Exercises

1. Demonstrate that the electric and magnetic fields inside a waveguide are mutually orthogonal.

2. Consider a ${\rm TE}_{mn}$ mode in a rectangular waveguide of dimensions $a$ and $b$ . Calculate the mean electromagnetic energy per unit length, as well as the mean electromagnetic energy flux down the waveguide. Demonstrate that the ratio of the mean energy flux to the mean energy per unit length is equal to the group-velocity of the mode.