Csilla, thank you very much!    I think i've figured it out!

Hi

Here's how I explain this to myself, in case it's helpful. In sequential ray-tracing, the Optical Path Difference is computed relative to a reference sphere radius. Hence you might say that a system has a wavefront error of lambda/2 say, compared to a sphere of radius 50 mm. These are just made up numbers to show the scale length difference between the optical path difference of the wavefront and its bulk radius of curvature. 

In POP, we use the same trick, by propagating a 'pilot' beam, which is a best-fit Gaussian matched to your input distribution. That pilot beam is propagated using the Skew Gaussian code to give all the bulk properties of the beam as it goes through the system: are we near the beam waist, far from it, etc. The phase of the pilot beam is always spherical, as the Gaussian beam calculation is purely paraxial.

The POP phase is then the difference between the real phase of the POP beam and this reference phase. Again, this allows you to see the 'difference' signal of maybe a wavelength or less, compared to the bulk curvature of the wavefront.

So, think of the pilot beam as being the reference arm of an interferometer, and you interfere your real wavfront with it. What you see are the differences in phase, and this is that the POP phase shows.

Hope that helps,

- Mark

Thank you Mark! 

Although in my question I uploaded a POP plot of 'Irradiance X-Cross section' , you managed to explain the pilot beam in terms of 'Phase difference'. I didn't have a look at the POP phase before, and when I open it, it looks like:

I don't understand how to analyze the phase difference quantitatively, but when I set the Waist smaller(from 2 to 1), the phase difference becomes smaller too:

So this POP phase diagram shows how ideal the real beam is, i.e. the smaller Waist, the closer the real beam gets to pilot beam.