understanding field plots of MNG metamaterial

Hello everyone,

Please locate the attached file which contains the simulated results (of HFSS) of negative permeable SRR metamaterial. The results contains S11 and S21 plot, extracted effective permeability (by NRW approach), Poynting vector plot, E-field and H-field plots.

Please help me explain the orientations of the above mentioned three vector plots.
Had it been a DNG metamaterial, there would have been a backward wave i.e. the propagation vetor (k) and the poynting vector (S) would have been in opposite directions.

Is this true for mu-negative materials as well? As there is no transmission but there is obvious reflection of incident wave in MNG materials, which i suppose explains the existence of backward wave for MNG materials. Am i correct?

Please explain the vector plots. I shall be highly obliged.

Thanks in advance.

View attachment Help_SRR.rar

Hi Ashish,

While DNG materials do support backwards waves, (since sqrt(ue) is still real), technically MNG materials will not, since sqrt(ue) is imaginary, hence the material only supports evanescent waves - i.e. no transmission. There will be reflections due to Bragg scattering and various impedance mismatches.

I am uncertain as to your setup, and so can't really explain your plots.. You have a diagram showing E and H in the same direction as k. Are the four side walls periodic boundaries? And are the top and bottom (y-direction) waveports?

Thanks for your reply.

Are the four side walls periodic boundaries? And are the top and bottom (y-direction) waveports?

Click to expand...

PEC walls are +z and -z
PMC walls are +y and -y
waveports are shown by arrows in +x and -x

You have a diagram showing E and H in the same direction as k.

Click to expand...

Can you explain how? as they are shown to be in three orthogonal directions.

I am uncertain as to your setup, and so can't really explain your plots.

Click to expand...

What information do you require for this.
the HFSS simulation is done in Driven Modal solution type, interpolating sweep in the range 1.5 GHz to 4.5 GHz.
The solution frequency is kept at 2.4 GHz.
The boundary conditions are used for the sake of testing the unit cell, and these are in accordance with D.R. Smith's and Zilokowski's works.

There will be reflections due to Bragg scattering and various impedance mismatches.

Click to expand...

Does these type of reflections also mean that vector k and S=ExH be opposite?

Please reply.

Thanks again.

Ok, my apologies, I see what you mean now. My first concern is that your transmission is only through 1 SRR cell in the k direction; I'm not sure how large of an impact this will have, but I typically use more than 5 cells in the propagation direction when dealing with periodic structures in order to get a good response.

The scattering and reflections will result in power S going in multiple directions, but the overall net power should still be in the direction of k. Can you compute the net Poynting vector of a cross-section in the ZY plane?

Thanks again for reply.

My first concern is that your transmission is only through 1 SRR cell in the k direction

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No, in the real scenario, i intend to use it in a periodic array configuration by placing it both above and below the patch antenna, in the hope of dual frequency operation and hence compactness (if any possible).

but I typically use more than 5 cells in the propagation direction when dealing with periodic structures in order to get a good response.

Click to expand...

My major motive is to just check whether the given selected structure is negatively permeable at my desired frequency or not? which i hope does not expect for much better S11 and S21 (except for them being <-10 dB, which is perfectly achieved here, and also such a notion is conceived by Smith and Zilokowski in their respctive papers).

The scattering and reflections will result in power S going in multiple directions, but the overall net power should still be in the direction of k.

Click to expand...

Can you tell me if i can observe the said effect if i analyze a DNG mematerial? i.e. them being oppositely directed.

One more query, somebody told me about negative phase velocity can be inferred if the phase of S21 is negative in the required frequency range. Can this a fact be proved by some theoretical reference? Please see.

Can you compute the net Poynting vector of a cross-section in the ZY plane?

Click to expand...

Very recently, i got to know how to plot Poynting vector in HFSS, can you just shed a little bit light how can i do this. Is this done by first selecting the geometry>>selecting ZY plane>>then plotting poynting vector...
0k..i must check it and report here soon.
Well how do you expect it to be like?

Please reply.
Thanks..

No, in the real scenario, i intend to use it in a periodic array configuration by placing it both above and below the patch antenna, in the hope of dual frequency operation and hence compactness (if any possible).

Click to expand...

So you will only be placing two cells in the Y-direction, with the "periodic" array being in the X-Z plane? Then I definitely would not simulate the unit-cells in this manner. An infinite array should behave much differently than two stacked cells. And I would still add additional cells in the k-direction.

My major motive is to just check whether the given selected structure is negatively permeable at my desired frequency or not? which i hope does not expect for much better S11 and S21 (except for them being <-10 dB, which is perfectly achieved here, and also such a notion is conceived by Smith and Zilokowski in their respctive papers).

Click to expand...

Do an eigenmode simulation. This will give you a much better idea of what is going on, and you can simulate in infinite array in how ever many dimensions you want. You will see a discrete frequency at which mu becomes negative, if it does at all.

Can you tell me if i can observe the said effect if i analyze a DNG mematerial? i.e. them being oppositely directed.

One more query, somebody told me about negative phase velocity can be inferred if the phase of S21 is negative in the required frequency range. Can this a fact be proved by some theoretical reference?

Click to expand...

Again, the eigenmode results will help you here. If you see a mode which slopes downwards in frequency with increasing propagation delays (Bd), you have a backwards wave mode guaranteed. As for the phase condition, I can see it being correct in the case of an ideal DNG medium, where k will incur positive phase with distance as opposed to negative, as usual. However, I think these mediums are far from this ideal.

Very recently, i got to know how to plot Poynting vector in HFSS, can you just shed a little bit light how can i do this. Is this done by first selecting the geometry>>selecting ZY plane>>then plotting poynting vector...

Click to expand...

To be honest, I'm not sure, I've just heard other people talking about it Someone else here should be able to help you with this.

thanks again..but i must admit now i am almost blown off..

Please help me in eigen mode solver, as i have never seen SRR based metamaterial simulation in this mode, which is commonly used for unit cell analysis of EBG. You seems to be pretty well known about Eigen mode solution to SRR unit cell simulation. Please give me some reference here as to what and how should the boundary conditions be like.

Moreover, i do not intend to extend the periodic array in Z direction, they will just be spread in the X-Y plane as in normal already done cases.

Please point out flaws in my current simulation technique of using PEC, PMC and waveports with Driven modal solution.

and any help in eigen mode solution is appreciable..

Thanks.

The problem with your setup seems to be that you are not simulating what you are describing. You have 1 cell in the direction of propagation, and an infinite number of cells in the "vertical" (z, as you described) direction - this isn't what printing an array of these on a substrate would look like.


The Eigenmode solver is pretty straight forward. Basically, you don't apply any sources, but it passively checks for resonance modes in your object. When I am dealing with Planar Metamaterials, I use the following basic setup:

- Make sure that your solution type is "Eigenmode"
If the plane of your cells is X-Y, and your unit cell has two SRRs "stacked" in Z,
- Draw a vacuum box around your cell, around a quarter of a wavelength in the Z-direction.
- Apply PMLs to the top and bottom (z-faces) of this vacuum box.
- With your unit-cell in the middle, apply two set of master slave boundaries to the X and Y facing faces of the vacuum box.
- Apply a Master boundary to one of the Y-faces, and apply a slave boundary on the other y-face. When setting up the slave boundary, use the "Input Phase Delay" option and set it to 0 degrees. This will make the cells appear to extend periodically in the Y-direction, with no phase across them (i.e., your surface wave is travelling in the X-direction).
- Apply another Master boundary to one of the X-faces, and a Slave boundary to the other X-face. Again, use the "Input Phase Delay" option, but this time, set the phase delay to a variable, "$Angle". This is the Bd angle that gives the phase across your cell in the direction of propagation.

Set up your solution with some minimum frequency and start with 2 modes (you can do more later for more info). If you have optimetrics, set it up to sweep $angle from 0 to 180 in steps of 5 degrees. Otherwise, you get to step in manually for each solution (under "Project Variables" Make sure to save fields under the last tab in optimetrics.

Then solve. The eigenmode simulator will show you the modes that correspond to a resonance, although there may be some fake "spurious" modes to the left of the light line (usually have a very low Q). By viewing the field profiles for each mode (under Field Plots -> "Edit Sources"), you can see exactly what is going on. By tracing out the frequency at which these modes occur for each Bd ($Angle), you can clearly see if the mode is forwards or backwards, as I explained in my last post.

Good Luck

Hey, I would surely use your great knowledge and expertise and would soon report the eigen mode solution results.

Moreover, I admit that my previous posts were quite confusing, but one thing is clear, i am to use SRR array spread in X and Y directions, either in below patch "or" above it, not both at a time, so there is no array in Z-direction.

But i must be using all the steps as mentioned by you for mode study.

Thanks a lot. Would soon be back with results.

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Hey, I would surely use your great knowledge and expertise and would soon report the eigen mode solution results.

Moreover, I admit that my previous posts were quite confusing, but one thing is clear, i am to use SRR array spread in X and Y directions, either in below patch "or" above it, not both at a time, so there is no array in Z-direction.

But i must be using all the steps as mentioned by you for mode study.

Thanks a lot. Would soon be back with results.

For Eigen mode solution of DNG metamaterial-SRR

Hello Planar Metamaterials,
hope you are doing great!!

Please locate the HFSS file of my version of Eigen mode solution file of DNG material.

Please note, that it is just for my understanding of Eigen mode simulation. Please Check the U and V vectors for Master and Slave boundaries, as I have not been able to find any guide on how and where to place these vectors, moreover they tend to make contact with PML boundaries, which HFSS prompts as a warning.

Please look into the design and correct it if possible. I have considered PML boundaries at +y and -y just to have infinite repetitions along y-axis and then applied Master-slave BC at remaining faces with variable phase along x-axis.

Please help once more, i shall be highly obliged.

View attachment Eigen_Mode_Part_1_MTM.rar

Hi Ashish, I'm doing great thanks

I'm dowloading your file.... but I can tell you right now that the U and V vectors need to be in the same direction (globally) for Master/Slave faces that are facing each other. These boundaries also have to completely overlap the PML.

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Hi Ashish,

I've reviewed your file - you were pretty close. The U/V vectors on the Z axis were backwards for one of the master/slave pair - I've corrected this. Also, you applied the Master/Slave boundaries directly to the vacuum box faces - as I indicated above, you want to draw a rectangle that covers the PMLs as well, and then apply the boundaries to the rectangles.

You probably also want your solution to converge to a delta F of < 1% for an accurate solution - I usually use 0.5%, and as well make sure it has a good number of maximum adaptive passes - I usually use about 20 (although it rarely gets that high). The default of 3 is pretty useless if you haven't specified a starting mesh. Your minium frequency should also be a good deal lower than what you're expecting - in your case, I set it to 2 GHz. You don't want to miss anything if your mode drops slightly in frequency. Also, don't forget to check "save fields" under the optimetrics options tab, otherwise you won't be able to view the field profiles when you're done.

I've uploaded the corrected file (Sorry, HFSS 13 not 12, hope it opens for you) - good luck!