I want to ensure the Apodization function used in the FDTD’s profile monitor. Is that a Gaussian function? Also, the Apodization time width we set in the monitor is the FWHM of this Gaussian function or just the gama factor in Gaussian function?
Yes, it is a Gaussian function and the width parameter specifies FWHM around the center time as shown on this figure:
You can read more about the apodization function on this KB page.