Dear Steven,
sorry for taking up this topic again, but I do not get sensible results when
putting in Meep the effective index as refractive index. In want to reduce a 3D
waveguide into 2D without resorting to too computing intensive 3D simulations.
The point is that it is a step-index structure, i.e. strictly neither
"homogeneous" nor with a given single "refractive index", since it is a rib
waveguide with a substrate a core and a cladding with different thicknesses and
refractive indexes. I calculated the effective index of the structure taking
this also as the effective index for the reduced 2D homogeneous waveguide
(hoping this will still be a reasonable approximation, is it?) Now, if in Meep
the scalar quantity labeled as "refractive index" is the group-phase index of
the dispersionless medium (ng), then I assume that this can not be equated with
the effective index (neff), per definition. As far as I know one way to get the
former from the latter is to use the
relation: ng=neff -Lambda*(dneff(Lambda)/dLambda)
(where the derivative is not a material but a modal dispersion, it exists also
in dispersionless media). I'm inclined to say that in doing these 3D-2D
reduction it is the calculated ng one must set in the Meep code, not neff.. If
so, please confirm just to be sure. If not, I would like to understand why not
and how to correctly handle the conversion of a (multiple-)refractive indexed
3D structure into a 2D simulation.
Best, Andreas.
Quoting "Steven G. Johnson" <[EMAIL PROTECTED]>:
> On Oct 1, 2008, at 3:34 PM, Andreas Francke wrote:
>> How should be the refractive index (or epsilon (* n n))) one sets in
>> Meep be considered? The effective index, the group index, the phase
>> index, or else?
>
> It's the refractive index, period. All of the other things you
> mention are properties of wave propagation and depend on the geometry.
>
> If you have a homogeneous medium with a
frequency-independent index n,
> then the group-velocity index and the phase-velocity index are all the
> same thing. "Effective index" means different things in different
> contexts, but in any context and with any definition, the effective
> index of a homogeneous dispersionless medium is just the refractive
> index, too.
>
> Steven
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