Hi gsun, thanks for your answer. Hi have a few things I need to clarify:
"1: simulate the whole device with regular output waveguide"
Do you suggest I should terminate the periodic structure at some x-position and couple the light into a uniform waveguide?

"2: modify the PML to have more absorption for your current settings. The newest version has this feature: auto scale pml parametersÔÇØ.
I read only yesterday about this new feature.
Do you mean that setting "auto scale pml parametersÔÇØ to enabled and setting "extend structure through pml" to disable (unlike in the image above) will allow me to run the simulation correctly with an extension of the structure into the pml layers (like in my image), without convergence issues?
Does that mean that if I use FDTD without the new feature, I need to find (by trials) some configuration of pml layers and dt factor (<0.99) for which I will get a stable simulation?

"due to the Bloch wave nature, the transmission in your current settings will have some change when you change the monitor location, even (though) the PML does not change." (I assume the word "though" is missing in your text)
I didn't show any monitors in my image. What monitor are you referring to?
My goal is to evaluate the distributions of EM fields that are generated deep inside the waveguide due to the light is coupled from the uniform waveguide (on the left). I intend to run the simulation with profile monitors close to the PML region; I assume that with correct PML layers there should be no back propagating waves and so the field distributions will represent the forward propagating modes (my geometry is tuned to have single mode operation at the wavelengths of interest). Are my assumptions correct?