Bodies of revolution. Write a 2D simulation to utilize the bodies of revolution method for a cylindrical waveguide, similar to Figure 12.10. Use the same waveguide parameters as in Problem 4.10. Include an absorbing boundary at the far end of the waveguide. Excite the waveguide with an r source at the edge of the waveguide (near the PEC boundary).
(a) Allow for only one expansion in φ (m = 1) and solve the update Equations (12.40). Why does m = 0 not work?
(b) Repeat (a), but add expansions one at a time, up to m = 5. In each case, plot the field pattern 5 cm down the waveguide and compare.
(c) Explore different methods for exciting the waveguide, i.e., different field components at different locations at the end of the waveguide. How does the excitation affect the relative amplitudes in each "mode"?
