Robert Koslover
Certified Consultant
Please login with a confirmed email address before reporting spam
Posted:
10 years ago
Oct 29, 2014, 11:49 a.m. EDT
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
Please login with a confirmed email address before reporting spam
Posted:
10 years ago
Oct 29, 2014, 2:07 p.m. EDT
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
Please login with a confirmed email address before reporting spam
Posted:
10 years ago
Oct 29, 2014, 11:07 p.m. EDT
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!
Please login with a confirmed email address before reporting spam
Posted:
10 years ago
Oct 29, 2014, 11:41 p.m. EDT
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.
