1. Waveguides

2. Waves in cylinder
In a waveguide whose cross-section is uniform along z-axis, variation of E, H is proportional to exp(-j z).
In a waveguide, transverse E and H can be obtained from Ez and Hz.

3. TM, TE mode
TM mode : Electromagnetic wave modes with Hz=0 are called TM modes (Transverse Magnetic). Those modes can be found from Ez.
TE mode : Electromagnetic wave modes with Ez=0 are called TE modes (Transverse Electric). Those modes can be found from Hz.

4. Eigen-function expansions in waveguides
TM modes
TE modes
TEM modes

5. Rectangular waveguide (TE mode)
Boundary condition

6. Field lines for some of the lower order modes of a rectangular waveguide. Reprinted from Fields and Waves in Communication Electronics, Ramo et al, © Wiley, 1965)

8. Example : WR-90 WR-90 X-band 8.2GHz~12.4GHz (2.286cm × 1.016cm)
5GHz input signal
Attenuation by a 3cm-long evanescent waveguide

9. Cavity resonator
Minimum frequency

10. Cylindrical waveguide
By separation of variables

11. Cylindrical waveguide mode

12. Cutoff frequencies of the first few TE and TM modes of a circular waveguide, relative to the cutoff frequency of the dominant TE11 mode.