Discussion Forum

We want to get photonic band gap, transmission and reflection spectra of 1D or 2D PC.

Could you help me how can I obtain band gap and Transmission/Reflection spectra of 1D or 2D photonic crystal? Or could you send me instruction about how can I get this?

Thank you for your help

To perform a bandgap simulation in COMSOL is very easy. Just model a unit cell and apply Floquet periodic boundary conditions in Eigenfrequency mode, select source and destinations boundaries and specify your x and y components of the propagating wave vector. Run the model for a selected number of eigenfrequencies. viola.


~Chris

To perform a bandgap simulation in COMSOL is very easy. Just model a unit cell and apply Floquet periodic boundary conditions in Eigenfrequency mode, select source and destinations boundaries and specify your x and y components of the propagating wave vector. Run the model for a selected number of eigenfrequencies. viola.


~Chris

Based on the above tips and the comsol library model "plamonic wire grating" i have tried to make a simple model of a square lattice of silica rods in air and solve for the eigenfrequencies at the gamma point of symmetry, but i am getting errors and i am not sure where i made a mistake.
I am not sure if i have to select all four boundaries as the Floquet-boundaries (i guess i should, since the structure is periodic in both x and y directions?) If i do this, i get the error

"Unknown function or operator.
- Name: mod1.emw.dst2src_pc1"

but if i only choose the left and right boundaries (top and bottom are periodic source- and destination ports) i get the error

"Undefined value found.
- Detail: Undefined value found in the stiffness matrix.
There are 1 equations giving NaN/Inf in the matrix rows for the variable mod1.emw.S1x.
at coordinates: (0,0), ...
There are 1 equations giving NaN/Inf in the matrix rows for the variable mod1.emw.S2x.
at coordinates: (0,0), ...
and similarly for the degrees of freedom, NaN/Inf in the matrix columns."

Any idea what i have done wrong? Every small hint is greatly appreciated :)

- Jens

Unfortunately I don't have the RF kit, I work with phononic systems so I can't open your model. But for a simple square unit cell, I usually have two instances of periodic conditions, one for the left-right boundaries and one for the top-bottom boundaries. Each instance of the periodic conditions will have 2 boundaries selected. For something as simple as a square you do not need to specify the destination boundaries, COMSOL will do it (although you can if you want). I assume you have defined parameters for propagation 'theta', 'k=m*pi/a', 'kx = k*cos(theta)', and 'ky = k*sin(theta)', where 'm' is very small for Gamma point and 1 for BZ boundary. Put 'kx' and 'ky' in the box for Floquet conditions. Assuming that is what you did, I don't know why you would get an error.


~Chris

Thanks for your reply Chris,

I already figured it out with the double Floquet BC's which indeed allows me to solve for the eigenfrequencies - but only if i leave out the ports alltogether.

Anyways, i am trying to reproduce the results in the attached band diagram (using the same parameters). If i have ky = 0 and sweep kx from 0 to pi/a, this should correspond to the Gamma -> Chi segment in the diagram. As i compare my results with the reference they match pretty well, but it seems like i only get the TM solutions out. What if i want the TE solutions as well? I don't understand why the periodic BC's would restrict the polarization.

- Jens.

Hi, Jens,

This is Jingjing, and I am exactly wanting to reproduce the band structure in your attachment. I have got some trouble in how to seperately plot TE and TM band structure. Also how did you build up the model in periodic condition? Also if it is possible, could you send me your comsol file of this? Thank you so much! Here is my file, and I plot a band structure that looks very different from it should be.

Thank you very much!

Jingjing

Unfortunately I don't have the RF kit, I work with phononic systems so I can't open your model. But for a simple square unit cell, I usually have two instances of periodic conditions, one for the left-right boundaries and one for the top-bottom boundaries. Each instance of the periodic conditions will have 2 boundaries selected. For something as simple as a square you do not need to specify the destination boundaries, COMSOL will do it (although you can if you want). I assume you have defined parameters for propagation 'theta', 'k=m*pi/a', 'kx = k*cos(theta)', and 'ky = k*sin(theta)', where 'm' is very small for Gamma point and 1 for BZ boundary. Put 'kx' and 'ky' in the box for Floquet conditions. Assuming that is what you did, I don't know why you would get an error.


~Chris

Thanks for your reply Chris,

I already figured it out with the double Floquet BC's which indeed allows me to solve for the eigenfrequencies - but only if i leave out the ports alltogether.

Anyways, i am trying to reproduce the results in the attached band diagram (using the same parameters). If i have ky = 0 and sweep kx from 0 to pi/a, this should correspond to the Gamma -> Chi segment in the diagram. As i compare my results with the reference they match pretty well, but it seems like i only get the TM solutions out. What if i want the TE solutions as well? I don't understand why the periodic BC's would restrict the polarization.

- Jens.

Unfortunately I don't have the RF kit, I work with phononic systems so I can't open your model. But for a simple square unit cell, I usually have two instances of periodic conditions, one for the left-right boundaries and one for the top-bottom boundaries. Each instance of the periodic conditions will have 2 boundaries selected. For something as simple as a square you do not need to specify the destination boundaries, COMSOL will do it (although you can if you want). I assume you have defined parameters for propagation 'theta', 'k=m*pi/a', 'kx = k*cos(theta)', and 'ky = k*sin(theta)', where 'm' is very small for Gamma point and 1 for BZ boundary. Put 'kx' and 'ky' in the box for Floquet conditions. Assuming that is what you did, I don't know why you would get an error.


~Chris

Thanks for your reply Chris,

I already figured it out with the double Floquet BC's which indeed allows me to solve for the eigenfrequencies - but only if i leave out the ports alltogether.

Anyways, i am trying to reproduce the results in the attached band diagram (using the same parameters). If i have ky = 0 and sweep kx from 0 to pi/a, this should correspond to the Gamma -> Chi segment in the diagram. As i compare my results with the reference they match pretty well, but it seems like i only get the TM solutions out. What if i want the TE solutions as well? I don't understand why the periodic BC's would restrict the polarization.

- Jens.