If you want to compute the enhancement of anything (e.g. absorption) due
to a structure, the most straightforward approach is similar to what you
would do in an experiment: compute that thing with the structure, and in
some control without the structure, and take their ratio.
e.g. since you are interested in emissivity of a surface, by Kirchhoff's
law you can instead compute absorbtivity. A surface will ordinarily have
periodic boundary conditions in two directions, so you will set up a cell
that is periodic in x and y with absorbing PML layers in z. Then, do
three calculations:
(i) with just vacuum, send in a pulse near from a planewave
source near the "top" of the cell (from the +z direction)
(for now, assuming normal incidence for simplicity)
and compute the transmitted flux F0 near the bottom of the
cell (-z direction). You will use F0 for normalization.
Also, save the flux in a plane near the top of the cell,
using save-flux, which you will subtract later to compute
reflection (see the waveguide bend in the Meep tutorial).
(ii) repeat the calculation with some solid material (e.g.
carbon) for z < 0 and vacuum above. Compute the transmitted
flux Ft and the reflected flux Fr, the latter using
load-minus-flux as in the tutorial to subtract the incident
fields. The absorbtivity is then A = 1 - |Ft/F0| - |Fr/F0|
(= 1 - T - R). This will be your "control"
(iii) Repeat the calculation for the structure you care about,
e.g. a surface with a lattice of spheres on top, and
compute the absorbtivity as in (ii).
Then the ratio of your answers in (iii) and (ii) is the enhancement of
absorptivity (= emissivity). Note that by using the fourier-transformed
flux of a pulse in this way you get the absorptivity spectrum over a whole
bandwidth at once.
Assuming dielectric materials (no metals), this should be doable on a PC.
Regards,
Steven G. Johnson
On Thu, 22 Nov 2007, PattiMichelle wrote:
> Hi All: I am a laboratory experimentalist in Los Angeles and was
> finding some very interesting enhanced-greybody emissions from
> micron-sized, monodisperse, perfectly spherical carbon particles when
> they are heated in a flame. I believe the emissions are enhancements in
> the absorption coefficient of the particles, both individually and in
> clusters, from the complex index of refraction of carbon in conjunction
> with the extreme symmetry of the particles. (I've seen some plots of
> single-sphere analytic solutions that suggest this, and nonspherical
> particles of the same material give no enhancement to wavelength plots
> of Q_abs.)
>
> I am looking at Meep as a potential way to investigate this, since
> computer power has become very cheap, but I'm not sure how to "get at"
> Q_abs (absorption coefficient) from a program like Meep. I was reading
> the Meep docs and it looked like I could run cases with and without
> particles present and ratio the fields. I would appreciate any
> suggestions for approaches with Meep and/or other software (although my
> budget doesn't allow for expensive commercial software). I'm not a Real
> Programmer, but I've written a lot of software to control my experiment
> controller and data reduction computers.
>
> Thank You Very Much, In Advance,
> Patti Sheaffer
>
> PS: I'm currently running through the setup documentation on a SuSE
> 10.3 Linux box.
>
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