On Mar 7, 2009, at 10:29 AM, adrian wrote:
Thanks Steven.
How about the definition for complex field in meep?
I tried to find it in meep reference but I need log in to that
page.
This doesn't make any sense to me --- I just checked, and I can view
the Meep Reference page without "logging in" to the page. See:
http://ab-initio.mit.edu/wiki/index.php/Meep_Reference#source
Is it:
Er+j*Ei=E0*exp(j*w*t) ?
I suspect that your question needs to be rephrased.
The "definition" of a complex field is just the field in response to a
complex current (or complex initial conditions).
For example, if you turn on force-complex-fields? and you put in a
complex current pulse, you get a complex-valued pulse in E, not a CW
field as in your formula above.
Perhaps what you meant to ask is how the complex current is defined
for a continuous-wave source. This is described at the link I defined
above: a CW current source is proportional to
exp(-i w t)
for an angular frequency w ( = 2 * pi * frequency). The resulting
electric field (after initial transients die away) will also be
proportional to exp(-i w t) in this case.
Similarly for Gaussian pulses, etcetera. The point is that Meep
follows the "physics" sign convention that an angular frequency w
corresponds to exp(-i w t) time dependence, not the "engineering" sign
convention of exp(+ i w t).
And when forced-complex-fields? is false, the normal value we
get is E0*cos(w*t), which should be equal to Er.
When force-complex-fields? is false, the complex current is replaced
by its real part. The corresponding electric field is also replaced
by its real part (in linear media).
Whether this is E0*cos(w*t) will depend on your current source. Even
if you have a CW current at a frequency w, the time dependence of the
*electric* field (after transients have died away) won't necessarily
be cos(w*t), because in general there is a phase difference between
the current and the resulting fields. So, in general for a CW source
you will eventually get fields proportional to cos(w*t - phi) for some
phases phi (depending on the field component, the position, and the
geometry).
The only thing Meep-specific in all of the above is the sign
convention for the frequency; everything else is simply a consequence
of Maxwell's equations.
Steven
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