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Describe why the total emission from dipoles with different polarization is an average in tutorial #2828

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2 changes: 1 addition & 1 deletion doc/docs/Python_Tutorials/Near_to_Far_Field_Spectra.md
Original file line number Diff line number Diff line change
Expand Up @@ -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, in an isotropic medium, the emission from dipoles with different polarization is incoherent. This is true whether the dipoles are located at the same or different positions within the QW.) In this example, only the $E_r$ polarization state is used.
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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:

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