On Jul 16, 2009, at 11:44 AM, liu wrote:
Anybody knows how to set material with Raman scattering?
There is no direct "Raman material" in Meep.
A reasonable way to handle stimulated Raman scattering, in the weak-
scattering (undepleted pump) approximation would be to do two linear
calculations. First, you do a linear calculation with your source
field to get the incident electric field at the location of the Raman
material. Then you multiply the field by the Raman susceptibility to
get a polarization at the scattered (Stokes or anti-Stokes)
frequency. Using this polarization as a source at the new frequency,
you can do a second linear calculation to compute the Raman-scattered
field.
(You could call this a first Born approximation, or some would use the
term "volume-current method".)
It might be possible to model a Raman-like process directly, in a
single simulation, by including an oscillating component (at the Raman
detuning frequency \Omega) in the dielectric function at some point --
the Fourier coefficients of this oscillation correspond mathematically
to Raman susceptibilities. Right now, doing an oscillating dielectric
function efficiently in Meep requires some trickery, however.
A full simulation of a Raman process would seem to require modeling
the populations of the atomic vibrational states corresponding to the
Raman bands, perhaps similar to how my colleague Peter Bermel has
modelled 2-level systems coupled to FDTD for lasing (P. Bermel, E.
Lidorikis, Y. Fink, and J. D. Joannopoulos, “Active materials embedded
in photonic crystals and coupled to electromagnetic radiation,”
Physical Review B, vol. 73, p. 165125, April 2006). We have some
effort underway to add a similar capability to Meep for saturable
gain, but it's not ready for release yet.
Steven
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