HFSS Metamaterial Near-Field Simulation

Hey Everybody,

I'm simulating a DNG metamaterial in HFSS 12.1. I've already investigated the far-field behavior by simulating a unit-cell, utilizing master-slave boundaries to force the unit-cell behavior to be replicated and forcing a plane wave to impinge upon the infinite sheet of metamaterial by utilizing perfect E and perfect H boundaries on my ports.

My Simulation Setup

I've linked to an image of my setup. The ports are the two thin boxes on the top and bottom of the unit-cell. Two opposite sides are defined as perfect E, say, the sides with normal vectors in the +/- x direction and the other two are perfect H, forcing a plane-wave to exist on the port. The master-slave boundaries are put on the unit-cell in a similar way. Sides with normal vectors in the +/- x direction are master and slave respectively.

This has worked perfectly for my far-field characterization of the metamaterial, but now I want to look at using this material as the substrate in a patch antenna, that is, I'm interested in the near-field behavior. I've tried simulating "large" sheets of unit-cells to replicate the master-slave behavior to no success: When I try to simulate structures larger than 5x5 unit-cells, I run out of computational power.

The physical material that I have is 12x12 unit-cells wide and, I believe, should accurately act as an "infinitely large" sheet of unit-cells. My question is: How do I simulate this in HFSS? I know it's possible to simulate arrays of antennas, but I do not want an array of antennas. I want only ONE radiating antenna (patch, in this case) and I want to see the S11 parameters when that patch radiates into an "infinitely large" substrate of metamaterials.

I've investigated using master-slave for this, as well, but it seems that any use of that replicates not only the behavior of the material inside the boundaries, but also the forcing radiation. If I were to simply stick a patch on top of my simulation now, I believe not only the metamaterial, but the patch as well would be effectively replicated by the master-slave boundary conditions.

Any ideas are greatly appreciated!

Hello,
Try to use H/E field symmetry in your structure to Reduce the structure size in HFSS and in this way you will simulate Half of your actual structure and ll get results of the whole structure. IN this way you will not run out of computational power.
/SC

Hey SC,

I'm sad to say that I don't believe there's much symmetry that I can exploit here. The fields should be periodic, but I'm not sure that necessarily means symmetric. Also, from what I've read about the symmetric E/H boundaries, they're made to go in the middle of a port and drastically altar port impedance.

Is there any clever way that I can use master-slave boundaries to accomplish this model of "infinite sheet" of metamaterial but NOT an infinite sheet of antenna patches?

Hi transquiltension,

Have you seen the HFSS document named 'Metamaterial' on ansoft site? If not i think you should have a look at Chapter 3 of the document as in that they have described in detail how to simulate a flat lens which consist of array of patches. That document is free and you can download it. If you have any problem in downloading it,do let me know i ll post it here. It might help you.

/SC

Hey SC,

I remember reading this paper a while ago and not getting much out of it. Since then I've learned a lot about metamaterials, computational electromagnetics and HFSS. I'll give it another read and see how it comes out.

Also, I'm going to try imposing E/H symmetry axes as you've suggested and see if I can get some reasonable results. I've got a few simulations that I already have results for: I'm going to see if I can get the same results using symmetry and if I do, then I can simulate the largest structures possible and simply impose symmetry.

I'll let you know how everything goes. Thanks a bunch!

- TT

Hey tranquiltension,
Do let me know how it goes or if you want to post your structure here,i will give it a try aswell. For sure there will be some symmetry to exploit in these structures.Its just the way how you arrange your structure. I am working on the same type of structures and its good to see someone who is on the same boat. Do let me know about how it goes.
/SC

Hey SC,

This chapter is rather helpful, but I'm confused about some things. Maybe we can discuss them here and clear them up? I hope I'm not confusing you or making myself sound stupid, although the latter isn't unheard of...

I'm not totally clear on this dispersion diagram that they're trying to get in section 3.2.3. I've done a little research and turned up this page that explains kind of what a dispersion diagram is:
EM: Talk - HFSS Tutorial 2
See also: EM: Talk - HFSS Tutorial 3

I've actually just spoken with a friend in the department and worked out what I find to be the usefulness of the dispersion diagram. Follow if you wish. It seems that a dispersion diagram is useful for finding the natural resonances of a system. Luckily, it is possible to simulate infinite sheets of structures using master-slave boundary conditions. This should allow for an understanding of how a material will act in the near-field and how it should act in as the substrate in an antenna (?) Also, we should be able to infer an index of refraction and (if we know something about our relative permeability) also an effective epsilon because Beta should be directly related to n and lambda.

Also, any ideas on why they're saying in HFSS Tutorial 3 that a negative slope on the dispersion diagram implies left-handed behavior? Wouldn't that imply reflections - ie: negative group velocity? I thought that left-handed behavior implied negative phase velocity, not group velocity.

This should be most helpful in designing a patch antenna with these materials.

I have yet to attempt the simulation based on symmetry. Sorry about that. I'll get to it shortly.

Thanks again and please let me know your thoughts.
- TT

Hey tranq,

At the start of the post you said that you have characterized your metamaterial perfectly. Doesnt it means that you have simulated your unit-cell structure in 'Eigen-mode solver' and got the dispersion diagram??? If not then you have to do it first in order to correctly characterize your metamaterial behaviour. If you want to really understand what dispersion diagram is then have a look here:

https://www.edaboard.com/threads/30740/

The tutorials you have pointed out on Emtalk site. I have seen them long long time ago and both of these tutorials are taken from the same document 'metamaterial' which i have referred to you before. For your other question about the left-handed behaviour, i will say to you again read chapter 1 of the same document to understand what left-handed metametrials are and how they work.

Here is another paper for you,its by Dan svien piper,the first guy who has given the concept of 'High-impedance surfaces with frequency bandgap' and used them as a groundplane with antenna to form low-profile antennas. Later on, all the commercial electromagnetic softwares updated their softwares to replicate his results using their tools because his invention becomes quite successful and still people are working on it. All the softwares documents/explanations are based on this paper. This guy has done it back in 1999 with his algos with no electromagnetic software tools. Read this paper you will understand the dispersion diagram,frequency bandgap, The theory behind these concepts and how to use them along antennas. if you dun understand anything out of it,just ask.

Forgot to add,

first characterize your metamaterial and get the 'dispersion diagram' and identify your 'bandgap'. This bandgap will stay the same,for it near-fiel/far-field thing is irrelative. The next step then would be to put antenna on top of it and see the effect. The high-impedance surface will act as a perfect reflector only in the 'band-gap' frequency range as 'image currents' will be in-phase rather than out-of-phase as in the case of a 'Metal reflector' where it is a must to place the metal reflector 'quarter-wavelength' away from the radiating source(antenna in your case).

The documents you are referring i have been through all this before. My advice to you is characterize your metametrial and optimize it for the frequency band in which you are interested. Then model your antenna separately and it must be operating in the same frequency range as that of band-gap you have for your metamaterial. Then you can directly manufacture both and put them together and measure the results. You will see that high-impedance surface will slightly shift the resonance frequency of your antenna and it ll increase its directivity. i have said to directly manufacture because sometimes due to computational power problems its not possible to simulate these High-impedance surfaces with your antenna as you always run out of memory unless you cleverly exploit symmetry in your structure. But if you have designed your surface perfectly it will work fine with antenna as ground plane even if u do not simulate both of them together.

Hope it might be helpful for you

/SC

Hey SC,

Thanks. I've downloaded Dan's paper and will read it ASAP. I'll also look through that whole Ansoft Metamaterails thing again. I'm at work presently and my work has very little to do with antennas (plasmas - the antenna is a side-project), so it may take me a while to get through all this stuff. I'll let you know as soon as I get through it and we'll discuss more.

I really appreciate all the help. I just wish I would've come here earlier.

Truly,
Tranq

Hey tranq,

Sharing knowledge is the best thing and this is how everyone makes progress. It sounds really interesting that a physics guy is working with antennas. just take your time and go through these things. I have replicated dans results in HFSS quite successfully,not all of them but just bad-gap of high-impedance surfaces and i can help you with 'eigen-mode solver' thing as much as i could. you are at the right place and you will progress quickly and in this process i will learn new things from you aswell.

BR,
SC

Hey SC,

So I've finally gotten around to all this stuff; It is not trivial at all. I've read Dan's paper and it's very good. I do think that I have a high-impedance ground plane despite it's dielectric nature. Because of the physical attributes of my metamaterial, however, it gives me some rather odd design constraints when I'm considering making an antenna. Perhaps you can shed some insight here as you seem to have much more experience with antennas than I.

At the beginning of this project, I arbitrarily decided to use a patch antenna and it seems it's not a bad choice, but if some other design allows me to more easily fabricate my antenna, I'll go with that. I figure I should have at least one cell between the radiating patch and my ground plane. My metamaterial has a minimum thicknes of 10mm (the thickness of a single unitcell) and can grow in steps of 5mm. The material seems to have resonances around 12GHz and 17GHz (based on far-field simulations - eigenmode simulations are presently running, but so far have found resonances approximately around these values.)

I'm following the design procedure suggested here:
**broken link removed**

I'm having a bit of trouble following the design procedure as I'm not sure of µ or ε. I've been told that for these materials, n ≈ -1.58. If I assume that µ ≈ -1 (arbitrarily) then I get ε ≈ -3.39. Is there any way to get these values more exactly from the eigenmode solver or from far-field simulations or perhaps from the dispersion diagram described in Chapter 3 of Ansoft's Left-Handed Design Guide? I wish I could assume that µ = -1, but I don't think I can since the blue set of spheres (see OP) experiences a magnetic resonance around 17GHz. This should affect the bulk µ, right?

Anywhom - If I continue with my design assuming µ = -1 and use the absolute value of ε (3.39), I get that my patch's L(eff) < ΔL, giving me an L < 0. Perhaps I should actually use the negative value of ε and see what comes out. I'm running out the door right now, but I'd like to get your thoughts on this and maybe see what you did.

As soon as I come back home I'll go through the design again with a negative ε and see if I get any better (more plausible) numbers. Any thoughts in the mean time will be very helpful.

Thanks,
TT

EDIT: Just went through with negative ε and got negative ε(reff). I'm not sure how to handle my negative epsilon. I get imaginary numbers everywhere. I'm still forced to use the absolute value...

Hi,

I do not follow you here completely. I believe we are on different wavelengths. But anyways, if you are interested in retreiving the parameters of your metamaterial,have a look at this discussion and download the paper mentioned here and study it.

https://www.edaboard.com/threads/190865/

But i am still not sure why you need it. If in Eigenmode solver you reseonant frequencies are around 12 and 17 Ghz.IT means you ll have a bandgap of around 1 or 2GHz not more than that.

You are trying to build a High-impedance surface so that you can use it as a groundplane with your patch antenna to reduce backward radiation and increase the directivity. IS it what you are aiming for or what is your final goal ???

/SC

Hey SC,

Okay - yes. My goals are very unclear right now. I'd like to try two things with my metamaterial:

1) Utilize it as a high-impedance ground plane such that I reduce backward radiation, and
2) Utilize it as a superstrate to improve overall antenna gain.

I won't be disappointed if I can only do one of these two, but I'd like to *try* both. The thread you've pointed me to was very helpful in determining Epsilon and Mu. It seems that I may not have left-handed propagation except in a very narrow band - I suppose this is to be expected. What's more is that I am unable to show that I have a negative index - I may not, in fact. The company that gave me these materials was sure they had a negative index, but it's beginning to look like they may not...

Anyways: There's still a resonance that experiences high impedance and one that experiences low impedance with left-handed behavior. So it seems like I should be able to utilize this material as both a high-impedance ground plane and as a superstrate to improve antenna gain...

We shall see, I suppose. I'll post back with more information.

Hey ,

Well your both goals are inter-related. You cant separate them while working with High-impedance surfaces or metamaterials. If you will use High-impedance surface as ground plane it will reduce backward radiation and in addition it will increase the diretivity of the antenna aswell(Svein piper paper has given the explanation and results related to it) and consequently gain aswell. Do remember that gain and directivity of antenna are related to each other with relation

Gain=K*directivity

where K is a constant which takes into account all the losses related to antenna(you can say it antenna efficieny factor aswell). Directivity doesnt take into account any losses whereas gain do. If antenna efficieny is equal to 100% which means K=1 then gain and directivity would be equal but in reality it never happens.

so when you will successfully design your high-impedance surface with bandgap in the operating range of your antenna then using it as ground plane with antenna will provide you both of your goals automatically. Hope you get what i mean here.

your other point,yes high-impedance surfaces are very narrowband especially for lower frequency ranges. uptill now i havnt seen a single paper with a very broad-band High-impedance surface. I do not know how you are analysing your Structure in HFSS but i will strongly suggest that trust on 'Eigen-Mode solver' results and 'Dispersion diagram' or 'Reflection-phase method' results obtained through HFSS. They will exactly characterize your metamaterial.