how to find propagation constant in waveguide with FDTD?

Hello,

You may use a shorted WG, some wavelength long. Excite it and look at the ISWR or VSWR pattern for sinusoidal excitation. This would at least give you the BETA component of GAMMA.

If you want ALPHA also, you may need a longer line to see a reduction in ISWR or VSWR. Based on the SWR, you can calculate the reflection coefficient and the loss.

Other option to assess the complex propagation constant is to use it as a resonator, but depending on available data on WG resonators this may be more elaborate.

If you have difficulties with the definition of 'propagation constant' then have a look at

Propagation constant - Wikipedia, the free encyclopedia

If not then

https://www.edaboard.com/thread152214.html

may be a start with respect to the FDTD side.