Describe why the total emission from dipoles with different polarizat…

…ion is an average in tutorial (#2828)

* describe why the total emission from dipoles with different polarization is an average in tutorial

* update to mention isotropic medium and polarization along principal axes

* remove unnecessary mention of principal axes

* Update doc/docs/Python_Tutorials/Near_to_Far_Field_Spectra.md

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Co-authored-by: Steven G. Johnson <[email protected]>

doc/docs/Python_Tutorials/Near_to_Far_Field_Spectra.md

@@ -662,7 +662,7 @@ if __name__ == "__main__":
 
 Note: in the case of a disc, the set of dipoles within the quantum well (QW) which spans a 2D surface only needs to be computed along a line. This means that the number of single-dipole simulations necessary for convergence is the same in cylindrical and 3D Cartesian coordinates.
 
-Note: for randomly polarized emission from the QW, each dipole requires computing the emission from the two orthogonal "in-plane" polarization states of $E_r$ and $E_\phi$ separately and averaging the results in post processing. In this example, only the $E_r$ polarization state is used.
+Note: randomly polarized emission from the QW requires computing the emission from the two orthogonal "in-plane" polarization states of $E_r$ and $E_\phi$ separately (for each dipole position) and averaging the Poynting flux in post processing. (The averaging is based on the principle that, for an isotropic emitter at a single location, the spontaneous emission can be modeled semiclassically as a random dipole for which orthogonal orientations are uncorrelated/incoherent (see e.g. [Milonni, 1976](https://doi.org/10.1016/0370-1573(76)90037-5)). In this example, we assume that the QW is only polarizable in-plane.) In this example, only the $E_r$ polarization state is used.
 
 The example uses the same setup as the [previous tutorial](#radiation-pattern-of-a-disc-in-cylindrical-coordinates) involving a dielectric disc above a lossless-reflector ground plane. The dipoles are arranged on a line extending from $r = 0$ to $r = R$ where $R$ is the disc radius. The height of the dipoles ($z$ coordinate) within the disc is fixed. The radiation pattern $P(r,\theta)$ for a dipole at $r > 0$ is computed using a Fourier-series expansion in $\phi$. The *total* radiation pattern $P(\theta)$ for an ensemble of incoherent dipoles is just the integral of the individual dipole powers, which we can approximate by a sum: