Hello Sumeet,
Based on the diagram you attached it would appear that your incidence plane is XY (propagation in XY and interface normal is Y). You are correct, if this is the case then the S (E field perpendicular to the incidence plane) would be the Ez group while the P( E fields parallel to the incident plane) would be the Ex/Ey group.
S – Ez, Hx, Hy
P – Ex, Ey, Hz
In regards to your question about the Poynting vector calculation things get a bit trickier.
S = E x H
which leads to
S = (EyHz-EzHy)x+(EzHx-ExHz)y+(ExHy-EyHx)z
If you have a source that is purely S or purely P polarized then you can neglect the field components of P when working on S, etc. This yields
S (S polarization) = -(EzHy)x+(EzHx)y
S (P polarization) = (EyHz)x-(ExHz)y
Note this separation cannot be done if your source contains field components of both polarizations.
In OptiFDTD the Poynting vector for an observation area is calculated along the direction normal to the plane. This means to get the polarizations above you should create an observation plane perpendicular to x and one perpendicular to y and get the fields from these. From there you can calculate the above equations.
Scott
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