Finite Difference Optical Waveguide Mode Solver
Finite Difference Optical Waveguide Mode Solver
(OP)
When solving the eigenvalue problem [A]*E =(beta^2/k0^2)*E, where beta is the prop constant, E the electric field and k0 the free space wavenumber:
Is there a limit on how small a discretisation step size you can take?
In my matrix [A] the main diagonal for a 2-D mesh is constructed by the expression:
n(x,y)^2 - 2/(xstep^2*k0^2) - 2/(ystep^2*k0^2)
Obviously when xstep or ystep and reduced to a small enough size this expresion produces a negative result, which gives purely imaginary eigenvalues which are incorrect. Does anyone know have I discretized the mesh incorrectly? Any help would be greatly appreciated. Thanks K.J
Is there a limit on how small a discretisation step size you can take?
In my matrix [A] the main diagonal for a 2-D mesh is constructed by the expression:
n(x,y)^2 - 2/(xstep^2*k0^2) - 2/(ystep^2*k0^2)
Obviously when xstep or ystep and reduced to a small enough size this expresion produces a negative result, which gives purely imaginary eigenvalues which are incorrect. Does anyone know have I discretized the mesh incorrectly? Any help would be greatly appreciated. Thanks K.J
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RE: Finite Difference Optical Waveguide Mode Solver
RE: Finite Difference Optical Waveguide Mode Solver
As it turned out my discretisation was fine, it was how I was getting the eigenvalues. I was looking for the 3 eigenvalues that were largest in magnitude. This was fine when the main diagonal was positive but when xstep was reduced further it went negative, the eigenvalues I was after were no longer lagest in magnitude, the negative ones were. It was one of those cases where you leave something for a while and come back to it the problem reveals itself.
All the best!