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Choosing the polarization vectors, Quantization of EM field

I think you can define the polarization vectors $\mathbf e_{\mathbf k}^{(1)}, \mathbf e_{\mathbf k}^{(2)}$ for the given $\mathbf k$ in any way, provided their dot product is zero. There is no need ...
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For unpolarized plane wave traveling normal incident from air to dielectric what are the reflection and transmission coefficients?

The amplitude reflection coefficients as calculated from the Fresnel formulae. There's one for s-pol, and one for p-pol, and at normal incidence one might expect them to be the same, but there is a ...
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For unpolarized plane wave traveling normal incident from air to dielectric what are the reflection and transmission coefficients?

Unless the dielectric material is anisotropic, light incident at 90 degrees to the surface has the same reflectivity for any polarization. This should be clear from the fact that the dielectric has ...
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Elliptical polarisation - unsure as to what quantity is on wikipedia page

An oscillating function can be associated with one component of a vector which is rotating in a complex “phase space”. $e^{iθ}$ = cos(θ) + i sin(θ), where θ = ωt + ϕ. In your question, the α's ...
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Why Does an Electric Field Arise In This Situation?

You have omitted the effects of electrochemistry, by which the application of a voltage difference between two pieces of metal facing one another in water will cause the formation of ions in the water ...
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Why Does an Electric Field Arise In This Situation?

The problem lies in the measurement method, not in the medium itself. As soon as you connect the battery, you will always have an electric field (actually also if you do not connect the battery), no ...
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Why Does an Electric Field Arise In This Situation?

Water conducts electricity, so the battery drives a steady current through the water. There is therefore a current desity $$ {\bf j}= \sigma {\bf E}= - \sigma \nabla \phi$ $$ where $\sigma$ is the ...
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How to convert from plus and cross polarization modes ($h_{+}$, $h_{×}$) to spin-weighted spherical harmonic $h_{lm}$?

Yes. (This answer assumes you want to go from $h_{\ell m}$ to $h_+$ and $h_\times$; in other words, to go from NR data to a predicted waveform that a detector like LIGO might see. If you want to go ...
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