Dispersion Curve calculation in HFSS

[usef_vahabzadeh]

Hello everybody,
I'm trying to calculate dispersion curve for a metamaterial. So, for the beginning and benchmark, I'm considering a very simple problem which is dispersion curve of free space. As everyone knows the dispersion curve for the free space should be a line with the slope of 45degree. Thus, I consider a vaccum box (epsilonr=1) with PEC boundaries at the two sides in x-directions and PML boundaries at two sides in y-direction and Master-slave boundary at the two ends in Z-direction. I have attached my HFSS simulation file. But, the result that I have obtained is very far from the expected solution(attached photo). I highly appreciate you to assist me and let me know about my mistake in my simulation. Thanks a lotView attachment HighEpsHMTM.zip

 

[DavidZlavan]

I have had problems simulating with HFSS in the past. Have you tried to simulate the same port in a known structure like a transmission line or a cavity and see correctly S parameters?

I am really interested to follow this topic. Just by curiosity, which type of metameterial would be? (If we are talking about metalines (2D) I highly recomend you ADS momentum.

 

[PlanarMetamaterials]

A few questions:

1) Why do you think the slope would be 45 degrees? The slope in the standard ω-κ format should be c, the speed of light.

2) Why are you using PECs on one side and PMLs on the other? PMLs should only be needed where an open boundary (which accepts radiation) is required. Since your plane wave will be propagating between your master-slave z-directed boundaries, this isn't the case -- I would use PMCs on the y-directed sides instead.

3) ADS Momentum? To obtain dispersion? Why?

 

[usef_vahabzadeh]

Thanks for your response. Yes, actually, I'm going to simulate a metamaterial and obtain its dispersion curve (not S parameters). Thus, having the dispersion curve, I can find the effective permitivitty and permeability at least for small frequencies. The metamaterial, for simplicity, can be an array of patches in x-y plane and the same array on top of that but with some lateral shift. I've not used ADS momentum and I'm not familiar with that.

I have had problems simulating with HFSS in the past. Have you tried to simulate the same port in a known structure like a transmission line or a cavity and see correctly S parameters?

I am really interested to follow this topic. Just by curiosity, which type of metameterial would be? (If we are talking about metalines (2D) I highly recomend you ADS momentum.

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Thanks for your reply.
1- yes, you are right. But assuming C=1 (normalization) then the dispersion curve will be k=omega, thus the slope will be one or 45degree.
2- I'm trying to simulate a metasurface, thus as a benchmark, I want to find dispersion curve for the free space. Thus, if the method works for the free, then it will work for my structure as well. The reason for considering PEC and PML boundaries is this: applying plane wave in, for example, x-direction will result in zero H field at both ends in x direction, thus we can put PEC in x-direction. And also that plane wave gives zero normal E-vector in y-direction, thus we can put PMC in both y ends. I tried using PMC at all four sides (all the boundaries in X and Y direction) but, unfortunately, I got an incorrect result like before.
Still, its a question for me how Can I find the dispersion curve of the vaccum!!!!

A few questions:

1) Why do you think the slope would be 45 degrees? The slope in the standard ω-κ format should be c, the speed of light.

2) Why are you using PECs on one side and PMLs on the other? PMLs should only be needed where an open boundary (which accepts radiation) is required. Since your plane wave will be propagating between your master-slave z-directed boundaries, this isn't the case -- I would use PMCs on the y-directed sides instead.

3) ADS Momentum? To obtain dispersion? Why?

 

[PlanarMetamaterials]

I missed your attached file in the original post. It appears that your only mistake was that you did not specify the unit of degrees ("deg") for your $phi variable.

Also, you meant to say PMC in your original post, not PML.

 

[anilkrpandey]

You can also try time-domain EM solvers like FDTD for this.

View attachment EBG_Anil.pdf

 

[usef_vahabzadeh]

Yes, you are right its PMC, not PML. And regarding your first point, since $phi is a project variable, it doesn't accept to select the unit of degree ("deg"). I tried it, but I couldn't set the unit as degree.

I missed your attached file in the original post. It appears that your only mistake was that you did not specify the unit of degrees ("deg") for your $phi variable.

Also, you meant to say PMC in your original post, not PML.

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Yeh, maybe its easy to find dispersion curve using those software. But, I don't have access to them since I don't have the license. And, actually, it must be obtainable with HFSS since its a very powerfull software and many people have calculated dispersion curve of complex structure. And its really a question for me why it doen't work? and where I'm making a mistake.

 

[PlanarMetamaterials]

Setting it to degrees worked for me. It then gave the proper dispersion curve.