Measuring intensity of superposed waves using complex amplitudes

In summary, the conversation discusses the calculation of intensity using the Jones formalism for the electric field with x and y components. The first result suggests that the intensity is given by E_{x}^{2} +E_{y}^{2} + 2E_{x}E_{y}\cos\phi, but the second result shows that this is not entirely correct as it does not take into account the relative phase. The correct expression for intensity is E_x^2 + E_y^2, where the phase does not have any influence.
  • #1
McLaren Rulez
292
3
Hi,

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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  • #2
How do you get your first result?
If you flip the sign of Ey, you modify your calculated intensity, which is wrong.
 
  • #3
The first result was using

[itex]I = (E_{x}e^{-i(kz-\omega t)}+ E_{y}e^{-i(kz-\omega t +\phi)})(E_{x}e^{i(kz-\omega t)}+ E_{y}e^{i(kz-\omega t +\phi)})[/itex]

Now that I think of it, this doesn't seem correct either. What is the correct expression for intensity?
 
  • #5
Are you sure about that? Is the phase completely irrelevant in the intensity calculation?
 

1. What is the concept of measuring intensity of superposed waves using complex amplitudes?

The concept involves using the complex amplitudes, which represent the magnitude and phase of each individual wave, to calculate the overall intensity of the superposed waves. This allows for a more accurate and comprehensive measurement of the combined waves.

2. How do you calculate the intensity using complex amplitudes?

The intensity is calculated by taking the square of the absolute value of the complex amplitude. In other words, the intensity is equal to the magnitude of the complex amplitude squared.

3. Why is it important to measure the intensity of superposed waves using complex amplitudes?

This method allows for a more precise measurement of the combined waves, taking into account both the magnitude and phase information. It also allows for a better understanding of the interference patterns that occur when waves are superposed.

4. What are some applications of measuring intensity using complex amplitudes?

This method is commonly used in fields such as optics, acoustics, and quantum mechanics to analyze and understand the behavior of superposed waves. It is also used in various imaging techniques, such as MRI and ultrasound, to enhance image quality.

5. Are there any limitations to measuring intensity using complex amplitudes?

One limitation is that this method assumes that the waves are perfectly coherent, meaning they have the same frequency, wavelength, and are in phase with each other. In reality, waves may not always meet these conditions, which can affect the accuracy of the measurement.

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