On Oct 11, 2008, at 7:02 AM, Andreas Francke wrote: > 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.
First, there is no such thing as "correctly" modeling a 3D structure by a 2D simulation, except for very restricted classes of 3D structures (typically with low-index contrast). The "effective index" technique that you are describing is simply an ad hoc heuristic, with no particular guarantees of accuracy of any kind -- it is simply a simple model that you hope will capture the essential physics of the more complicated system. It is important to keep in mind that this is not rigorous. So, it comes down to what characteristics of the 3d system you want to try to fit, and how best to fit them. Again, this is ad hoc; there are no "correct" answers. What I would suggest is to do a fit. Say that you want to match two things: the dispersion relation, and the lateral field profile or decay rate or something like that. You have two parameters: the waveguide index and the cladding index (here, I'm talking about the actual refractive indices). Using MPB or some similar tool, choose these two indices to fit the desired characteristics of the 3d waveguide as closely as possible in your desired frequency range. Steven _______________________________________________ meep-discuss mailing list [email protected] http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
