On Sat, 20 Oct 2007, adrian wrote:
>     I'm wondering the definition of complex fields.
>  Typically, in time domain, E(r,t)=E(r)cos(wt). But how about the 
> complex fields?
>  Are they just simply represented as E(r,t)=E(r)exp(-jwt) or something 
> else?

Either real or complex fields can be any function of time, depending on 
the sources.

However, if you put in a time-harmonic source, a continuous-wave source in 
Meep, then the time dependence should be asympototically exp(-iwt) for a 
frequency w.

> In addition, how to find out the eigen mode? In tutorial, one just 
> exited one resonant mode and saw the field pattern. However, if the 
> input is continuous, then the field pattern will include the source 
> itself. So I don't think that field pattern is real eigen mode. But if 
> one just turned off the source and record the field pattern after a 
> couple of periods, then the field will decay with time, if so, how do we 
> get the exact spatial distribution of eigen mode? More specifically, how 
> can we separate the time argument from the field pattern?

Put in a narrow-band gaussian pulse and look at the field pattern when the 
pulse has turned off.   Even if you have a resonant mode, assuming it is 
sufficiently long-lived then you should still have the field pattern 
(multiplied by the decay coefficient).  As long as the pulse source is 
narrow-band enough, no other modes should be excited significantly.

Regards,
Steven G. Johnson

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