Calculating Amplitude of Elliptically Polarized EM Wave

In summary, the conversation discusses an eliptically polarized EM wave with an electric field given by \vec{E}=A\cos(kz-\omega t)\vec{e}_x+B\sin(kz-\omega t)\vec{e}_y, where A and B are amplitudes of the x and y components. It is mentioned that the amplitude of the whole beam can be reported, but not the intensity. This is similar to asking for the magnitude of a voltage source with a time function of V = A\cos (\omega t) + B\sin(\omega t), which has two out of phase components. It is suggested that an RMS value may be used for power calculations.
  • #1
TriTertButoxy
194
0
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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  • #2
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.
 
  • #3


To calculate the amplitude of the whole beam, you would need to use the Pythagorean theorem to find the resultant amplitude. This can be done by squaring both the x and y components, adding them together, and then taking the square root of the sum. In this case, the resultant amplitude would be √(A^2 + B^2). This represents the overall strength of the electric field in the elliptically polarized EM wave. It is important to note that this amplitude may change over time as the wave propagates.
 

1. What is an elliptically polarized EM wave?

An elliptically polarized EM wave is an electromagnetic wave that has both electric and magnetic components that vary in magnitude and direction over time. This results in a wave that appears to trace out an elliptical path as it travels through space.

2. How is the amplitude of an elliptically polarized EM wave calculated?

The amplitude of an elliptically polarized EM wave can be calculated by finding the maximum value of the electric or magnetic field at any given point in space and time. This is typically represented by the height or width of the elliptical path traced out by the wave.

3. What is the significance of the amplitude of an elliptically polarized EM wave?

The amplitude of an elliptically polarized EM wave represents the strength of the electric and magnetic fields that make up the wave. It can also affect the intensity of the wave, which is a measure of its energy.

4. How does the amplitude of an elliptically polarized EM wave affect its polarization?

The amplitude of an elliptically polarized EM wave does not affect its polarization. The polarization of a wave is determined by the orientation of its electric and magnetic fields, not their strength. However, changes in amplitude can affect the shape and size of the elliptical path traced out by the wave.

5. Can the amplitude of an elliptically polarized EM wave be negative?

Yes, the amplitude of an elliptically polarized EM wave can be negative. This simply means that the electric or magnetic field is pointing in the opposite direction as the positive amplitude. This can happen if the wave is traveling in the opposite direction or if there is interference from another wave.

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