A.Taflove's book "Computational Electrodynamics" explains well about dispersion in numerical schemes. But how can numerical wavenumber be actually be calculated, when only spatial steps and timesteps are know?
All analysis made so far are for free space. For waveguides, velocity changes to a specific phase velocity of a propagating mode. But what if more than one modes are propagating at once?
what if you consider an case of fiber optic cable (an dielectric wave guide), I feel there may be you got hint for it.
It's not a problem. A fiber optic cable is also waveguide. Unfortunately all methodologies are about the free space 1-D scheme
can't understood the free space 1-d scheme. Like in case of an optical waveguide we consider an varying index (difference) that change (under certain boundary condition)
result in multiple mode that propagates through the guide. (if depending factor are only either wavelength & index & radius )
I can only think of complex analysis in 3d varying effect of index or radius on multiple propagating mode
It's a different thing. Numerica wavenumber doesn't really exist. It's a way to study the influence of discretization in space and time to the results
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