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Suppose we have the x and y components of the electric field being described as [itex](E_{x}e^{i(kz-\omega t)}, E_{y}e^{i(kz-\omega t +\phi)})[/itex], what is the intensity?

I think the correct answer is [itex]E_{x}^{2} +E_{y}^{2} + 2E_{x}E_{y}\cos\phi[/itex]. However, I am not sure how to deal with this using the Jones formalism. In that, the intensity is given by [itex]E^{\dagger}E[/itex] which would give

[tex]\begin{pmatrix} E_{x}e^{-i(kz-\omega t)} & E_{y}e^{-i(kz-\omega t +\phi)} \end{pmatrix} \begin{pmatrix} E_{x}e^{i(kz-\omega t)}\\ E_{y}e^{i(kz-\omega t +\phi)}\end{pmatrix} =E_{x}^{2} +E_{y}^{2} [/tex]

Clearly, the above answer is independent of the relative phase and I think it cannot be right because of that. So what is the correct way to calculate the intensity using Jones formalism? Thank you

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# Measuring intensity of superposed waves using complex amplitudes

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