Hi Steve,
I think your response to Matt demands a follow up. Matt's problem (as
well as ours) involves periodic boundaries. In our simulations we
clearly see that a periodically continued line source only produces a
plane wave (CW) without artifacts for specific combinations of
wavelength and k vector. These coincide very well with what we would
naively expect from periodic boundaries, i.e. sin(prop. angle) = n
lambda/period. To us this is an indication that the periodic BC are
implemented without correcting for phase mismatch at the boundaries in
order to compensate for this problem, and we are unaware of any way to
invoke such a correction.
As a consequence we do not expect the suggested approach (repeat for all
angles: short pulse propagation -> Fourier analysis) to work correctly,
since only a discrete set of frequencies for each angle (or k) produces
correct results. Anything we are missing here?
Thanks,
Markus
Steven G. Johnson wrote:
On Wed, 28 Mar 2007, matt wrote:
My trouble with this is that it isn't compatible with the periodic
plane wave excitation:
I can create a planewave with oblique incidence and periodic
boundaries, but only if the source is very narrowband (df is small).
A large df doesn't work because the periodic boundaries are frequency
specific.
For a gaussian source, a small df practically makes it a continuous
source, producing the same results.
No, that's not true. A small-df Gaussian is still a Gaussian. It
still goes to zero at both the beginning and end of the simulation,
unlike a CW source. Note that, however, you would want to use
stop-when-decayed to wait until the fields die away, rather than
running for a fixed time.
Moreover, a Gaussian is in some sense the optimal shape if you want to
maximize localization in both frequency and time.
However, it's still better to use a short pulse, as described below.
The reason you'd want this is to be able to calculate the scattering
properties for a particular angle of incidence.
Your reasoning is incorrect here.
Assuming you have linear materials, you should get the same results if
you put in a narrow-band Gaussian and look at only one frequency
component of the Fourier transform, or put in a broad-band Gaussian
and look at only one frequency component of the Fourier transform.
The latter has the advantage that it requires a shorter simulation for
the fields to die away.
Morever, if you want the scattering properties as function of both
frequency and angle, then the short pulses have a further advantage.
Each simulation with a short pulse and fixed k gives you a broad
spectrum result, each frequency of which corresponds to a different
angle. Then you repeat the simulation for a range of k's, and at the
end you'll have a 2d dataset of transmission/reflection vs. both
frequency and angle.
Steven
_______________________________________________
meep-discuss mailing list
[email protected]
http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
_______________________________________________
meep-discuss mailing list
[email protected]
http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
