Homework
HW4-1.  In their interaction with electromagnetic radiation, the alkali metals behave approximately as dilute plasmas.  Estimate the plasma frequency for sodium, looking up the relevant quantities.  Show that it explains the result that sodium is transparent at wavelengths less than about 210 nm.  What part of the electromagnetic spectrum is this?  Sketch a graph showing both the phase velocity and the group velocity in such a material as functions of radiation frequency.
9.26 - Derive and play with the equations for a waveguide
9.27 - No TE00 mode
9.28 - TE modes in rectangular wave guide
HW4.2 - Suppose a rectangular waveguide is filled with a dielectric which undergoes breakdown (sparking) at 10 kV/m. Calculate the maximum power that can be carried by the TE10 mode without breakdown if the dimensions of the waveguide are 5 cm x 5 cm.  Assume the frequency is twice the cutoff frequency.
9.29 - Group velocity of wave guide modes

Examples class
9.30 - TM modes in rectangular wave guide

Bonus
9.38 - resonant cavity
B4.1 - Determine the TM and TE modes of propagation in a cylindrical waveguide with a circular cross section, by separation of variables in polar coordinates. The radial functions are Bessel functions regular at r = 0. Determine the first few cutoff frequencies of each type of mode, and note any degeneracies.