The Solution

In Figure 4.3, “Inhomogeneous Waveguide Solution” we can see the z component of a solution. The mode and the eigenvalue for this solution is given on the right hand corner of the information bar. In this case, the mode is 1 (remember modes start from 0) and the eigenvalue is 0.007. Once you know the eigenvalue, you can calculate the cutoff and other parameters.

Figure 4.3. Inhomogeneous Waveguide Solution

Inhomogeneous waveguide solution

For each mode you will see 3 contour plots. They are the x, y and z components of the electric field. For a TM mode, like the one given in Figure 4.3, “Inhomogeneous Waveguide Solution”, you will not see anything for the x and y components. However, for a TE mode, you will see the x and y components only. You will not see a nice contour plot like the above so do not be alarmed. In order to see each mode you have to select Popup->Next Eigenmode from the popup menu. It is also possible to switch to the next eigenmode by pressing n in the keyboard.

You can see solution to another eigenvalue problem in Figure 4.4, “Problem with 5000 unknowns”. This uses ARPACK for the solution. The problem size was 5000 by 5000. If you had used normal direct solution methods to solve this problem, it would have been nearly impossible. So use your judgment in choosing the correct solver according to the problem at hand.

Figure 4.4. Problem with 5000 unknowns