I have tried using PML boundary and applying master and Slave boundary to only surfaces in the direction of propagation , Am I correct. I am not getting proper results. Please Help
In order to get the dispersion relation, you need to sweep the phase in the direction of propagation across the corresponding master/slave boundaries (called primary/secondary in the new HFSS versions). You can then plot the frequency vs. phase for the desired modes. If you want, you can also convert this phase to a phase constant based on the length of the structure.
I also want to point out that generally if the structure is lossy the eigen mode solver will not give you the full dispersion relation as it would involve complex frequencies (imaginary frequency due to loss). If the structure is lossless, you will have real frequencies only and then the dispersion relation would be correct and can be found as I pointed out above. Since you're dealing with a leaky-wave antenna you will have loss due to radiation and the eigen mode solver will not give you the full picture of the dispersion relation. The phase constant may be approximately correct but you will not be able to directly compute the attenuation constant.
I attached an example that you might find helpful of the eigen mode solver used to find the dispersion relation of the first two modes in a rectangular waveguide.
1)make a very short cross-section.
but not too short since you may loose precision. and not too large, since the Brillouin zone may trim the dispersion curve too much.
In case of metamaterial antenna, it is the unit cell.
2)apply periodic conditions to the faces, which are normal to the propagation axis. The phase between slave and master should be a parameter.
3)Sweep that parameter with parametric sweep, or with a script, you will get a set of eigenfrequencies for every shift.
4)convert that shift to the phase number, since you know the distance between the faces.
5)plot that.
P.S.
"if the structure is lossy the eigen mode solver" WILL GIVE you the correct dispersion relation, since the lossy solution is still the exact solution. It will not just be that beautiful as the lossless ideal case. But solving the wave equation on paper with the loss factors involved will give you the same curve. Of course, computing the attenuation constant is not direct. But since there are complex roots, you get real and the Neper frequency, and it has the same meaning against time, as the attenuation constant against distance. I guess the latter may be extracted with some effort directly in the report editor. I do not remember, did I do that, or not in the past; time flies....
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