Is the Plane Wave Decomposition of a Vector Field Accurate?

In summary, plane wave decomposition is a method used in optics to break down a complex electromagnetic field into individual plane wave components. This technique involves representing the field as a combination of individual plane waves and analyzing their properties to better understand the overall behavior. It has various applications in optics and other fields, but it does have limitations, such as assuming linearity and homogeneity of the field. It can also be used for non-monochromatic waves, but it cannot analyze fields with discontinuities or sharp changes in amplitude or phase.
  • #1
Niles
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Hi

When we decompose e.g. the vector potential A into a sum of plane waves, then is it correct to say that we are describing an arbitrary vector field A, since we have decomposed it into its Fourier (= plane wave) components?Niles.
 
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  • #2
I'm sure there are some restrictions- I don't think *all* functions can be written as a converging Fourier series. I don't know what the official rules are, tho.
 

FAQ: Is the Plane Wave Decomposition of a Vector Field Accurate?

What is plane wave decomposition?

Plane wave decomposition is a technique used in the field of optics to break down a complex electromagnetic field into its individual plane wave components. This method is often used to study the properties of light waves and their interactions with different materials.

How does plane wave decomposition work?

In plane wave decomposition, a complex electromagnetic field is represented as a combination of individual plane waves. These plane waves have different amplitudes, phases, and polarizations, and when added together, they create the original field. By analyzing the properties of each individual plane wave, we can better understand the overall behavior of the electromagnetic field.

What are the applications of plane wave decomposition?

Plane wave decomposition has many applications in optics, including studying the properties of light waves, analyzing the effects of diffraction and interference, and designing optical components such as lenses and mirrors. It is also used in other fields such as acoustics and radio wave propagation.

Can plane wave decomposition be used for non-monochromatic waves?

Yes, plane wave decomposition can be applied to non-monochromatic waves, such as those with a range of frequencies. In this case, the complex electromagnetic field is represented as a superposition of plane waves with different frequencies, allowing for a more detailed analysis of the wave's properties.

Are there any limitations to plane wave decomposition?

While plane wave decomposition is a useful tool for studying electromagnetic fields, it does have some limitations. It assumes that the field is linear and homogeneous, which may not always be the case. Additionally, it cannot be used for fields that have discontinuities or sharp changes in amplitude or phase.

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