Coupled."
I hope this can help you (if it not to late) or others to come.
Best,
Thibault Wildi
Hi Zeinab,
Hopefully the following example be helpful to you.
Regards.
https://www.comsol.com/model/bandgap-analysis-of-a-photonic-crystal-798
Thanks Abdulllah,
Yes, it is exactly the file that I am trying to use it as my reference. I do not have any problem to follow the instructions given in the file and get the same results... my problem is how I should normalize the field for a 3D case...!
Sincerely,
Zeinab
Hey Zeinab! Did you find a solution for that? I am struggling, because what I actually want is to be able to follow the bands. If I only sweep in the momentum k, I cannot get a picture where I know to which band belong the eigenfrequencies found if there are crossings (can be done with treatment of the data, but it is anoying). I see that in the tutorial for the photonic crystal they do something to follow the bandsm but since it is mixed with the dispersive nature of the material I cannot see which steps are needed for each aspect. So I wanted to just use the same scheme with the dumb refractive index of a constant. But I do not manage to make it work in 3D.
If you found the way, it could be really helpful!
Sincerely,
Guillermo
Dear Guillermo,
Actually, I could not solve my problem...
As far as I am concerned if you have constant refractive indices, you do not need that part which solves a nonlinear equation to find the frequency... Am I right?
Also, I think there should be examples for cases without considering dispersion... such examples are simpler to be understood and followed, please search the example library to find them.
Good Luck,
Zeinab
Dear Zeinab
As far as I know it is unfortunately the only band diagram example. I know very well how to calculate the band diagrams for non-dispersive media (which is what interests me). The problem is that I do not know how to follow the bands (which is important when computing group velocity). If out of the tutorial you know how to just do that, that is what I need!
Thanks!
Guillermo
Dear Guillermo,
From the above link, the tutorial from Comsol, page 23, under solution 2, it is mentioned that:
"From the Predictor list, choose Constant. This makes the solver first try with the solution found for the previously calculated k value. This is preferred, as even though the states can be degenerate, the field solutions are orthogonal. Thus, the solver is forced to follow the right band."
If you set the setting of parametric study properly, you should be able to get the right band. Have you noticed to these lines in the tutorial?
Good luck
Hi folks, my photonic crystal design has a triangular lattice. In this case how and will I define b1 and b2? It is possible to get these results after the project is already built, in my case a coupler. Somebody help me there, please.
Guillermo Arregui Bravo, Zeinab Jafari did you find the solution to the problem?
Thanks!
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