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How to plot the permeability?

Posted 29 oct. 2014, 02:01 UTC−4 RF & Microwave Engineering Version 4.4 4 Replies

Kanyu Zhang
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Hi all,

I'm making a simulation about meta-material. And now I try to plot a graph about the permeability (real part).
I try to do this by some ways, but all of this ways are only plotted the permeability of the material I used.
I want to plot the permeability of the meta-material I made not the material I used.

PS: The graph like Fig 6. in this paper
ieeexplore.ieee.org/xpls/icp.jsp?arnumber=6766276&tag=1

If anyone have the experience about this or any idea, please suggest me.

Thanks
Zhang
4 Replies Last Post 29 oct. 2014, 23:41 UTC−4
Robert Koslover Certified Consultant
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Posted: 1 decade ago 29 oct. 2014, 11:49 UTC−4
I haven't worked with metamaterials, but I'll take a cautious guess. (And I encourage others here to correct my answer, if I get it wrong.) A metamaterial permeability is, if I understand correctly, actually an *effective* permeability that applies within a certain frequency range and over a region of space that is large enough to contain the electrically-small, and typically periodic, structures that cause it to occur. I.e., it is not a true, local, point-like (aka, intrinsic) material property. And that means you need to go back to what permeability means, which is presumably the ratio of the bulk B to bulk H. (i.e., B=mu_0*mu_r*H). So, I guess what I would do, is: (1) pick a carefully-sized small volume (small compared to the problem space and small compared to a wavelength, but large compared to the mesh size, and large compared to the metamaterial unit-structure scale-size), then (2) compute spatial averages of B and H within that selected volume, and (3) compute B(ave)/H(ave) there, which should yield the effective mu_0*mu_r. I *think* that approach should work, if you choose your integration volumes and mesh sizes right. If you try this method, please let the rest of us here know if it actually gives the correct answers for fiducial cases (e..g., cases already reported in the literature). Best regards.
I haven't worked with metamaterials, but I'll take a cautious guess. (And I encourage others here to correct my answer, if I get it wrong.) A metamaterial permeability is, if I understand correctly, actually an *effective* permeability that applies within a certain frequency range and over a region of space that is large enough to contain the electrically-small, and typically periodic, structures that cause it to occur. I.e., it is not a true, local, point-like (aka, intrinsic) material property. And that means you need to go back to what permeability means, which is presumably the ratio of the bulk B to bulk H. (i.e., B=mu_0*mu_r*H). So, I guess what I would do, is: (1) pick a carefully-sized small volume (small compared to the problem space and small compared to a wavelength, but large compared to the mesh size, and large compared to the metamaterial unit-structure scale-size), then (2) compute spatial averages of B and H within that selected volume, and (3) compute B(ave)/H(ave) there, which should yield the effective mu_0*mu_r. I *think* that approach should work, if you choose your integration volumes and mesh sizes right. If you try this method, please let the rest of us here know if it actually gives the correct answers for fiducial cases (e..g., cases already reported in the literature). Best regards.
Edgar J. Kaiser Certified Consultant
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Posted: 1 decade ago 29 oct. 2014, 14:07 UTC−4
Robert,

as always a profound contribution from you. I am planning some work with anisotropic magnetic metamaterial in AC/DC and will probably try a similar approach.

Cheers
Edgar

--
Edgar J. Kaiser
emPhys Physical Technology
www.emphys.com
Robert, as always a profound contribution from you. I am planning some work with anisotropic magnetic metamaterial in AC/DC and will probably try a similar approach. Cheers Edgar -- Edgar J. Kaiser emPhys Physical Technology http://www.emphys.com
Robert Koslover Certified Consultant
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Posted: 1 decade ago 29 oct. 2014, 23:07 UTC−4
Thanks for the generous compliment, Edgar.
And good luck with your meta-material work!
Thanks for the generous compliment, Edgar. And good luck with your meta-material work!
Kanyu Zhang
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Posted: 1 decade ago 29 oct. 2014, 23:41 UTC−4
Hi Robert,

As your enlightening suggestion, the permeability for meta-material is the effective permeability.
Then, I have tried to find some paper about the effective permeability of meta-material.
And now I have found this paper, maybe it is helpful for others.
journals.aps.org/prb/pdf/10.1103/PhysRevB.65.195104


Thank you　Robert
and these authors of the paper.
Hi Robert, As your enlightening suggestion, the permeability for meta-material is the effective permeability. Then, I have tried to find some paper about the effective permeability of meta-material. And now I have found this paper, maybe it is helpful for others. http://journals.aps.org/prb/pdf/10.1103/PhysRevB.65.195104 Thank you　Robert and these authors of the paper.

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