Calculating Amplitude of Elliptically Polarized EM Wave

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SUMMARY

The amplitude of an elliptically polarized electromagnetic (EM) wave can be calculated using the electric field representation given by the equation \(\vec{E}=A\cos(kz-\omega t)\vec{e}_x+B\sin(kz-\omega t)\vec{e}_y\). The overall amplitude of the beam is determined by the vector sum of the x and y components, specifically calculated as \( \sqrt{A^2 + B^2} \). This approach aligns with the method used for calculating the magnitude of a voltage source with time function \(V = A\cos(\omega t) + B\sin(\omega t)\). The discussion emphasizes that the focus is on amplitude rather than intensity, which is a separate consideration.

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  • Understanding of electromagnetic wave theory
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  • Knowledge of amplitude and phase relationships in waveforms
  • Basic concepts of RMS (Root Mean Square) values in power calculations
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Suppose I have an eliptically polarizied EM wave, whose electric field can be written as

[tex]\vec{E}=A\cos(kz-\omega t)\vec{e}_x+B\sin(kz-\omega t)\vec{e}_y,[/tex]

where the constants [itex]A[/itex] and [itex]B[/itex] are amplitudes of the [itex]x[/itex] and [itex]y[/itex] components of the beam, respectively.
How would I report the amplitude of the whole beam?

(Please note that I am not looking for intensity of the beam -- I know how to report that).
 
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This question is similar to asking, what is the magnitude of a voltage source with time function:

[tex]V = A\cos (\omega t) + B\sin(\omega t)[/tex]

There are two out of phase components superimposed on each other. In my opinion, it would only make sense to have some RMS value if you are doing power calculations.
 

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