UPML in cylindrical coordinates. Derive an equivalent of the UPML in 2D cylindrical coordinates, for the rmax boundary and the z = 0 and zmax boundaries. Implement this PML in Problem 4.9, for the half-wave dipole and monopole problems. Note that for the monopole you will not need the PML at z = 0.
Problem 4.9
3D circular waveguide in cylindrical coordinates. Create a simulation space for a circular waveguide in 3D cylindrical coordinates. Let the radius of the waveguide be 2.7 cm, and design it for a frequency of 10 GHz. Excite the waveguide at one end with a hard source at a frequency of 10 GHz, where the source field is defined along a line through the cross-section of the waveguide. Plot a snapshot of the field patterns a few wavelengths down the waveguide; what modes exist in this waveguide? Repeat for frequencies of 8 GHz and 12 GHz and compare the results.