Dear Steven,
It seems impossible to make both omega_p.^2 and gamma positive in our case. The
harminv give no result when we use a narrow bandwidth source(df=0.02), whereas
harminv works when a relatively board bandwidth source(df=0.1) is used. Maybe I
can't convince myself. What is your opinion?
Li
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Today's Topics:
1. Re: Is that Ok to set the epsilon in this way? (Steven G. Johnson)
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Message: 1
Date: Sat, 29 Mar 2008 19:50:31 -0400
From: "Steven G. Johnson" <[EMAIL PROTECTED]>
Subject: Re: [Meep-discuss] Is that Ok to set the epsilon in this way?
To: [email protected]
Message-ID: <[EMAIL PROTECTED]>
Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes
On Mar 29, 2008, at 8:15 AM, phcgroup wrote:
> We want to use the doping silion in our simlution. We describe
> doping silion by drude mode and get negative omega_p.^2 and positive
> gamma, so the gamma is positive and delta-epsilon is negative in
> meep. However, harminv can't give any result. We change omega_p.^2
> and gamma so that we get negative gamma and positive delta-epsilon
> in meep, whereas this model is not accurate(but the model is
> accurate at a specific wavelength which is our interested). Harminv
> give some results. My question is can we set the epsilon in this
> way? I am not sure this method is right, because the source is a
> pulse which contains much frequency signals and the material
> responses all frequency signals.
If you look at:
http://ab-initio.mit.edu/wiki/index.php/Dielectric_materials_in_Meep
you'll see that dispersive materials are implemented using an
auxiliary differential equation (ADE) to evolve a corresponding
polarization density as a driven, damped harmonic oscillator (see the
ODE for P_n). Here, \gamma is a damping term.
If \gamma is positive, you have a gain in the polarization ODE, so the
ADE will be unstable and I would be a little surprised if Meep gave
useful results in this case. So, you really need to constrain your
fits so that gamma is positive.
However, if you are only interested in the response at a specific
frequency, assuming you have no nonlinearities, then only the
dielectric function at that frequency really matters (as long as it is
stable at other frequencies). Sure, the pulse you put in contains
lots of frequencies and most of those frequencies have a "wrong"
values of epsilon, but the analysis ultimately depends on only the
frequency where you get your mode of interest. This is a consequence
of linearity. (To convince yourself of this, try putting in a pulse
of a narrow bandwidth around the frequency that harminv identified in
the first simulation---you should get the same result from harminv for
that mode, modulo small numerical differences....in general, harminv's
"fitting" procedure works better the fewer modes you excite).
Steven
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