Re: negative dielectric constant

[Kevin Thomas <kjt@cray.com>]

Allen,

I can't address your main question about a negative dielectric
constant, but I can confirm your suspicion that the dispersive
materials feature in LC is not yet functioning.  You can create
models with dispersive materials (Debye or Lorentz), but the
simulation does not run correctly.  Basically, all the plumbing
is there for the FDTD implementation, but it doesn't work.

-- 
Kevin Thomas    kjt@cray.com   tel 1-651-605-9072
http://lc.cray.com/~kjt/        or 1-800-284-2729 x6059072


Date: Thu, 19 Jul 2001 00:44:23 -0500 (CDT)
From: Allen Lee <allentc@ece.rice.edu>
To: <lc-users@maori.colorado.edu>
Subject: negative dielectric constant

Hi LC users, I'm trying to use LC and a home-grown fdtd code to look at
the diffraction of small metal structures at near-infared wavelengths. The
problem I am encountering is that for the materials/wavelengths I'm
working with, the real part of the dielectric constant is negative (like
a plasma, for example).  As you might guess, when I try simulating this
material by illuminating it with a plane wave, the algorithm becomes
unstable and the fields rapidly diverge to infinity.

The LC wizard warns me about my material settings, and I've looked a bit
at the stability of the standard FDTD algorithm, and it looks like this
instability is what one would expect from standard FDTD and these
material parameters.

One weird thing is that in the "literature" some authors make it sound
like standard FDTD _can_ be used for materials w/negatve real permittivity
(like a plasma), so long as frequencies where FDTD coefficients become
singular are avoided. This sort of makes sense, only I get the instability
regardless of incident frequency, both on LC and in my home-grown code
where I know exactly what the update coefficients are. It seems to me that
since the incident plane wave is not infinite in extent, it contains some
high-frequency components that eventually get amplified and blow up the
fields (just like if you use a time step beyond the Courant limit).

Here are my questions-- any help is much appreciated.
- This instability is what one would expect to see using a negative
permittivity, right? I see the same thing with a positive loss term
(conductivity).
- If so, how can I model this material? My understanding is that I can do
a full treatment of the material as a dispersive material, but that seems
like more work than necessary, because I'm really only interested in one
incident frequency at a time. Is there some way to avoid the instability
by starting the material parameters at false values and then "bringing
them back" as time passes? Also, it doesn't look like LC's dispersive
materials is functional yet.

Thanks a bunch,
Allen
allentc@ece.rice.edu