Not realy: the textbook oversimplifies this relation for plane wave only, and it does not depend on space. However, in simultion,the Poynting vectors are a funciton of space, so Px, Py and Pz are power density (Poynting vector), not the power. Power is the integration of P dot source normal over the monitor plane, as show in the link of the first reply: the script command "transmission".
You should be able to find a textbook for such relationship. You can also search online for Optical Intensity.
Please note that in most cases Lumerical's tranmission is always normalized to the source power.
In addition, the forum policy is for "one question one answer" for better reference. So if you have quesitons different from the first post, please write a new post. Thank you!
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