On Jul 14, 2009, at 11:08 AM, Alexandre Besnier wrote:
Good morning,
I'm a student and I work currently on your software Mpb, I try to
make a rectangular lattice of 0.204µm x 0.561µm size, and I would
like to understand units give by band diagram.
On your wiki pages you say that frequency is given in c/a unit, but
I don't understand several things :
- In band diagram, if I obtain frequency = 1, that say a=c, ie
a=3.10^8 meters ?
No, it means that frequency = 1 (c/a). Since frequency = c / lambda,
this means that
c/lambda = 1 (c/a)
and thus
lambda = a
Put another way, the frequency in MPB's units is exactly the same as a/
lambda (where lambda = vacuum wavelength).
- Normally, "a" is the lattice period, but with rectangular
lattice, I have two periods, so what is "a" compared with my two
periods ?
"a" is whatever unit of distance you want; it doesn't have to have
anything to do with the lattice constant(s).
You are perfectly free to use a=1um, for example, and then specify the
size of your computation cell as 0.204 x 0.561, and give all distance
units in microns. In this case the frequencies returned by MPB are
equivalent to 1/(lambda in microns).
- In the page "Mpb User Tutorial/A few words on units", you say
at the last paragraph : "Thus, the corresponding vacuum wavelength
is a over the frequency eigenvalue." It is not "Thus, the
corresponding vacuum wavelength is c over the frequency
eigenvalue." ? Because frequency * lambda = c ?
See above. This is a consequence of using c/a units of frequency.
| Finally, if I would like to have frequency in Hz, what I have to do
to convert it ?
Multiply Meep's units by c/a in SI units.
Steven
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