Re: Modeling of fields in waveguides

Phil Hobbs wrote:
> Rolf Wester wrote:
>
> > Thank you very much for your helpfull reply. I still have a question 
> > concerning the filed components. If I have axial and transversal 
> > symmetry I get uncoupled wave equations for the field components. 
>
>
> Axial and cylindrical symmetry, or axial symmetry and a stack of planar 
> layers (e.g. a slab guide) will lead to a Laplacian that separates. 
> Rectangular symmetry, e.g. a rectangular guide, doesn't let you separate 
> the Laplacian outside the rectangle.  It can't, partly on account of the 
> jumps in the perpendicular E and tangential D--the jumps occur only at 
> the rectangle's edges, so the field
> outside the rectangle can't be the product of two one-variable functions 
> in x and y.
>
> > If I solve the wave equation for the Ex component how do I get the 
> > other field components Ey, Ez, Hx, Hy and Hz? I'm not sure whether the 
> > procedure I outlined above is correct. Are there any field components 
> > that are 0 everywhere (transversal electric -> Ez = 0)? My problem is 
> > how can I be sure to get all the nonvanishing field components 
> > correctly when only solving the wave equation for a single component 
> > (or may by Ex and Ey).
>
>
> Dielectric guides are intrinsically more complicated than metal guides. 
>  For example, a circular metal cylinder has two families of modes, TE 
> and TM, and the axial component of the (non-transverse) field can be 
> used as a potential function to derive all the other components.  In 
> step-index optical fibres (which are about the simplest dielectric 
> guides going), there are not two but four families of modes (EH, HE, TE, 
> and TM).  Things get uglier in a hurry for more complicated guides.
>
> The usual method is to use a mode solver to get the eigenmodes of the 
> waveguide, and then construct a suitable analytic approximation after 
> having a look at the fields, if you can find one.  Plugging in a 
> functional form *a priori* is liable to lead to poor results, unless 
> you're sure that it approximates the true fields well.  Sines and 
> cosines are non-starters.  There's a very good book, "Introduction to 
> Optical Waveguide Analysis: Solving Maxwell's Equation and the 
> Schrdinger Equation" by Kenji Kawano & Tsutomo Kitoh, that I'm working 
> through slowly myself.  Professor Siegman put me on to it.
I'm going to bye it.
> > Regarding your last paragraph what numerical scheme would you 
> > recommend, FE, FD, ..?
>
>
> It depends.  Mode solvers aren't hard to write, but I haven't done one. 
> My simulation expertise mainly centres round optimizing FDTD simulators 
> for design synthesis, so I don't have much advice to give here.  FDTD is 
> great for relatively small things (roughly, things that will fit inside 
> a 100-wavelength cube), is easy to code, runs pretty fast for a 3-D full 
> EM solver, and so on, but uses a boatload of memory and is much slower 
> than BPM.
>
> Cheers,
>
> Phil Hobbs

Hi,

thanks again for your comprehensive reply. It made things much clearer 
for me.

Regards

Rolf Wester