Re: negative permeability and permittivity

["Timothy S. Sullivan" <sullivan@KENYON.EDU>]

I just got back from the March Meeting and attended a session on Friday
where Sheldon Shults gave a brief reprise of the talk he gave earlier in
the week. I checked a few concepts with his collaborator David Smith
after the session. I'll try to summarize what I heard.

First, this fit in with a theme of the meeting called "Metamaterials".
Metamaterials are composite of structured materials whose component
sizes are smaller than the wavelength of the exciting wave. Thus, the
man-engineered material responds to the wave with some *effective*
dielectric constant and magnetic permeability to an electromagnetic
wave, for example. An example given was that natural materials might
have physical contraints that prevent them from having simultaneously a
large value of dielectric constant and high permeability. But a
composite material composed of a high dielectric material and a
different high permeability material will respond to EM waves of
wavelength longer than the size of the individual material domains as if
the material were composed of a material of effectively high values of
both properties. Another example given was that of a material that was
used as the ground plane of an antenna. The surface was structured so
that EM waves parallel to the surface had a band gap (analogous to
electron band gaps in solids) so that waves wouldn't propagate parallel
to the surface. This turns out to be a way to more effectively radiate
energy in one direction only.

So, first, the announcement of materials with negative dielectric and
permeability are only materials in this "metamaterial" sense. Second, as
someone has already pointed out, the effectively negative values are
only for AC fields, not DC. So no problems with negative energy
densities.

I'll try to describe the experiment as best I can. All mistakes and
misconceptions expressed below are strictly my own.See
http://www.aip.org/physnews/graphics/html/composite.html for a diagram.
(Link copied from Doug Craigen's message.)

Imagine passing microwaves through a "comb" of parallel wires as in the
demonstration of polarization that often comes with microwave kits for
physics labs. If the polarization fo the waves is parallel to the wires
then we have seen that the microwaves won't propagate through the comb.
The comb can be thought of as a medium with an effective dielectric
coefficient. The negative epsilon gives the wavevector k (=
sqrt(mu*epsilon)omega/c) an imaginary component and when you plug this
into exp(ikx) this gives a real part which corresponds to damping.
Shults does this measurement with only the parallel wires shown in the
diagram and sees basically no energy transmitted through the structure
(within their measurement capabilities).

It then turns out that split conducting rings placed with their normals
parallel to the magnetic field vector in the microwave act as an
effective medium with negative permeability. This is demonstrated in
much the same way as for the electric field case. They take out the
parallel wires from the apparatus as shown in the experimental diagram
and observe almost zero transmision through the structure. Again, the
negative permeability gives a real part to k and hence damping.

Now, put the wires and the rings together. Now microwaves propagate
through the system. The two effectively negative quantities multiplied
together again give a real value and hence no damping (at least from
this source).

The other relationship that they discuss that is non-intuitive is the
relationship between the Poynting vector S and the wavevector k. In
"normal" materials they are parallel (ignoring anisotropic materials
where you might say they are almost parallel in this context.) In the
materials Shults describes they are antiparallel. Thus, k is in the
direction of ExB and S is in the direction of ExH still hold, but the
effectively negative permeability gives opposite sign to the directions
of k and S.

Perhaps the surprising claim is one that they have not yet demonstrated.
It would essentially reverse our usual thoughts about Snell's Law. For
example, we are familiar with the demonstration that a light ray
travelling through a flat slab of material will emerge parallel to its
incident direction. Not so if the medium has an effectively negative
dielectric coefficient. In fact, if this is right, a flat slab could be
made to focus incident waves. (I haven't thought about this enough to
give a better explanation.) This would actually be a more vivid
demonstration of something surprising as the direction of k in a one
dimensional material is really pretty abstract, as opposed to the
direction of S, say.

While I was talking to David Smith we were approached by Yablonovich
from UCLA (the creator of the first optical photonic band gap material.)
His comment to Smith was that this phenomena, or at least something very
much like it, was already known from plasma physics.

My sense is that there really isn't any new fundamental physics here,
but that this is a radical change in the way people are *thinking* about
how to engineer the interaction of EM waves and materials. The first
impact will be felt in the microwave regime where length scales are long
and there is a lot of money for wireless communications. Already
demonstrated are the use of effective material concepts to improve
antenna design. One group is already designing active components into
the effective medium. Simulation shows that they can tailor the
microwave reflectivity or tranmittance of a thin slab to be pretty much
whatever they like. They suggest a patch of this material on a military
aircraft would give a friend-or-foe interrogation system that doesn't
rely on active transmission from the queried plane. Then people will
push this into the IR using integrated circuit technology. Visible is a
little farther down the road as it will rely on advances occuring in
nanostructured materials fabrication. But there is already a
demonstration of fiber optic cable where dispersion is much reduced
because of confinement of the light wave (fiber optic communciation uses
a lot of 1.5 micron IR) to an air core using photonic band gap
techniques.

Tim Sullivan
sullivan@kenyon.edu



Ludwik Kowalski wrote:
> Peter Schoch asked about "a negative permeability".
>
> A dielectric with negative permeability would allow me
> to build a capacitor with negative C storing negative
> energy proportional to V^2. Crazy! I would not hesitate
> to say this to your student. Somebody is probably using
> the familiar word for something else. This is always
> an invitation to trouble.
> Ludwik Kowalski