COMSOL band structure of photonic crystal waveguide

In summary, the conversation discusses the process of creating a band structure for a planar photonic crystal with finite thickness. The main challenge is adapting a method used for a purely 2D crystal to a quasi-3D problem. The use of variable floquet periodic BCs for the x-direction boundaries and PEC or PMC BCs for the top and bottom parts of the cell is mentioned. The tutorial used as a reference involves ramping k by force feeding the previous frequency into the current parametric solver and using an integration coupling variable with an ODE on the frequency. The problem of the solver halting due to unknown variables is addressed and the suggestion to use a newly created discussion forum for help is given. Some users express interest in
  • #1
BrillouinPie
2
0
Setup:
I'm trying to make the band structure for a planar photonic crystal with finite thickness, i.e., a quasi-3D problem.

I only want the x-direction band structure. So, I'm using variable floquet periodic BCs for the x-direction boundaries, and 0 degree floquet periodic BCs for the y-direction. The top and bottom parts of the cell have either PEC or PMC BCs.

I'm trying to adapt the method used here: http://www.comsol.com/showroom/documentation/model/798/

This tutorial shows how to a make band diagram for a purely 2D photonic crystal. The main idea in the tutorial is following a particular band while ramping k by force feeding the previous frequency into the current parametric solver. Their method also uses an integration coupling variable with an ODE on the frequency, by normalizing the z-comp of the electric field (they're using 2D > RF Module > In-Plane Wave > TE waves > eigenfrequency).

Problem
:
I try to adapt the problem by normalizing the entire electric field using: Ex*conj(Ex) + Ey*conj(Ey) + Ez*conj(Ez). For subdomain ICs I use Ex(to) = Ex, etc., for all parts of the E-field.

When I try to run the parametric solver and ramp k, the solver immediately halts, saying that it doesn't know what Ex, Ey, and Ez are.

Any ideas?
 
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  • #2
Nothing specific to this problem, but an FYI: COMSOL has started a discussion forum (as of only a week ago) where you might be able to get help from active users.

http://www.comsol.com/community/

You should be able to use the forum if you are a registered user with an account. Be sure to read and follow the Guidelines posted at the bottom of the welcome thread.
 
  • #3
Oh great. Thanks!
 
  • #4
Dear Sir,

I am a started using COMSOL. And I would like to do the band structure for a planar photonic crystal as well. Can you be so kind to share the document from COMSOL web you got to me?

Thanks in advance!
David
 
  • #5
I am also trying to do this. I haven't got the arrors you have but the computation time seems to be never ending, but perhaps that's because the mesh is very fine and it's a 3D problem.

Have you made sure you are using a 3D RF module where the dependent variables are Ex, Ey and Ez? Because in the 2D problems the two mode polarisations decouple and there is only a single variable Ez (or Hz). Such decoupling does not occur in 3D and you need a full vectorial treatment (although from your post it seems as though you already knew that).

I'll keep you posted and if I get the thing working I can send you my scripts if you wish.
 
  • #6
Can you please load your code so that I may learn how you were able to accomplish this? Thank you.
 
  • #7
I didn't actually write any code. I just used the GUI and followed the instructions for the 2D case, but changed the geometry I drew. Unfortunately the file, with the mesh and results is too large to upload here.

The most important thing to realize when doing things in 3D is the the mesh on the periodic boundary condition boundary pairs must be identical. This is not done automatically and you must thus mesh one boundary then manually copy the mesh from it to another when there is a periodic pair. Once you have done all the periodic pairs then mesh what's remaining using "Mesh remaining free". If you do not do this your computation will not converge.
 

1. What is a photonic crystal waveguide?

A photonic crystal waveguide is a type of optical waveguide that uses a periodic structure of dielectric materials to control and manipulate the propagation of light. It is typically made up of a lattice of air holes or other defects in a dielectric material.

2. How does COMSOL calculate the band structure of a photonic crystal waveguide?

COMSOL uses a finite element method to numerically solve the Maxwell's equations for the periodic dielectric structure of the photonic crystal waveguide. This allows for the calculation of the photonic band structure, which describes the allowed energy states for light propagating through the waveguide.

3. What are the key parameters that affect the band structure of a photonic crystal waveguide?

The band structure of a photonic crystal waveguide is primarily affected by the lattice type, the geometry of the waveguide, and the index contrast between the dielectric materials. Other factors such as the refractive index of the materials and the wavelength of light also play a role.

4. Can COMSOL simulate the band structure of a photonic crystal waveguide for different operating conditions?

Yes, COMSOL allows for the simulation of the band structure of a photonic crystal waveguide under various operating conditions, such as different wavelengths of light, different refractive indices of the materials, and different lattice types. This allows for the design and optimization of photonic crystal waveguides for specific applications.

5. How can the band structure of a photonic crystal waveguide be used in practical applications?

The band structure of a photonic crystal waveguide can be used to design and optimize various photonic devices, such as filters, lasers, and sensors. It can also be used to understand and engineer light-matter interactions, leading to advancements in fields such as telecommunications, optical computing, and quantum information processing.

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